Electro -optic microdisk RF -wireless receiver

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Content ELECTRO-OPTIC MICRODISK RF-WIRELESS RECEIVER Copyright 2004 by Mani Hossein-Zadeh A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) December 2004 Mani Hossein-Zadeh Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3155423 Copyright 2004 by Hossein-Zadeh, Mani All rights reserved. INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3155423 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication To My parents Maman and Papa Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements First and foremost, I would like to express my deepest gratitude to my parents Jamileh and Mahmoud and to Iliga for their unconditional love, encouragement, and the many sacrifices they have made for me. Their patience, love and support always created a warm and safe atmosphere, conducive to a happy life, and to studies in particular. They raised me to work hard towards realizing my dreams, and yet to be content with what I have; to be honest with those around me and myself; to never sacrifice my values for success. I will never find words adequate enough to express my gratitude, deep respect, and endless love for them. I would also like to thank my aunts, uncles, and cousins in Los Angeles, without whom I would not have been able to adapt to my new life. My acknowledgements would be endless if I were to name them all. Needless to say, their love and encouragement during my studies supported me through the financial and emotional adjustments I faced when I first arrived. I could not have survived without them then, and they continue to be a great source o f strength for me now. I would like to thank my dissertation advisor Professor A. F. J. Levi for offering me the opportunity to work on this exciting project within his research group. His constructive criticism and original ideas were my main drive to becoming a professional researcher. I have learnt much from him and hold him in great respect. I would like to thank Dr. David Cohen to whom I owe most o f the Lab management and technical skills I learned. He patiently explained to me everything from basic measurement to advanced techniques. His presence as a friend and teacher transformed the learning process into a truly enjoyable experience. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I would like to thank my colleague Fernando Harriague. Not only was he a great Lab mate, but a wonderful friend, a true brother. I always enjoyed our conversations that spanned topics as diverse as physics, politics, and social issues. I would like to thank Kim L. Reid for taking care of all the administrative tasks during the project. More importantly she was always there as a caring friend and gave me the feeling o f having a sister by my side. I would like to thank my friend and Lab mate loan Georma who did most o f the work for antenna design and fabrication. I particularly appreciate his help with CST (a commercial EM simulation software). He was a true friend and knowledgeable colleague. I would like to thank Dr. Bindu Madhavan. A friend and colleague from whom I learned subjects as diverse as integrated circuits and spiritual development. His great suggestions always helped me make the best decisions at the most crucial times. I would like to thank Dr. John D. O ’Brien and Stephan Haas for graciously agreeing to serve on my dissertation committee. I would like to thank past members o f my research group for their useful comments and suggestions: Dr Sumesh Thiyagarajan, Dr Barath Raghvavan, Dr Panduka Wijetunga, Yuliang Du, Alex Tarasyuk, Jeff Sondeen, Ashirvad Bahukhandi, Kundan Patidar and Karan Gupta. I would especially like to thank Kundan for helping me make the PCB board for the photoreceiver, and Karan for assistance in video transmission and the video editing software. To all those who have supported me in various ways and whom I love, thank you. iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Dedication................................................................................................................................ii Acknowledgements........................................................................................................... iii List of Tables......................................................................................................................... ix List of Figures........................................................................................................................x Abbreviations................................................................................................................... xxvi Abstract...............................................................................................................................xxvii 1 Introduction 1.1 M otivation.................................................................................................................. 1 1.1.1 Photonic RF-signal processing...................................................................... 1 1.1.2 RF-subcarrier links in wireless LANs and fiber-feed backbone networks........................................................................................................ 3 1.1.3 Indoor wireless.................................................................................................. 6 1.2 B rief survey o f the related to p ic s......................................................................... 7 1.2.1 Mach-Zehnder m odulator............................................................................... 8 1.2.2 Microsphere optical resonators...................................................................... 11 1.2.3 M icrodisk and microring optical resonators............................................... 12 1.2.4 RF microring resonator.................................................................................... 15 1.2.5 Wireless receivers............................................................................................ 17 1.3 Resonant optical m odulator.....................................................................................20 1.3.1 Optical resonance............................................................................................. 20 1.3.2 Electrical resonance.......................................................................................... 25 1.3.3 Resonant electro-optic m odulation............................................................... 27 1.4 M icrodisk and microring modulator.................................................................. 35 1.4.1 LiNb0 3 microdisk m odulator........................................................................ 36 1.4.2 Polymer microring m odulator...................................................................... 37 1.4.3 Semiconductor microdisk modulator............................................................ 39 1.5 Microdisk photonic RF receiver............................................................................ 41 1.6 Summary...................................................................................................................... 45 1.7 References....................................................................................................................47 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 LiN b03 microdisk modulator 2.1 Introduction.............................................................................................................. 56 2.2 M icrodisk optical resonator.................................................................................. 57 2.2.1 Physical, electronic and optical properties of LiNbCE............................. 57 2.2.2 L iN b03 microdisk...............................................................................................61 2.3 Optical coupling........................................................................................................62 2.3.1 W hispering - Gallery m odes......................................................................... 63 2.3.2 Evanescent optical coupling........................................................................... 69 2.3.3 Prism coupling to W G m o d e s...................................................................... 71 2.3.4 Critical coupling and intrinsic loss............................................................... 80 2.3.5 Other optical coupling techniques................................................................ 84 2.4 DC response................................................................................................................87 2.4.1 DC shift.............................................................................................................. 87 2.4.2 Optical bistability............................................................................................ 92 2.5 RF resonator............................................................................................................... 96 2.5.1 Linear and half-ring RF resonator................................................................ 97 2.5.2 Ring resonator....................................................................................................101 2.5.3 Voltage gain and RF critical coupling.......................................................... 115 2.6 Fundamental FSR modulation...............................................................................121 2.6.1 Physics and modeling....................................................................................... 122 2.6.2 Frequency response and bandwidth..............................................................127 2.6.3 Experimental results......................................................................................... 128 2.7 Flarmonic FSR modulation................................................................................... 142 2.7.1 Introduction........................................................................................................ 142 2.7.2 Experimental results.........................................................................................145 2.8 Stabilization...............................................................................................................149 2.9 Summary.....................................................................................................................151 2.10 References................................................................................................................. 153 3 Microdisk modulator in RF-optical link 3.1 Introduction...............................................................................................................159 3.2 RF-optical link....................................................................................................... 160 3.3 Video and data transm ission........................................................................... 165 3.4 Planar antenna and antenna arrays.................................................................... 169 3.4.1 Patch antenna................................................................................................. 169 3.4.2 Patch antenna array..................................................................................... 175 3.5 Wireless video and data transmission.............................................................. 182 3.6 Noise analysis....................................................................................................... 185 3.7 Summary............................................................................................................... 192 3.8 References............................................................................................................. 194 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 Optical down-conversion 4.1 Introduction......................................................................................................... 196 4.2 Nonlinear photodetection....................................................................................... 197 4.3 Down-conversion through optical filtering ......................................................200 4.3.1 Introduction.........................................................................................................200 4.3.2 Self-homodyne RF down-conversion...........................................................206 4.3.3 Optical heterodyning........................................................................................213 4.4 Down conversion through nonlinear optical modulation............................... 219 4.4.1 Introduction.........................................................................................................219 4.4.2 Nonlinear optical modulation with MZ m odulator....................................226 4.4.3 Nonlinear optical modulation with microdisk m odulator........................ 231 4.4.4 Comparison.........................................................................................................236 4.5 Microdisk photonic self-homodyne RF receiver.............................................. 239 4.5.1 M odeling................................................ '...........................................................239 4.5.2 Experimental results .......................................................................................242 4.5.3 Noise in microdisk photonic self-homodyne receiver............................. 248 4.6 Sum m ary................................................................................................................... 252 4.7 References.................................................................................................................255 5 Conclusion and future work 5.1 Introduction.................................................................................................................257 5.2 Self-homodyne photonic RF receiver ............................................................... 258 5.3 Microdisk photonic receiver: potential improvements....................................260 5.3.1 M icrodisk modulator.........................................................................................261 5.3.2 Photoreceiver......................................................................................................264 5.3.3 Integration and final design........................................................................... 266 5.4 Alternative electro-optic materials...................................................................... 275 5.4.1 Polymers..............................................................................................................276 5.4.2 Semiconductors ...............................................................................................277 5.4.3 S B N ......................................................................................................................283 5.5 Millimeter-wave photonic transceiver............................................................... 285 5.6 Summary.................................................................................................................... 291 5.7 References.................................................................................................................292 Glossary................................................................................................................................. 296 Appendix A B ib lio g r a p h y .........................................................................................299 vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables Table 1.1 Summary o f Fabry-Perot formulas..................................................................23 Table 1.2 Summary o f main formulas o f series and parallel resonant circuits 27 Table.2.1 Bulk properties o f LiNbC> 3.................................................................................59 T able 2.2 DC-shift and pE o for different disks................................................................90 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures Figure 1.1 (a) Shows the propagation loss o f the electromagnetic waves in air as a function o f frequency. Two absorption peaks are observed at 23 and 60 GHz (Source: phased array-based systems and applications, Nicholas Fourikis, pp. 27-28, John Wiley & Sons, 1997). (b) A schematic diagram showing the concept o f fiber-feed backbone networks and the function o f wireless-optical modulator in the n etw o rk .................................................................................................... 4 Figure 1.2 (a) Video redistribution for households based on RF-photonic receiver system, (b) Application o f RF-photonic receiver in an indoor wireless LA N .......................................................................................................................................... 6 Figure 1.3 Convergence o f four principal technologies in microdisk optical m odulator................................................................................................................................. 8 Figure 1.4 (a) Photograph o f a state-of-the-art low-drive voltage (V* = 0.9 Volt) 40 Gb/s LiNb0 3 MZ modulator [15]. (b) A semiconductor MZ modulator fabricated on a Sl-InP substrate. Cross-sectional geometry o f the n-i-n InP waveguide (left) and a photograph o f the fabricated chip (right) [20]...................... 10 Figure 1.5 (a) Photograph o f a 235 pm radius silica microsphere photonic resonator showing angle polished-fiber couplers [25], (b) Photograph o f a silica microsphere coupled to tapered-fibers as an add-drop filter. Over coupling o f this device results in low loaded optical-g o f 4 x l0 4 for broadband applications [26] 12 Figure 1.6 (a) Photograph o f LiNb0 3 microdisk ( D - 1 mm), (b) Photograph o f an InP microdisk vertically coupled to parallel waveguides (D = 30 pm)[34], (c) Photograph o f an InP microdisk laterally coupled to parallel waveguides (D = 4 pm) [34], (d) An SEM cross-sectional view o f a buried microring resonator [35]. (e) Photograph o f a microdisk laser (D = 1.6 pm) [37]. (!) Photograph of an ultra-high-g (108 ) toroidal silica microdisk.(.D = 150 pm) [31] .......................... 14 Figure 1.7 (a) Photograph o f microstrip ring resonators side-coupled to a microstrip line on a printed circuit board (PCB). (b) A ring resonator on top o f a LiNbCA disk (D = 5.8 mm), side coupled to a microstrip line on a PC B ................. 16 Figure 1.8 Block diagrams o f wireless receiver architectures, (a) Direct conversion (homodyne) receiver, (b) Super heterodyne receiver, (c) Dual conversion superheterodyne receiver................................................................................ 18 ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure. 1.9 (a) Geometry o f a Fabry-Perot standing wave resonator. Input electric field is E\, reflected field is Er and transmitted field is Et. The cavity is o f length L and the reflectivity o f the two mirrors is R\ and R2. (b) Geometry o f a circular traveling wave resonator....................................................................................... 22 Figure 1.10 (a) FSR o f a LiNbCL average size microdisk optical resonator against its diameter, (b) FSR o f polymer, LiNbCL and semiconductor microdisk optical resonators against their diameter.......................................................................... 24 Figure 1.11 (a) Series resonant circuit, (b) Parallel resonant circuit, (c) Open ended microstrip resonant circuit...................................................................................... 26 Figure 1.12 (a) An electrically resonant MZ-modulator. 10 dB enhancement through electrical resonance has been achieved [70], (b) An optically resonant modulator. 5 dB enhancement compared to a straight waveguide o f length equal to the ring has been reported [60]...................................................................................... 29 Figure 1.13 Qualitative behavior o f the frequency response based, (a) Linewidth modulation: the RF carrier frequency is smaller than Avfwhm /2. Polymer and semiconductor microring and microring resonators work in this regime, (b) No modulation: the RF frequency is larger than optical bandwidth but smaller than the optical free-spectral-range so the RF-optical sidebands are filtered out by the optical transfer function, (c) FSR modulation: The RF- optical sidebands are within the adjacent resonances. LiNbCL microdisk modulator works in this regim e......................................................................................... 32 Figure 1.14 (a) Ideal frequency response o f a resonant optical modulator (solid line) and a traveling wave optical modulator (dashed line), (b), (c) and (d) Digital modulation bandwidth of microdisk modulator against optical quality factor in baseband and FSR modulation regim es......................................................... 34 Figure 1.15 Photograph o f a LiNbCL microdisk modulator (D - 5.8 mm) with RF-ring resonator and single-prism optical coupling.................................................... 36 Figure 1.16 (a) Layout photograph o f the fabricated device showing polymer microring waveguide (D — 500 pm) vertically coupled to perpendicular straight waveguides, (b) Schematic diagram o f the device cross-section showing the material system and dim ensions........................................................................................ 38 Figure 1.17 The schematic diagram o f a photonic RF-wireless receiver..................................................................................................................................... 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.1 LiNbCb molecular structure. Niobium atoms are represented as dark gray small spheres, Lithium as light gray small spheres and Oxygen as large spheres, (a) Vertical view o f the LiNb0 3 conventional hexagonal unit cell, (b) View along c (or z) axis. (c) Octahedral oxygen structure o f LiNb 0 3 [5].............................................................................................................................................. 58 Figure 2.2 (a) Photograph o f a LiNbOs disk with optically polished sidewalls. (b) 3D picture o f the disk sidewall surface taken by interferometric surface profdometer (4). nm scale scratch marks due to mechanical polishing are clearly visible...................................................................................................................................... 62 Figure 2.3 (a) Geometry o f the microdisk resonator and definition o f the coordinate system used (notice that 9 is measured relative to the equatorial plane unlike the conventional definition where it is measured relative to the z-axis. This new definition has been chosen because it is more convenient for WG resonances that are confined around the equator). Also shown is the definition o f the TE and TM polarized resonances, (b) Normalized modal distribution for I = m = 24 that is the projection o f spherical harmonic Y2 4,24 on a unit sphere (longitudinal and equatorial cross section)...................................................................... 64 Figure 2.4 WGM power distribution in vz plane, for microdisks with different diam eters.................................................................................................................................. 66 Figure 2.5 (a) Frustrated total internal reflection, (b) Evanescent prism coupling to surface waves.................................................................................................... 70 Figure 2.6 (a) Diamond microprism dimensions, (b) Single-prism coupling. (c) Double-prism coupling, (d) Interference effect in single-prism coupling 72 Figure 2.7 Schematic diagram o f the experimental arrangement used for optical coupling m easurem ent.......................................................................................................... 73 Figure 2.8 (a) Top view photograph o f a 5.13 mm diameter LiNb0 3 microdisk in contact with two microprisms, (b) The detected TE WG optical spectrum, (c) High coupling efficiency (> %15) and a clean TE spectrum obtained with the same set up after accurate alignment (optical input power in both cases is about 1200 pW )................................................................................................................................. 74 Figure 2.9 TE mode spectrum obtained using a single prism for coupling light in and out o f the microdisk. The quality factor o f the second measurement (bottom) is the highest Q observed.................................................................................... 76 xi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.10 (a) Photograph o f the toroidal L iN b03 microdisk, (b) The microdisk dimensions and the sidewall profile, (c) TE mode spectrum obtained using a two prism coupling scheme. Although the spectrum is very clean the coupling efficiency is low («% 3)....................................................................................... 77 Figure 2.11 Optical output power spectrum o f a single prism coupled L iN b03 microdisk (D = 3 mm, h = 0.4 mm), (a) Detected transmission dips when the output fiber is tuned to the overlap region o f the WG cone and the total reflection cone, (b) Detected WG peaks when the output fiber only collects optical power from the W G cone....................................................................................... 79 Figure 2.12 Observation o f WG modes inside the L iN b03 disk (h = 700 pm, D = 5.85 mm) using He-Ne laser............................................................................................ 80 Figure 2.13 (a) Generic description o f a single waveguide coupled ring resonator, (b) Typical transfer function o f a waveguide-resonator system 81 Figure 2.14 (a) Transmitted optical power spectrum of 3 mm diameter and 0.4 mm thick microdisk optical resonator, (b) Simulated optical output power against coupling factor for different values o f distributed loss factor, (c) Simulated optical quality factor against coupling factor for different values of distribute loss factor.............................................................................................................. 82 Figure 2.15 Geometry o f direct coupling to W G modes through a plano-convex ZnSe lens.................................................................................................................................. 85 Figure 2.16 (a) Photograph o f the experimental arrangement used for testing a half-disk coupler, (b) The toroidal half-disk (D = 6 mm) coupled to a microdisk (D = 2 mm), (c) He-Ne laser light coupled to the WG resonance o f the 2 mm microdisk through a toroidal half-disk coupler............................................................... 86 Figure 2.17 (a) Schematic diagram showing the E-field lines in the vicinity of the microdisk sidewall (the curvature and fringing effect have been exaggerated), (b) The modified design where the microdisk is mounted on a cylindrical ground plane...................................................................................................... 89 Figure 2.18 (a) Photograph o f the microdisk resonator mounted on a cylindrical ground plane, (b) Measured optical output spectrum at 0 V and 5 V DC bias voltages.................................................................................................................................... 90 Figure 2.19 (a) simulated resonant shift o f the transmission dip for a microdisk resonator with: k = 0.0999, a = 0.0075 cm '1 , P 0 jin = 50 pW, p E o = 0.5, h = 0.4 m m ............................................................................................................................................ 91 xii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.20 (a) Photograph o f the LiNb0 3 microdisk modulator, (b) Experimental arrangement used for demonstrating the bistable behavior o f the microdisk optical resonator with a feed-back loop........................................................ 93 Figure 2.21 (a) Measure optical output-power as a function o f optical input- power for indicated values o f peak-to-peak voltage feedback (Fft) and optical Q- factor. (b) Results o f simulation for the ideal case where just one set o f modes has been excited inside the disk.......................................................................................... 95 Figure 2.22 Photograph o f the first RF-resonator (linear) used for modulating the W G modes inside the LilNbCE disk........................................................................... 97 Figure 2.23 (a) Photograph o f the microdisk modulator designed based on side coupled semi-ring RF resonator, (b) The measured Su spectrum for the open- ended microstripline side-coupled to the semi-ring, (c) The result o f simulating the resonant E-field (magnitude) distribution on a cut-plane located in the middle of the disk, (d) The structure used in the simulation. Dielectric substrate thickness = 0.508 mm, dielectric constant = 2.94, microstrip linewidth = 1.2 mm, disk thickness = 0.7 mm, semi-ring resonator width = 1 .2 mm, resonator angle = 90 degree.................................................................................................................................. 98 Figure 2.24 Schematic diagram showing the voltage distribution around the semi-ring RF resonator.......................................................................................................... 100 Figure 2.25. Geometry o f microstrip ring resonator side-coupled to a microstripline on a uniform dielectric substrate.............................................................. 102 Figure 2.26. (a) Ring on uniform dielectric substrate (RTD 6006): s, = 6.15, dielectric thickness (hs ) = 0.508 mm, microstripline width (wi) = 0.8 mm, ring diameter = 6.11 mm, gap size (g) = 0.32 mm. (b) The simulated S21 for the ring shown in (a), (c) Measured S21 • Resonant frequencies up to the third harmonic are shown.................................................................................................................................. 103 Figure 2.27. Geometry o f ring resonator on LiNbCE side-coupled to a microstripline (top view and side view )............................................................................ 105 Figure 2.28 (a) Photograph o f the ring resonator on LiNbCE microdisk side- coupled to the microstripline. (b) S21 measurement results for ring and semi-ring on the LiNb0 3 microdisk shown in (a)............................................................................. 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.29 Simulated £-field distribution on a cut plane passing through the middle o f a LiNbOi microdisk when the fundamental resonance o f the ring resonator is excited, (a) 2-D E-field magnitude distribution, (b) 3-D view o f the E-vectors distributed around the disk. The E-vectors are plotted on a log scale.............................................................................................................................................108 Figure 2.30 The .E-field distribution for the fundamental mode o f the ring resonator and equivalent linear resonance....................................................................... 108 Figure 2.31 The accumulated electro-optical phase for a photon that enters the resonator at the peak o f the voltage oscillation after traveling for 10 cycles (solid line). The dashed line shows the accumulated electro-optic phase for a photon in a traveling wave m odulator................................................................................................. 109 Figure 2.32 S21 measurement results for ring and half ring on LiNbCh ................................................................................................................................................... I l l Figure 2.33 Resonant frequency as a function o f gap size for the even mode o f a ring resonator (w = 300 pm) on a LiNb0 3 microdisk with a diameter o f 3 mm and a thickness o f 0.4 mm (approximated line equation: f RF = 15.292g (l007S) ................................................................................................................................................... 113 Figure 2.34 (a) Schematic diagram o f the configuration used for tuning the RF resonant frequency, (b) Results o f S21 measurement for different volumes o f air cylinder (z„ is changed), (c) Resonant frequency as a function o f za........................ 114 Figure 2.35 Q rf.u and Q r f measurement points in the reflection and transmission coefficient magnitude planes as a function o f coupling factor r\ and the definition o f various terms used [43].......................................................................... 118 Figure 2.36 CST simulation results for ring resonlator on a LiNbCb microdisk with a diameter o f 5.13 mm and a thickness o f 0.4 mm. (a) The coupling factor (r|) against gap size (g). (b) Q„ and Qi against coupling factor, (c) The E-field oscillations amplitude against g .......................................................................................... 119 Figure 2.37 (a) Experimental results o f S-parameter measurements for a LiNbCb with a diameter o f 3 mm and a thickness o f 0.4 mm for three different values o f g. (b,c,d) The calculated quality factor, coupling factor, and the E-field oscillation amplitude (calculated using Eq. 34) against the gap size............................................................................................................................................ 120 Figure 2.38 Schematic diagram o f the microdisk modulator representing the parameters involved in the modulation process............................................................. 124 xiv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.39 (a) The electro-optic transfer function o f a microdisk modulator (h — 0.4 mm, k = 0.1, a = 0.0075 cm '1 , P 0j;n = 50 pW, Gv = 6. (b) The simulated DC-shift (AA.dc) based on measured value...................................................................... 125 Figure 2.40 Evolution o f the LiNbCE microdisk optical modulator, (a) Direct RF feeding, non-planar, double-prism optical coupling, (b) Linear RF-resonator, non-planar, double prism optical coupling, (c) Half-ring RF-resonator, semi- planar, double-prism optical coupling, (d) Half-ring RF-resonator, planar, double-prism optical coupling, (e) Full-ring RF-resonator, semi-planar, single prism optical coupling, RF through put. (f) Full-ring RF-resonator, semi-planar, single-prism optical coupling, RF-throughput, controlled RF coupling.................. 129 Figure 2.41 Measured S21 for a semi-ring and ring at fundamental resonance and the simulated even mode (left inset) field distribution on the ring. The right inset shows the detected modulated power with semi-ring and ring resonators................................................................................................................................. 131 Figure 2.42 Close up photograph o f the 8.7 GHz LiNbCL microdisk modulator (Fig. 39-d)............................................................................................................................... 132 Figure 2.43 Single frequency modulation result at/ rf = A v FSr = 8.7 GHz. The LiNbOa microdisk has a diameter o f 5.13 mm and thickness o f 0.4 mm. (a) Spectrum o f optical detector output voltage. The detected modulation has a bandwidth o f 90 MHz with a maximum o f about 420 pV at 8.73 GHz. The RF- resonator is a full-ring and the input RF power is 0 dBm (1 mW). (b) Spectrum of the optical resonance. The maximum coupled optical power is about 14 pW, and the optical bandwidth is about 85 MHz (mode slope is 30 pW /pm). (c) Detected optical voltage output (at 8.7 GHz) against RF input power. In this experiment a semi-ring RF-resonator is employed. The inset is the corresponding optical m ode................................................................................................. 133 Figure 2.44 Detected modulation at resonance and at RF frequencies detuned from resonance.................................................................................................................... 135 Figure 2.45 (a) Optical output spectrum at different optical input powers, (b) Detected RF voltage against P0,ma\ when the laser output is tuned to the middle o f the mode slope (dashed line in (a))................................................................................. 136 Figure 2.46 (a) Photograph o f the microdisk modulator, (b) S-parameter measurement results for the microstrip line side coupled to the RF ring resonator.....................................................................................................................................137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.47 Linearly modulated optical intensity against peak-to-peak input voltage (and RF power). The inset shows the modulated optical mode. At Vpp = 0.56 V, the optical power in the linear region o f the optical mode is 100% modulation, (b) Demodulation RF power against input RF pow er.......................... 138 Figure 2.48 Optical spectrum o f the detected RF power at very low RF input pow ers...................................................................................................................................... 140 Figure 2.49 (a) the optical spectrum o f the selected WG mode. The maximum modes slope (S) is 80 pW /pm and its line width is 0.33 pm corresponding to a bandwidth o f 45 MHz and a loaded optical Q o f 4 .7 x l0 6. (b) Frequency spectrum o f the detected RF voltage at 0 dBm received RF power, (c) M easured .S'-parameters for the microstripline side coupled to the ring resonator..................... 141 Figure 2.50 Simulated F-field magnitude and F-ficld vectors on a cut plane passing through the middle o f the LiNbC>3 microdisk for even ( a ) and odd (b) second harmonics. (D = 5.13 mm, h = 0.4 m m )............................................................ 143 Figure 2.51 (a) Simulated ^’ -parameters around the second-harmonic o f a side- coupled ring resonator, (b) The amplitude o f the is-field oscillation in the middle o f the disk at angular positions E and O shown in Fig. 2.50....................................... 144 Figure 2.52 (a) Photograph o f the experimental arrangement. Disk diameter = 5.8 mm, disk thickness = 0.74 mm, FSR = 7.6 GHz. (b) Second-harmonic modulation at 2xFSR = 15.2 GHz. The inset shows the results o f measurement. As may be seen the fundamental resonance o f the ring is off by 100 M Hz (7.7 GHz as opposed to 7.6 GHz), while the second-harmonic is exactly equal to 15.2 GHz. This explains the weak modulation observed at 7.6 GHz. (The injected RF-power to the microstrip line is 0 dBm )................................ 146 Figure 2.53 Measured signal to noise ratio (of amplified signal) as a function o f input RF power at fundamental (fR F = 7.6 GHz) and second-harmonic (fR F = 15.2 GHz) o f the ring. The inset shows S21 spectrum when the even second harmonic o f the ring (f = 15.2 GHz) is excited................................................................................. 147 Figure 2.54 (a) RF frequency spectrum o f the detected third harmonic modulation (3xAvF sR = 3x 8.7 GHz = 26.1 GHz), (b) The spectrum o f the modulated optical mode, (c) S21 measurement result showing the 3K l resonance of the ring................................................................................................................................. 148 Figure 2.55 (a) Schematic diagram showing the feedback loop arrangement. (b) Experimental results showing the effect o f the feedback loop on output power fluctuations....................................................................................................................150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.1 Basic operation o f wired (a) and wireless (b) RF-optical links. Depending on the signal-to-noise-ratio required at each stage, amplifiers may be used in some interfaces......................................................................................................... 161 Figure 3.2 Schematic diagram showing the signal flow in an RF-optical link that uses the microdisk optical m odulator....................................................................... 162 Figure 3.3 Schematic diagram o f the experimental RF-optical link designed for investigating the LiNbCh microdisk modulator performance........................................ 164 Figure 3.4 Photograph o f the 8.7 GHz LiNbCh microdisk modulator. (I) -- 5.13 mm, h — 0.4 m m ).................................................................................................................... 165 Figure 3.5 (a) Measured phase margin o f the output at 10 Mb/s (NRZ 27 - 1 PRBS) for 10 mW and 2.5 mW modulating RF power. The inset shows representative input and output eye-diagrams. (b) Measured RF signal spectrum before and after microdisk modulator using 2.5 mW RF pow er................................ 166 Figure 3.6 Measured sensitivity o f BER to modulating RF power (measured RF power within 150 MHz bandwidth centered at 8.685 GHz). The inset is the detected optical output power against input laser wavelength.......................................167 Figure 3.7 Optical output eye-diagrams at 50 Mb/s (a) and 100 Mb/s (b) (NRZ 2' - l PRBS). The modulating RF-power is 40 mW and 60 mW respectively 168 Figure 3.8 Demonstration o f video transmission through microdisk based RF- optical link. (a) The original image, (b) The transmitted im age............................... 168 Figure 3.9 (a) The definition o f E- and //-radiation planes, (b) A typical example o f the radiation patterns o f a rectangular microstrip patch antenna [1]............................................................................................................................................. 170 Figure 3.10 Top view and side view o f spatial distribution o f F-field in a rectangular microstrip patch resonator showing that the F-field lines effectively behave like two dipole arrays.............................................................................................. 171 Figure 3.11 Different techniques used for feeding the patch antenna: (a) The tapered microstrip feed, (b) Multisection impedance matching, (c) Inset micro strip feed........................................................................................................................ 172 xvii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.12 (a) Photograph o f the patch antenna (with tapered line feed) attached to microdisk modulator, (b) *S ji measurement results for receive and transmit patch antennas as well as the semi-ring resonator showing good resonant frequency matching. The antenna g-factor is about 25 and the semi ring g-factor is about 70...................................................................................................... 174 Figure 3.13 (a) Photograph o f the single patch with inset line feed, (b) S\ i measurement result (Q = 26,/ r f = 8.73 GHz)................................................................ 175 Figure 3.14 (a) Photograph o f the fabricated four-patch antenna array (made on a 0.508 mm thick dielectric substrate with s = 2.94 and loss tangent = 0.00119). (b) 5 * 1 1 measurement result showing a Q o f about 20 at 8.68 GHz resonant frequency, (c) Simulated S\ \ and 3D radiation pattern o f the four-patch antenna u s in g ......................................................................................................................................... 177 Figure 3.15 (a) Measured radiation pattern o f the 4-patch antenna array and the definition o f radiation planes, (b) Simulated radiation pattern o f the 4-patch antenna, (c) Received RF power as a function o f the distance between receivers and transmit antennae. The RF-power injected to the transmit antenna is 10 dBm and the radiation is measured along z-axis (x=y = 0)......................................... 178 Figure 3.16 (a) Photograph o f a serially fed 10-patch antenna array, (b) Schematic diagram showing the simulated 3 dB angular width o f the main radiation lobe.......................................................................................................................... 180 Figure 3.17 (a) Measured radiation pattern o f the 10-patch antenna array and the definition o f radiation planes, (b) Received RF power as a function o f the distance between receive and transmit antenna. The RF-power injected to the transmit antenna is 10 dBm and the radiation is measured along z-axis (x = y = 0) 181 Figure 3.18 Schematic diagram and photograph o f the short wireless-optical link based on single patch and microdisk modulator..................................................... 182 Figure 3.19 (a) shows the BER measurement results at 10 Mb/s (NRZ 27 - 1 PRBS) as a function o f injected RF-power to the transmit antenna, (b) The measured eye-diagram at 18 dBm RF input pow er....................................................... 183 Figure 3.20 (a) Wireless RF-optical link using patch antenna arrays and the microdisk modulator, (b) The measured BER (at 10 Mb/s NRZ 27 - 1 PRBS) as a function o f the distance between two antenna (received optical power = 100 pW, injected RF power to the transmit antenna = 1W). (c) The measured eye- diagram at z =10 ft. The average optical output power is about 30 pW ................... 184 xviii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.21 (a) Schematic diagram o f signal and noise flow in microdisk RF- wireless receiver, (b) Values o f parameters required for noise calculation, (c) BER against signal-to- noise ratio [15]........................................................................... 186 Figure 3.22 BER calculations as a function o f RF input power for different optical g-factors, disk thicknesses, and voltage gain factor. In all cases optical coupling efficiency (p) is 15%, RIN is -150 dB/Hz, optical input power is 5 mW, detector responsivity is 0.8 A/W, detector dark current is 10 nA, temperature is 300 K, detector impedance is 10 kQ and detector amplifier noise-figure is 3 dB. The sensitivity is defined as the RF-power at which the SNR is unity, (a) Effect of optical 0-factor on BER performance, (b) Effect of disk thickness on BER performance. (c) Effect o f RF resonator voltage gain factor on BER perform ance............................................................................................................................ 190 Figure 3.23 Calculated influence o f laser RIN on BER and sensitivity (Q = 2 x 106 and other parameters are the same as in Fig. 15). (a) BER performance with different values o f RIN as a function o f RF input power, (b) Sensitivity with different values o f RIN as a function o f Gv.................................................................... 191 Figure 4.1 Schematic diagram o f the frequency spectrum o f an optical carrier modulated with an RF signal. The RF signal is an RF sub-carrier modulated by a single-tone baseband. The amplitude of each frequency component is written as a function o f optical E'-field and the modulation indexes..........................................201 Figure 4.2 Schematic diagram o f a RF-subcarrier optical-link that uses optical filtering for optical down-conversion............................................................................... 203 Figure 4.3 The transmission spectrum o f the Fiber Bragg Grating (FBG) employed in the optical down-conversion experiment. (Center wavelength: 1553.3 nm, Slope: 1 dB/pm, Reflection Band width: 0.26 nm )...................................204 Figure 4.4 RF down-conversion by optical filtering (a) The measured spectrum o f the FBG transmission and the modulated optical signal, (b) RF-spectrum of the detected signal (c) The simulated spectrum o f the detected signal. In this the simulation the RF carrier frequency is only ten times smaller than the optical frequency and the baseband signal is ten times smaller than the RF-carrier frequency, to make the FFT calculations faster............................................................. 205 Figure 4.5 (a) The transmission spectrum o f the FBG filter and the location of the wavelength components o f the modulated optical carrier, (b) Frequency spectrum of the transmitted carrier RF signal fed into the MZ modulator, (c) The spectrum o f the detected signal after filtering for the optical spectrum shown by dashed gray lines in (a), (d) The spectrum o f the detected signal after filtering for the optical spectrum shown by solid black lines in (a)........................................... 209 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.6 The magnitude o f the detected baseband signal (black triangles) and its second-harmonic (gray diamonds) against RF modulation index...........................210 Figure 4.7 The measured BER performance o f the self-homodyne receiver that employs pre-detection optical fdtering for photonic down-conversion...................... 211 Figure 4.8 Measured BER o f the down-converted data against received RF power. The RF carrier is 14.6 GHz and the transmitted data is 10 Mb/S 27-l NRZ PRBS. The photonic down-conversion is achieved using a linear modulation in a microdisk modulator and FBG filter. The microdisk has an FSR o f 14.6 GHz and a F h m m o f 0.6 V ........................................................................................212 Figure 4.9 Measured eye diagrams o f the down-converted data from 14.6 GHz RF carrier using microdisk modulator and FB G ............................................................ 212 Figure 4.10 Active down-conversion using optical filtering and local oscillator. (a) Schematic diagram o f the system architecture. A second laser with the same power as the main laser but with a shifted wavelength (Av = / R F , / R ,.: the RF carrier frequency) is combined (50/50) with the modulator output before passing through the FBG filter, (b) The simulated optical output intensity spectrum. The RF signal has a transmitted carrier modulation format (RF-carrier is not suppressed). By using the optical local oscillator the baseband signal becomes larger (by a factor o f 5). hi order to reduce the calculation complexity o f the FFT, in this simulation the RF carrier frequency is only ten times smaller than the optical frequency and the baseband signal is ten times smaller than the RF- carrier frequency.................................................................................................................... 215 Figure 4.11 (a) Schematic diagram o f the experimental arrangement to test the feedback loop thermal phase control in a homodyne detection scheme. 90% of the laser power goes to the passive arm and 10% goes to the active arm. Due to optical insertion loss in MZ modulator iV T ’i is about 40. 5% o f the detected signal is fed to a RF-power detector (that generates a voltage proportional to the received RF power). The output voltage from the power detector is used as the reference in a control circuit to drive the appropriate current through the heating element and change the phase accordingly, (b) The measured eye diagrams with and without the passive arm. Data amplitude is amplified by a factor o f 5.8 that is in very good agreement with the calculated gain................................................217 Figure 4.12 Schematic diagram o f the photonic self-homodyne RF receiver. The transmitted carrier RF signal is received by the antenna and is directly fed to a square-law optical intensity modulator. Through nonlinear optical modulation the optical output intensity spectrum contains the baseband and high frequency components that are filtered out by the response o f the low-speed photodetector.......................................................................................................................... 220 xx Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.13 (a) Calculated down-conversion efficiciency ( P o ,n J P n . m J 2}) versus RF modulation index (mi), (b) Second-harmonic suppression ratio against m. The electrical (after detection) and optical suppression ratios are related through P e,cot/ P e,2wb O 'o)t/*2e)b) cc(P o ,a b /P o 2 .a b ) ...................................................................................................................... 223 Figure 4.14 (a) The output optical power o f a microdisk modulator against the input voltage and the frequency spectrum o f the photocurrent generated by the voltage in equation 4.7. (b) The current across a conventional diode against the input voltage and the frequency spectrum o f the current generated by the voltage in equation 4.7.......................................................................................................................... 225 Figure 4.15 (a) P0,0m versus A(3Z/7t characteristic o f a Mach-Zehnder modulator, (b) The DC response o f the MZ modulator used in our experiments. The circles are the measured data points while the solid line is the calculated response using equation 4.16 assuming P 0,m ax = 468 pW, ( j > = 2.375 rad and VK = 5.2 V. The dashed curve is the parabola defined by /V 2F2 /2 where M is the second derivative o f the equation 4.16............................................................................. 226 Figure 4.16 Experimental arrangement for studying photonic down-conversion through nonlinear modulation in an MZ m odulator...................................................... 228 Figure 4.17 (a) Calculated and detected rms voltage at baseband and the second-harmonic o f the baseband as a function o f mi. The calculation is based on square-law optical modulator model, (b) Calculated and measured rms voltage at baseband and the second-harmonic o f the baseband (V2) as a function of the total received RF power at mi = 1.2...................................................................... 229 Figure 4.18 Measured eye-diagrams at 10, 50 and 100 Mb/s (PRBS NRZ 27-1). The data is down-converted from a 7.6 GHz RF carrier through nonlinear optical modulation in an MZ modulator....................................................................................... 230 Figure 4.19 Simulated optical output power spectrum of microdisk modulator at linear (a) and nonlinear (b) operation regime. The RF input power is a 1 GHz RF carrier modulated by a 100 MHz (single frequency) baseband signal........................................................................................................................................ 231 Figure 4.20 Nonlinear modulation with microdisk modulator. The microdisk is fed by a 0 dBm single frequency RF signal ( / r f = 8.7 GHz = optical free spectral range o f the disk). When the laser wavelength is set to the middle o f the optical mode slope the modulation is linear and is only observed at 8.7 GHz (right). If the laser wavelength is tuned to the W G resonant frequency, modulation becomes nonlinear and a second-harmonic o f the input RF frequency (17.4) is generated while the linear component decreases (left)................................................... 232 xxi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.21 Calculated optical output intensity o f an ideal microdisk modulator as a function o f RF input voltage (Gv = 6). The dashed and the dotted lines are generated as the first (/Vi) and second (N2) Taylor coefficients in an expansion of the optical transfer function (solid line). The laser is biased to the extreme nonlinear operating regime Z|aser = Zres............................................................................. 234 Figure 4.22 (a) Calculated baseband modulated optical power against RF input power for a microdisk modulator with an electro-optic transfer function similar to Fig. 4.21. (b) The down-converted voltage and power gain against received RF power for a microdisk optical RF receiver (R = 0.9 A/W), Z j = 700KQ, Q = 4 .8 x l0 6, Fhmm =0.4 V olt)................................................................................................... 236 Figure 4.23 (a) Calculated optical output power against the RF voltage for a MZ modulator with a Ft o f IV and insertion loss o f 4dB. The gray line is the approximated hyperbola (A V ^F2. The dotted blocks shows the small signal region, (b) Calculated optical output power against RF voltage. The microdisk has a F h m m o f 0.55 V and insertion loss o f 10 dB. The optical input power is 1 mW. (c) Calculated value o f N 2 versus F h m m and V% assuming the MZ has an insertion loss o f 4 dB and microdisk modulator has an insertion loss o f 10 dB ................................................................................................................................................ 238 Figure 4.24 The simulated magnitude o f N2 as a function o f F Hm m for different values o f insertion loss. The optical input power is 1 m W ........................................... 239 Figure 4.25 Simulated signal flow in a self-homodyne RF receiver, (a) Modulated optical transfer function when the laser emission wavelength (Z|asci) is centered at one o f the microdisk optical resonant wavelengths and the modulator is fed by the data modulated RF carrier. The RF carrier frequency is 10 GFIz and is modulated by a 62.5 Mb/s data stream with a modulation index o f m\ = 0.8. The modulation amplitude is exaggerated to show the down- conversion mechanism, (b) Spectrum o f the transmitted-carrier RF input signal. The inset shows the original data stream in a short time interval (640 ns). (c) Calculated spectrum o f the optical output intensity. Nonlinear modulation generates the baseband signal and high-frequency components around 20 GFIz. The photodetector bandwidth o f 0.1 GHz (dashed line) filters out the high- frequency components and only the baseband is converted to an electric signal. The inset shows the detected data stream again in a 640 ns time interval............... 241 xxii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.26 (a) Photograph o f the LiNbCh microdisk modulator, (b) A close-up view o f the modulator showing the microstripline, LiNb0 3 microdisk, microprism, microring RF resonator and the output fiber, (c) Schematic diagram o f the experimental arrangement used for photonic RF down-conversion measurements. The RF modulation index (m\) is tuned using the DC bias on the mixer. The laser is a tunable single mode laser with a resolution o f 0.1 pm and linewidth o f less than 0.5 MHz. The RF filter eliminates any low frequency component generated due to nonlinearities in RF devices. The local oscillator frequency is 14.6 GHz that is equal to the optical free spectral range o f the microdisk modulator............................................................................................................. 243 Figure 4.27 The measured and calculated baseband modulated optical power versus total RF input power. The inset shows the optical spectrum o f the WG resonance chosen for down-conversion (Q = 2.7 x l0 6, Ni — 2 .2 3 x l0 '2 mW /V2) ......................................................................................................................................244 Figure 4.28 (a) Measured baseband modulated (10 MHz) optical output power against m\ for three optical modes with different optical quality factors, (b) Measured second and third Harmonic suppression ratios (electrical) against m\................................................................................................................................................. 245 Figure 4.29 Measurement results o f photonic data down-conversion in LiNbCE microdisk modulator, (a) The frequency spectrum o f the input RF signal and down-converted signal. The RF carrier frequency is 14.6 GHz and it is modulated by a 10 Mb/s 27-l NRZ PRBS bit stream, (b) The BER sensitivity of the photonic RF receiver. The RF power is the measured RF power within 10 MHz bandwidth centered around 14.6 GHz. The right inset shows the input and detected data in time domain. The left inset shows the optical spectrum o f the selected W G resonance...........................................................................................................247 Figure 4.30 Measured eye diagrams at 10 Mb/s, 50 Mb/s and 100 Mb/s (received RF power = -15 dBm ).......................................................................................... 248 Figure 4.31 Schematic diagram showing the signal and noise flow in the photonic self-homodyne receiver.........................................................................................249 Figure 5.1 Simulated value o f F h m m as a function of (a) Gv , (b) Q and (c) h using the electro-optic transfer function ( / e o ) ................................................................... 262 Figure 5.2 Relative alignment o f the laser wavelength and WG resonant wavelength for linear and nonlinear m odulation............................................................ 264 Figure 5.3 Schematic diagram o f signal flow (frequency domain) in the photonic RF receiver in the presence o f the optical filter...............................................266 xxiii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.4 Schematic diagram o f two microdisk photonic self-homodyne RF receiver architectures: (a) DNOM, where the microdisk is biased at nonlinear modulation regime and (b) DOF where the microdisk is biased at linear operating regim e.................................................................................................................... 267 Figure 5.5 (a) Band pass filter in a DNM photonic RF receiver decreases the shot noise by eliminating the high frequency components, (b) Band stop filter in a DOF photonic RF receiver eliminates the optical carrier and one o f the RF- optical sidebands......................................................................................................................268 Figure 5.6 (a) Spectral response o f optical filters with different number o f ring resonator, (b) The multi ring resonator bandpass optical filter fabricated on hydex material system [3].................................................................................................... 268 Figure 5.7 (a) Flybrid integration o f a L iN b03 microdisk photonic RF receiver on a silicon bench, (b) Monolithic integration o f a semiconductor microdisk photonic RF receiver based on compound semiconductor material system 270 Figure 5.8 Estimated power consumption using commercially available technology (gray blocks), and costume design technology (dotted line)................. 271 Figure 5.9 (a) Calculated receiver sensitivity against Fhmm f°r 3 different values o f optical insertion loss (-10db, -5 dB and -10 dB). The optical input power (P0,in) is 1 mW and the sensitivity o f the photoreceiver is -40 dBm. (b) Calculated receiver sensitivity against optical input power ( P 0 , i n ) for two microdisk modulators with Fhmm o f 0.45 V and 0.1 V. Again the sensitivity of the digital photoreceiver is -40 dBm. (c) Calculated receiver sensitivity against sensitivity o f the digital photoreceiver for an optical input power ( P 0 , i n ) o f 1 mW and a F h m m o f 0.1 V )...................................................................................... ’................... 274 Figure 5.10 The voltage dependence o f the effective refractive index variation and the corresponding phase shift for a N-AlGaAs/n-GaAs/P-AlGaAs waveguide modulator with length o f 800 pm at X = 1.06 pm [7], Lines correspond to the theoretical calculations. The dots are the experimental data for TE mode and triangles for TM m ode..................................................................................281 Figure 5.11 Calculated refractive index change generated by Kerr (a) and Franz-Keldysh effect in silicon [1 9 ]................................................................................ 283 Figure 5.12 (a) Photograph o f the waveguide-output and the rectangular waveguide o f the photonic 120GHz oscillator [26]. (b) Micrograph o f the transformer connecting the UTC-PD and the rectangular waveguide. (c) Relationship between the measured mm-wave output power and input optical power at 120 GHz for several bias voltages [26]............................................................. 287 xxiv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.13 Schematic diagram o f a photonic mm-wave transm itter........................288 Figure 5.14 Schematic o f the photonic wireless link [28]......................................... 289 Figure 5.15 Photonic generation o f the transmitted carrier signal by means o f optical modulation and photom ixing................................................................................ 290 xxv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abbreviations BW Bandwidth cw Continuous wave DC Constant power DD Direct detection DSC Double sidebands suppressed carrier RF modulation fonnat FBG Fiber Bragg grating FP Fabry-Perot IF intermediate frequency MZ Mach-Zehnder optical modulator NRZ Non-retum-to-zero PRBS Pseudo-random beat stream PM Polarization maintaining RoF RF over fiber RF Radio frequency WG W hispering Gallery xxvi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract A self-homodyne photonic receiver for transmitted carrier wireless links is demonstrated. The key innovations in this photonic RF-receiver are the design and implementation o f a resonant L iN b03 microdisk electro-optic modulator and novel RF down-conversion techniques that exploit the sensitivity o f the microdisk for efficient RF down-conversion in the optical domain. By careful RF and optical design, simultaneous photonic and RF resonance is achieved in a LiNbCf microdisk modulator resulting in a sensitivity o f -80 dBm at 14.6 GHz. Two photonic RF down-conversion techniques are proposed to extract the baseband information from a RF signal that has a transmitted carrier modulation format. In the first approach we use an optical filter to modify the optical output spectrum o f the microdisk modulator. Photodetection o f the subsequent optical signal generates the baseband photocurrent. In the second technique the RF carrier and sidebands are mixed through nonlinear optical modulation in the microdisk and the down- converted signal is detected using a photodetector. In both cases the bandwidth o f the photodetector and electronic circuitry are limited to that o f the baseband signal. Receiver operation is demonstrated by demodulating up to 100 Mb/s digital data from a 14.6 GHz RF carrier frequency. Power efficiency, small volume, light weight and elimination o f high-speed electronic components are the main specifications o f the photonic RF-receiver that make it useful for applications like wireless LANs, fiber-feed backbone networks or video distribution systems. xxvii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 Introduction 1.1 Motivation 1.1.1 Photonic RF signal processing Microwave links are essential parts o f today’s radio communication and radar systems. A factor limiting use o f mm-wave carrier frequencies in these links is the high attenuation o f RF signals in microwave cables and low efficiency o f conventional electronic devices. The design complexity and cost of fabricating solid-state electronics based signal processing devices and circuits increases significantly at mm-wave frequencies. RF-photonic technology is an alternate approach that employs an optical carrier in hybrid microwave-photonic links to transmit and distribute RF-signals as well as performing some signal processing functions photonically [1-10]. The primary task in a RF-photonic system is up- conversion from RF to optical frequencies or optical modulation. Direct modulation of laser sources becomes highly inefficient at mm-wave frequencies and external optical modulators, especially conventional LiNbC^ Mach-Zehnder (MZ) modulators, are the best alternative. Recently the bandwidth, efficiency and size of MZ-type modulators have been dramatically improved by better RF design and employing semiconductor electro-optic materials [15,20]. In RF subcarrier optical links information is carried within a limited bandwidth around a high-frequency RF- 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carrier. This is an opportunity to employ the high sensitivity offered by resonant optical modulators. Resonant modulators use either optical or electrical resonance to enhance the interaction length or modulating voltage at the expense o f loosing bandwidth [55-80], These modulators can only modulate within a limited bandwidth around discrete frequencies separated by RF or optical free-spectral-range o f the resonator. Resonant modulators are typically smaller than regular MZ modulators and by careful design their sensitivity can be maintained up to mm-wave frequencies where MZ modulators face significant RF-optical phase mismatch. Processing microwave and mm-wave signals in the optical domain has been the subject o f research for the past few years [1-3]. One o f the most interesting applications o f photonic RF processing is RF frequency conversion. RF frequency conversion in the optical domain has many advantages such as optical isolation from environmental RF noise and signals, independence from carrier frequency and elimination o f high-speed electronic circuitry. Frequency conversion in the optical domain is mainly achieved through optical filtering and nonlinear modulation. Photonic generation o f pure RF and mm-wave signals is another attractive application o f RF-photonics [3,4], Mixing infrared lasers in a high-speed photodiode is a powerful technique to generate a RF signal. Tunability over a wide range o f frequencies, simplicity o f the design, small volume, purity o f the RF spectrum are among the most promising features o f photonic RF generators. The high-frequency limit o f these generators is mainly imposed by the photodiode response. Recently the advent o f the uni-traveling carrier photodiode has noticeably increased the 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. operational frequency o f the photonic generators. The state-of-the art UTC-PD based photonic mm-wave source can generate a 90 GHz signal by mixing two DFB lasers [4]. The power and phase stability o f these devices is determined by the relative phase fluctuations o f the laser sources. An accurate and stable phase locking mechanism is a crucial requirement for a reliable RF or mm-wave source. A resonant LiNbCL microdisk modulator uses simultaneous electrical and optical resonance and hence benefits from both voltage-gain and enhanced electro-optic interaction length. This feature increases the sensitivity o f a microdisk modulator compared to other types o f modulators, and makes it a good candidate for a RF- photonic receiver. In this thesis it will be shown that LiNbCL microdisk modulators can be used in an all-optical receiver design that exploits their sensitivity in combination with optical signal processing techniques to receive and down-convert the data from an RF signal. 1.1.2 RF subcarrier links in wireless LANs and fiber-feed backbone networks A wireless local area network (LAN) is a data communication system implemented as either an extension to, or as an alternative to a conventional wired LAN. The majority o f wireless LAN systems use Radio Frequency (RF) transmission technology. Wireless LANs are typically fed through the wired LAN. The radio 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. access point consists of a bridge and a base station, and acts as the interface between the wired LAN and the wireless LAN. The requirement of high data rates and cell isolation push the carrier frequencies into mm-wave. A tm ospheric absorption of miHmnster-rang© waves W avelength tm m ) 30 2 0 10.0 S.O 6.05.0 4.0 3.0 1.0 0 ,8 100 40 20 10 _ Average atmospheric _ absorption o f m illim eter-ran g e wav© {horizontal propagation* / I °'1 % 0.04 0.02 0.01 0.004 0 .002 0 - 0 0 1 HgQ A-km a ltitu d e 150 200250300 400 (a) Customer units Optical fibers Base station ^ ) Central office Base station Base station b Wireless optical modulator (b) F igure 1.1 (a) S h o w s the propagation lo ss o f the electrom agnetic w a v es in air as a function o f frequency. T w o absorption peaks are o b served at 23 and 6 0 G H z (Source: phased array-based system s and app lication s, N ich o la s Fourikis, pp. 2 7 -2 8 , John W iley & Son s, 1997). (b) A schem atic diagram sh o w in g the co n cep t o f fiber-feed backbone netw orks and the function o f w ireless-o p tica l m odulator in the network. 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The propagation loss is high at mm-wave frequencies (Fig. 1.1(a)) so each base station will have a smaller coverage radius (5-10 km for micro-cellular and 1 km for pico-cellular). Adjacent cell interference is minimized and the network has a high degree o f frequency reuse. However, having small radio cells also means that numerous radio access points (or base stations) are required to cover a large area. Also, broadband wireless networks require a high capacity feeder network. The deployment and maintenance o f such a system using today’s copper based wired LANs is economically unattractive. An alternative is they are replaced by a high capacity optical fiber infrastructures [5-8]. RF over fiber (RoF) is the best candidate for this purpose (Fig. 1.1(b)). An important component in RoF systems is a low-power wireless optical modulator that can efficiently modulate the optical carrier using the weak RF power received by the antenna (typically 1-10 pW). Microdisk modulators can be made sensitive enough to operate at very small RF-powers (SNR o f 10 dB at -70 dBm RF power is demonstrated in this thesis), which makes it a useful component in these types o f links. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.1.3 Indoor wireless A video transmission system is an example o f a simple millimeter-wave application because it is a one-way redistribution system for received terrestrial or satellite broadcast video signal, and it is the first common millimeter-wave application in house-hold use [10]. Satellite broadcasting Terrestrial broadcasting serv ices \ serv ices W ireless optical receiver RF transm itters R e c e iv e r s .. C A T V services ( a ) W ireless optical receiver 2 D patch antenna array ( b ) F ig u re 1.2 (a) V id eo redistribution for h ou seh old s based on R F -photonic receiver system , (b) A p p lication o f R F -ph otonic receiver in an indoor w ireless L A N . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 1.2(a) illustrates the concept o f a mm-wave video transmission system for household use. Terrestrial, satellite-broadcast and/or cable television (CATV) signals are redistributed through the house by using mm-waves and optics [10]. A small low power RF-photonic receiver can be connected to each display device to receive the modulated carrier and recover the video signal. An indoor wireless data distribution system is another potential candidate for employing a RF-photonic receiver. Fig. 1.2(b) shows an example where a data modulated RF-carrier is transmitted by a directional antenna that broadcasts to all users. A small RF-photonic receiver is attached to each computer to receive the RF- signal and send the down-converted data to the computer. 1.2 Brief survey of the related topics LiNb0 3 microdisk optical modulator employs principles, techniques and physical concepts that have been the subject o f research for many years. Consequently, a brief survey o f the most important related research is useful. Fig. 1.3 shows four major concepts and technologies that are combined in a LiNbC>3 microdisk resonant modulator. In this section the main aspects o f these subjects are discussed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MZ LiNbOs electro-optic modulator RF ring resonator Microdisk modulator WG optical resonator Resonant modulation Figure 1.3 C on vergen ce o f four principal tech n o lo g ies in m icrodisk optical m odulator. 1.2.1 Mach-Zehnder modulator Traveling wave Mach-Zehnder (MZ) amplitude modulators are widely used in high speed optical communication systems. Conventional MZ interferometric modulators rely on two physical effects to vary the light intensity. The effects are voltage dependence o f light velocity in electro-optic materials (known as Pockels effect) and optical interference. Such modulators are typically composed of two Ti-diffused optical wave-guide arms fabricated in a LiNb0 3 wafer. The waveguides are typically 8x6 pm 2 in cross section with a loss of 0.1 dB/cm (the optical mode is 7x4 'y pm located about 2 pm below the surface) [9]. The electric field is applied with CPW 1 1 : i or CPS (2 ) structures. Performance is characterized by bandwidth, drive voltage (Vn), optical insertion loss and chirp. One of the main challenges for increasing the sensitivity at high frequencies is to maintain RF-optical phase 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. matching for a long distance. The effective optical and RF refractive index o f LiNb0 3 are different so there is an inherent mismatch between the optical and microwave velocities. As a result, the maximum achievable drive frequency decreases as the modulator length is increased. Conversely, to lower the drive voltage and power, a long device length is required. Thus a performance tradeoff is made between maximum drive frequency and required drive power. A large amount of effort has been dedicated to solve this problem resulting in lower drive voltages (factor o f 5) during the past 10 years [11-15]. Fig. 1.4(a) shows the picture o f a LiNbCh MZ modulator with a Vn o f 0.9 V at 40 Gb/s, which has been developed using a new design concept featuring a wide-gap and a long CPW electrode [15]. On the other hand these devices are relatively big and bulky (lcm xlcm xlO cm ) and hard to integrate with microphotonic devices. Integration with planar antennas is another issue, which makes using a conventional MZ modulator for certain wireless applications questionable. MZ modulators have been also fabricated using III-V compound semiconductor materials [18-20]. These modulators are typically smaller than LiNb 0 3 and they can be monolithically integrated with other microphotonic devices such as lasers and photodetectors. Fleterostructures for electro-optic phase modulation are typically made o f AlGaAs or InGaAsP compounds. A detail explanation o f the electro-optic effects in III-V structures is presented in Chapter 5. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) P h a s e - s h i f t recsG,- L = 3 , 0 m r n E lec trica l o u tp u t 5 0 - Q te rm in a tio n E lectrical input n-lnP S l-lnP i-MQW Xpt=1.37 pm BCB E lectrode O ptical input O p tic a l o u tp u t n-lnP S l-lnP E lec trica l o u tp u t Electrical input 5 0 - o te rm in a tio n ( b ) F ig u re 1.4 (a) Photograph o f a state-of-th e-art low -drive v o ltage (V„ = 0 .9 V olt) 4 0 G b/s L iN b 0 3 M Z m odulator [15 ]. (b ) A sem icon ductor M Z m odulator fabricated on a S l-ln P substrate. C ross- section al geom etry o f the n-i-n InP w a v eg u id e (left) and a photograph o f the fabricated chip (right) [20], Recently an InP-based Mach-Zehnder has been introduced with a bandwidth larger than 40 Gb/s and a Vn of 2.2 V [20], The length of the active arm in this modulator is about 3 mm. Fig 1.4(b) shows the cross-sectional geometry o f the active waveguide and a photograph of the MZ modulator chip (0.8 mm x 4.5 mm). 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.2.2 Microsphere optical resonator Microsphere resonators are very small (25 pm to 4 mm radius) optical resonators usually made o f fused silica. They are interesting because o f the ability to support confined high-Q Whispering G allery (WG) modes. Quality factors exceeding Q = 101 0 have been reported for these microresonators [21]. The long photon lifetime inside the microsphere is the key feature that makes it very attractive for various optical and opto-electronical applications. Challenges that must be overcome for practical applications are fabrication and optical coupling to Whispering-Gallery modes. Basic understanding o f the ultimate Q o f optical resonators and mode analysis has been investigated since mid 1990’s [21-23], Different schemes have been used to couple light into and out o f resonators, such as prism coupling, tapered-fiber coupling [26,27], angle polished fiber coupler [25] and planar single mode waveguide coupler [24], Among them the tapered-fiber coupling seems to be the most promising due to high coupling efficiency (98%) and geometrical compatibility with photonic circuit and filter designs. Fig. 1.5(a) is the photograph o f a microsphere coupled to two angle polished fiber couplers and Fig. 1.5(b) shows a microsphere resonator coupled to two tapered-fiber couplers in an add-drop filter configuration. Experimental results indicate that optical coupling loss of less than -3 dB is routinely achievable with this method [26]. Microspheres suffer from coupling stability and geometrical incompatibility with planar structures that will keep them from being commercially feasible. 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ( a ) ( b ) F ig u re 1.5 (a) Photograph o f a 2 3 5 pm radius silica m icrosphere ph otonic resonator sh o w in g angle p o lish ed -fib er couplers [25 ]. (b) Photograph o f a silica m icrosphere cou p led to tapered- fibers as an add-drop filter. O ver cou p lin g o f this d ev ice results in lo w loaded op tical-(2 o f 4 x l 0 4 for broadband app lication s [26]. 1.2.3 Microdisk and micro ring optical resonator Microdisk optical resonators are disk shaped Whispering-Gallery optical resonators. Medium size disks (1-10 mm diameter, 0.1-1 mm thickness) can be made from bulk material using special grinding and polishing techniques. Small size resonators (10- 200 pm diameter and 10-50 pm thickness) can be made using standard lithographic patterning and etching techniques. The principle advantage of the small disks is that they can be integrated with other monolithic microphotonic deices. But since most electro-optic crystals cannot be deposited and also the etching techniques do not provide the desired surface roughness quality to achieve very high opticai-Q, currently for certain applications medium size disks are the only candidates. Prism 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coupling and etch eroded half-block coupling are the main methods for coupling to medium size disks. Fig. 1.6(a) is a photograph o f a L iN b03 microdisk with a diameter o f 1 mm and a thickness o f 0.2 mm. Small size InP microdisk optical resonators have been fabricated using optical lithography and wafer bonding techniques [33,35]. The diameter o f these devices is typically between 4 to 12 pm and they can be vertically (Fig. 1.6(b)) or laterally (Fig. 1.6(c)) coupled to ridge waveguides fabricated on the same substrate and work as add-drop filters or switches [61,62]. The quality factor of these disks is around 6000 and is limited by surface roughness o f the etching process used in fabrication. Semiconductor microdisks can be used as active switches since their refractive index and loss can be changed by free carrier injection; consequently the optical 2-factor and the resonant wavelengths may be controlled by current flow [61]. Due to high index contrast, the air-guided structures (the waveguide and the microring are surrounded by air) are not always favorable in terms of optical losses and coupling efficiencies. Recently a buried InP/InGaAs microring resonator with a Q o f 105 has been demonstrated. Fig. 1.6(d) is the SEM cross-sectional view o f the buried InP microring resonator [35], Multi-quantum well microdisk lasers employ the WG optical-modes o f a microdisk [36-38]. Fig. 1.6(e) shows a microdisk laser with radius R = 0.8 pm and lasing wavelength of X « 1.5 pm. Detailed studies and modeling o f these active optical devices have revealed much o f the physics governing device operation. 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ( e ) ( f ) Figure 1.6 (a) Photograph o f LiNbO:, m icrodisk (D = 1 m m ). (b ) Photograph o f an InP m icrodisk vertically cou p led to parallel w a v eg u id es (D = 3 0 p m )[3 4 ]. (c ) Photograph o f an InP m icrodisk laterally cou p led to parallel w a v eg u id es (D = 4 p m )[3 4 ], (d ) A n SE M cro ss-sectio n a l v ie w o f a buried m icroring resonator [35]. (e) Photograph o f a m icrodisk laser (D = 1.6 pm ) [37 ]. (f) P hotograph o f an u ltra -h ig h -0 (1 0 8) toroidal silica m icrodisk.(Z ) = 150 pm ) [31], The CW room-temperature operation o f optically pumped InGaAs/InGaP microdisk lasers has been reported [38]. Monolithic microring and microdisk resonators have 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. been also fabricated based on Si-SiCh [28-30]. The diameter o f these ring resonators is typically 8-50 pm and their 0-factor strongly depends on the fabrication techniques. Recently a SiC>2 toroidal microdisk has been reported with a 0 o f 108 (Fig. 1.6(f)) [31]. These resonators have been mostly used for add-drop optical fdter design [29,30,31], Ring resonators with a 0 - factor of about 105 have been also fabricated based on polymer materials [32], The diameter o f these rings is between 50 and 500 pm and they are vertically coupled to polymer waveguides. Since they are made o f electro-optic polymers, they can be used as modulators (section 1.4.2) 1.2.4 RF microring resonator RF ring resonators are ring shaped microstrip structures used as resonant elements in RF filter design [39]. Previously, most o f the research in this subject has been on resonant frequency, 0-factor estimation and excitation methods for ring based RF filter design [39-43]. Several schemes have been developed to couple RF power into and out o f the ring resonators. O f these, magnetic side coupling and capacitive gap coupling are the most commonly used methods. Ring resonators are also used in electro-optic devices. G. K. Gopalakrishnan et al. have investigated the microwave optoelectronic interactions in a m icrostrip ring resonator by m onolithically integrating a Schottky diode photodetector into a microstrip ring resonator [45]. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The semi-ring resonator [44] hasn’t been used as much as the ring resonator for filter design. However, since its resonant frequency can be easily tuned (by trimming the length), it has been used in initial designs o f the microdisk modulator where RF- optical frequency matching is an important issue [74,75,79,80]. Fig. 1.7(a) shows a photograph of microstrip ring resonators side coupled to a microstrip line on a printed circuit board (PCB). Fig. 1.7(b) shows a ring resonator on top o f a LiNb0 3 microdisk that is side-coupled to microstrip line fabricated on a PCB. The typical Q- factor o f these ring resonators is between 50-150, depending on the surface roughness o f the ring, ring size and properties of the substrate material. The geometrical compatibility and relatively high-(9 makes these resonators a good choice to provide voltage gain (through resonance) in a microdisk modulator. M icrostripline I M icrostrip line R ing resonator R ing resonator L iN b 0 3 m icod isk ( a ) ( b ) Figure 1.7 (a) Photograph o f m icrostrip ring resonators sid e-co u p led to a m icrostrip line on a printed circuit board (P C B ). (b ) A ring resonator on top o f a L iN b 0 3 disk (D = 5.8 m m ), side cou p led to a m icrostrip line on a PCB. 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.2.5 Wireless receivers A well-designed radio receiver must satisfy the following requirements [47]: (A) High gain (-100 dB) to restore the low power o f the received signal to a level near its original baseband value. (B) Frequency selectivity, in order to receive the desired signal while rejecting adjacent channels, image frequencies, and interference. (C) Down-conversion from the received RF' frequency to an IF frequency for processing. (D) Detection o f the received analog or digital information. (E) Isolation from the transmitter to avoid saturation. Because the typical power level from the receive antenna may be as low as -100 to - 120 dBm, the receiver may be required to provide power gain as high as 100 to 120 dB. The global system for mobile communication (GSM) standard (3 ) requires a minimum sensitivity o f -102 dBm and a dynamic range of 62 dB (4). This much gain should be spread over RF, IF and baseband stages to avoid instabilities and possible oscillation. It is generally good practice to avoid more than about 50-60 dB o f gain at any one frequency band. The fact that amplifier cost generally increases with frequency is a further reason to spread gain over different frequency stages. Here we present an overview o f some o f the most important types o f RF wireless receiver architectures: Direct conversion receiver. The direct conversion receiver, shown in Fig. 1.8(a), uses a mixer and local oscillator to perform frequency down-conversion with zero IF frequency. The local oscillator is set to the same frequency as the desired RF signal, 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which is then converted directly to baseband. The direct conversion receiver is sometimes called a homodyne receiver. For AM reception the received baseband signal would not require any further detection. RF amp j j >P Baseband amp Mixer Baseband LO ( a ) V IF amp RF amp Mixer BPF Demod LO ( b ) t! R F am p Mixer BPF ^ Mixer BPF 2' ^ IF 1st LO 2n d LO Demod 2 LO ( c ) Figure 1.8 B lo ck diagram s o f w ireless receiver architectures, (a) D irect co n version (h o m o d y n e) receiver, (b ) Super heterodyne receiver, (c) D ual co n version superheterodyne receiver. Superheterodyne Receiver. By far the most popular type o f receiver used today is the superheterodyne architecture shown in Fig. 1.8(b). In this design the intermediate frequency (IF) is not zero. A midrange IF allows the use of an IF amplifier. Tuning is conveniently accomplished by varying the frequency o f the 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. local oscillator so that the IF frequency remains constant. At microwave and mm- wave frequencies it is often necessary to use two stages of down-conversion to avoid problems due to LO stability. The dual-conversion superheterodyne receiver o f Fig. 1.8(c) employs two local oscillators and mixers to achieve down-conversion to baseband with two IF frequencies. Self-heterodyne Receiver. Recently a novel receiver design has been proposed for mm-wave indoor wireless video distribution [48,49]. In this architecture the local oscillator is transmitted along with the signal. The signal is down-converted to IF frequencies by mixing the received local oscillator and the signal in a self-mixer. So the high-frequency local oscillator is eliminated. The term self-heterodyne implies a heterodyne receiver that relies on self-mixing rather than mixing with a local oscillator. In Chapter 4 we will show that by eliminating the IF stage the self-mixing technique may be employed in a self-homodyne photonic receiver that down-coverts the baseband information in optical domain. Currently one o f the main challenges in wireless receiver design is to increase the carrier frequency and design efficient wireless links at mm-wave frequencies [50- 54], Recently a 24 GHz CMOS front-end has been demonstrated in a 0.18pm process that consist o f a low-noise amplifier (LNA) and a mixer that down-converts an RF input o f 24 GHz to an IF o f 5 GHz [53], Today’s frequency performance limitations o f CMOS technology has led to use o f alternative material systems for 60 GHz applications. Preliminary studies and experiments show a 60 GHz transceiver circuit based on SiGe bipolar technology is achievable [54]. 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The NEC group has developed a 60 GHz transmit/receive electronic analog RF front-end module using 0.15 pm gate-length AlGaAs/InGaAs heterojunction FETs w ith /m ax > 220 GHz for electronic circuitry and a Ba(M g,Ta)03 dielectric resonator to stabilize a fixed frequency, low phase-noise, local oscillator (LO). The packaged device occupies a volume o f 900mm3 and consumes 400mW power [51]. Operation at carrier frequencies above 60 GHz is an opportunity for new system design as well as a change in device technology because the conventional electronic devices lose their efficiency to a level that cannot easily be compensated for by novel system designs. Processing the received RF/mm-wave signal in the optical domain is a promising alternative to conventional electronic with the potential benefit o f reduced power consumption as well as reduced device volume. In this thesis we investigate some of the possibilities o f employing photonic technology in wireless receiver design. 1.3 Resonant optical modulator 1.3.1 Optical resonance In an optical resonator energy is confined in a small volume by means o f multi- reflections at low loss and high reflectivity interfaces. The photons are trapped in the resonator for a relatively long period o f time (compared to the time for a single pass 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. through the resonator). The resonance boundary conditions impose a constraint on the frequency o f the resonant photons thus only photons within a limited bandwidth around certain frequencies can resonate in the cavity. Spatial confinement, long photon lifetime and frequency selectivity are the main traits of the optical resonance that can be used in many photonic devices. The average amount o f time that a photon stays in the resonator is called photon life time (xp ) and can be estimated as xp = Q /a, where Q is the quality factor o f the resonance and co is the photon frequency. The number of photons inside the resonator can be written as [65]: N ( t) = N Q e - (mlQ)l (1.1) where N is the number of photons in the resonator at time /, N o is the initial number of photons in the cavity. So at time t = xp the number o f photons in the cavity (initially N o ) reduces to ( l/e)No. The photon lifetime (xp) can also be written as [65]: ( 1.2 ) p I - s where t r t is the photon roundtrip time and S is the survival factor or the number of photons surviving in a roundtrip. Evidently a long photon life time or high-Q requires a low-loss resonator. For a resonator with an effective refractive index n, xp can be translated to an effective length Zeif= xpc/n that is the characteristic length a photon travels before escaping from the resonator. In electro-optic applications, the long photon lifetime can be used to enhance the interaction between the electro-optic medium and the photon in a very small volume. 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A well-known optical resonator is the Fabry-Perot (FP) resonator. It is a linear resonator with two reflecting boundaries. The spectrum o f the transmitted optical power through a Fabry-Perot resonator is a series of equally spaced peaks. The frequency interval between the peaks is called the free-spectral-range (FSR). The full-width-half-maximum (FWHM) o f each peak is A v Fw h m = Q /vr c s where vre s is the resonant frequency. The FSR and the Q o f a Fabry-Perot resonator are determined by the mirror reflections, and the length of the resonator. Fig. 1.9(a) shows the geometry o f a Fabry-Perot resonator. Input k i T ransm itted Ei R { R2 ------ Input r ................................1 Transm itted „ ------ --------------------J £t ► R eflected -------- ---------- ► E L C ou pled out-*-------------^ ( a ) ( b ) Figure. 1.9 (a) G eom etry o f a Fabry-Perot standing w a v e resonator. Input electric field is E -„ reflected field is Et and transm itted field is Et. T he cavity is o f length L and the reflectivity o f the tw o mirrors is and R2. (b) G eom etry o f a circular traveling w ave resonator. The input optical power is coupled to the resonator through a mirror o f reflectivity R\. The reflected and transmitted power spectrum can be calculated in terms of the resonator length, loss factor inside the resonator, and mirror reflections. Table 1.1 summarizes the main parameters o f a Fabry-Perot resonator and their relations. Ring resonators are another important category of optical resonator. The main difference between a ring resonator and a Fabry-Perot resonator is the fact that the electromagnetic field in a Fabry-Perot resonator has a standing wave distribution but in a ring resonator it can be a traveling wave. In a ring resonator the reflecting 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. surfaces are distributed around the periphery of the resonator and the traveling wave is continuously reflected while it travels around the resonator. If the ring resonator has a spherical geometry the lowest order fundamental traveling resonance is WG mode. Coupling into and out of a ring resonator can be achieved by means o f evanescent coupling from a media that has a larger refractive index than the resonator T a b le 1.1 Sum m ary o f Fabry-Perot form ulas Q uantity R elation w ith other param eters R ound-trip phase shift (R T P S ) n co L U — c T ransm itted pow er T — . E \ 2 T _ E , 2 ( \ - ^ R tR 2 ) 2 + 4 ^ R tR 2 sin 2 0 R eflected pow er R = E X n _ ( V * , ~ ^ R 2 ) 2 + 4^ R , R 2 sin 2 0 E, 2 ( \ - ^ R , R 2 Y + 4 sin 2 9 Q uality factor 0 - ..... "■ Ircn L (/?, R 2 ) 4 A A V FWHM 3 ~ 1 N) 1- (7? ,Z2) - F in esse F _ G ,v« ^ d l n L n:(R[R 2) 4 A V FWHM r — - ----------— ......................... ^ / A V FWHM 1 - ( R , R , ) / 2 Free spectral range (F SR ) A V FSR = 0 , 2nL Thus the input/output coupling mirrors in a Fabry-Perot resonator (R\ and Rj) are replaced by the couplers (ki and K 2). Fig. 1.9(b) shows the basic geometry o f a ring resonator. By carefully replacing the reflectivity (R\) with coupling factor (Kj) and the length (Z) with circumference (2nR) most formulas from Table 1.1 can be used for a ring resonator. Notice that the optical power coupled out from the second 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coupler in a ring resonator is equivalent to the reflected optical power in the Fabry- Perot resonator. The FSR o f a ring resonator can be written as: A v is, Sit 2nL , where R is the ring radius. Fig. 1.10(a) shows the FSR against the disk diameter for an average size ring resonator made o f LiNbC>3 (n = 2.14). H c4 m U h 80 60 O 40 0 0.5 1.5 2.5 3.5 4.5 5.5 Disk diameter (mm) ( a ) 10 8 6 4 2 0 P olym er P olym er -LiNbOj InP, G aA s 0.8 0.6 0.4 0.2 InP, G aA s 50 100 150 200 5 15 25 35 45 Disk diameter (pm) Disk diameter (pm) ( b ) Figure 1.10 (a) F S R o f a L iN b 0 3 average size m icrodisk optical resonator against its diam eter, (b) F SR o f polym er, L iN b 0 3 and sem icon ductor m icrodisk optical resonators against their diam eter. Fig. 1.10(b) shows the FSR o f a microring resonator made of polymer (n = 1.5), LiNb0 3 and semiconductor (n = 3.4) against their diameter. 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.3.2 Electrical resonance An electrical resonator is the equivalent o f an optical resonator at relatively low frequencies (MHz-GHz). The main difference is that in most electric resonators the wavelength is similar in value to the resonator dimensions or larger (k/L > 1), while in most optical resonators the wavelength is much smaller than the resonator dimensions (k/L « 1). So even in RF resonators with ring geometry the resonances are standing waves. Due to this difference the behavior o f RF resonator is better understood as the energy exchange between electric and magnetic field oscillations rather than a traveling wave. The operation o f most electronic resonators can be explained in terms o f lumped- element resonators o f circuit theory. The most basic resonant circuits are series and parallel RLC resonant circuits. Fig. 1.11(a) and (b) show series and parallel RLC resonators respectively. Table 1.2 summarizes the relation among the key parameters of series and parallel RLC resonators. For opto-electronic applications the most commonly used resonator structures are microstripline based. 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.11 (a) S eries resonant circuit, (b) Parallel resonant circuit, (c) O pen ended m icrostrip resonant circuit The simplest microstripline resonator is an open ended rectangular patch on a dielectric substrate (Fig. 1.11(c)). Because of its application in RF filter design, various aspects of this resonator have been the subject o f research for a long time [66,67], The properties o f the microstrip resonator are determined by its geometry and permittivity and the loss tangent o f the dielectric substrate. In a resonant electro optic modulator, we intent to use these resonators to control and amplify the T-field in certain regions. Using the relations in Table 1.2, one can easily derive the voltage across the capacitor in a series RLC circuit at resonance (co = coq): This equation shows that a series RLC resonant circuit can amplify the voltage with a (1.3) factor proportional to Vg. So any distributed element circuit whose equivalent 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. circuit may be simplified as a series lumped element resonant circuit, in principle, will have the same voltage amplification factor (°cVg). It is evident that C, R and L should be derived in terms of the geometrical and dielectric properties o f the distributed element resonant circuit. T a b le 1.2 Sum m ary o f m ain form ulas o f series and parallel resonant circuits Q uantity S eries RLC resonator Parallel RLC resonator A v erage m agnetic energy stored in the inductor (W„) 1 1 r 1 W = \v\~ a \ \ 2 r 4 co L A v era g e electric energy stored in the capacitor (W e ) 1 i 12 w, = -\V ,\ C 4 I U ll | - O P ow er loss - s P = ’ 2 R U n load ed quality factor (QkI’ JI) w +w loss W + W Q h,-.v = < *> \ m = M a> 0R C * loss R esonant freq uency (co0) 1 4 l c 1 V Z Z 7 Input im pedance (Zin) z ,„ = R + j(» L - y - 7 7 coC ( 1 1 V ' Z,„ = - + ---------+ jcoC y R jcoL ' 1.3.3 Resonant electro-optic modulation Resonant optical modulators use resonance to enhance the electro-optical interaction through am plified E-field and/or longer interaction length. These m odulators can be divided into three main categories depending on the nature of the resonance that is employed in their design: electrical, optical or both. Electric resonance increases the 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. E-field intensity and optical resonance increases the interaction length, in both cases frequency bandwidth is sacrificed for modulation efficiency. Resonant modulators can only perform efficient modulation within limited bandwidth around discrete RF center frequencies defined by integer multiples o f optical free spectral range or RF resonant frequencies. Operation in simultaneous electrical and optical resonance operation requires a resonant RF equal to the optical FSR or an integer multiple of the FSR. The modulation bandwidth is limited by the highest quality factor (which in most cases we will consider is the optical Q). The concept o f resonant modulation has been investigated since 1962 [58] and many resonant modulators have been developed using different types o f electrical and optical resonators [55-80], Although MZ modulators with bandwidth in excess o f 40 GHz have been demonstrated [15], such devices exhibit only modest RF conversion efficiency. Wireless communication typically doesn’t require M Z’s broadband response. For example Personal Communication Systems (PCS) standards require only 60 MHz bandwidth around the center frequency o f 1.9 GHz, allowing great potential for optimization o f modulation efficiency through resonant enhancement. Fig. 1.12(a) shows the schematic diagram o f an electrically resonant modulator. In this configuration the RF-resonance is achieved by introducing impedance discontinuities at RF input and output ports o f the electrode in an MZ modulator. RF resonance occurs at 540 MHz with a bandwidth o f 92 MHz. 10 dB enhancement over a regular impedance matched traveling wave modulator has been reported [70], 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RF in O ptical O ptical D C bias Load- Load-Mismatch Output Input 50 f l M odulated ring sectio n C oupler In ( a ) ( b ) F ig u r e 1 .1 2 (a) A n electrica lly resonant M Z -m odulator. 10 dB enhancem ent through electrical resonance has b e e n a ch iev ed [70], (b) A n o p tica lly resonant m odulator. 5 dB enhan cem ent com pared to a straight w a v eg u id e o f len gth equal to the ring has b een reported [60]. Fig 1.12(b) shows an optically resonant modulator where a ring resonator is side- coupled to one arm o f a MZ modulator. The ring is made o f 25 InGaAsP/InP quantum-wells and its refractive index is sensitive to applied F-field across the ring. A semi-ring metal electrode that is placed on top o f the ring provides the modulating Zs-field. The ring effectively increases the electro-optic interaction length in the active arm and enhances the sensitivity o f the device. The optical-g o f the resonator is 4500 and 5 dB enhancement compared to a straight waveguide o f length equal to the ring has been reported [60], It is important to mention that in optically resonant modulators (unlike MZ modulators) Vn is not a well-defined quantity since the device does not work based on MZ interference principle. Instead there is a Lorentzian transfer function whose 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resonant wavelength changes as a function o f applied electric field. In this case the voltage F f w h m required to shift the resonance by A v f w h m (where A v f w i i m = Q! vres, vres: optical resonant frequency) may be used to quantify the modulator performance. Another definition used as a measure o f modulator sensitivity is the variation o f the optical intensity with respect to voltage at the half-transmission point: . dP„ dV For a MZ modulator this quantity is related to VK by: y - ( dP Ut 0 ,0 1 1 / \ dV \ 1 1 2 ) [59]. This relation can be used to define an equivalent Vneq for a resonant modulator. If one uses the bandwidth/voltage ratio ( fu d F f q) as the figure o f merit for an electro optic modulator, traveling wave MZ modulators outperform resonant modulators [59], Although using as a figure of merit is a reasonable choice for broadband optical communication applications, it is not a suitable choice for RF- subcarrier optical links where a limited bandwidth around a high-frequency carrier is usually required. Modulation bandwidth limitation imposed by optical resonance The modulation bandwidth o f an optically resonant modulator is limited by spectral linewidth and the free spectral range. Using the optical transmission spectrum o f the modulator, the modulation spectrum can be qualitatively explained as follows: The optical transmission spectrum o f the modulator is a series of equally spaced Lorentzians with linewidths of A v f w h m ( A v f w h m = Q! vres) separated by A v f s r as shown in Fig. 1.13 ( A v f s r = c/2nR ne = l/xrt. xrt = optical roundtrip time of the 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resonator). Through the modulation process optical power is coupled out from V |ascr (optical carrier frequency) into optical sidebands viaser ± / r f . All o f these frequencies (viascr ± / r f , viaser) have to be resonant inside the microdisk so that optical energy cannot be pumped into them. The optical transmission spectrum can be used as a fdter that modifies the optical spectrum o f the modulated signal. Assuming the laser frequency is tuned to v,„- A v f w h m /2 (middle o f the slope), when / r f < A v f w n m /2 both sidebands would be inside the m-th resonance so the output will be modulated (Fig. 1.13(a)). Now as we increase / r f the optical power in the sidebands decreases until they are completely filtered out (Fig. 1.13(b)). So low frequency modulation is allowed with a bandwidth o f about A v f w h m / 2 . If we continue increasing/ r f , at / r f ~ A v f s r again the sidebands become resonant (Fig. 1.13(c)). It is obvious that since the spectral linewidth is A v Fw h m , the modulation bandwidth around A v f s r is A v f w h m - The same situation is periodically repeated around/ r f = mx A v f s r is an integer). We may conclude that only R F frequencies less than A v f w i i m / 2 and within a A v f w h m bandwidth centered around integral multiples o f the optical FSR can modulate the optical mode. W e refer to the low frequency modulation as linewidth modulation and the modulation at mx A v f s r (m ^ 0) as FSR modulation. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Optical power \- 4 — A V FWHM V m + ! Frequency .Optical power A v f w h m < / r f < 2 A v |.\s r V m + i Frequency Optical power A v f s r + A v f w h m > ./ r f > A v f s r - A u f w h m V m + i Frequency F ig u re 1.13 Q ualitative behavior o f the frequency resp on se based, (a) L inew idth m odulation: the RF carrier frequency is sm aller than A v FWHm /2 . P olym er and sem icon d u ctor m icroring and m icroring resonators w ork in this regim e, (b ) N o m odulation: the RF frequency is larger than optical bandw idth but sm aller than the optical free-spectral-range so the R F -optical sideban ds are filtered out by the optical transfer function, (c) F SR m odulation: T he R F -optical sideban ds are w ithin the adjacent resonances. L iN b 0 3 m icrodisk m odulator w orks in this regim e. Fig. 1.14(a) shows the ideal frequency response of a resonant optical modulator (solid line) and a traveling wave optical modulator (dashed line). 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In both cases we assume the RF and optical waves are phase matched and the high frequency response o f the modulator is limited by electrical losses. We should point out that here we want to have a qualitative estimation o f the modulation and the details strongly depend on the specific modulator design. As may be seen at high- frequencies where the sensitivity o f the traveling wave modulator is reduced we expect better sensitivity from the resonant modulator, even though within a small bandwidth around /m x A v f s r .. The bandwidth limitation imposed by A v f w h m and A v f s r may challenge the usefulness o f employing high-(9 resonant modulators for broadband optical communications where data rates as high as 40 Gb/s are currently achieved by traveling wave modulators. However in most RF-subcarrier links and also wireless communications broadband is unnecessary. In such circumstances resonant microdisk modulators offering efficient modulation around a high frequency carrier may represent a competitive technology. Since the center frequencies (/wxAvfsr) are determined by the refractive index and the diameter o f the disk, the RF carrier frequency imposes limitation on the disk size and the electro-optic material. For example Fig. 1.10(b) shows that for current wireless applications, where the carrier frequency is between 1 GHz 1 and 60 GHz, the small size polymer and semiconductor microdisks cannot be used for FSR modulation because their FSR is in THz regime. In contrast, the FSR of the average size LiNbCT microdisks is about 5 to 50 GHz and so is suitable for many wireless applications. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. — T raveling w ave M Z m odulator — O ptically resonant m odulator O ptical am plitude m odulation RF frequency Sem icon d u ctor m icrodisk (InP) [61] m 51 -------- L inew idth / co' o 41 m o d u la tio n 1 X> i o (U 31 FSR modulation d> 1 i - Q 21 11 ! To ; D I i --------------------------- 5000 13000 21000 29000 37000 45000 O ptical quality factor (Q) ( b ) P olym er [56] and all-buried InP/InG aA sP m icrodisk [63] Linewidth modulation [•SR modulation 2.0E+04 i.OE+04 1.4E+05 2.0E+05 2.6E+05 O ptical quality factor (Q ) (c) 250 Linewidth modulation F SR m o d u la tio n 4 C 200 .o 5 — 150 <u c 5 s — L iN b 0 3 m icrodisk [7 4 ,7 5 ] 100 03 1.5E+06 3.5E+06 5.5E+06 7.5E+06 9.5E+06 O ptical quality factor (Q) (d) Figure 1.14 (a) Ideal frequency response o f a resonant optical m odulator (so lid lin e) and a traveling w ave optical m odulator (dashed line), (b), (c) and (d) D igital m odulation bandw idth o f m icrodisk m odulator against optical quality factor in baseband and F SR m odulation regim es. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig 1.14 (a), (b) and (c) show the digital modulation bandwidth o f baseband and FSR modulation as a function o f optical-^ for microdisk modulator technology we have developed. The digital modulation bandwidth (data rate) is estimated knowing that if the analog bandwidth is about 70% o f digital bandwidth an acceptable BER (below 10"';) can be achieved. As may be seen semiconductor microdisk modulators can provide a bandwidth of about 20 Gb/s using baseband modulation (assuming the electronic properties do not limit the modulation speed). H igh-0 polymer modulators have a modulation bandwidth o f about 3 Gb/s again in the baseband modulation regime [56]. L ow -g polymer modulators may have bandwidths as high as 15 GHz [64] but their sensitivity is too low for practical applications. Due to its high quality factor, L iN b03 microdisk modulator has a bandwidth o f about 100 Mb/s using FSR modulation. 1.4 Microdisk and microring optical modulators The microdisk modulator is a traveling-wave optical resonator made o f electro-optic material with an electrode structure that provides the modulating //-field in the optical mode region. Because o f the high quality factor o f whispering-gallery (WG) modes inside the microdisk (106 - 107) the photon lifetime is large and therefore efficient electro-optic interaction becomes possible in a small volume. If the electrode is also designed as a RF-resonator with a fundamental resonant frequency 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equal to the optical free spectral range o f the microdisk, simultaneous RF-optical resonance can be achieved, which makes the modulator more sensitive. 1.4.1 LiN b03 microdisk modulator The first microdisk modulator reported was fabricated in LiNbCb [74,75] and to our knowledge it is the only modulator that is both optically and electrically resonant. It consists o f a microdisk optical resonator, a RF resonator and coupling structures for optical and RF coupling to these resonators. LiNbO-, disk RF output M icroring resonator S id e-co u p led ggtfj m icrostrip line m icrop n sm OUtDUt LaSer inPUt F igure 1.15 Photograph o f a L iN b 0 3 m icrodisk m odulator (D = 5.8 m m ) w ith RF-ring resonator and sin gle-p rism optical coupling. The optical resonator is fabricated from a disk shaped z-cut LiNbCb. Fig. 1.15 shows the photograph of a LiNbCh microdisk modulator. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The basic geometry o f the LiNbCh resonator is a disk of radius R, and thickness h. The sidewalls o f the disk are optically polished with a radius o f curvature Rs, which is typically equal to the radius o f the disk (since the disk is usually made by thinning a sphere down to the desired thickness). The RF resonator is a full-ring or half-ring copper electrode placed on top o f the disk with a radius equal to the radius o f the disk. Light is coupled into and out o f the disk by using a single or double prism coupling method. RF power is coupled to the half-ring (or ring) by side coupling to a microstrip line that can be open or 50 Q terminated. TE polarized (E-ficld parallel to c-axis) optical W G modes inside the microdisk are exited with a single mode DFB laser (A , = 1550 nm) and detected with a cleaved (or lensed) fiber. The fundamental resonant frequency o f the standing wave RF-resonator is equal to the FSR o f the disk. Therefore, by feeding the microstrip line at / r f = A v f s r , simultaneous electrical and optical resonance is achieved. It has been shown that, unlike the M ach-Zehnder modulator, the microdisk can perform efficient optical modulation without use o f a reference arm to convert phase to amplitude modulation [80]. 1.4.2 Polymer microring modulator Polym er m icroring m odulators have been recently developed based on sim ilar principles as LiNbCL microdisk modulator [56,64] but they use electro-optic polymers instead o f LiNbCL as their active media. These materials have been 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. previously used for making regular MZ modulators [16,17]. Fig. 1.16 shows the layout and the cross section o f the fabricated device. A micro-ring waveguide made of electro-optic polymer material (M l) is vertically coupled to the input and output ridge-waveguides made of a different material (M2). The space between the waveguides and the microring resonator is filed with a third material (M3) that has a lower refractive index than M l and M2. A gold-ring on top o f the device provides the modulating f-field around the ring. output Au electrode U pper and low er clad dings '/A A u electrod e 5 pm 5 pm P olym er Rinj M l ► M 2 input E n M3 F ig u re 1 .1 6 (a) L ayout photograph o f the fabricated d ev ice sh o w in g polym er m icroring w a v eg u id e (D = 5 0 0 pm ) vertically cou p led to perpendicular straight w a v eg u id es, (b) S chem atic diagram o f the d e v ice cro ss-sectio n sh ow in g the m aterial system and dim ension s. It is important to notice that in this case the ring is not an RF-resonator because it is much smaller than the microwave wavelength and its high-speed behavior is mainly capacitive [64], So the polymer microring resonators are optically resonant modulators similar to the MZ modulator in Fig. 1.12(b). 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The FSR and optical-Q o f the ring as well as coupling efficiency between the wave guide and the resonator are determined by refractive index contrast (M2-M3 and M l- M2), size and spacing. Maximum possible refractive index contrast using polymer materials is about 0.3. The typical Q o f these devices is about 5-8x104. The Q and hence the sensitivity of polymer microdisk modulators depends o f the device diameter, optical mode polarization (TE or TM) and the resonant wavelength. At A ,ies = 1300 nm a polymer microdisk with a 1.5 mm diameter has a Q o f 6.2x104 for TE polarized modes (E - field perpendicular to the disk surface) and a Q o f 7.6x104 for TM polarized modes [56]. These Qs correspond to bandwidths o f 3 GHz and 4 GHz respectively. The FW HM-shift-voltage ( F f w h m ) is about 4.86 Volt for this device. At /,rc s = 1550 nm the Q drops to almost half o f its value at 1300 nm and the F f w h m is about 16 V. Reducing the microdisk diameter increases the bending loss and therefore decreases the Q. A 3 mm diameter polymer microdisk has a Q o f 4 .7 x l0 4 for TE polarized modes (F-field perpendicular to the disk surface) and a Q o f 5.8xl04 for TM polarized modes [56], 1.4.3 Semiconductor microdisk modulator Microdisk optical modulators have been also fabricated based on III-V semiconductor materials. One o f the first examples is an InP microdisk resonator 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vertically coupled to two parallel waveguides [62] similar to the one shown in Fig. 1.6(b). The microdisk has a radius o f 10 pm, an optical-(2 o f about 5500 (Avfwhm 0.27 nm), and a FSR o f 10 nm. The change in effective refractive index in this microdisk is achieved by free carrier injection (FCI). It is also possible to incorporate quantum wells with emission wavelength near 1550 nm to define a gain region that can controls optical loss in the W G cavity. The measured response o f the FCI device shows a modal index change o f -2x10'3 /mA. The maximum tuning range is limited by the cavity heating. Increasing the drive current in a microdisk with active QW region near the bandgap decreases the loss in the cavity and increases the Q. At around 10 mA injected current the device acts as an amplifier and increases the optical power in the drop channel. Applying a reverse bias on the active microdisk, shifts the absorption edge towards longer wavelengths by a slope o f about 0.06 nm/V corresponding to an index change of about 4x10 ~ 4. Any o f these changes may be used for switching or modulating the coupled optical power to the drop or transmission channel. When free carrier injection is used to change the refractive index, the modulation bandwidth is limited by the minority carrier lifetime. So achieving a large modulation bandwidth requires use o f other electro-optic mechanisms in the semiconductor. An externally applied electric field can change the refractive index of a p-n junction by changing the depletion. Recently a semiconductor microdisk modulator has been demonstrated that uses this mechanism for electro-optic modulation [63], The active microdisk is made o f a InGaAsP p-n junction and has a 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Q o f about 8500 ( A v f w h m - 0.18 nm). Using this device a modulation bandwidth of about 8 GHz has been achieved at a modulation voltage of less than 1 V. 1.5 Microdisk photonic RF receiver In a photonic RF-receiver, the intent is to replace all the electronic components o f a conventional RF receiver with photonic elements that, in principle, they are smaller and consume less power. Processing RF and mm-wave signals in the optical domain reduces the design and performance issues associated with high-frequency electronics. In a photonic receiver, the carrier frequency may be extended from a few GHz to mm-wave frequencies without any major change in system architecture since eventually the signal is processed in the optical domain. The photonic RF receiver also benefits from optical isolation wherever protection from interference with environmental and unwanted signals is required. The 60 GHz transmit/receive electronic analog RF front-end module developed by NEC [51] consumes 1.2 W o f which 0.4 W is used for the receiver with a digital bandwidth o f 10 Mb/s, sensitivity o f 10 pW and a volume o f 900 mm 3. We will show that a photonic receiver can provide the same sensitivity and bandwidth in a smaller volume and less power consumption. In the photonic RF-wireless receiver shown in Fig. 1.17, the electromagnetic radiation detected by the receiving antenna modulates a laser beam. Through signal 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. processing in the optical domain using optical filtering, optical mixing, and photodetection, the electrical baseband information signal is extracted from the received RF/mm-wave signal. Three mechanisms may be used to extract the baseband information in the optical domain: 1) The intensity o f the optical carrier (laser) is linearly modulated by the received RF/mm-wave signal and is then detected with a nonlinear photodetector that generates a photocurrent proportional to the square o f the optical power. Through nonlinear photodetection the up-converted carrier and sidebands are mixed resulting in a baseband modulated photocurrent. In this approach a very sensitive optical intensity modulator and a high-speed photodetector are required. The photodetector should operate in a strong nonlinear regime that may require a modified photodetector design. 2) The intensity o f the optical carrier (laser) is linearly modulated by the received RF/mm-wave signal and is then fed to an optical filter that filters out the optical carrier and the higher frequency sideband. When this modified optical signal is fed to a photodiode, the baseband photocurrent is generated. In this approach a very sensitive optical amplitude modulator and optical filter with proper role-off and a low-speed detector are required. Since the photodetection is linear, a conventional photodetector can be used. 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ; Nonlinear down-conversion Antenna V Multipole filter B aseband a m plifier Laser T IA Microphotonic modulator L aser d iod e w ith low E fficien t optical couplini H igh v o lta g e gain RF resonator M ultip lication takes place here. C on ventional optical m odulator requires high -sp eed pin (up to RF carrier frequency) Figure 1.17 T he schem atic diagram o f a photonic R F -w ireless receiver . 3) The intensity o f the optical carrier (laser) is nonlinearly modulated by the received RF/mm-wave signal. Due to nonlinear modulation the output intensity will be baseband modulated and the baseband photocurrent is generated in a low-speed photodetector. In this approach optical filters are not required but they can be used to improve the noise performance o f the receiver. In such photonic receiver designs employing a transmitted carrier RF modulation format there is no need for a local oscillator. The mixing occurs in the optical domain and the baseband current is generated by a photodetector. In the 2n d and 3rd approach the bandwidth o f the photodetector is limited to that of the baseband and no high-speed electronic components are required. A sensitive modulator that can convert a weak detected RF-power from the antenna (pW regime) to optical modulation is a key component in all of these architectures. 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The high sensitivity due to simultaneous optical and electrical resonance, small size, operation in the RF carrier frequency range of 5 GHz to 60 GHz makes the LiNb0 3 microdisk modulator a suitable candidate for this task. It is useful to describe gain in the photonic RF-wireless receiver in the context o f a conventional electronic RF-wireless receiver architecture. The gain in the photonic receiver is mainly provided by the RF-to-optical conversion in the modulator and optical-to-electrical baseband conversion in the photoreceiver. So basically the total gain is a combination of the modulator and photoreceiver sensitivity. For every photonic down-conversion method we can define a RF-to-baseband optical gain as: This gain is directly proportional to modulator sensitivity and also the chosen mechanism for down-conversion. The detector sensitivity is normally quantified as responsivity (R) that is the ratio between the photocurrent and the input optical power. So if we define the gain of the wireless receiver as the ratio between the down-converted baseband power and the received RF power, the overall gain o f the photonic wireless receiver can be written as: where Z i is the load impedance and A is the down-converted baseband power. One of the most important parameters o f a wireless receiver is sensitivity. Sensitivity is defined as the minimum detectable RF power at the receiver input such that there is a sufficient signal-to-noise ratio (SNR) at the output of the receiver for a given application. So each wireless standard may require a different sensitivity. Baseband modulated optical power (1.4) Received RF power (1.5) 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Current wireless links are mainly digital, so the minimum SNR is translated to the maximum bit error ratio (BER) that is required in the link. In a digital photonic receiver it is convenient to use a digital photoreceiver to detect the data modulated optical power because it contains all the digital electronic circuitry integrated with the photodiode. The sensitivity (S'd) of a digital photoreceiver is defined as the minimum data modulated optical power required to have certain BER ( 10"'J) in the output. So assuming that the maximum BER required in the wireless link is the same as the BER at which Ni is measured, the sensitivity of the photonic wireless receiver can be written as: g Receiver sensitivity = — -— (1.6) G ri. ' o h 1.6 Summary A combination of wireless system design methodologies, optical modulation and optical signal processing techniques, can result in a novel RF/mm-wave photonic wireless receiver design with reduced volume, low power consumption and no sophisticated electronic devices and circuitry. Such a photonic receiver potentially can be used in wireless LAN’s, fiber-feed backbone networks and indoor wireless data/video distribution systems. We have proposed three different approaches to photonic baseband down-conversion from a RF/mm-wave signal. All o f these 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. methods require efficient optical intensity modulation around a high-frequency carrier. Resonant optical modulators are among the best candidates for this task. To our knowledge the LiNbCb microdisk optical modulator is the most sensitive resonant optical modulator. In this thesis we explore various aspects o f employing a LiNbCh microdisk modulator in an all-optical wireless receiver. The design and implementation o f a sensitive LiNbCf microdisk modulator is explained in Chapter 2. Chapter 3 presents the experimental results o f LiNbC>3 microdisk modulator performance in a RF-optical link. In Chapter 4 we explore the various methods for all-optical down-conversion through theory and experimental results. Finally, Chapter 5 summarizes the potential improvements that may define the road to a practical monolithic photonic RF receiver. We will also address the future challenges toward an all-optical wireless link. 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.7 References R F -ph otonic (lin ks and signal processing') [1] B. Vidal, V. Polo, J. L. Corral, and J. Marti, “Efficient architecture for WDM photonic microwave filters,” IEEE Photon. Technol. Lett., vol. 16, pp. 257-259, Jan. 2004. [2] P. O. Hedekvist, B.-E. Olsson, and A. Wiberg, “Microwave harmonic frequency generation utilizing the properties o f an optical phase modulator,” J. o f Lightwave Technol., vol. 22, pp. 882-886, March 2004. [3] A. Hirata, M. Harada, and T. Nagatsuma, “ 120-GHz wireless link using photonic techniques for generation, modulation, and emission o f millimeter- wave signals,” /, o f Lightwave Technol., vol. 21, pp. 2145-2153, Oct 2003. [4] H. Ito, T. Ito, Y. Muramoto, T. Furuta, and T. Ishibashi, “Rectangular waveguide output unitraveling-carrier module for high-power photonic millimeter-wave generation in the F-band,” J. o f Lightwave Technol., vol. 21, no. 12, pp. 3456-3462, Dec 2003. [5] G. H. Smith, D. Novak, C. Lim, “A millimeter-wave full-duplex W DM /SCM fiber-radio access network,” OFC technical digest, pp. 18. [6] H. Ogava, D. Polifko, and S. Banba, “Milimeter-wave fiber optic systems for personal radio communication,” IEEE Trans, on microwave theory> and techniques, vol. 40, no. 12, pp. 2285-2293, Dec 1992. [7] D. Novak, G. H. smith, C. Lim, H. F. Liu, R. B. Waterhouse, “Optically fed millimeter-wave wireless communication,” OFC ’98 technical digest, pp. 14. [8] M. Hossein-Zadeh, and A. F. J. Levi, “Mb/s data transmission over a RF Fiber- Optic link using a LiNb03 microdisk optical modulator”, Solid-State Electronics, vol. 46, pp 2173-2178, 2002. [9] “RF photonic technology in optical fiber links”, Edited by W illiam S. C. Chang. Cambridge university press, 2002. [10] J. Oreilly and P. Lane, “Remote delivery o f video services using mm-waves and optics,” IEEE J. o f Lightwave Technol., vol 12, no 2, pp. 369-375, Feb 1994. 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M ach -Z hender m odulator [11] E. L. Wooten, K. M. Kissa, A. Y.-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeir, D. Mack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of Lithium Niobate modulators for fiber-optic communications systems,” IEEE J. o f Selected Topics in Quant. Electron., vol. 6, no. 1, pp. 69-82, Jan-Feb 2000. [12] T. Nakazawa, “Low drive voltage and broad-band LiNbCE modulator”, Microwave photonics, international conference, pp. 45-48, 2002. [13] K. Noguchi, O. Mitomi, and H. Miyazawa, “Millimeter-wave TkLiNbCE optical modulators,” /, o f Lightwave Technol, vol. 16, no. 4, pp. 615-619, April 1998. [14] O. Mitomi, K. Noguchi, and H. Miyazawa, “Broadband and low driving- voltage LiNbCE optical modulators,” IEE Proc.-Optoelectron., vol. 145, no. 6, pp. 360-364, Dec 1998. [15] M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, “Low-drive voltage LiNbCE 40-Gb/s modulator,” IEEE LEO S news letter, vol. 17, no. 1, pp. 12-13, Feb 2003. [16] D. Chen, D. Bhattacharya, A. Udupa, B. Tsap, H. R. Fetterman, A. Chen, S. Lee, J. Chen, W. H. Steier, F. Wang, L. R. Dalton, “High-frequency polymer modulators with integrated finline transitions and low V , ” IEEE Photonics Lett., vol. 11, no. 1, pp.54-56, Jan 1999. [17] S.-S. Lee, S. M. Gamer, V. Chuyanov, H. Zhang, W. H. Steier, F. Wang, L. Dalton, A. H. Udupa, and H. R. Fetterman, “Optical intensity modulator based on a novel electro-optic polymer incorporating a high p [ 1 chromophore,” IEEE J. o f Quant. Electro., vol. 36, no. 5, pp. 527-532, May 2000. [18] R. G. Walker, “High-speed III-V semiconductor intensity modulators,” IEEE J. o f Quantum Electron., vol. 27, no. 3, March 91. [19] M. Fetterman, C-P. Chao, and S. R. Forrest, “Fabrication and analysis o f high- contrast InGaAsP-InP Mach-Zehnder modulators for use at 1.55-pm wavelength,” IEEE Photonics Technology Lett., vol. 8, no. 1, Jan 1996. [20] K. Tsuzuki, T. Ishibashi, T. Ito, S. Oku, Y. Shibata, R. Iga, Y. Kondo, and Y. Tohmori, “40 Gb/s n-i-n InP Mach-Zehnder modulator with a 7 t voltage o f 2.2 V,” Electron. Lett., vol. 39, no. 20, pp. 1464-1466, Oct 2003. 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Optical resonators: Microspheres, Microdisks and Microrings [21] M. L. Gorodetsky, A. A. Savchenkov, and V. S. 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Vahala, “Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system,” IEEE Photon. Tech. Lett., vol. 11, pp. 686-687, 1999. [27] M. Cai, P. O. Hedekvist, A. Bhardwaj, and K. Vahala, “5-Gbit/s BER performance on an all fiber-optic add/drop device based on a taper-resonator- taper structure,” IEEE Photon. Tech. Lett.,vol. 12, no. 9, pp. 1177-1187, 2000. [28] B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact S i-S i02 microring resonator optical channel droppingfilters,” IEEE photonics technol. Lett., vol. 10, no. 4, pp.549-551, April 1998. [29] J. V. Hryniew icz, P. P Absil, B. E. Little, R. A. W ilson, and P. -T . Ho, “H igher order filter response in coupled microring resonators,” IEEE photonics technol. Lett., vol. 12, no. 3, pp. 320-322, March 2000. 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [30] B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P . Lain, “Microring resonator channel droping filters,” IEEE J. Lightwave Tech., vol. 15, no. 6,pp. 998-1005, June 1997. [31] D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high- Q microcavity on a chip,” Nature, vol. 421, pp. 925-928, Feb 2003. [32] P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters and modulators,” IEEE J. o f Lightwave Technol., vol. 20, no. 11, pp 1968-1974, Nov 2002. [33] K. Djordjev, S.J. Choi, S. J. Choi, and P. D. Dapkus, “H igh-0 vertically- coupled InP microdisk resonators,” IEEE Photonics Technology Letters, vol. 14, no.3, March 2002, pp.331-333. [34] www.csl.usc.edu (Compound semiconductor lab. University o f Southern California). [35] S. J. Choi, Q. Yang, Z. Peng, S. J. Choi, and P. D. Dapkus, “High-(9 buried heterostructure microring resonator,” IEEE/LEOS, summer topical meetings, 2004, CTHF1. Sem iconductor microdisk lasers [36] S.L. McCall, A. F. 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Rosenbaum, “Mode chart for microstrip ring resonators,” IEEE trans. on microwave theory and techniques, vol. MTT-21, pp 487-489, July 1973. [42] G. K. Gopalakrishnan, and K. Chang, “Novel excitation schemes for the microstrip ring resonator with low insertion loss,” Electron Lett., vol. 30, no 2, pp 148-149, Jan 1994. [43] K. Chang, S. Martin, F. Wang, and J. L. Klein, “On the study o f microstrip ring and varactor-tuned ring circuits,” IEEE trans. on microwave theory and techniques, vol. MTT-35, no 12, pp 1288-1295, Dec 1987. [44] I. Wolf, and V. Tripathi, “The microstrip open-ring resonator,” IEEE trans. on microwave theory and techniques, vol. MTT-32, no. 1, pp 102-107, Jan 1984. [45] G. K. Gopalakrishnan,B. W. Fairchild, C. L. Yeh, C.-S. Park, K. Chang, M. H. Weichold, and H. F. Taylor, “Experimental investigation o f microwave- optoelectronic interactions in a microstrip ring resonator,” IEEE trans. on microwave theory and techniques, vol. MTT-39, no 12, pp 2052-2060, Dec 1991. [46] P. A. Bernard, andJ. M. Gautray, “Measurment of dielectric constant using a microstrip ring resonator,” IEEE trans. on microwave theory and techniques, vol. MTT-39, no 3, pp 592-594, March 1991. W ireless receiver [47] D. M. Pozar, “Microwave and RF design o f wireless systems,” John W iley & Sons, Inc., 2001. [48] J. Park, Y. Wang, and T. Itoh, “A microwave communication link with self heterodyne direct down-conversion and system predistortion,” IEEE Trans. On Microwave Theory and Tech, vol. 50, no. 12, pp. 3059-3063. Dec 2002. [49] Y. Shoji, K. Hamaguchi, and H. Ogawa, “Millimeter-wave remote self heterodyne system for extremely stable and low-cost broad-band signal transmission,” IEEE Trans, on Microwave Theory and Tech., vol. 50, no. 6, June 2002. [50] K. Kojucharow, H. Kaluzni, and W. Nowak, “A wireless LAN at 60 GHz-novel system design and transmission experiments,” Microwave symposium digest, IEEE M TT-S international, vol. 3, pp. 1513-1516, 1998. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [51] K. Ohata, T. Inoue, M. Funabashi, A. Inoue, Y. Takimoto, T. Kuwabara, S. Shinozaki, K. Maryhashi, K. Hosaya, and H. Nagai, “Sixty-GHz-Band ultra miniature monolithic T/R modules for multimedia wireless communication systems,” IEEE Trans, on Microwave Theory and Tech., vol. 11, no. 12, pp. 2354-2360, Dec 1996. [52] S. K. Reynolds, B. Floyd, T. beukema, T. Zwick, U. Pfeiffer, and H. Ainspan, “A direct-conversion receiver IC for WCDMA mobile systems,” IEEE J. Solid- State Circuits, vol.38, pp. 1555-1560, Sept 2003. [53] X. Guan, A. Hajimiri, “A 24-GHz CMOS Front-End,” IEEE J. Solid-State Circuits, vol.39, pp. 368-373, Feb 2004. [54] S. Reynolds, B. Floyd, U. Pfeiffer, T. Zwick, “60 GHz transceiver circuits in SiGe bipolar technology,” ISSCC 2004, session 24, pp. 442. R eson ant m odulators (op tica l resonance) [55] J. J. Huang, T. Chung, M. Lerttamrab, S. L. Chuang, and M. Feng, “ 1.55-j.tm asymmetric Fabry-Perot modulator (AFPM) for high-speed applications,” IEEE Photon. Technol., vol. 14, no. 12, pp. 1689-1691, Dec 2002. [56] P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters and modulators,” J. o f Lightwave Technol., vol. 20, no. 11, Nov 2002 [57] N. Shaw, W. J. Stewart, J. Heaton, and D. R. Whight, “Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators,” Electron. Lett., vol. 35, no. 18, pp 1557-1558, Sept. 1987. [58] E. I. Gordon and J. D. Rigden, “The Fabry-Perot electo-optic modulator,” The Bell system technical journal, pp. 155-179, Jan. 1963. [59] I. L. Gheorma and R. M. Osgood, Jr., “The fundamental limitations o f optical resonator based high-speed EO modulators,” IEEE Photon. Technol., vol. 14, no. 14, pp. 795-797, June 2002. [60] M. H. Kwakemaak, A. N. Leopre, H. Mohseni, H. An, Z. A. Shellenbarger, J. H. Abeles, J. - 0 , S. L. Rommel, and I. Adesida, “Eletrco-refractive low loss MMI-coupled ring resonators,” CLEO 2003 technical digest. [61] Kostadin Djordjev; Seung June Choi, Sang Jun Choi, and P. Daniel Dapkus, “Active semiconductor microdisk devices,” IEEE J.l o f Lightwave Technology, vol.20, n o .l,p p . 105-113, Jan 2002. 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [62] K. Djordjev, S. S. Choi, S. J. Choi, P. D. Dapkus, “Novel active switching components,” 28th European Conference on Optical Communication (ECOC 2002), September 2002, Monday - paper 2.3.5 [63] T. Sadagopan, S. J. Choi, S. J. Choi, and P. D. Dapkus, “High-speed, low- voltage modulation in circular WGM microresonator,” IEEE/LEOS, summer topical meetings, 2004, MC2-3. [64] P. Rabbiei, W. Steier, C. Zhang, C.-g. Wang, H. J. Lee, E. H. Turner, and P. J. Maloney, “Polymer micro-ring modulator with 1 THz FSR,” CLEO 2002 technical digest. [65] J. Verdein, “Laser electronics,” Prentice H a ll, 1995. R eson ant m odulators (electrical resonance') [66] T. Itoh, “Analysis o f microstrip resonators,” IEEE trans. on microwave theory and techniques, vol. 22, no. 11, pp. 946-952, 1974. [67] A. Gopinath, “Maximum Q-factor o f microstrip resonators,” IEEE trans. on microwave theory and techniques, vol. 29, no. 2, pp. 946-952, 1981. [68] R. Krahenbuhl, and M. M. Howerton, “Investigations on short-path-length high-speed optical modulators in LiNbCE with resonant-type electrodes,” J. Lightwave Technol., vol. 19, no. 9, pp. 1287-1297, Sep 2001. [69] T. Kawanishi, S. Oikawa, K. Higuma, Y. Matsuo, and M. Izutsu, “ LiNbCE resonant-type optical modulator with double-stub structure,” Electron. Lett., vol. 37, no. 20, pp. 1244-1246, Sep 2001. [70] Y. S. Visagathilagar, A. Mitchel, and R. B. Waterhouse, “Fabry-Perot type resonantly enhanced Mach-Zehnder modulator,” Microwave Photonics, MWP ’ 99. International Topical Meeting on, vol. 1, pp. 17-20, 1999. [71] G. K. Gopalakrishnan, and W. K. Bums, “Performance and modeling o f resonantly enhanced LiNbCE modulators for low-loss analog fiber-optic links,” IEEE Trans, on Microwave Theory and Techniques, vol. 42, no. 12, pp. 2650- 2656, 1994. 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R esonant m odulator (electro -o p tica l resonance) [72] T. Kawanishi, S. Oikawa, K. Higuma, Y. Matsuo, and M. Izutsu, “Low-driving- voltage band-operation LiNbCL modulator with lightwave reflection and double-stub structure,” Electron. Lett., vol. 38, no. 20, pp. 1204-1205, Sept 2002 . [73] J. H. Abeles, “Resonant enhanced modulator development,” DARPA/MTO R- FLICsprogram: K ickoff meeting, Aug 2000. [74] D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, “High-(9 microphotonic electro-optic modulator,” Solid-State Electron., vol. 45, pp. 1577-1589, 2000. [75] D. A. Cohen, M. Flossein-Zadeh, and A. F. J. Levi, “Microphotonic modulator for microwave receiver,” Electron. Lett., Vol. 37, no.5, pp 300-301, 2001. [76] M. Hossein-Zadeh, and A. F. J. Levi, “A new electrode design for microdisk optical modulator,” CLEO 2003 technical digest. [77] T. F. Gallagher, N. H. Tran, and J. P. Watjen, “Principles o f a resonant cavity optical modulator,” Appl. Optics Lett., vol. 25, no. 4, pp 510-514, Feb 1986. [78] L. Maleki, A. Savchenkov, V. Ilchencho, T. Handley, and A. Matsko, “Novel photonic filter and receiver based on Whispering Gallery mode,” Microwave- photonics c o n f. [79] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Sub microwatt photonic microwave receiver,” IEEE photonics technol., vol 14, no. 11, Nov 2002. [80] D. A. Cohen, “Lithium Niobate microdisk modulators,” PhD dissertation, USC 2001, (www.usc.edu/alevif Technical notes (1) CPW: coplanar waveguide structure where as opposed to the microstripline structure the ground planes are located on both sides o f the signal line and on the same plane. (2) CPS: coplanar stripline. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (3) The GSM (Global system for mobile communication) was developed by European standard committee. The European GSM is currently being developed in the United States in the 1900 MHz band is named PCS 1900. (kabuki.eecs.berkeley.edu/~weldon/ papers/spec/gsms6.pdf) (4) The sensitivity is defined as the minimum detectable signal power (typically specified in units o f dBm) at the receiver input such that there is a sufficient signal to noise ratio at the output o f the receiver for a given application. (kabuki.eecs.berkeley.edu/~weldon/ papers/spec/gsms6.pdf) 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 LiNb03 microdisk modulator 2.1 Introduction This chapter describes the design and operation o f a LiNbCE microdisk modulator. The physics behind the operation and interaction o f the RF and optical elements are explored using both simulation and experiment. We start with the LiNbC>3 microdisk physical properties and their importance in the modulation process. A brief explanation o f the microdisk resonator optical modes and coupling from a fiber- launched electromagnetic field is followed by the experimental results o f prism coupling to different disks and a discussion o f novel coupling schemes. Electro- optical interaction in the microdisk is introduced by studying the DC shift o f an optical resonance. Bistable behavior is demonstrated as an example o f the slow- speed electro-optic response o f a microdisk optical resonator. The RF-resonator is the second element o f the microdisk modulator that is considered. RF-resonator design strongly influences modulation efficiency. After a brief review o f the different electrode structures that have been tested in the preliminary experiments, a ring resonator is introduced. Resonant frequencies, RF coupling, voltage gain, E- field distribution, even and odd harmonics are among the most important aspects o f the ring resonator operation that are addressed in this section. Experimental results 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are presented to support the simulation and analytical studies. The physics o f resonant electro-optic modulation and its application to the microdisk modulator is the next topic covered in this chapter. A simple model for the behavior o f the modulator based on DC-shift is described. This model is very helpful for evaluating the role o f the different parameters in modulation efficiency. In chapter three and four the same model is used to analyze the noise performance o f the microdisk based RF-photonic link and the concept o f direct RF down-conversion by nonlinear optical modulation. Finally the results o f linear and harmonic optical modulation experiments using a LiNbCL microdisk modulator are described. 2.2 Microdisk optical resonator 2.2.1 Physical, electronic and optical properties of LiN b03 Crystalline Lithium Niobate (LiNbCfi) is a commonly used electro-optic material in optical modulators. Its optical, electrical and mechanical characteristics such as low loss at RF and optical frequencies, high electro-optic coefficient, mechanical robustness and stable crystal structure at room temperature make it an excellent candidate in many electro-optical devices including microdisk modulators. At room temperature, well below its ferroelectrics curie temperature (~1210°C), LiNbCL is a 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. negative uni-axial crystal with crystal symmetry of the trigonal 3m point group and R3C space group [1], Fig.2.1 shows the LiNbC>3 crystal structure. ( a ) ( b ) ( c ) F ig u re 2.1 L iN b 0 3 m olecular structure. N io b iu m atom s are represented as dark gray sm all spheres, Lithium as light gray sm all spheres and O x y g en as large spheres, (a) V ertical v ie w o f the L iN b 0 3 con ven tion al h exa g o n a l unit cell, (b) V ie w alo n g c (or z) axis, (c) O ctahedral o x y g en structure o f L iN b 0 3 [5], LiNb0 3 is birefrigent and therefore sensitive to the polarization o f an electromagnetic wave propagating through the material. Its optical index of refraction at wavelength X = 1550 nm along the extraordinary axis is «c = 2.138 and nv = 2.21. along the ordinary axis. LiNbC>3 is an insulating crystal that is essentially transparent to wavelengths from approximately 400 nm to 5000 nm. The RF permittivity o f LiNbC>3 is high compared to materials such as optical polymers, III-V semiconductors, and common microwave substrates such as alumina. 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table.2.1 Bulk properties of LiNb03 Property Value Notes Optical index o f refraction (0*) 2.223 X = 1550 nm Optical index o f refraction (E*) 2.143 X = 1550 nm RF permitivity (0 ) 42.5 - 43 100 MHz - 140 GHz RF permitivity (E) 26-28 100 MHz - 140 GHz Electrical conductivity lx lO 8 (Q-cm)"1 DC Thermal conductivity 5.6 W/m.K Thermal expansion coefficient (0 ) 14x10‘6 K '1 Thermal expansion coefficient (E) 4x1 O ’6 K '1 Thermal effect on index (0 ) 1.85xlO'6 K '1 l/n 0(dno/dT) Thermal effect on index (E) 1.6xl0‘6 K"1 l/n e(dne/dT) Electro-optic coefficients r33 = 30.8 pm/V r2 2 = 3.4 pm/V rn = 8.6 pm/V r5j = 28.0 pm/V Nonlinear-optic coefficients d3i = 11.6 d2 2 = 5.60 d33 = 8.60 Piezoelectric coefficient d ]5 = 69.20 pm/V d3 ) = -0.85 pm/V d2 2 = 20.80 pm/V d3 3 = 6.00 pm/V Defined as dij/d3 ( ) Pyroelectric coefficient -4x10~ 5 (C/K-m2) Dielectric loss tangent along c-axis 0.004 * E: e-wave where it-field is polarized along c-axis * O: o-w ave where E -field is polarized perpendicular to c-axis Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. However it is low compared to some other electro-optic materials such as Strontium Barium Niobate (SBN). SBN60 has a r 33 o f 235pm/V and an RF permittivity o f 880 along c-axis. The bulk L iN b0 3 crystal properties are summarized in Table. 2.1 [1-8]. The measured value o f the dielectric loss tangent for L iN b0 3 is small enough (« 0.004 in the range DC 100 GHz) that this is a minor source o f loss compared to conductor loss [8 ], For electro-optic applications mechanical stress in L iN b0 3 is an important parameter that must be kept low enough to avoid changes in the modulator bias point through the acousto-optic effect (stress couples to refractive index). Refractive index change caused by high optical power density can also be a problem for such modulators, because it also causes changes in the bias point. This mechanism is wavelength dependent, for a regular Ti-diffused L iN b0 3 wave guide (optical mode dimension « 7 x 4 pm), less than one mW (power density o f 3 .5 x l0 3 W/cm ) at 632 nm wavelength can cause significant index change, while at 1320 nm wavelength the waveguide can be stable at up to optical power o f 400 mW power (power density o f 1.4xl0 6 W /cm2) [3,8]. L iN b0 3 exhibits pyroelectric response (generation o f an electric field due to temperature change) along the c-axis. W hen the temperature on one surface o f the crystal is changed, a large potential difference between z-surfaces o f the crystal can cause rapid changes in the bias point o f a modulator. For L iN b03, the induced electric field magnitude is about 1.73xl0 5 V/m.K. 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.2.2 LiN b03 microdisk A core element o f the microdisk modulator is a L iN b0 3 microdisk optical resonator that supports very high-2 Whispering-Gallery (WG) optical resonances. The microdisk resonator is fabricated from a z-cut LiNb0 3 cylinder. As shown in Fig. 2.2(a), the basic geometry is a disk o f diameter D, and thickness h. For devices presently under test, 0.1 mm < h < 1 mm and 1 mm < (D = 2R) < 6 mm. The sidewall o f the disk is optically polished with a radius o f curvature R, typically equal to the radius o f the disk. In addition, the equator o f the disk’s sidewall should be accurately maintained at height hi2. Polishing curved sidewalls to an optical finish in LiNbCh is not a standard practice and it is very difficult to achieve the surface quality needed for high-2 operation. Fig. 2.2(b) shows a 3D picture o f the sidewall surface roughness for a typical microdisk. (h = 0.4 mm, D = 3 mm). The peak-to- peak value (4 ) (Sy) o f roughness is about 5.1 nm and the rms value (4 ) (Sq) is about 0.846 nm. With this surface quality, loaded optical-2s up to 3 x l0 6 (unloaded optical 2 o f about 7 x l0 7 ) have been achieved. This corresponds to a distributed loss o f 0.0075 cm ' 1 or 0.03 dB/cm. If an electric field o f magnitude Ec is applied along the c-axis, the optical refractive indices change according to: A A / 77 Meo 1*3 3 /if /2 A/7A |' 1 1 oo r ] yE (J2 where, from Table 1 r 33 « 30.8 x 10' 12 m/V and r ]3 ~ 8 . 6 x 10' 12 m/V. 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. h - 100 ( xm -700 )xm LiNb03 < > D = 2 - 6 mm FSR: 7 GHz- 22 GHz (a) Sy = 5.1 nm Sq = 0.846 nm e-axis 0.4 mm 2.82 mm D irection o f light propagation (b) F ig u re 2 .2 (a) Photograph o f a L iN b 0 3 disk w ith op tica lly polish ed sid ew a lls, (b) 3 D picture o f the disk sid ew all surface taken by interferom etric surface p r o filo m e te r < 4). nm scale scratch m arks due to m ech anical p o lish in g are clearly v isib le. 2.3 Optical coupling Efficient optical coupling to optical modes of a microdisk resonator is essential for successful device operation. M odulation can only be efficient if energy coupling to WG modes occurs without introducing large coupling losses that decrease the optical 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Q. In this section the WG resonance structure in the microdisk resonator and a method for evanescent coupling to them are described 2.3.1 Whispering Gallery (WG) resonances WG resonance structure A dielectric sphere is an open cavity supporting tunneling leaky waves. In the presence o f high dielectric contrast (between the sphere and surrounding medium), we can neglect the radiation part and focus only on the bound portion o f the field and find the resonant modes of the sphere. Assuming that the direction o f the polarization is constant along a fixed set o f spherical coordinates, the Helmholtz equation can be separated for high-order confined modes in the following way [14]: ¥ q ,m 0 % o, (p) = A'v'/a (>')/'o ( ^ K , (< p) (2 .1) V R (2 .2 -c) where: (2.3) (2.4) 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vqim represents either the Eq or Hq, corresponding to TE and TM polarized modes respectively. c-axis h / / ✓ c-axis (z) (a) x ■y X (b) F ig u re 2 .3 (a) G eom etry o f the m icrodisk resonator and definition o f the coord in ate system used (n o tice that 0 is m easured relative to the equatorial plane unlike the con ven tion al defin ition w h ere it is m easured relative to the z-axis. T his new d efin ition has been ch o sen becau se it is m ore co n v en ien t for W G resonances that are con fin ed around the equator). A lso sh ow n is the definition o f the T E and T M polarized resonances, (b ) N o rm a lized m odal distribution for / = m = 2 4 that is the projection o f spherical harm onic Y 2424 on a unit sphere (longitud in al and equatorial cross section ). The it-field vector of a TE resonance is polarized along 9 (for equatorial propagation this is the same as the z direction) and the .E-field vector o f a TM resonance is polarized in the xy plane. The Hn is the Nth order Hermite polynomial. The electromagnetic solutions to the disk resonator are found from those of a sphere by simply defining the disk to be a sphere with part o f the top and bottom 6 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. hemispheres removed (the geometry o f this resonator is shown in Fig. 2.3(a)). A sphere’s mode is described in terms o f three integers /, m and q. The value o f q counts the number o f field maximum in the radial direction and l-m + 1 ( I m I < /) is the number o f field maxima in the polar direction, perpendicular to equatorial plane and between the two poles. The resonant wavelength is determined by q and /. The mode has a propagation constant Pi and its projection on the equator is commonly referred to as the “propagation constant” because it is the wave vector in the net direction o f propagation. Note that an ideal microsphere (microdisk) is a traveling wave optical resonator (when X « R that is almost always true). W hispering- Gallery (WG) modes are solutions with large values o f / and m and small values o f /- m and q (q « I), this means that they are highly confined in r and 0 directions very close to the equator and the sidewall while their propagation is described by a function o f < ( > . For these modes p/ = pm = m/R (R is the sphere radius and m is a positive integer). This condition can be used to calculate the approximate resonant frequency o f the W G modes, m essentially corresponds to the number o f optical wavelengths that fit into the microdisk’s circumference. The mode labeled by I = m and <7 = 1 is called the fundamental mode and it only has one maximum in each direction (it is Guassian in nature). Fig. 2.3(b) shows the modal distribution for l = m = 24. While this is helpful to visualize the fundamental mode, in practice an average size disk (2 mm < 2R < 6 mm) has a value o f / that is usually greater than 5000. Using equation (2) we can approximately calculate the mode size for the fundamental and low order (l-m < 1 0 ) W G modes inside the sphere. Fig. 2.4 shows 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the definition o f the fundamental mode profile parameters and their values for three LiNbC>3 disks with different sizes commonly used in our experiments [47], 5rFW H M is the full-width-half-maximum of the power distribution along the radial direction and 5 0 f w h m is the full width half maximum along the polar direction. I - m, q = 1 X = 1550 nm ne = 2.14 S r FW HM 2R (mm) R - S O f w h m (pm) SR FW H M (pm) r m (pm) / (= m) 2 17.8 4.06 3.31 8660 3.5 24 4.99 4.00 15120 5.84 30 5.80 4.58 25260 F ig u re 2 .4 W G M pow er distribution in xz plane, for m icrodisk s with different diam eters. For microdisk modulator applications, we are interested in WG modes with TE polarization (E-field parallel to z-axis) because the elecro-optic coefficient of LiNbCb is larger along the c-axis. The resonance frequencies o f TE WG m odes in a sphere with a refractive radius R (R » X ) and a refractive index n surrounded by air (n= 1) can be obtained from [24]: 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 2 J10(/ + 0 .5 )i 32y2(w2 - 1)2 (/ + 0.5)3 where aq denotes the r/-th zero o f Airy function, c is the speed of light, and v /q is the frequency o f the mode. For the fundamental and low order modes we can use the approximation: m(X/n) = nD (/ = m) (2.6) and calculate the free spectral range frequency A v f s r using: Avfsr = c/(nnD) (2.7) Losses and quality factor The optical loss mechanisms in the LiNbC>3 microdisk resonator (or any spherical optical resonator) are: Rayleigh scattering, surface scattering and material loss. It has been shown that even for small spheres the Rayleigh scattering is suppressed for WG modes [20]. For medium size disks since (R » X) loss due to finite curvature becomes small, since the resonator dimension is significantly greater than the optical resonant wavelength. Flence for optical wavelengths near X - 1550 nm, the unloaded (intrinsic) quality factor o f optical dielectric resonators with a diameter greater than 1 0 pm is typically limited by attenuation due to scattering from surface imperfections and material loss. The distributed optical loss for WG modes can be derived from the photon lifetime in the resonator. Assuming the number o f photons present in a WG mode decays exponentially in time (due to intrinsic optical losses) we can express the unloaded optical quality factor o f that mode as Q„ = cotp where t p is the 1/e photon lifetime and c o = 2 7tv/( / We can also define a distributed loss constant per unit length a = n/cxp (c: is the speed of light and n is the effective 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. optical refractive index for the corresponding optical mode). So Qu and the distributed loss are related as: a = no)/cQu (2.8) The loaded optical quality factor Q o f an optical mode can be calculated based on the measured full-width half maximum o f the spectral peak at the resonant optical frequency vre s = v!t], Q = v res/A v FwHM (or Q = rires/A A 1WnM)- The typical loaded Q- factor values that we observe for optically polished LiNbCb micodisks is between 2 x l0 6 and 7 x l0 6 (see section 2.3.3). Experimentally we measure the loaded Q and if we insert the measured Q in equation 2.8 to calculate a , the optical coupling loss will be included in the distributed loss. In section 2.3.4 we will show that the loaded quality factor o f a critically coupled W G mode can be used to calculate the intrinsic distributed loss in the microdisk resonator. The high quality o f the optical modes reveals the small magnitude o f the surface roughness of the sidewalls — a fact confirmed by surface profilometer measurements (2.2.2). The high quality o f sidewall surface is not only important for high-Q optical resonance but also to guarantee the traveling-wave nature o f the W G modes. It is well known that surface roughness can generate back-scattered optical-waves that couple energy into modes with negative wave-vectors (effectively increasing the VSWR) [21]. In a microdisk modulator the energy coupled to modes circulating in the opposite direction do not contribute to the optical modulation process. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3.2 Evanescent optical coupling Light must be coupled to the WG modes without disturbing their propagation around the disk or reducing their high-Q. In principle it is not possible to couple energy into any resonator without coupling some energy out; hence there is always a certain amount of loss associated with coupling. The objective here is to reduce the coupling loss and more importantly, to avoid as much as possible any physical perturbation. Evanescent coupling in which an exterior field tunnels into the sphere, appears to be the most promising approach. The excitation o f whispering gallery modes is achieved via evanescent fields. The mechanism for this type o f coupling is that o f frustrated total internal reflection. As may be seen in Fig. 2.5(a) light in medium 1 (refractive index - n \ ) incident on the interface of medium 1 and 2 (where n\ > ni) is totally reflected if 9 (angle with respect to normal) is greater than the critical angle. But an evanescent field will exist beyond the interface (in medium 3) with a skin depth o f 6 given by: ' : - (2.9) 4/r2 “ sin — 1 If a third medium is present within a distance g0 from medium 1 where g„ < 8 , then light will couple to the third medium with an angle ( j ) where 4> and 0 follow the regular Snell’s law meaning: n\sin (9) = uasin (()> ). This phenomenon is called 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ‘frustrated total internal reflection’ and can be used to couple light to WG modes inside the disk. Fig. 2.5(b) shows how an equilateral prism with a refractive index n/ > nj and angle 0 C (where 0 C is the critical angle for the n\ and m interface) placed in the vicinity of medium 3 (g„ < 5), can couple light into (and out of) optical waves propagating parallel to the interface. Since the wave vector of WG modes is almost tangential to the microdisk surface, a prism that has a higher refractive index than LiNb0 3 can be used for coupling light from free space to these modes. There are numerous other methods for evanescent coupling of light into guided modes [9,10,11,15,16,17], but because o f the large refractive index of LiNb0 3 , the prism coupling approach is the most convenient. go <5 ( 8 skin depth) (WGM) ( a ) ( b ) F ig u re 2 .5 (a) Frustrated total internal reflection, (b ) E van escen t prism co u p lin g to surface w a v es 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3.3 Prism coupling to WG modes In our experiments we use small diamond prisms with the dimensions shown in Fig. 2.6(a). The refractive index o f diamonds is near 2.4 and is thus larger than the refractive index o f LiNbCh for both TE and TM modes (ne = 2.14, n0 - 2.23). The use o f diamond microprisms to couple to W G modes inside a LiNbCf disk, is equivalent to setting n3 = 2.14 and n\ = 2.4 in Fig. 2.5(b). The skin depth (8 ) for a diamond-air interface excited by X = 1550 nm radiation is about 135 nm. It is possible to use a single prism to couple light into and out o f the microdisk (Fig. 2.6(b)) or to use one prism to couple in and another one to couple out (Fig. 2.6(c)). The detection o f coupled WG peaks using two prisms is easier since the reflected part o f the input that is not coupled and coupled light do not interfere. However, since two prisms are in contact with the microdisk, the Q is smaller due to the larger coupling loss, and the portion o f the optical WGM power that is coupled out through the first prism does not contribute to the modulated signal. In a one-prism coupling scheme this problem does not exist but experimental results show that the WGM cone coupled out o f the disk and the totally reflected beam cone have spatial overlap (Fig. 6 (c)), therefore, depending on the location o f the collecting fiber the detected output spectrum can be WGM peaks, transmission dips or just the reflected beam. This effect adds to the complexity o f the alignment o f the output port. Also experimental results show that two-prism coupling generally results in a cleaner mode structure. In chapter 4 we will demonstrate that using transmission dips in a 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. one-prism coupling scheme is a better choice for nonlinear modulation and optical down-conversion due to reduced DC optical power at resonance. F ig u re 2 .6 (a) D iam ond m icroprism dim ension s, (b ) Sin gle-prism coupling, (c ) D ou ble-p rism cou p lin g, (d) Interference effect in single-prism coupling. Fig. 2.7 depicts the schematic diagram o f the typical experimental arrangement used for optical coupling and mode structure characterization. The laser light is generated using a DFB laser (line width = 3 MHz). After passing through an optical isolator and a polarizer, the light is coupled to a lens system through a cleaved end. We use the polarizer to selectively excite the TE modes (E-field parallel to c-axis, which is normal to the top surface o f a z-cut microdisk). As mentioned previously, this 0 .5 3 8 m m L iN b 0 3 disk Prism O utput optical c o u p ,er beam 0 .4 4 2 m i t f ^ ( a ) ( b ) O utput optical beam (peaks on resonance) O utput prism Input prism coupler coupler L iN bO r , disk Input optical beam Interferenci W G M s anc beam (dips W G M s Total internal reflection (c ) (d) 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. polarization is preferred because o f the large magnitude o f the LiNbCL electro-optic coefficient along the c-axis. Matched pair lenses Cleaved (or lensed) fiber x y z stage v y Microprism x y z stage | isolator Oscilloscope Optical modes D etector Polarization controller Signal generator Laser Laser controller F ig u re 2 .7 Schem atic diagram o f the experim ental arrangem ent used for optical co u p lin g m easurem ent. The lens system is an IR coated matched pair with a focal length o f 11 mm (we have also tried 6 mm) mounted on a xyz stage. The laser beam is focused on the input prism and evanescently couples to the WG modes inside the disk. The modes are coupled out through the second prism and collected with a cleaved fiber (or lensed fiber) that is also mounted on a xyz stage. In a one-prism coupling scheme, the same prism is used for coupling into and out o f the disk. Finally the output goes to a detector and is monitored with an oscilloscope. 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Output microprism L iN b 0 3 microdisk (a) 30 A -fsr = 6 7 .8 7 pm 25 15 o. 10 -a 5 Q 0 0 0.02 0.04 0.06 0.08 0.1 W a v elen g th (1550+...nm) (b) Q = 3 .4 x 1 0 0.02 0.04 0.06 0.08 W avelength ( 1550.05 +...nm) 0.1 (c) F ig u re 2 .8 (a) T op v iew photograph o f a 5.13 m m diam eter L iN b 0 3 m icrodisk in contact w ith tw o m icroprism s, (b ) T he detected T E W G optical spectrum , (c) H igh co u p lin g effic ie n c y (> % 15) and a clean T E spectrum obtained w ith the sam e set up after accurate alignm ent (op tical input pow er in both ca ses is about 1200 pW ) 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To sweep the laser wavelength, a triangular voltage signal is fed to the laser power supply that modulates the current and consequently the laser wavelength (the power is also modulated but we can normalize it). By triggering the oscilloscope with the same signal we can observe the frequency spectrum on the oscilloscope. After careful alignment and finding the desired spectrum, we change the light source to a high-resolution tunable laser (line width < 0.5 MHz, wavelength resolution < 0.1 pm) and scan a small part o f the spectrum to measure details o f the mode structure. Fig. 2.8(a) shows a photograph o f a LiNbCb microdisk (D = 5.13 mm and h = 400 pm) in contact with two microprisms. Fig. 2.8(b) shows a typical TE W G mode spectrum. The measured FSR is in very good agreement with the calculated value using equation 2.7, assuming ne = 2.14, for a 5.13 mm diameter disk the measured value is 67.87 pm and the calculated value 69.24 pm. This is consistent with the effective refractive index o f the TE WG modes being almost the same as the bulk extraordinary refractive index (A-field along c-axis). Fig. 2.8(c) shows another TE mode spectrum for the same disk. As may be seen the maximum optical power is 2 times greater and the spectrum has fewer features. Achieving such a good coupling requires a very accurate alignment o f all optical elements with pico-motor drivers (l). In both cases (Fig. 2.8(b) and(c)), the input optical power is about 1200 pW , By taking into account the losses through the system, specially reflection from prism surfaces and power lost in the first coupler, one may estimate optical coupling efficiency o f 15%. Note that in all cases we define the coupling efficiency (p) as the ratio o f the maximum optical power detected and the total power injected into the 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. input prism. The same experimental arrangement can be used to demonstrate one prism coupling by removing one prism and moving the other to the middle o f the microdisk. Fig. 2.9 shows the TE mode spectrum obtained with the one-prism coupling scheme. As expected, the measured optical Q in both cases is larger than observed when using a two prism coupling scheme and also more modes have been coupled out resulting in a complex spectrum. The laser input power is about 1400 pW in both cases but the maximum coupled power in the second case. a. 0.02 0.04 0.06 0.08 W a v elen g th (1550+...nm) 10 8 6 4 2 0 Q = 4 .2 x 10 v \j J W 0 .0 6 0 .0 6 5 0 .0 7 W a v e le n g th (1 5 5 0 + ...) nm 0 .0 8 0 .0 8 2 0 .0 8 4 0 .0 8 6 0 .0 8 8 W a v e le n g th ( l5 5 0 + ...n m ) 0 0.02 0.04 0.06 0.08 0.1 W a v e le n g th (1550+ ...nm ) F ig u re 2 .9 TE m ode spectrum obtained usin g a sin g le prism for co u p lin g light in and out o f the m icrodisk. T he quality factor o f the seco n d m easurem ent (bottom ) is the high est Q ob served . 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. One may see that when we try to couple more light into one mode, many other modes are excited and hence there is a trade-off between a clean spectrum and the maximum coupled optical power to a certain mode (with the exception of some special cases that are mostly unrepeatable). We have also studied optical coupling to a toroidal (the side wall curvature is smaller than the disk radius R) LiNbOs miocrodisk. 0 .7 4 m m 6 m m R = 0 .5 m m 0 . 2 m m Q uality area . 0 . 1 m m / ( a ) 0) 5 o o. 3 O h 3 O 13 u o- O 0 .1 6 0 .1 4 0.12 0.1 0 .0 8 0 .0 6 0 .0 4 0.02 0 -f s r = 6 0 .1 6 pm 2 = 2 x 1 0 ' A_ _ 0 0.02 0 .0 4 0 .0 6 0 .0 8 0.1 W a v elen g th (1 5 4 0 + ...n m ) ( C ) F ig u re 2 .1 0 (a) Photograph o f the toroidal L iN b 0 3 m icrodisk, (b) T he m icrodisk d im en sio n s and the sid ew a ll profile, (c) T E m ode spectrum obtained usin g a tw o prism co u p lin g sch em e. A lthou gh the spectrum is very clean the cou p lin g effic ie n c y is lo w («% 3). 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.10(a) shows the photograph o f the microdisk and Fig. 2.10(b) is a schematic diagram showing the details and dimensions o f the sidewall. The sidewall curvature is about 10 times smaller than the disk radius, resulting in strong confinement along 0. This should result in a cleaner spectrum due to the absence o f extra transverse modes (different values o f m) that could resonate in a regular microdisk. Fig. 2.10(c) shows a TE mode spectrum obtained by the two prism coupling method. Although the mode structure is cleaner the coupling efficiency is very low (~ %3). The low coupling efficiency is a result o f mode mismatch between the incident beam that has a Gaussian profile and the small cross section area o f the WG mode. Decreasing the waist size in a Gaussian beam does not improve the efficiency because it simultaneously increases the beam divergence. As mentioned previously, using a single prism coupling scheme, the optical spectrum of the collected output power can be a series o f transmission dips or peaks depending on the position o f the output fiber. Fig. 2.11 shows the spectrum o f the TE optical output power from a single prism coupled LiNbCE microdisk (D = 3 mm, h = 0.4 mm). In Fig. 2.11 (a) the output fiber is located at the overlap o f the WG cone and the totally reflected cone (Fig. 2.6(d)) while in Fig. 2.11(b) it only collects the W G optical power. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. W a v elen g th (1550+...nm ) o CL klmili lUli /j p W l k t o o 0.02 0.04 0.06 0.08 W a v elen g th (1550+..nm ) ( b ) o.i F ig u re 2.11 O ptical output pow er spectrum o f a sin gle prism coupled L iN b 0 3 m icrodisk (D = 3 m m , h = 0 .4 m m ), (a) D etected transm ission dips w h en the output fiber is tuned to the overlap region o f the W G co n e and the total reflectio n con e, (b) D etected W G peaks w h en the output fiber on ly c o lle cts optical pow er from the W G con e. Fig. 2.12 shows photographs of visible (red) scattered light from WG modes inside a 6 mm diameter (h = 700 pm) excited by a He-Ne laser ( X = 623.2 nm). A single prism is used to both couple in and out the laser light from a 30 mW He-Ne laser. The laser is focused on the prism using an 11 mm focal length matched pair lens. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u re 2 .1 2 O bservation o f W G m od es inside the L iN b 0 3 disk (h = 7 0 0 pm , D = 5 .85 m m ) usin g H e-N e laser. In the photograph we can also see the scattered light from the collecting (output) fiber that shows the WG modes are coupled to the fiber. In the bottom-right picture of Fig. 2.11 the output fiber is decoupled (moved slightly up) and only WG modes inside the disk are observable. 2.3.4 Critical coupling and intrinsic loss When the output fiber is tuned to the interference region where transmission dips are observed, the single-prism coupled microdisk can be, treated as an effective optical 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ring resonator side coupled to a waveguide. The generic description o f this system is schematically shown in Fig. 2.13(a). The corresponding optical transfer function may be calculated using the general relation for coupling between an optical resonator and a dielectric waveguide [12]. The transmitted optical power ratio (T = Po\/Po,in = |£t|2/|£in|2) is written as: a 2 + \t\2 - 2a\t\cos(7ikD) P = ------ ^ — ----------------- (2.10) 1 + a |r| - 2a\t\cos{7ukD) where D is the microdisk diameter, k is the wave vector of the WG optical resonance, a = exp(-cmD) is the inner circulation loss factor (E-A =axel0xE^ 9 = 7rDnc /Arcs) and t is the transmission coefficient (t = Et/Em). a is the total distributed loss factor that combines the scattering losses and absorption. If the coupling mechanism is lossless i/2 the optical coupling factor ( k ) may be expressed as ( 1 - tt*) . t,m ax W avelen gth (X) -res ( b ) input ■>— output ( a ) F ig u re 2 .1 3 (a) G eneric description o f a sin g le w a v eg u id e coupled ring resonator, (b ) T yp ical transfer fun ction o f a w aveguide-reson ator system . It is important to notice that all parameters except D are different for different WG resonances. The optical transfer function (equation 2.10) defines a series o f resonant transmission dips that are equally spaced by the optical free spectral range o f the 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. microdisk resonator ( A v f s r = c/nnD) as shown schematically in Fig. 2.13(b). Each resonance has a Lorentzian shape with full-width-half-maximum wavelength A / . f w h m around its resonant wavelength Xre s and a loaded optical Q = A.rcs/A A ,F W H M limited by k and a . Loaded Q can be estimated using the general relation derived for Fabry-Perot (FP) resonators [19] and by changing the factor R/R2 to ta: D^fta Q = n 2n (2 .11) (l - ta R c , n is the refractive index o f the optical resonator along the optical mode polarization. 40 30 Q. 20 10 0 100 90 95 85 a = 0 .0 0 5 5 cm' a = 0 .0 0 7 5 cm" a = 0 .0 0 9 5 cm" a = 0.0115 col' Q. 3 o 0 0 .15 C oupling factor 0.2 0.25 0.05 W a v elen g th d etun in g (pm) (a ) x lO 6 a = 0 .0 0 5 5 cm' a = 0.0 0 7 5 cm " 1 a = 0 .0 0 9 5 cm " 1 a = 0 .0 1 1 5 cm" 0.1 0.15 0.2 Coupling factor 0.25 ( b ) ( c ) F ig u re 2 .1 4 (a) Transm itted op tical pow er spectrum o f 3 m m diam eter and 0 .4 m m thick m icrodisk optical resonator, (b) Sim ulated optical output pow er against co u p lin g factor for different valu es o f distributed loss factor, (c) Sim ulated optical quality factor against co u p lin g factor for different valu es o f distribute lo ss factor. 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.14(a) shows part o f the transmission spectrum for a single-prism coupled LiNbCb microdisk with a diameter D - 3 mm and a thickness h = 0.4 mm. For a TE mode o f the LiNbCE microdisk resonator, n should be replaced by ne that is the unperturbed value o f the extraordinary refractive index ne ~2.14. As may be seen, at the resonant wavelength o f the third mode, the transmitted optical power is zero so that one may infer the mode is critically coupled. The measured transmitted optical power and loaded Q may be used to calculate the intrinsic distributed loss o f a resonant mode. For example the critically coupled mode in Fig. 2.14(a) has a Q of 2 .8 x l0 6. Now if we use equations (2.10) and (2.11) to plot the transmitted optical power and the loaded Q versus the optical coupling factor ( k ) for different values of distributed loss factor (a), we see that there is a unique value o f a which results in critical coupling and a certain value o f loaded Q for the same coupling factor. Fig. 2.14(b) and 2.14(c) show the simulated transmitted optical power and loaded Q for the same microdisk and different values o f a . As may be seen, the mode is critically coupled at a = 0.0075 cm ' 1 and has a loaded Q of about 2 .8 x l0 6 at k = 0.12. So, using simulation results and the measured Q value o f the critically coupled mode, we have simultaneously estimated the value o f k and a for the mode. We can calculate the unloaded quality factor (Qu) of an optical mode using the estimated value o f a and equation (2.8). The critically coupled mode in Fig. 2.14(a) has a Qu o f about 1.2xl07. 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3.5 Other optical coupling methods Coupling methods such as tapered fiber [9], etch-eroded fiber coupler [11] and waveguide coupler [16] that have been successfully used for coupling light into silica microspheres, do not work for LiNb0 3 microdisks because o f its high refractive index. These techniques are based on evanescent-coupling and as mentioned before (2.3.2) the incident light should enter the resonator from a medium with a higher refractive index (compared to the resonator). It may be possible to use a Ti-diffused waveguide on LiNbCf that is pigtailed to single mode fibers. By accurately designing the waveguide dimensions and tuning the propagation constant, it is possible to achieve high efficiency coupling to WG modes in an average-size LiNbCb microdisk. Another possibility is to improve the efficiency o f the prism coupling by tailoring the gap between the prism and microdisk’s sidewall. It has been shown that using cylindrically shaped prisms the coupling to planar waveguides can be improved up to 92% [10,17,18], Notice that as opposed to prism coupling to slab-waveguides, the coupling-gap is already tapered in the microdisk case. Assuming that the prism is in contact with the disk and knowing the skin depth for a diamond prism («135 nm at X = 1550 nm), we can easily calculate the coupling length (about 30 pm for D = 2.9 mm). By shaping the base o f the prism we can tune this length to achieve optim um coupling efficiency. Since it is difficult to polish diamond prisms, ZnSe crystal may be a good candidate for this task. ZnSe has a zinc blend structure and a refractive index o f 2.435. ZnSe is transparent in a wide 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. wavelength window from 500 nm to 22 pm. Plano-convex ZnSe lenses (spherical or cylindrical) are commercially available and so, for these and other reasons it might be possible to use them instead of prisms and take advantage o f the fact that they can also be used to focus the beam. Fig 2.15 shows a possible configuration where a plano-convex ZnSe lens might be used to focus a free space collimated beam and couple it to WG modes inside the microdisk. The collimated beam is easily generated using a pigtailed collimator. F ig u r e 2 .1 5 G eom etry o f direct co u p lin g to W G m o d es through a p la n o -co n v ex Z n S e lens. The main parameters of this design that have to be optimized are the lens radius (Ri) and the center offset (y). Using a basic wave tracing matrix for a spherical air-ZnSe interface and the ABCD law for guassian beams one may calculate the proper value of R/ and y for generating a guassian beam with a waist size o f w at the contact point of the microdisk and plano-convex lens. The value o f the beam waist size (w) has to be chosen according to the WG mode profile. Consider that the beam axis is passing through the center of the lens, and therefore, there is no deviation due to refraction at W G M Incident collim ated beam Z nSe P la n o -co n v ex lens L iN b 0 3 m icrodisk 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the air-ZnSe interface. The beam should enter the interface with an incident angle equal to the ZnSe-LiNbCT critical angle (9C = 60°), so knowing this angle and If we can easily calculate y. The last possibility that we describe here uses a LiNbC>3 half-disk to couple to a full- dislc. Coupling non-resonant WG modes o f a half-disk from free space using a cleaved fiber or a cylindrically shaped fiber is easy and very efficient. Since the wave vectors o f the WG mode inside the half-disk and the WG mode in the full-disk are similar, if both disks are in contact the touching point should act as a directional coupler in analogy with regular fiber couplers and splitters. ( b ) ( c ) F ig u re 2 .1 6 (a) Photograph o f the experim ental arrangem ent used for testin g a half-d isk coupler, (b ) T he toroidal h alf-disk (D = 6 m m ) cou p led to a m icrodisk (D = 2 m m ), (c ) H e-N e laser light cou p led to the W G resonance o f the 2 m m m icrodisk through a toroidal h alf-disk coupler. 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We have done some preliminary work on this scheme but the measured coupling is very weak due to mode mismatch (we didn’t have two identical disks). Fig. 2.16(a) shows a photograph o f the first experimental arrangement used for investigating the half-disk coupling scheme. The half-disk and the microdisk have diameters o f 6 mm and 2 mm respectively. Fig. 2.16(b) shows another arrangement where a toroidal half-disk (made by grinding the microdisk shown in Fig. 2.10) is coupled to the 2 mm microdisk. Fig. 2.16(c) shows Fle-Ne laser (red light, X = 623.2 nm) coupled to the microdisk through the toroidal half-disk. 2.4 DC response Study o f DC electrical-optic response o f the W G modes in the microdisk is useful since it provides information regarding the strength o f the electro-optic interaction inside the disk without the complication o f the microwave design issues o f a RF modulator. This section covers the low-speed electro-optic response in a LiNb0 3 microdisk optical resonator. 2.4.1 DC shift If we place a conductive ring on top o f a microdisk (of the same radius) mounted on a ground plane, a DC voltage on the ring will generate an C-field (mainly along z- 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. direction) around the disk where the W G modes are propagating. Since LiNbCh is an electro-optic material, the E-field changes its refractive index and consequently the resonant wavelengths o f WG modes. Using equation (2.6) (Sec. 2.3.1) we can estimate this change for TE WG modes: We have used ne because we are interested in large r33 and hence modes that are TE polarized. Since in most telecom applications the laser wavelength is around 1550 nm usually Xm = / . 0 = 1550 nm. The refractive index change may be estimated using Ane = n 3 r33£ efl/2 (U3 = 30.8 x 1 0 ’ 12 m/V) so: Eef |- is the magnitude o f the E-field along the z-axis in the equatorial plane o f the microdisk where the WG mode is traveling. Ideally, in the absence o f fringing and other perturbing factors the E-field intensity in the middle o f the disk should be equal to V/h (V is the applied voltage). But due to a fringing field effect, the E-field in the vicinity o f the sidewall has a component along r (Er). The magnitude o f Er varies along the z-axis and is zero at the equatorial plane. Simulation shows that for a 400 pm thick LiNbCE disk, Er is about 8 times smaller than Ez at z ~ ± 100 pm from the equatorial plane. The air gap between the ring and the microdisk surface will also reduce the E-field intensity inside LiNb0 3 . We summarize all these effects and the overlap integral between optical mode and the E-field in a correction factor called the optical-mode-electric-field overlap correction factor pE o so: Xm = nDnc/m => AXm = uDAnJm => AXm = Xm (A n j ne) (2 .12) (2.13) Eeff- Peo(V/h) (2.14) 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. When V - 1 V AXm is called the DC shift or Aloe- This DC shift is an important parameter in a microdisk modulator because it quantifies the electro-optic response of the modulator and is helpful for calculating the RF modulation response. The measured value of the DC shift for a WG resonance of a microdisk can be used to estimate the corresponding pE0. The desired value o f p E o should be close to 1 but in most cases it is less than 0.5. pE O is determined by many parameters and it also varies slightly for different WG resonances. It is possible to improve p E o by using a geometry that forces the C-fields to better overlap the optical mode region. For example in our latest design we mount the microdisk on a cylindrical ground plain with the same radius as the disk and we observe a slightly larger DC shift. F ig u re 2 .1 7 (a) S chem atic diagram sh o w in g the £ -fie ld lin es in the v icin ity o f the m icrod isk sid ew all (the curvature and fringing effect have b een exaggerated), (b) T he m odified d esig n w here the m icrodisk is m ounted on a cylind rical ground plane. Fig. 2.17(a) shows the old design where the microdisk was mounted on a large ground plane and Fig. 2.17(b) shows the modified design. Table 2.2 shows the results of the DC shift measurements for the microdisk modulators tested in our lab. O ptical m ode E lectrode E lectrode O ptical mode_ (a) (b) 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The last microdisk was mounted on our modified design and has the largest Peo- Fig. 2.18(a) shows a photograph o f the microdisk resonator (D = 3 mm, h = 0.4 mm) mounted on a cylindrical ground plane. T a b le 2 .2 D C -sh ift and p E o for different disks D = 2R (m m ) li(m in) AX (p m /V ) (m easured) AX (pm /V ) (calculated ) P e o 5.13 0.4 0 .0 9 0 .2 7 0 .33 5 .8 4 0 .7 4 0 .0 6 0.15 0 .4 2 .9 0.4 0.05 0 .2 7 0 .1 8 2 .9 5 0 .4 1.3 0 .2 7 0 .4 8 Fig. 2.18(b) shows the measured optical output spectrum o f the microdisk in Fig. 2.18(a) at 0 V and 5 V DC bias. The resonator is coupled through a single prism and the output fiber is tuned to the WG cone to detect WG peaks. ( a ) 0 V o lt 0 .6 7 pm H . o 3 9 13 15 5 7 W avelen gth detu n in g (pm) ( b ) F ig u re 2. 18 (a) Photograph o f the m icrodisk resonator m ounted on a cylind rical ground plane, (b ) M easured optical output spectrum at 0 V and 5 V D C bias voltages. We can also simulate the DC shift (A A ,D c) using equation (2.10) and the voltage dependent vector: 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.19 shows the simulated WG resonant wavelength shift for a microdisk resonator with following parameters: k = 0.0999, a = 0.0075 cm '1 , PQ jn = 50 pW, Peo = 0.5, h = 0.4 mm. When the electric field is applied A ,m -» A ,m ± A A ,m (the sign depends on the relative direction of the ii-field and c-axis). The simulated values are in good agreement with values obtained from equation (2.13). In section 2.6 we will use the same approach to calculate the optical modulation amplitude in a microdisk modulator. 4 3 — 0 V a. AA.dc = 0 .1 3 pm o. 0 L ...... 1 5 5 0 .0 3 1 8 1 5 5 0 .0 3 2 8 1 5 5 0 .0 3 3 3 1 5 5 0 .0 3 2 3 W avelength (nm) F ig u re 2 .1 9 (a) sim ulated resonant shift o f the transm ission dip for a m icrodisk resonator with: k = 0 .0 9 9 9 , a = 0 .0 0 7 5 cm ’1 , P0 in = 50 pW , p E0 = 0 .5 , h = 0 .4 mm. To simulate a double-prism coupled microdisk resonator or a single-prism coupled resonator with an output alignment for detecting WG peaks, we have to use a different transfer function that corresponds to a microdisk coupled to two waveguides. This is because the output beam is not propagating in the same direction as the reflected beam so they do not interfere. 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The corresponding transfer function may be written as: C = rrrj 4 -------------- (2.16) 1 + a |/j - 2a\t\ cos{nkD) The parameters in this equation are the same as in equation (2.10). The optical spectrum represented by equation (2.16) is a series of peaks rather than dips. 2.4.2 Optical bistability Bistable optical devices are of great interest for their possible applications to all- optical signal processing for optical computing, optical thresholding and memory. The most common intrinsic bistable optical devices consist o f a Fabry-Perot (FP) resonator containing nonlinear media. To date optical bistability has been observed in different types of nonlinear resonators using materials with various nonlinearity mechanisms [27-32], Here we demonstrate the bistable behavior o f the LiNb 0 3 microdisk resonator when configured as part o f an electrical feedback loop. This differs from the FP case in that we are using a traveling wave resonator. The reason for our interest is that the high-g should, in principle, make a sensitive device. However, there will be a trade off between speed o f response and sensitivity. Fig. 2.20 (a) is a photograph o f the microdisk modulator used in our experiment. The microdisk resonator has a diameter of 5.8 mm and a thickness of 0.74 mm. The measured DC shift for this configuration is about 0.09 pm/V (Table 2.2). The experimental arrangement to measure electro-optic non-linearity is shown in Fig. 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.20(b). The voltage applied to the electrode is a function of resonator optical output power. Optical input power to the resonator is, provided by a frequency-stabilized laser diode whose output is intensity modulated to create a 500 Hz triangle wave. Optical output power is detected using a photodiode. To study electro-optic bistability, amplified detector output voltage is fed back to the disk electrode. ( a ) feed-back LiNbOi, disk with circular electrode » _J micoprisrr DFB laser diode output ( b ) F ig u re 2 .2 0 (a) P hotograph o f the L iN b 0 3 m icrodisk m odulator, (b) E xperim ental arrangem ent used for dem onstrating the bistable behavior o f the m icrod isk optical resonator w ith a feed -b a ck loop. Fig. 2.21(a) shows the measured optical output-power as a function of optical input- power for the indicated values o f peak-to-peak voltage feed-back (F^) and optical Q- factor. The electro-optic system shows a slight non-linearity when Vn, = 1.5 V, using 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. an optical mode with Q = 7.5xl05, and significant bistability and hysteresis behavior when V fb - 3.0 V, using an optical mode with Q = 106. The arrows indicate the sense o f the hysteresis loop. Fig. 2.21(b) shows results o f simulation for the ideal case where just one set o f modes has been excited inside the disk. The simulation shows a behavior similar to the experimental results o f Fig. 2.21(a). Since two-prism coupling technique is employed used in this experiment, equation (2.16) is used to calculate the optical output power as a function o f optical input power. The optical output power can be written as C x P o in where C is a function o f P 0,in because k is proportional to Vfb and Vn , is proportional to the optical output power. Fib creates an electric field along the z-direction equal to Ey = Vn, / h which changes the refractive index at incident optical wavelength X q - 1550 nm from ne- 2.138 to ne = M e - nJr^Ez / 2. Consequently the WG wave vector k (=27tnJX$) depends on Vfb. Flence, with feed-back, the transfer function (C) becomes a function of optical output power as well as wavelength. The optical output power P 0 ut(^) of the system is calculated by applying a discretized triangular input signal and solving the equation P0 U t(X) = C(A,,T> 0u t)x f> o,in(ro) iteratively. The laser wavelength is set to be X ,res-A A .FW H M / 2 where /,re s is one o f the resonant wavelengths o f the microdisk resonator, and A A .f w m m / 2 is the spectral line width o f the optical resonance. 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.15 JO u < 0) £ o a . - 4-* = 3 Cl + - » = 3 O 15 o H. O K ft = 3 .0 V ( 0 = 1O 6 ) K fb = 1.5 V ( g = 7.5 x 1 0 5 ) 0 ■ 0 .1 5 -0.025 0 O ptical input pow er (A rb.) (a ) 0.025 _Q K fl) = 3 .0 V ( 0 = 1O 6 ) Kn, = 1 .5 V (0 = 7.5xlO5) Input pow er (Arb.) ( b ) F ig u re 2.21 (a) M easure optical output-pow er as a function o f optical input-pow er for indicated valu es o f p eak-to-p eak v o lta g e feed b ack ( F(ll) and optical g -fa cto r. (b ) R esults o f sim ulation for the ideal case w here ju st one set o f m o d es has been ex cited inside the disk 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5 RF resonator The key characteristics o f the modulating Zs-field for an efficient electro-optic interaction with WG optical modes inside the disk may be summarized as: 1) Proper RF E -field spatial distribution. 2) RF oscillation frequency equal to m0xAvpsR (/«,,: integer). 3) Large interaction length. 4) Large magnitude. 5) Good overlap with the optical mode (large (3 E o)- The role o f a good RF resonator is to generate an F-field that satisfies all these requirements. We show that the microstrip ring resonator can fulfill all requirements with minimal complexity. It is very important to note that in a conventional MZ modulator both optical and electrical waves are traveling along an open linear trajectory and they are velocity matched for broadband operation. In contrast, in a microdisk modulator, the optical wave is a resonant traveling wave that circulates around the microdisk. Given the large difference between the RF resonant wavelength, A .RF = c T u r f .c A v f s r ) , and resonant optical wavelength, Z rcs = c/(nevrcs), it is not easy to create a traveling wave RF resonance around the disk. In our microdisk modulator the RF field is a standing wave and the phase matching between the optical and RF waves is achieved by frequency matching ( / r E = iw 0xAvfsr) and appropriate spatial distribution o f the F-field. 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5.1 Linear and half-ring RF resonator Fig. 2.22 shows the linear standing-wave resonator design, which was been used for the first demonstration of optical modulation with simultaneous electrical and optical resonance in a microdisk [47]. The RF power is fed to the central open-ended microstrip and gradually couples to two linear resonators. RF input Linear R F-resonators L iN bO j m icrodisk F ig u re 2 .2 2 Photograph o f the first R F-resonator (linear) used for m odulating the W G m od es inside the L ilN b 0 3 disk. About 2/3 of each resonator’s length is on the PCB board (sr = 2.94, thickness = 0.508 mm). The remaining length (1/3) is curved with a radius R (equal to the microdisk radius) and covers about 2/5 of the disk. The frequencies o f both resonators are tuned to A v f s r - Although we observed optical modulation using this configuration, their low efficiency (and complexity of RF tuning) caused us to replace the linear resonators with a semi-ring resonator. 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M icrostrip line Sem i-ring resonator L iN b 0 3 disk F req u e n c y (G H z) ( b ) ( d ) F ig u r e 2 .2 3 (a) P hotograph o f the m icrodisk m odulator design ed based on sid e cou p led sem i-ring RF resonator, (b ) T he m easured ST spectrum for the open -en d ed m icrostripline sid e-co u p led to the sem i-ring, (c) T he result o f sim ulating the resonant £ -fie ld (m agnitude) distribution on a cut- plane located in the m iddle o f the disk, (d) T he structure used in the sim ulation. D ielectric substrate thickness = 0 .5 0 8 m m , dielectric constant = 2 .9 4 , m icrostrip linew idth = 1.2 m m , disk thick n ess = 0 .7 m m , sem i-rin g resonator w idth = 1.2 m m , resonator angle = 90 degree. Fig. 2.23(a) shows the photograph o f a microdisk modulator that uses a semi-ring as the RF-resonator. The resonator is placed on the LiNbC>3 microdisk while the side- coupled open terminated microstrip line is fabricated on a PCB board (s, = 2.94, thickness = 0.508 mm). The outer radius o f the semi-ring (R0) is equal to the microdisk radius in order to maximize the overlap between the E-field and the optical mode. The length of the semi-ring is chosen such that its fundamental resonant frequency ( / r f ) is equal to the optical free spectral range frequency ( A v f s r ) 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. that is 7.6 GHz for this disk. Experimentally it has been found that this length is very close to half o f the disk circumference. Fig. 2.23(c) shows a diagram o f the configuration used for simulating the E'-field distribution on the RF-resonator. The dimensions are slightly different than those o f the actual experimental arrangement, but qualitatively the predicted behavior matches the experimental results. We used Ansoft HFSS software (3 ) for this simulation. As may be seen, when the ring is fed at its fundamental resonant frequency, the magnitude o f the iAfield in the disk is larger than the magnitude o f the /Afield underneath the line. The /Afield magnitude is plotted on a cut-plane that passes through the middle of the disk. This proves that the resonance in the ring amplifies the E-field. The amplification depends on the intrinsic quality-factor o f the ring and the coupling efficiency to the microstrip line. To measure the resonant frequencies o f the semi-ring and estimate the (7-factor we use the standard RF reflection measurement (,Si i) with a RF network analyzer. Fig. 2.23(b) shows a typical Sn spectrum obtained for the semi-ring shown in Fig. 2.23(a). Fig. 2.24 shows a schematic diagram o f the voltage distribution around the semi-ring. The E-Held is a standing wave and, due to the open boundary condition, its maxima are located at open ends o f the semi-ring (points A and B). Similar to an open circuit length o f transmission line, the semi-ring resonator behaves as a parallel RLC resonant circuit (see section 1.3.1). 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A B F ig u re 2 .2 4 S chem atic diagram sh o w in g the v o ltage distribution around the sem i-rin g RF resonator Unlike a Mach-Zehnder modulator it is not possible to lock the optical phase to the maximum o f the £ -field. However, by choosing / rf = A v f s r , the photon roundtrip time ( t r t ) would be equal to the RF period ( 7r f ) and therefore the electro-optic phase accumulation per roundtrip is maximized. The fundamental resonant frequency o f a semi-ring (with a length equal to %R') may be written as: f RFJ = c/2nR’ nRF (2.17) where R != (R0+R\)/2 is the half-ring mean radius and nRy is the effective RF refractive index. Since the extraordinary RF refractive index o f LiNbC/ (/-zrf.c = 5.1) is larger than the optical (ne = 2.14), matching optical FSR and RF resonant frequency of a semi-ring is a difficult task but if we relax the limitation on ring length it is possible to tune the frequency by tuning the length. In practice by reducing the half-ring length by about 5-10 %, we were able to match the frequencies. Because of this relatively easy tuning technique, the semi-ring 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resonator was the first resonator successfully employed in the microdisk modulator design [47,48]. More details about the physics o f resonance in side coupled ring/half ring resonators are discussed in the next section. The main disadvantages o f the semi-ring as a RF-resonator are a reduced quality factor due to electromagnetic radiation from the open ends, poor coupling efficiency at high frequencies, and the fact that only half o f the full photon roundtrip is used for electro-optic interaction. A ring resonator solves the latter two problems by closed loop operation and interacting over the full photon roundtrip. 2.5.2 Ring resonator Microstrip ring resonators are widely utilized in measurement applications as well as filter, oscillator and antenna design [41,42,44,45]. Compact size, low radiation loss, high quality factor and geometrical compatibility make the ring resonator a perfect candidate for disk and ring shaped optoelectronic devices. A ring resonator with the same diameter as the microdisk can generate the modulating A-fiekl around the full photon path length. Several methods have been developed for coupling RF power to ring resonators [36,38,44], In our design the metal ring resonator is placed on top of the microdisk and is side coupled to a microstrip line on a dielectric substrate. To understand the details o f microstrip-ring physics we start with a side-coupled microstrip-ring system on a uniform dielectric substrate. 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.25 shows the geometry of a ring resonator with a mean radius o f R' = (R0+R\)/2 and a width o f wr = R0 - R, on a dielectric substrate with a relative permittivity o f ss and a thickness hs. For an isolated narrow such that wJ2R <0.1 isolated ring the dominant resonant modes are TM mio and the field components are E-, Hr and //,|, for these modes [37]. The resonant frequencies of these modes can be simply calculated from: where c is speed of light, w rf is a positive integer and n ^ x is the effective refractive index of TM mio mode. «rf.c may be calculated using the effective dielectric constant of a microstrip line given approximately by [46]: F ig u re 2 .2 5 . G eom etry o f m icrostrip ring resonator sid e-co u p led to a m icrostripline on a uniform d ielectric substrate. It is also possible to use the W heeler’s effective permittivity [37]: fnF,m = mRF c/(2n R ’ nRFe) (2.18) (2.19) z-axis RF power T 8 eff= 1+<7(SS -1) (2.20) 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where q is called the filling factor. Experimentally it has been shown that for Zd ~ 9.9, q is proportional to (w/2R)0 09 and (W/zs) 0 09 [37], Equation (2.20) is useful for more complex cases where Equation (19) fails. In this situation, experimental results are typically used to estimate the filling factor. Fig. 2.26(a) shows the photograph of a side coupled ring resonator fabricated on RTD 6006 dielectric substrate with a 8 S = 6.15, hs = 0.508 mm. dB - 4 -6 8.1 ( i l l z 8.5 9 7 7.5 8 Frequency (G H z) ( a ) ( b ) 2 0 ■ 2 ■ 3 ■ 4 ■ 5 ■ 6 ■ 7 15.59 G H z 7 .8 2 G H z 2 2 .8 2 G H z 5 10 15 20 2 5 Frequency (GHz) (c) Figure 2.26. ( a ) R ing on uniform d ielectric substrate (R T D 6006): s, = 6 .1 5 , d ielectric th ick n ess (/;, ) = 0 .5 0 8 m m , m icrostripline w idth (wi) = 0 .8 m m , ring diam eter = 6.11 m m , gap size (g ) = 0 .3 2 mm . (b) T he sim ulated S2i for the ring sh o w n in (a), (c) M easured S2i • R esonant freq uencies up to the third harm onic are show n. 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.26(b) is the simulated 6 2 1 using CST electromagnetic simulator (2). The fundamental resonance o f the ring resonator occurs at / r f =8.1 GHz. Fig. 2.26(c) shows the measured S21 through the microstripline. The RF resonances (TMno, TM 2 1 0, TM 310) appear as dips in the transmitted RF power spectrum. The measured fundamental resonance is about 7.82 GHz that is very close to the simulated value. If we use equation (2.19) to calculate seff and substitute into equation (2.18) we find that /r f i = 7.91 GHz. This agreement validates our assumptions and the approximations in Equations (2.18) and (2.19). The slight (1%) difference between calculation and measurement is mostly due to errors in ring width and diameter measurements. Also the resonant frequency calculated using equation (2.18) is the intrinsic resonant frequency o f an isolated ring. Coupling to the microstrip line changes the resonant frequency (loading effect) similar to any other loaded oscillator. When a ring resonator is strongly coupled to a microstripline (small gap sizes), the symmetry breaks due to the proximity o f the microstripline to the ring and two coupling configurations are possible, depending on whether induced magnetic field or induced electric field is maximum at the resonator near the microstripline. The broken symmetry splits each mode into two modes with slightly different resonant frequencies: even and odd modes [36]. Odd modes have lower frequencies and are capacitively coupled to the line, while the even modes have higher frequencies and are magnetically coupled to the line [35], The coupling strength depends on mode order. The different coupling mechanisms result in different loading factors and hence different frequency shifts and loaded Os. Resonant 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. frequencies cannot be calculated using equation (2.18), although this relation may still be used to get a rough idea about the resonant frequencies. It is evident that calculating the loaded 0 -factors and resonant frequencies as a function of geometrical parameters and mode nature is an involved task. We will explore this issue as we continue to analyze the ring resonator on a L iN b0 3 microdisk. In the microdisk modulator design, the ring is placed on a L iN b0 3 microdisk. The role o f the ring is to provide an T-field normal to the disk surface and localized to the disk circumference where the highly confined optical WG modes are traveling. Microstripline Optical input LiNb03 disk Microprism Optical output Ring resonator Optical mode 0 LiNbCk disk 01 I h Ground F ig u re 2 .2 7 . G eom etry o f ring resonator on L iN b 0 3 sid e-cou p led to a m icrostripline (top v iew and sid e v iew ) 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In our design we use a side-coupled microstripline to couple energy to a resonance of the RF ring resonator. Fig. 2.27 shows a schematic diagram of the ring, microdisk and the microstripline. This configuration is more complicated than the side-coupled ring on a uniform substrate (in Fig. 2.25) because the ring and line are on two different high contrast dielectric materials with an air gap in between. Fig. 2.28(a) shows a typical experimental arrangement for characterizing the performance of the ring resonator on the LiNbCb microdisk. V R = 2 .9 mm h = 0 .7 4 mm s , = 6 .1 2 g = 0.3 mm wr = 0.5 mm w/ = 0 .7 5 mm hs = 0.5 mm 0 -2 -4 -6 -8 -10 -12 Ring - - Semi-ring 20 5 10 15 / ) ,= 7 .7 2 G H z f2e= 1 4.60G H z 4 . = 2 0 .4 0 G H z //„ = 7 .1 3 G H z f2o= 14 .1 0 G H z f3a= 2 0 .1 3 G H z Frequency (GHz) ( b ) Fig. 2 .2 8 . (a) Photograph o f the ring resonator on L iN b 0 3 m icrodisk sid e-co u p led to the m icrostripline. (b) S 2! m easurem ent results for ring and sem i-ring on the L iN b 0 3 m icrod isk sh ow n in (a). 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We use S-parameter measurement (An and S2\) to estimate the resonant frequency and the quality factor o f the RF resonances. Fig. 2.28(b) shows the measured S2\ for the ring in Fig. 2.28(a) as well as a semi-ring on the same microdisk. The resonant dips up to the third harmonic o f the ring are shown in this figure. For the ring resonator (solid line) we observe two dips (one small and one large) due to even-odd mode splitting. The coupling strength o f the ring as indicated by the depth o f the resonant dips is better at higher frequencies than that o f the semi-ring, and the width of the resonant dips is smaller for the ring due to a better quality factor. These observations prove the validity o f our argument regarding the superiority o f the ring resonator especially at high frequencies. Before analyzing the electromagnetic behavior o f this system we will examine simultaneous RF-optical resonance in this configuration. As mentioned in section 1.3, an optically resonant modulator can only modulate light at RF frequencies equal to m0xAvFSR but an efficient modulation also requires a proper spatial distribution o f the oscillating E-field to maximize the accumulated electro-optic induced phase shift at each roundtrip. Fig. 2.29 shows the simulated resonant .E-field distribution on a cut-plane that passes through the middle o f the disk. Fig. 2.29(a) shows the 2-D E-field magnitude distribution and Fig. 2.29(b) shows a 3-D view o f the E-vectors distributed around the disk. Since we want to satisfy the frequency matching condition /rf,™ = twrfxAvfsr for low values o f mR F (mR F < 10), the RF wavelength, XrF)„ = c/(ne^ x f RPlu), is not small enough (compared to ring circumference: 2nR) for resonant traveling wave operation. 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) (b) F ig u re 2 .2 9 Sim ulated £ -fie ld distribution on a cut plane p assin g through the m iddle o f a L iN b 0 3 m icrodisk w h en the fundam ental resonance o f the ring resonator is excited , (a) 2 -D £ -fie ld m agnitude distribution, (b ) 3 -D v iew o f the .E-vectors distributed around the disk. T he E -vectors are plotted on a lo g scale. So, similar to the semi-ring resonator, the ring resonator is a standing wave resonator and the locations of the maximum and minimum are fixed by the broken symmetry of the feed point. In Fig. 2.30 the voltage distribution along a linear standing wave resonator, that is equivalent to the ring resonator, is shown. M B A 'A F ig u re 2 .3 0 T he £ -fie ld distribution for the fundam ental m ode o f the ring resonator and equ ivalen t linear resonance. 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The traveling optical wave (WG resonance) will always experience a position dependent E-field intensity during its round trip. A voltage oscillation on a ring resonator that is excited by a single tone at its fundamental resonant frequency ( / r f . i ) can be expressed as: V = Vm cos(kRFx,)cos(coRFt) (2.21) The electro-optic induced phase shift for a photon that enters the microdisk resonator at point ‘A ’ may be written as: (p - ^ cos(kRFx ,) cos(coRFt) (2 .22) where = n ^ x ^ E ^ H = ( 1/2 ) Peo!h (Eq. 14) and x/ ^(c/njt. If we integrate equation (2.22) over ten optical roundtrip times (10xp) that are also equal to the ten RF periods (10TR F = 1 0 / / r F) , then: X 1 0 'x (27T ^ //,rc.,) 6 o 4 jy o > N u < D < D 0 -2 -4 -6 T raveling w ave — Standing w ave A / M / y y y \ -1 -0 .5 0.5 1 (2.23) 0 W < • F ig u re 2.31 T he accum ulated electro-op tical phase for a photon that enters the resonator at the peak o f the v o ltage o scilla tio n after traveling for 10 c y cles (so lid line). T he dashed line sh o w s the accum ulated electro -o p tic phase for a photon in a traveling w a v e m odulator. Fig. 2.31 shows the calculated value o f ( j) against RF-optical detuning ( I nc-URF | ). 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. So when / r f = A v f s r or ne = hrf, the phase shift is maximized but its magnitude is still half o f the value that can be obtained in a conventional velocity matched traveling wave electro-optic phase shifter. When both optical and RF waves are traveling, their phase can be locked in such a way that the optical phase shift per unit length is written as: An A, \ -o /Lo V ^ n J 2 e 33 h R F (2.24) where p'Eo is the overlap factor and h is the gap size between the electrodes. For the microdisk modulator we use the refractive index change and the transfer function to calculate the optical power modulation. The modulated effective optical refractive index o f TE modes in a frequency matched ( / r f = A v f s r ) microdisk- microring system can be written as: «e(0 = ne „ + = nm + \ nl ^ ^ f i L x K ,c o s (2.25) 2 n The new factor Ps is a correction factor that accounts for the standing wave nature of voltage oscillation. As shown in Fig. 2.31 in a standing ring resonator based modulator Ps = 0.5. In equation (2.24) this factor doesn’t exist because o f the traveling wave nature o f the RF wave. We now turn our attention to the resonant frequencies of the microring resonator. The microdisks used in our experiments are z-cut (the c-axis is parallel to the z-axis and normal to the disk flat surface). The bulk dielectric constant o f LiNbC/ along the c-axis (z in Fig. 2.24 that is also the f?-field direction for TMmi0 modes) is nR F = 5.1 at frequencies between 1-50 GFIz [2], If LiNbCh is used as the substrate in a microstripline structure (Fig. 2.32(a)), the effective permittivity is reduced. For 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. example for a 0.4 mm thick substrate and a linewidth of 0.3 mm using equation (2.19), Setf - 17.45 and nR F > e = 4.18. But a ring resonator on a L iN b0 3 microdisk has a cross-section similar to that shown in Fig. 2.32(b). For this configuration seir cannot be calculated by a simple formula so we use CST simulation software (2 ) to estimate the propagation constant and derive «R F. 4 L iN b0 3 L iN b0 3 L iN b0 3 ( a ) ( b ) ( c ) F ig. 2 .3 2 . S 2i m easurem ent results for ring and h a lf ring on L iN b 0 3 For a similar substrate thickness and line width nR F c = 3.76, If we move the line further to the edge and create a 50 pm overhang in the air (which is equivalent to increasing the inner and outer radius o f the ring), then nR F decreases to 3.56. This shows that by tailoring the ring/microdisk design one may reduce ttR F c to more closely match the optical refractive index (ne = 2.14). Also the optical mode propagates at a radius almost equal to the disk radius (R) while the mean ring radius is R' = (R0+R\)/2. So as to satisfy the frequency matching condition (AvF sR = , / r f i ) , /? ] > F e should be larger than nc by a factor R/R' (for a disk with a diameter o f 3 mm and a ring with a width of 0.3 mm, R/R '= 1.11). Another important factor that needs to be taken into account in RF frequency tuning 111 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is that the loaded resonant frequency is larger than the value estimated by equation (2.18) due to side coupling to the microstripline. As we mentioned before, strong side-coupling results in separate degenerate even and odd modes in the microring and the loading effect is different for these modes. Taking into account the loading effect and the geometry of the resonator, one may expect that the resonant frequencies of the side-coupled ring on a dielectric disk should have the form: / L O and /le are unknown functions that should be evaluated based on a particular geometry. / is equivalent to equation (2.19) for a regular microstrip line but it gives smaller values of effective permittivity for given values o f n\ h and sr due to the absence of dielectric on one side o f the line as well as other design factors. To calculate / the wave equation for asymmetric microstripline should be solved. / o and /le are loading factors for even and odd modes as a function o f the gap size (g) between the disk and line. These functions can be evaluated using experimental data. For example Fig. 2.33 shows resonant frequency measurement for the fundamental even mode o f a ring resonator on a LiNbCb disk side-coupled to a microstripline with different coupling gap (g) sizes. In this experiment gx = 0.1 mm, D = 3 mm, wT = 0.3 mm, w\ = 0.75 mm, h = 0.4mm, hs = 0.5 mm, and ss = 6.12. The c (2.26) where: £ eff = f s i f r ’ t, / W ,) (2.27) (2.28) 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. experimental results show that tuning the gap over a wide range (600 pm) doesn’t change the resonant frequency more than 200 MHz. 14.75 I 14.7 G — 4 — » c ^ cS N I o 1465 C D w u, 1 5 I 14.6 C S -o C £ 14.55 150 350 550 750 Gap size (pm) F ig u re 2 .3 3 R esonant frequency as a function o f gap size for the ev en m ode o f a ring resonator (w = 3 0 0 pm ) on a L iN b 0 3 m icrodisk w ith a diam eter o f 3 m m and a thickness o f 0 .4 mm. (approxim ated line equation: f iF = \5.292g 0 0 0 7 3 ) If we use equation (2.26) to estimate the fundamental resonant frequency o f a ring resonator with Rx = 2.75 mm, R0 = 3.05 mm and «RF,e = 3.56 (that corresponds to the configuration shown in Fig. 2.31(c)) on a 3 mm diameter and a 0.4 mm thick LiNbC>3 microdisk with a A/L =100 MHz dten /rf i = 10.14 GHz. The optical free spectral range for this disk is 14.6 GHz so that a factor o f 1.44 reduction in nR F ,e (2.07 in eefr) is required to achieve RF-optical frequency matching. In our proof of principle experiment we solve this problem by fabricating the ring separately. When the ring is placed on top of the disk an effective air gap exists between the ring and LiNbCb surface due to the surface roughness o f the ring and the 113 A Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. microdisk. This air gap reduces seff. By properly choosing the ring size, gapsize, surface roughness and fine tuning the location o f the ring on the disk, we were able to tune the fundamental RF resonant frequency o f the ring very close to A v i? s r .. Notice that tuning the fundamental resonance doesn’t guarantee fap,m = wrfxAvfsr for all values o f »7rf because, as opposed to optical resonant frequencies, the RF resonant frequencies aren’t exact multiples of the fundamental resonance because of different loading factors and even-odd splitting. 5 .9 8 m m 4 .1 7 m m RF input C opper ring L iN b 0 3 T unable v olu m e o f air cylinder Brass (a) RF output 250 MHz f N t / D -10 8.5 9 9.5 10 F re q u e n c y (G H z ) (b) K 9.35 ® 9.3 k * 9.25 c u 3 cr 9.2 9.15 9.1 g 9.05 p 4 1000 2000 za (m m ) (c) 3000 4000 F ig. 2 .3 4 (a) Schem atic diagram o f the configuration used for tuning the RF resonant freq uency, (b) R esults o f S 21 m easurem ent for different v o lu m es o f air cylinder (za is changed), (c ) R esonant frequency as a function o f z„. 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We also explored an alternate approach to RF resonant frequency tuning by changing the ground plane design. Fig. 2.34 (a) shows a schematic diagram o f the new arrangement. A tunable air cylinder beneath the disk changes the effective permittivity and consequently the resonant frequencies. In the actual experiment, a brass cylinder that can move along the z-axis has been used to change the air-cylinder height (za). Notice that the air cylinder is not centered. Fig. 2.34(b) shows the results o f S21 (throughput) measurements for different values o f za. As may be seen, the minimum (which represents the resonant frequency) decreases as we increase za. Fig. 2.34(c) shows the resonant frequency against za. For za > 3 mm the resonant frequency changes only slightly. This tuning method is useful for fine-tuning the RF-resonant frequency but, since the maximum tuning range is limited (about 250 MHz in this case), still other techniques should be used for RF-optical frequency matching. 2.5.3 Voltage gain and RF critical coupling In addition to generating the proper voltage distribution around the disk, the RF resonator also provides voltage gain. At resonance, the amplitude o f the voltage oscillation (Vm) on the ring is larger compared to the input RF voltage amplitude (Fjn). The voltage amplitude on the ring is a function of the ring quality factor and 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RF coupling coefficient. The voltage gain is defined as Gv = and it can be estimated from S parameter measurements. The average stored energy (if) in a resonator can be expressed as: Where ( T r p . u is the unloaded quality factor and P | oss i s the energy lost in the resonator per second, not withstanding coupling loss: P\ is the power lost in the microstripline. The energy stored in the ring-microdisk capacitor can be expressed as a function o f the voltage and geometrical parameters: Where A is the ring area (%R0-nR\). The extra factor (1/4) is a result o f having a time and space varying voltage distribution (we are using the RMS values o f the voltage in the conventional formula for static energy storage in a capacitor). pe is a factor that connects the actual capacitance and the capacitance calculated assuming the ring-microdisk-ground is a parallel plate capacitor (C = srsoA/d). pc can be estimated either by simulation or measuring the optical modulation. The capacitance per unit length (C ') for a microstripline can be written as: C ' = nuy/cZ,, (Zn is the characteristic impedance o f the line and c is the speed o f light). nR F and Z0 can be calculated from simulation results and pc = C/C. For a 0.3 mm wide microstip on a 0.4 mm thick LiNbCb substrate, pc « 2.8. Since, in our experiments the ring resonators are hand made and mechanically tuned on the disk, pc should be evaluated separately for each modulator. (2.29) (2.30) (2.31) 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Using equations (2.30) and (2.31): Vm = l l hP! - Q^ ^ (2.32) V P c COm ' S c ,R F S o ^ - We can rewrite equation (2.30) in terms o f the microstripline loss factor (ZT, P oul = (l/Lj)P in ): p , „ „ = p j 1 -|S „ r - |S 2 ,r - 1 . 5 ( i p i ) ] (2,33) V L r J The voltage gain Gv =Vm /Vin, where Vln (input voltage amplitude) is related to the input RF power through Vm =(2Zo Prf)05 in which Z0 is the microstripline impedance. Here we have assumed that the microstripline is properly terminated with a matched impedance. Using equation (2.33) in equation (2.32): G = — = I 4 h P l '> ^ R 'Z lIl (2.34) K, \ ^ Z ocoRF£eMe0A where P |o ss 'is the loss factor given by: P' h iv f a a L -1 N L t- r lo ss V J (2.35) The .V-paramctcrs and L \ can be directly measured using the network analyzer. The quality factor o f a dielectric resonator that is magnetically coupled to a microstripline may be determined using the measured .S'-parameters [43]. Since the even mode of the ring resonator is also magnetically coupled to the microstripline, we can use the method described in Ref. 43 to determine the unloaded quality factor that is needed in equation (2.32). Fig. 2.35 shows the measurement points for loaded and unloaded quality factors in the reflection and transmission coefficient magnitude planes as a function of coupling factor p and the definition o f various terms used. The coupling factor is defined as S) i,/S'2 i0 = r\ where .S ) i„ and Sfi0 are measured values o f reflection and transmission at resonance. 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Also r| relates the various quality factors by the well-known relation [43]: QRF. U ~ Q r f ( 1 + 1 1)~ >]Qexl (2.36) Qi{h\u & Qrf m easurem ent points in dB S i.( d B ) S 21 (d B ) R eflection T ransm ission F ig u re 2 .3 5 Qw.a and Qrf m easurem ent points in the reflection and transm ission c o efficie n t m agnitude plan es as a function o f cou p lin g factor r] and the definition o f various term s [43]. Equation (2.34) may not be accurate enough for calculating the exact value of Vm but it is very useful for evaluating the effect o f different parameters on the voltage gain. When 5'iio= -S ? 10 = 0.5 and r| =1, the ring is critically coupled to the microstripline. In this situation the stored energy (and therefore Fm ) is maximized. The RF coupling factor can be tuned by changing the gap size (g) between the microdisk and the microstripline to achieve critical coupling. We have simulated the ^-parameters and the E-field intensity inside a microdisk using the CST electromagnetic sim ulator(2). Fig. 2.36 shows the simulation results. The LiNbCb microdisk has a diameter of 5.13 mm and thickness of 0.4 mm. As may be seen when g = 380 pm (p = 1), the E- field amplitude is maximized. When r\> 1 (S\ i0 > S21 0) the ring is over coupled, and 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. when r) < 1 (.S) |0< Si \0) it is under coupled. We can calculate (3 C using equation (2.32) and the simulation results. The average value of (3 C in this case is 2.7. 2.00 S 1.50 £ »-oo C a , 0 .5 0 3 o u 0.00 s' > 2.0E+05 > 200 | 100 200 300 400 500 Gap size, g, (pm) (b) A A 600 200 400 600 Gap s ize, g , (pm) ( c ) F ig u re 2 .3 6 C S T sim ulation results for ring resonator on a L iN bO j m icrodisk w ith a diam eter o f 5.13 m m and a th ick n ess o f 0 .4 m m . (a) T he cou p lin g factor (r|) against gap size (g ). (b ) Q„ and Qt against co u p lin g factor, (c) T he £ -fie ld o scilla tio n s am plitude against g. As expected, the absolute values o f resonant frequency derived from the simulation are smaller than the optical FSR and they decrease as we increase the gap size (loading effect). Since the resonant frequency also changes as a function o f g, it is difficult to have RF-optical frequency matching and RF critical coupling sim ultaneously. As mentioned in section 2.4.1, mounting the microdisk on a cylinder improves the DC-shift. The same arrangement also allows us to tune the gap size since the brass 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. cylinder can move relative to the microstripline. We use an experimental arrangement similar to the one shown in Fig. 2.28 to study RF coupling. Fig. 2.37(a) shows experimental results of .S'-parameter measurements on a LiNb0 3 structure with a diameter of 3 mm and a thickness of 0.4 mm for three different values o f g. Fig. 2.37(b), 2.37(c) and 2.37(d) are the calculated quality factor, coupling factor and the /(-field oscillation amplitude (calculated using equation 2.34) as a function o f against the gap size. We have used the value o f (3 C derived from the simulation results (Fig. 2.36). PQ -o 3 § C 3 a i 00 2 g = 2 5 0 pm — g = 3 5 0 pm • g = 4 5 0 pm 4 6 8 -10 14.8 14.9 14.4 14.5 14.6 14.7 15 2.00 I — o o 1.50 ,0 3 < + H on c 1.00 "a. 3 o 0.50 U Frequency (GHz) ( a ) 180 J 130 3 a 80 30 200 300 400 500 Gap size, g , (pm) ( b ) 200 300 400 500 Gap s ize, g ,(pm) ( c ) 5 4.8 c d 4 6 o o 4 > 4.4 o > 4.2 o < v V 200 300 400 500 Gap s ize, g , (pm ) ( d ) F ig u re 2 .3 7 (a) E xperim ental results o f S-param eter m easurem ents for a L iN b 0 3 w ith a diam eter o f 3 m m and a thick n ess o f 0 .4 m m for three different valu es o f g . (b ,c,d ) T he calculated quality factor, co u p lin g factor, and the £ -fie ld o scilla tio n am plitude (calculated usin g Eq. 2 .3 4 ) against the gap size. 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In this case at a gap size o f g = 350 pm, the ring is critically coupled to the line. The estimated voltage gain at critical coupling condition is 4.9. We should point out that whenever ^-parameters are expressed in dB they represent the relative transmitted and reflected power as opposed to voltage amplitude. So the critical coupling condition S\]0= £ 2 1 0 = 0.5 becomes < S ,n 02= Sixo2 = -6 dB. If instead o f matched termination, we open terminate the microstripline then, in an ideal situation the standing wave ratio would be infinite. In this case, the voltage amplitude on the line is 2 F j n (instead o f Fjn). By properly tuning the location o f the voltage maxima on the line, we can improve the voltage gain (ideally by a factor o f 2). This is achievable by tuning the length o f the open end. 2.6 Fundamental FSR modulation Modulation in resonant optical modulators is fundamentally different from traveling wave optical modulators because in the latter case at least one o f the waves (optical or microwave) is a resonance inside a microwave or optical resonator. Resonance enhances the electro-optic interaction but imposes a limitation on the frequency response. As mentioned before, in an optically resonant modulator, effective modulation only occurs within a limited bandwidth (BW) around a discreet set of frequencies defined by the optical free spectral range (FSR) and optical 0-factor. If the modulating RF frequency ( / r f ) is very close to A v f s r the behavior o f the 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. microdisk modulator may be explained using a simple model based on the optical transfer function o f an optical resonator and electro-optic modulation o f the effective optical refractive index. This section covers the theoretical and the experimental aspects o f linear modulation at the fundamental frequency o f the microdisk modulator. 2.6.1 Physics and modeling Our previous work on LiNb0 3 microdisk modulators [47-48] uses general principles o f resonator-coupler systems to derive the modulation response in the time domain. Although this approach is very accurate, it requires time consuming calculations because it is based on evaluating the interference o f the traveling waves inside the disk after a large number o f round trips around the disk (details o f this calculation can be found in section 3.4 o f Ref. 47). In the previous calculations the RF- resonance hasn’t been treated properly because, instead of modeling the modes o f the ring resonator, the modulation has been modeled based on a periodic metal-electrode structure. One possible approach to a more complete model is to use the same time- domain model o f a resonator-coupler combined with RF resonance o f a ring resonator. Theoretically this should result in a complete model for expressing modulator response for all harmonics (m0x A v f s r ) as a function o f RF quality factor, 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RF coupling factor, optical quality factor, optical coupling coefficient and the geometrical parameters. A second approach is to use the optical transfer function o f the microdisk modulator (in frequency domain) with an electro-optically modulated refractive index. This approach is applicable only i f / R F is very close to m0xAvF sR so that we can ignore the restriction imposed on the modulation by the frequency response. We choose the second approach as it leads to a very simple model in which the role o f all measurable parameters and their impact on modulator efficiency is clearly demonstrated. The main disadvantage o f this simple model is the absence o f bandwidth calculations. Basically we assume the bandwidth is limited by the optical-Q. To analyze the modulator performance, it is helpful to review the role o f different device parameters contributing to the modulation process. Fig. 2.38 is a schematic diagram o f the modulator illustrating important parameters that influence modulation performance. The efficiency o f electro-optic interaction between optical whispering gallery modes and the applied electric field is directly proportional to the following factors: 1) Interaction time or length. The interaction time is the photon lifetime inside the resonator xp = Q/co0 where Q is the quality factor o f the optical resonator. 2) .E-field oscillation amplitude inside the mode region that can be written as: E m = $m (G vV m /h). 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u re 2 .3 8 Schem atic diagram o f the m icrodisk m odulator representing the param eters in volved in the m odulation process. In section 2.3.3 we mentioned that the transfer function o f the microdisk optical resonator can be a series o f transmission dips (equation 2.10) or a series o f coupled peaks (equation. 2.16) depending on the optical coupling method and alignment. In each case the optical transfer function is expressed as a function of optical coupling factor (k) the circulation loss factor (a), and microdisk refractive index for TE modes («e). So at a given wavelength (Aq), the time variation o f the optical output power ( 8 P 0,out) can be written as a function of time variation o f the refractive index ( 5 n e) (equations (25) and (34)): ne(t) = ne + 8nc{t) = nc + ^ n 3 er3 3 x G„Vm c o s (2.37) 2 h So knowing p E O (from DC shift measurement), Gv (from S’ -parameter measurement), the optical Q (or the distributed loss factor a ) and the optical coupling factor (k) we can calculate the modulated optical power as a function o f RF input voltage amplitude (VR F ). P0,out=fBo(VR F ) (2.38) / bo is called the electro-optic transfer function of the optical resonance. 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.39(a) shows the simulated electro-optic transfer function for an optical resonance (transmission dip) in a microdisk LiNbC>3 with a thickness o f 0.4 mm. The laser wavelength is tuned to A res + 0 . 2 5 A ^ f w h m - Fig. 2.39(b) shows the simulated DC shift based on experimental results. The optical input power ( P 0,in) is 50 pW, Gv = 6 and Q = 3 x l0 6. The dashed and the doted lines are respectively the first ( 7 V i ) and the second ( A C ) derivatives of/eo- It is evident that an efficient linear modulation (P0,out ,o c Fri) requires a small second derivative and a large first derivative. A a s e i “ T es + 0.25A X f w h M — ov o Q . A k Dc = 0 .1 3 p m 1550.0323 1550.0328 W av elen g th (nm ) 1550.0318 RF Voltage (V) ( a ) ( b ) F ig u re 2 .3 9 (a) T he electro-op tic transfer function o f a m icrodisk m odulator (h = 0 .4 m m , k = 0 .1 , a = 0 .0 0 7 5 cm"1 , P0; m = 50 pW , G v = 6. (b) T he sim ulated D C -sh ift (A k D c) based on m easured value. As may be seen in Fig. 2.39(a) at Frf = 0, N\ is maximum and N 2 is zero. This is the optimized condition for linear modulation and is a result o f proper tuning o f the laser w avelength (kiasci) relative to the resonant w avelength (k rcs). W hen the laser wavelength is tuned to the linear regime we may simplify the calculations further by using the first derivative: 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. P o ,m = 2 M p sFi„ (2.39) P 0,m is the peak-to-peak value o f the modulated optical power. Although A /i can be derived from /eo, but an easier way to estimate N\ is to write it as a function o f the voltage (Gv) gain, the DC shift, ps, and the mode slope for the corresponding optical mode: Po.m = 2Gv Pskm xAxAkoc (2.40) S is the optical mode slope (usually measured in pW/pm) near the laser wavelength. This equation is used to calculate the modulated optical power for a known value of Gv or to estimate Gv based on the measured value o f P(xm . If a coupled optical peak with a symmetric spectral profile is used for modulation, we can estimate the mode slope based on the measured optical-Q in the following way: Q ~ ^-res/A ^-FW H M & S — Po.nmd A ^-F W H M — ^ S — (Q x Po,max)l ^rcs Then equation (2.40) can be rewritten as: Po.m = 2Gv PsV i„ ^(QPo.nmd K es)x&^DC (2-41) Where T> 0,m ax is the optical output power at resonance. This equation clearly shows the role o f all critical parameters in the linear modulation process (the same simplification is possible if we use a transmission dip). 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.2 Frequency response and bandwidth The calculated optical power in equation (2.38) is independent o f the modulating RF frequency. However in practice optical and electrical responses of the microdisk and the ring resonator impose limitations on the modulation bandwidth. In section 1.3.3 the effect o f the optical transfer function on the RF frequency response o f an optical resonator was explained based on a simple fact: the RF side bands (194 THz + / r f ) generated by optical modulation must be resonant inside the microdisk resonator. As a result the optical transfer function is effectively a RF bandpass filter with pass band frequencies o f bandwidth A v f w h m = vres IQ around / m0 x A v i $ r . One way to include the frequency response into our simple model is to filter in frequency domain. W e can calculate the Fourier transform o f the modulated optical power from equation (2.38) and filter it through the microdisk optical transfer function (f0). Then frequency dependent modulation amplitude can be derived from the inverse Fourier transform o f the filtered frequency spectrum: Pour{tJR F ) =Bopt(fR F ) x P 0 J 0 J t ) = T 'x {/o(<d)x<F / e o ( F r f ( 0 ) ] ! (2.42) The RF frequency response o f the microstripline-ring system also has a frequency dependent voltage gain factor Gv(f\*s), but usually this bandwidth is larger than the optical bandwidth. In our calculations we assume that the optical bandwidth dominates the frequency response o f the system and if A v f s r = / rf then 2?opt = 1. 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.3 Experimental results To observe and measure the modulation performance of the L iN b03 microdisk modulator we employ the same arrangement used for studying the optical coupling and WG modes (Fig. 2.7). The only difference is that the output fiber is attached to a 10/90 single mode power splitter. 10 percent o f the optical output power goes to a low-speed photo detector for monitoring the mode and the location o f the laser wavelength relative to the resonant wavelength, and 90 percent is sent to a high speed detector to measure the modulated optical power. Fig. 2.40 shows the evolution o f the microdisk optical modulator structure. Fig. 2.40(a) shows the first and the simplest setup. There is no microstrip structure and the disk is fed directly with, SMA connector. The two-prism optical coupling method has been used and the optical input lens, output fiber and microprisms were mounted on four separate xyz stages controlled by picomotors(1). Fig. 2.40(b) shows a setup with the linear RF-resonators explained in Sec. 2.5.1 and with the same opto mechanical arrangement but the disk is mounted on the ground-plane o f the PCB board (a small part of dielectric material is removed) so the resonators can be coupled to the central microstrip feed line. Fig. 2.40(c) shows the semi-planar setup with half-ring RF resonators. We use the term semi-planar because the microprisms, microdisk and the PCB board are mounted on a common brass substrate to make the device smaller and more robust. Flowever, the optical input and output stages are on separate mounts. 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u re 2 .4 0 E volu tion o f the L iN b 0 3 m icrodisk optical m odulator, (a) D irect RF feed in g , non- planar, dou ble-p rism optical coupling, (b) L inear R F-resonator, non-planar, d ou b le prism optical coupling, (c ) H alf-ring R F-resonator, sem i-planar, double-prism optical cou p lin g, (d ) H alf-ring R F-resonator, planar, double-prism optical coupling, (e ) Full-ring R F-resonator, sem i-planar, single-prism optical cou p lin g, RF through put. (f) F ull-ring R F-resonator, sem i-planar, sin g le prism op tical co u p lin g , RF-throughput, controlled RF coupling. Fig. 2.40(d) shows a planar-setup in which all components are mounted on the same brass substrate. In this configuration the optical input and output are manually 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. controlled with two small x-y-z stages, there is no picomotor involved and optical alignment can be maintained for a long time. Although the planar setup is stable, due to the lack o f accurate control on the input and output launch positions, it is hard to achieve high optical coupling efficiencies. The best optical coupling (15%) has been achieved with configurations (a) and (b) because of the high degree o f freedom and accuracy o f the mechanical motion. Fig. 2.40(e) shows the latest version o f the planar setup where a single prism is used to couple in and out and there is a RF" output port that allows RF throughput (S21) measurement. Fig. 2.40(f) is designed to control RF-coupling by changing the relative height and distance between the ring resonator and the side-coupled microstrip line. The LiNbCh microdisk is mounted on a brass cylinder and it can move independently o f the RF board. As explained in section 2.4.1 this semi-planar configuration increases the optical DC shift. The single prism technique is used for optical coupling and is similar to the arrangement (b) and (c). To characterize the modulation performance o f the LiNbC>3 microdisk modulator we measure the detected modulated voltage at different RF powers and frequencies. The detector used in our experiments has a responsivity R = 280 pV/pW at 8 GFlz that reduces to about 260 pV /pW around 15 GHz. A single mode tunable laser with a line width < 0.5 MHz provides the input optical power at wavelength X0 = 1550 nm. The wavelength is tunable within a 0.1 nm range (around center wavelengths between 1525 nm and 1575 nm) with an accuracy o f 0.3 pm. By controlling the laser wavelength we can find the optimum position in the mode spectrum (largest 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. slope) in order to maximize the modulation. We use a RF tracking source to sweep the frequency near / r f = A v f s r for RF-bandwith measurements. For measuring modulation as a function of input RF power, the RF frequency is set to / R F = A v f s r where the modulation is maximum and the power is changed while the relative position o f the laser wavelength is fixed. The first experiment is a comparison between the ring and semi-ring performance. The disk used has a diameter o f D = 5.8 mm and thickness h = 0.720 mm. Optical coupling in and out using the arrangement shown in Fig. 2.40(e) gives a maximum coupled power of 100 pW. The optical Q is near 3x10 6 and Avfsr ~7.6 GHz (for TE WG modes). Fig 2.41 shows the measured S21 through the microstripline that is coupled to a ring and semi-ring. 0 -2 -4 -6 -8 - 10 -12 -14 -16 -18 -20 -ring •sem i-ring Odd mode Ficc|ucncv(GH/0 6.5 7.5 8 8.5 Frequency(GHz) 9.5 10 F ig u re 2.41 M easured S2i for a sem i-ring and ring at fundam ental resonance and the sim ulated ev en m ode (left inset) field distribution on the ring. The right inset sh ow s the detected m odulated pow er w ith sem i-ring and ring resonators. 131 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. As may be seen, the even mode of the ring and the fundamental resonance o f the semi-ring are tuned to A v f s r - The left inset shows the simulated £ -field distribution in the middle of the disk at fundamental even mode. The right inset shows the detected RF power from the detector showing modulation improvement replacing the semi-ring with a ring. Fig. 2.42 is a close up photograph o f the 8 . 7 GHz microdisk modulator in a full planar arrangement (Fig. 2.39(d)). The LiNb0 3 microdisk employed, has a diameter of 5.13 mm, A v f s r of 8 . 7 GHz and a thickness o f 0.4 mm. I . * F ig u re 2 .4 2 C lo se up photograph o f the 8.7 G H z L iN b 0 3 m icrodisk m odulator (F ig. 3 9 -d ). Fig. 2.43 shows the single frequency modulation results for the microdisk modulator illustrated in Fig. 2.40. Fig. 2.43(a) shows the spectrum o f the detected voltage (left). The detected modulation has a bandwidth of 90 MHz with a maximum of about 420 pV at 8.73 GHz. Fig. 2.43(b) shows the spectrum o f the modulated optical resonance 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Detected modulation 450 400 > S 350 ei> 300 = 250 4 2 0 0 5 150 S 100 .73 G H z ^ 9 0 M H z Full ring 9.5 8 8.5 9 ^ 16 f 14 % 12 ^ 10 .§ 8 o ° ■ O A . < D ^ o o 2000 < L > is 1500 > -a < > W a v e le n g th (1 5 5 0 + ...n m ) C -* <y O- -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 0 10 12 14 RF pow er (dB m ) ( c ) F ig u re 2.43 Single frequency m odulation result a t / R F = A v Fs r = 8.7 G H z. T he L iN b 0 3 m icrodisk has a diam eter o f 5.13 m m and thickness o f 0.4 mm . (a) Spectrum o f optical d etecto r output voltage. T he detected m odulation has a bandw idth o f 90 M H z w ith a m axim um o f about 420 pV at 8.73 G H z. T he R F -resonator is a full-ring and the input R F pow er is 0 dB m (1 m W ). (b) Spectrum o f the optical resonance. The m axim um coupled optical pow er is about 14 pW , and the optical bandw idth is about 85 M H z (m ode slope is 30 pW /pm ). (c) D etected optical voltage output (at 8.7 G H z) against RF input pow er. In this experim ent a sem i-ring R F -resonator is em ployed. T he inset is the corresponding optical m ode. 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The maximum coupled optical power is 14 pW and the optical bandwidth is about 85 MHz (mode slope is 30 pW/pm). As expected, the optical modulation band width is limited by the optical Q. The RF- resonator in this case is a full-ring (as opposed to what is shown in the photograph) and the injected RF power is OdBm (1 mW). Fig. 2.43(c) shows the detected voltage (at 8.7 GHz) against RF input power for the same modulator but with a semi-ring resonator. The inset is the corresponding optical mode with a slope o f 120 pW /pm and maximum coupled optical power o f 110 pW. As may be seen, although the optical mode slope is about 4 times bigger in Fig. 2.42(b) with 0 dBm RF power, the detected modulation is about 1100 pV that is only 2.5 times larger than the maximum detected modulation in Fig. 2.42(a) (420 pV). Since the detected voltage is proportional to modulated optical power, this again indicates that the ring resonator is modulating more efficiently then the half-ring resonator. Fig. 2.44 shows the Sz\ and optical modulation measurement results at different fundamental resonant frequencies. It is clear that when the fundamental resonance of the ring resonator is detuned from A v FSr = 8 .6 8 GHz, the /7-field amplitude and consequently the optical modulation efficiency drop. In section 2.6.1 we showed that the optical modulation is linearly proportional to Ai.max (the resonant optical output power o f the modulated optical mode). To test the validity o f this prediction we use a variable optical attenuator between the laser and optical input to the microdisk modulator. In this way we can control P 0,m ax without perturbing the laser wavelength alignment relative to the resonant wavelength. 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. .68 G H z ; ,675 G H z i ,672 G H z .335 G H z 4 s = 8 .8 1 5 G H z 5.00&05 8400 8500 8600 8700 8800 8900 9000 Frequency (MHz) o . - 1 0 1 '-2 0 1 -30 -40 8.2 M ' C S 84 8 .6 8 G H z 8 6 8 8 o 1 0 1 5 -20 4 S = 8 .6 7 5 G H z -2 5 8 2 8,4 9 8 6 8 . .8 F re q u e n c y (G H z ) 0 -5 -10 c £ T '1 - 5 5 -20 c/i -25 -30 -35 -40 8.2 8 4 8.6 8 8 9 Frequency(G H z) 0 -10 -20 -335 G H z : -30 •40 8.2 8.4 8.6 8..8 9 Frequency(GHz) - 1 0 -35 8.2 84 8 6 F ig u re 2 .4 4 D etected m odulation at resonance and at RF freq uencies detuned from resonance. Fig. 2.45(a) shows the optical output spectrum at different optical input powers. The detected RF voltage against P 0,m ax is shown in Fig. 2.45 (b). During modulation, the laser wavelength is located almost in the middle o f the mode slope (dashed line). The linear behavior o f P 0,m o d as a function of P 0,m ax demonstrates the validity of equation (2.41). 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. £ 2 5- O J £ o 1.5 CL O O , i O l - o id 0.5 - a 0 s O ■ Poi.i= 1.5 mW P0 ,n = 1.2 mW ~ Po.in= 1 mW Po.i«= 0-75 mW P o .m = 0.3 mW 0 1 1----- --i ----------r 0.0555 0.0557 0.0559 0.0561 0.0563 0.0565 0.0567 0.0569 W a v elen g th (1550+...nm ) ( a ) 6 0 0 > 5 0 0 3- & 400 3 0 0 o > T3 £ 200 < u u Q 1 0 0 0 0.5 1 1.5 2 M aximum pow er at reso n a n ce (pW ) ( b ) 2.5 F ig u re 2 .4 5 (a) O ptical output spectrum at different optical input pow ers, (b) D etected RF v o lta g e against Po m ax w hen the laser output is tuned to the m iddle o f the m ode slo p e (dashed line in (a)) High-sensitivitv 14.55 GHz microdisk modulator The microdisk modulator arrangement shown in Fig. 2.46(a) is our optimized m echanical design for a better perform ance. In sections 2.4.1 and 2.5.3 we show ed that mounting the microdisk on a cylindrical ground plane enhances the DC-shift and adds an extra degree o f freedom for controlling the RF coupling gap size, g. The 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. voltage gain provided by the critically coupled ring resonator and enhanced electric- field distribution increases the sensitivity o f the microdisk modulator. The L iN b03 microdisk used in this arrangement is 400 pm thick, 3 mm in diameter and has an optical free spectral range of 14.55 GHz. The copper ring resonator has an outer diameter of 3 mm and width o f 300 pm. RF output M icrostrip line R ing resonator 3 mm b—1 L iN b 0 3 M icroprism ( a ) m " O s — < D S 03 U 03 Cl i C/5 -10 14.2 14.4 14.6 14.8 15 Freqency (GHz) ( b ) Fig. 2 .4 6 (a) Photograph o f the m icrodisk m odulator, (b) S-param eter m easurem ent results for the m icrostrip line sid e cou p led to the RF ring resonator 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.46(b) shows the measured S\\ and S21 for the microstrip line side coupled to the RF ring resonator. The RF energy stored in the ring at resonance ( / rf = 14.6 GHz) is maximized by tuning the gap size (g ). X a C 3 u- a > * o ^ ■ 3 ^ s ^ O, o ~ o < D 0 3 ■ O o s & 0.2 0.4 12 Q = 4 x l0 ( 10 8 6 a 4 2 0 • — 0.0044 H 0,0049 0.0054 W a v e le n g t h 1550+... ( 11m) 0 . 6 V p p .in (V ) 0.8 1.2 ( a ) C O 3 u. o j * o Q. P i -a •73 o E < u Q 1 0 0 -10 -20 -30 -40 -50 -60 -70 A A A A A A A A A A A A A A A A -70 -60 -50 -40 -30 -20 -10 0 10 Input RF pow er (dBm ) ( b ) F ig. 2 .4 7 L inearly m odulated op tical intensity against peak-to-peak input v o lta g e (and RF p ow er). T he inset sh o w s the m odulated optical m ode. A t Vpp = 0 .5 6 V , the optical pow er in the linear region o f the optical m ode is 100% m odulated, (b ) D em odu lated RF pow er against input RF pow er. 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.47 shows the variation o f the modulated optical power against peak-to-peak voltage o f the input signal. The inset shows the modulated optical mode with a Q = 4 x l0 6. As may be seen at Vp p = 0.56 V the linear portion o f the optical mode is completely modulated. Saturation o f the linearly modulated optical power with increasing Vp p occurs because o f increasing second-order harmonic generation due to nonlinear modulation. The optical intensity modulation is detected using a high speed analog optical receiver with a responsivity o f 260 pV/pW at 15 GHz. The calculated effective interacting voltage based on DC shift and detector responsivity is Fjn = 3 V at -1 dBm RF input power ( Vpp =0.56 V) RF input power representing a voltage gain o f 5.3 at resonance. The voltage gain calculated based on S-parameter measurements is 5.5. Fig. 2.47(b) shows the demodulated RF power against input RF power. The modulation saturation occurs around 0 dBm received RF power. Fig. 2.48 shows the frequency spectrum o f the detected RF power at very low RF input powers. In this experiment an RF amplifier with a gain o f 20 dB is used after the detector to amplify the weak detected RF power. At -67 dBm received RF power, the signal-to-noise ratio o f the detected RF power is about 13 dB. Both saturation voltage and sensitivity measurement results shown in Fig. 2.47(b) and 2.48 indicate a 10 dB improvement compared to the best results reported previously for a 9 GHz LiNbCb microdisk modulator [49]. 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -50 -5 7 dB m -62 dB m -6 7 dB m -7 2 dB m -7 7 dB m 14.5 14.55 14.6 14.65 14.7 14.75 14.8 Frequency (G H z) F ig u re 2 .4 8 O ptical spectrum o f the detected RF pow er at very low RF input pow ers. In an additional single frequency experiment with the 14.6 GHz microdisk modulator we selected a symmetric and clean WG resonance to estimate the voltage gain (Gv). Fig. 2.49(a) shows the optical spectrum of the selected mode. The maximum slope (S) of the mode is 80 pW /pm and its line width is 0.33 pm corresponding to a bandwidth o f 45 MHz and a loaded optical Q o f 4.7x106. Fig. 2.49(b) shows the frequency spectrum o f the detected RF voltage at 0 dBm received RF power. 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 25 20 7pm o. 15 D. 1 0 5 0 ■0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 ^ 4.00E-04 > m 3.00E-04 > 2.00E-04 -o ( O | 1.00E-04 u ^ Q 0.00E+00 - 14.5 F requency (GHz) F requency (GHz) ( b ) ( C ) F ig u re 2 .4 9 (a) the optical spectrum o f the selected W G m ode. T he m axim um m o d es slo p e (S) is 80 pW /p m and its line w idth is 0 .3 3 pm correspon ding to a bandw idth o f 45 M H z and a loaded optical Q o f 4 . 7 x l 0 6. (b) Frequency spectrum o f the detected RF v o lta g e at 0 dB m received RF pow er, (c) M easured 5-param eters for the m icrostripline side coupled to the ring resonator The measured modulation bandwidth is 50 MHz which again validates the assumption that the modulation bandwidth is limited by the optical bandwidth. After correcting the modulated voltage and input RF power to compensate for the RF cable losses we calculated a Gv = 5.12 using the measured values o f S, V -m and A 7.< jc in equation (2.40). Fig. 2.49(c) shows the measured ^-parameters for the microstripline side coupled to the ring resonator. W a v elen g th d etun in g ( a ) (pm) m -a V £ c e D. 14.6 14.7 14.8 0 ■ 2 ■ 4 ■ 6 8 -10 -12 -14 14.4 14.6 14.8 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7 Harmonic FSR modulation 2.7.1 Introduction The fundamental modulation frequency o f a microdisk modulator is defined by its diameter and thus, high frequency modulation requires smaller disks. Modulation at harmonic frequencies ( » ? 0 x A v f s r , m 0 = 2 , 3 , . . . ) is an alternative way o f increasing the modulation frequency o f a microdisk modulator without decreasing the microdisk diameter. The main requirement for harmonic FSR modulation is RF resonant frequency tuning. For efficient harmonic modulation at »20 x A v f s r , the mth harmonic o f the RF resonator has to be tuned to m0x A v f s r - Due to even-odd mode splitting,/ r F,„, is not exactly equal to /«rfx/R F /. Fig. 2.50 shows the simulated A-field magnitude and fs-field vectors for even (a) and odd (b) second harmonics on a cut plane passing through the middle o f a LiNbC>3 microdisk. The microdisk has a diameter D = 5.13 mm and a thickness o f h = 0.4 mm. The position o f the maximum and minimum oscillation amplitudes o f the even mode is rotated 90 degree relative to those o f the odd mode. In principle both even and odd modes could be used for optical modulation but in most cases the resonant frequency o f the even mode is w 0x A v Fs r and its coupling to the microstripline are stronger. 1 4 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u re 2 .5 0 Sim ulated £ -fie ld m agnitude and £ -fie ld vectors on a cut plane passing through the m iddle o f the L iN b 0 3 m icrodisk for even ( a ) and odd (b) secon d harm onics. (D = 5 . 13 m m , h = 0 .4 m m ) Fig. 2.51(a) shows the simulated ^-parameters around the second-harmonic of a side- coupled ring resonator. Although the simulated resonant frequencies are off (for a 5.13 mm diameter 2 x A v f s r is 1 7 . 4 GHz) the qualitative behavior of the E - field inside the disk and the A-parameters are predicted properly. As may be seen the even second-harmonic is critically coupled (S) i = S21 = -6 dB). Fig. 2.51(b) shows the amplitude of the E-field oscillation in the middle of the disk at angular positions E and O shown in Fig. 2.50. Due to critical coupling, the amplitude o f the E-field for the even mode is larger than the odd mode oscillation am plitude. Once the RF resonant frequency o f either odd or even resonance is tuned to the 7 7 2 0xAvfsr (where m0 is the same as the RF resonance order tnuj) the optical modulation mechanism can be treated similar to the fundamental modulation. 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 dB i "~\ i \ / ' y r " \ A ' ........ \ / i .......... A..JL. L : 521 j ^ . ...j 5 | 1 .........! ....................../ ' i A ........... ! . \ ..... / V . / ! \ -20 _ 10.5 10.6 10.8 E -field (V /m ) li Frequency GHz O ) 11.2 11.4 11.5 7e+004 6e+004 3e+004 le+004 10.5 10.6 10.8 1 1 11.2 11.4 11.5 Frequency GHz ( b ) F ig u re 2.51 (a) Sim ulated 5-param eters around the second-h arm on ic o f a sid e-co u p led ring resonator, (b ) T he am plitude o f the 5 -fie ld o scilla tio n in the m iddle o f the disk at angular p o sitio n s E and O sh ow n in Fig. 2 .5 0 . The main differences in this case are: (1) the E-field distribution factor (3 S is smaller due to more E-field variations around the microdisk. (2) Gv is smaller due to frequency dependent losses o f the RF com ponents (m icrostripline + ring). H ow ever we can still use the same formalism with new correction factors to evaluate the modulation performance. 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7.2 Experimental results Fig. 2.52 is a photograph o f the experimental arrangement used for our harmonic modulation measurements. The disk size and other parameters are the same as Fig. 2.23. Optical coupling in and out is achieved using a single prism. The laser light from a single mode tunable laser with (line width « 500 MHz) is focused on the prism surface by a lens system and collected from the other side with a cleaved fiber. The optical Qs observed are about 3-5x10 6 and A v Fs r -7 .6 GHz (for TE WG modes). A copper ring electrode (R = 2.9 mm, wr = 0.5 mm) is placed on top o f the disk and is side coupled to a microstrip line. Using the experimental arrangement in Fig. 2.52(a) we have modulated the laser light (wavelength = 1550 nm) at the fundamental and second-harmonic frequencies o f the ring. The optical mode used for this experiment has a (9 = 3x10 6 and maximum optical power P 0 ,m ax = 30 pW. During modulation, the RF output port was open ended to create a standing wave on the microstrip line and increase the voltage on microstrip line. Fig. 2.52(b) shows the detected RF-power spectrum while the second-harmonic o f the RF-ring resonator is tuned to 2 x v f s r = 15.2 GHz. The inset is representative o f throughput measurement (S2 1) and shows that the fundamental at frequency 7.7 GHz and second-harmonic at frequency 15.2 GHz o f ring resonator are excited. The modulation observed at 15.2 GHz is experimental proof o f higher harmonic modulation using the RF-ring resonator modes. The fundamental resonance o f the 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ring resonator is about 100 MHz detuned relative to A v f s r =7.6 GHz, which explains the weak modulation observed at 7.6 GHz. RF input RF output R ing resonator LiNbCh disk M icroprism L aser input O ptical output ( a ) 15.2 G H z : 2.00E-04 > ■ a .50E-04 7 .7 G H z 15.2 G H z o •p 1.00E-04 U 1 ) 1 l > Q 5.00E-05 -18 7 .6 G H z F requency (G H z) 6 7 8 9 10 12 13 14 15 16 F r e q u e n c y ,/^ , (GHz) ( b ) F ig u re 2 .5 2 (a) Photograph o f the experim ental arrangem ent. D isk diam eter =5. 8 m m , disk thickness = 0 .7 4 m m , F SR = 7 .6 G H z. (b) S econd-h arm on ic m odulation at 2 x F S R = 15.2 G H z. T he inset sh o w s the results o f S 2 1 m easurem ent. A s m ay be seen the fundam ental resonance o f the ring is o f f by 100 M H z (7 .7 G H z as o p p o sed to 7 .6 G H z), w h ile the second-h arm on ic is ex a ctly equal to 15.2 G H z. T his explain s the w eak m odu lation o b served at 7 .6 G H z. (T he injected R F -pow er to the m icrostrip line is 0 dB m ) 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.53 is the measured signal to noise ratio (S/N) at the fundamental ( v f s r = 7.6 GHz) and the second-harmonic ( 2 x A v f s r = 15.2 GHz). The R F-0 o f the second- harmonic was about 80. * , 4 * ' fundam ental fR F = 7 .6 G H z Second-h arm on ic fRF= 15.2 G H z F re q u e n c y (G I Iz) -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 RF input pow er (dB m ) F ig u re 2 .5 3 M easured signal to n o ise ratio ( o f am p lified sign al) as a function o f input RF p o w er at fundam ental ( f R F = 7.6 G H z) and second-h arm on ic ( f R F = 15.2 G H z) o f the ring. T he inset sh o w s S 2i spectrum w h en the ev en seco n d harm onic o f the ring ( f = 15.2 G H z) is excited . To our knowledge, no result has been reported at higher harmonics previously and this is the first demonstration of efficient modulation at 2 x A v Fs r for an electro-optic resonant modulator. A comparison between the second-harmonic modulation results with half-ring and ring resonators indicates that use o f the ring electrode modulates the WG modes about 8 times better than the half-ring at 2 x A v Fs r . Fig. 2.54 shows the third-harmonic modulation results for the 8.7 GHz microdisk modulator. Fig. 2.54(a) shows the RF frequency spectrum of the detected third harmonic modulation ( 3 x A v Fs r = 3x 8.7 GHz = 26.1 GHz). 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.50E-04 > 2 .0 0 E -0 4 B W ~ 75 M H z IP 1 .50E -04 1.00E -04 ■ o 5 .0 0 E -0 5 0 .0 0 E + 0 0 26 26.1 2 6 .2 26.3 a. o " O s - < D p o > ~ o 0s- o F requency (G H z) ( a ) g = 3 .1 x l0 6 (AA, = 0.5 pm ) ! 0.09 0.092 0.094 0.096 W a v elen g th (1550+...nm) ( b ) Qw,-= 80 (B W = 3 0 0 M H z) -10 -15 26.1 G H z -20 24 25 26 27 28 Frequency (GHz) (c) F ig u re 2 .5 4 (a) RF frequency spectrum o f the detected third harm onic m odulation (3 x A v F S R = 3 x 8.7 G H z = 26.1 G H z), (b ) T he spectrum o f the m odulated optical m ode, (c) S 2i m easurem ent result sh o w in g the 3 ld resonance o f the ring. Fig. 2.54(b) shows the spectrum o f the modulated optical mode with a Q o f 3 .1 x l0 6. The S21 spectrum result in Fig. 2.54(c) shows that the 3rd resonance of the ring resonator is tuned to 3 x A v f s r . 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.8 Stabilization In this section we describe an active stabilization circuitry designed to eliminate thermal and mechanical drift during microphotonic modulator operation. Knowing the system response to the optical mode, drift in resonant frequency can be detected by detecting a small portion o f the average optical output power and measuring the power variations. Since the optical modes in the LiNbCh disk can be tuned via the electro-optic effect by applying a DC electric field, it is possible to compensate for any thermal or mechanical drifts using DC shift. In this way the laser wavelength can be locked to a specific position in the optical mode. During modulation the ring electrode is resonating at RF frequency ( / rf = A v f s r )- Hence, the DC voltage should be applied in such a way that it does not influence the RF resonant mode. This has been achieved by applying the voltage via a very thin gold wire that is attached to a zero-field position on the ring. When the even mode o f the ring is excited, this position is at the coupling area where the distance between the microstripline feed and the ring is minimum. Fig. 2.55(a) shows a schematic diagram o f the experimental setup. We have used a 10/90 splitter to monitor the optical output power. However, in principle, a smaller portion of the optical power can be used (around 1%) minimizing the impact on the modulated power. 149 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R ing resonator ,aser RF output 90% G old Splitter w ire F eedback am plifier R F in p u t P hotodetector R eference v o ltage (a) 10 % detected optical power (ptW) F-ded-bitek-dti LOO.O 150.0 200.0 250.0 30 0.0 350.0 4 2 3 ./ T im e(sec ) (b) F ig u re 2 .5 5 (a) Schem atic diagram sh ow in g the feed b ack loop arrangem ent, (b ) E xperim ental results sh o w in g the effect o f the feed b ack loop on output pow er fluctuations. A differential amplifier is used to compare a reference voltage with the detected voltage and to apply an appropriate voltage on the disk. By changing the reference voltage we can lock the laser wavelength to any position on the mode. The optical peak power and the quality factor determine the slope o f the mode. In our 150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. experiments, a typical optical mode with a quality factor o f Q = 3 x 106 has a slope o f about 120 pW/pm. For a disk o f 5.13 mm diameter and 400 pm thickness the ring generates a DC shift of about 0.1 pm/V. So, if we choose the reference voltage in a way that the output o f the differential amplifier is zero while the wavelength is tuned to the selected mode location, a 10 V peak-to-peak signal swing in amplifier output is more than enough to compensate for typical drift values. Fig. 2.55(b) shows the temporal variation of average optical power with and without the feedback loop. As may be seen, when the feedback loop is operational, the output power is very stable and the modes resonant wavelength is locked. This simple feedback circuit makes the modulator output very stable with respect to thermal and mechanical drift. This results in improved BER performance as well as improved RF-photonic link signal to noise ratio. 2.9 Summary In this chapter many aspects o f the microdisk modulator have been reviewed. We studied optical W G resonances in a LiNbCh microdisk resonator and optical coupling techniques for the exciting them. We investigated the theoretical and experimental aspects o f the RF-ring resonator and its impact on the electro-optic interaction in a microdisk optical resonator. The DC electro-optical response o f W G resonances was used to develop a simple semi-empirical method to calculate the magnitude o f the 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. modulated optical power as a function o f measurable parameters. The low-speed bistable behavior o f the disk was demonstrated using a feedback loop. The efficiency o f the microdisk modulator was significantly improved by using a combination o f careful opto-mechanical design, feedback stabilization, and employing the RF-ring resonator. A sensitive 14.6 GHz LiNbC^ microdisk modulator was demonstrated that outperforms all previously reported devices. Comparison between experimental and theoretical calculations demonstrate the validity o f the semi-empirical model. In chapter 4 this model is used to estimate the down-conversion efficiency in the novel LiNbCh microdisk photonic RF mixer. 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.10 References L ithium N io b a te properties [1] R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary o f physical properties and crystal structure,” Appl. Phys. A, vol. 37, pp 191-203, 1985. [2] W. M. Robetrtson, G. Arjavalingam, and G. V. Kopcsay, “Broadband microwave dielectric properties o f LiNbCL,” Electron. Lett., vol. 27, pp. 175- 176. [3] L. Wan, Y. Yuan, “Observation o f dynamic photorefractive effect in lithium niobate waveguides,” Optics communications, vol 73, no. 6, pp. 439-442, Nov 1989. [4] K. K. Wong, “Properties o f lithium niobate,” INSPEC, institution o f electrical engineers, 1989. [5] A. M. Prokhov and Y. S. K uz’minov, “Physics and chemistry o f crystalline lithium niobate,” The Adam Hilger series on optics and optoelectronics, 1990. [6] M. Lee, “Dielectric constant and loss tangent in LiNbOj crystals from 90 10 147 GHz,” Appl. Phys. Lett., vol. 79, pp. 1342-1344, 2001. [7] A. Mendez, A. Garcis-Cabanes, E. Diegues, and J. M. Cabrera, “Wavelength dependence o f electro-optic coefficients in congruent and quasi-stoichiometric L iN b03,” Electron. Lett., vol. 35, pp. 498-501, 1999 [8] “RF photonic technology in optical fiber links,” Edited by W illiam S. C. Chang. Cambridge university press, 2002. O ptical cou p lin g [9] M. Cai, O. Painter, and K. J. Vahala, “Fiber-coupled microsphere laser,” Optics Lett., vol. 25, no. 19, pp.1430-1432, Oct. 2000. [10] A. V. Chelnokov and J. M. Lourtioz, “Optimised coupling into planar waveguides with cylindrical prisms,” Electron. Lett., vol. 31, no. 4, pp. 269- 271, Feb. 1995. 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [11] J. P. Laine, B. E. Little, H. A. Haus, “Etch-Eroded fiber coupler for Whispering-Gallery mode excitation in high-Q silica microspheres,” IEEE Photon. Technol., vol. 11, no. 11, pp. 1429-1430, Nov. 1999. [12] A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett., vol. 36, no. 4, pp. 321-322, Feb. 2000. [13] C. Liao, Y. D. Zhang, “Spherically tapered prism-waveguide coupler,” Appl. Optics, vol. 24, no. 20, pp. 3315-3316, Oct. 1985. [14] B. Little, J. P. Laine, H. A. Haus, “Analitic theory o f coupling from tapered fibers and half-blocks into microsphere resonators,” J. o f Lightwave Technol., vol. 17, no. 4, pp. 704-714, April 1999. [15] J. -P. Laine, B. E. Little,D. R. lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Photon. Technol. Lett., vol. 12, no. 8, pp. 1004-1006, August 2000. [16] V. S. Ilchenco, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical Whispering-Gallery modes,” Optics Lett., vol. 24, no. 11, pp. 723-725, June 1999. [17] M. L. Gorodetsky and V. S. Ilchenco, “Optical microsphere resonators: optimal coupling to high-Q Whispering-Gallery modes,” J. o f Opt. Soc. Am. B, vol. 16, no. l,p p . 147-154, Jan. 1999. [18] R. Ulrich, “Optimum excitation o f optical surface waves,” J. o f Opt. Soc. Am., vol. 61, no. 11, pp. 1467-1476, Nov. 1971. [19] J. Verdein, “Laser electronics,” Prentice Hall, 1995. Surface roughness and scattering [20] M. L. Gorodetsky and A. D. Pryamikov, “Rayleigh scattering in high-Q microspheres,’V . o f Opt. Soc. Am., B, vol. 17, no.6, pp. 1051-1057, June 2000. [21] B. E. Little and J. P. Laine, S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Optics Lett., vol. 22, no. 1, pp. 4-6, Jan. 1997. 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [22] B. Little and S. T. Chu, “Estimating surface-roughness loss and output coupling in microdisk resonators,” Optics Lett., vol. 21, no. 17, pp. 1390-1392, Sept. 1996. [23] M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Optics Lett., vol. 21, no. 7, pp. 453-455, April 1996. W G m o d es [24] S. Schiller and R. L. Byer, “High-resolution spectroscopy o f whispering gallery modes in large dielectric spheres,” Optics Lett., vol. 16, no. 15, pp. 1138-1440, Aug. 1991. [25] J. C. Knight, N. Dubreuil, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Haroche, “Maping whispering-gallery modes in microspheres with a near-field probe,” Optics Lett., vol. 20, no. 14, pp. 1515-1517, July 15 1995. [26] M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators :precession approach for spherical mode analysis and emission patterns with prism couplers”, Optics comm., vol. 113, pp. 133-143, Dec. 1994. E lectro-op tic bistab ility [27] P. W. Smith, E. H. Turner, and P. J. Maloney, “Electro-optic nonlinear Fabry- Perot devices,” IEEE J. o f Quanum Electron., vol. 14, no. 3, pp. 207-212, March 1978. [28] R. S. Jameson and W. T. Lee, “ Operation of an all-optical bistable device dependent upon incident and transmitted optical power,” IEEE J. o f Quantum Electron., vol. 25, no. 2, pp. 139-143, Feb. 1989. [29] P. W. Smith and E. H. Turner, “A bistable Fabry-Perot resonator,” Appl. Phys. Lett., vol. 30, no. 6, pp. 280-281, March 1977. [30] T. Ikegami and K. Kubodera, “Nonlinear optical devices for switching applications,” Communications, 1990. IC C 90 IEEE international conference on, v o l . 3, pp. 1152-1156, Apr. 1990. [31] P. W. Smith, E. H. Turner, and B. B. Mumford, “Nonlinear electro-optic Fabry- Perot devices using reflected-light feedback,” Optics Lett., vol. 2, no. 3, pp. 55- 57, March 1978. 155 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [32] K. Ogusu and S. Yamamoto, “Nonlinear Fabry-Perot resonator using therm o optic effect”, IEEE J. o f lightwave technol., vol. 11, no. 11, pp. 1774-1780, Nov. 1993. R F resonator [33] I. Wolf, and V. Tripathi, “The microstrip open-ring resonator ”, IEEE trans. on microwave theory and techniques, vol. MTT-32, no. 1, pp. 102-107, Jan 1984. [34] S. G. Pintzos, and R. Pregla, “ A simple method for computing the resonant frequencies o f microstrip ring resonators ”, IEEE trans. on microwave theory and techniques, vol. MTT-26, no. 10, pp. 809-813, Oct 1978. [35] S.-L. Lu, and A. M. Ferendeci, “ Coupling parameters for a side-coupled ring resonator and a microstrip line ”, IEEE trans. on microwave theory and techniques, vol. 44, no. 6, pp. 953-956, June 1996. [36] S.-L. Lu, and A. M. Ferendeci, “ Coupling modes o f a ring side coupled to a microstrip line ”, Electron. Lett., vol. 30, no. 16, pp. 1314-1315, August 1994. [37] Y. S. Wu, and F. J. Rosenbaum, “ Mode chart for microstrip ring resonators ”, IEEE trans. on microwave theory and techniques, Vol. MTT-21, pp. 487-489, July 1973. [38] G. K. Gopalakrishnan, and K. Chang, “ Novel excitation schemes for the microstrip ring resonator with low insertion loss”, Electron. Lett., vol. 30, no 2, pp. 148-149, Jan 1994. [39] L.-H. Hseieh, and Kai. Chang, “ Equivalent lumped element G,L,C, and unloaded Q ’s o f closed- and open-loop ring resonators”, IEEE trans. on microwave theory and techniques, vol. MTT-50, no. 2, pp 453-460, Feb 2002. [40] G. K. Gopalakrishnan,B. W. Fairchild, C. L. Yeh, C.-S. Park, K. Chang, M. H. W eichold, and H. F. Taylor, “Experimental investigation o f microwave- optoelectronic interactions in a microstrip ring resonator”, IEEE trans. on microwave theory and techniques, vol. MTT-39, no. 12, pp. 2052-2060, Dec 1991. [41] K. Chang, S. Martin, F. Wang, and J. L. Klein, “On the study o f microstrip ring and varactor-tuned ring circuits”, IEEE trans. on microwave theory and techniques, Vol. MTT-35, no. 12, pp. 1288-1295, Dec 1987. 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [42] P. A. Bernard, and J. M. Gautray, “Measurment of dielectric constant using a microstrip ring resonator”, IEEE trans. on microwave theory ancl techniques, vol. MTT-39, no 3, pp. 592-594, March 1991. [43] A. Klianna, and Y. Garault, “Determination o f loaded, unloaded, and external quality factors o f a dielectric resonator coupled to a microstripline”, IEEE trans. on microwave theory and techniques, vol. MTT-31, no 3, pp. 261-264, March 1993. [44] K. Chang, “Microwave ring circuits and antennas”, W iley series in microwave and optical engineering, John W iely & Sons Inc, 1996. [45] W. C. Chew, “A broad-band annular-ring microstrip antenna,” IEEE Trans. Antennas and Prop., vol. AP-30, Sept 1982. [46] D. M. Pozar, “Microwave engineering,” John Wiely & Sons Inc, 1998. LiNbCL m icrod isk m odulator [47] D. A. Cohen, “Lithium Niobate microphotnic modulators”, Ph.D dissertation, USC May 2001. < http://www.usc.edu/alevi> [48] D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, “High-Q microphotonic electro-optic modulator,” Solid-State Electronics, vol. 45, pp.1577-1589, 2001. [49] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Sub microwatt photonic microwave receiver”, IEEE photonics technol., vol 14, no. 11, Nov 2002. Technical notes (1) Picomotor actuator from New Focus .. Angular resolution < 0.6 mrad M inimum incremental motion < 3 0 nm (2) CST MICROW AVE STUDIO: electromagnetic field simulation software based on FTDT, from Computer Simulation Technology. (3) H FSS (V8): electromagnetic field simulation software based on finite element method, from Ansoft. 157 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (4) The roughness is measured by “Interferometric surface profiler” from AD E phase shift. The roughness parameters Sy and Sq are defined as: Peak-Peak h eig h t: Sy = zm ax-zm m Root MeanSquare : Sq = [(1/A/) Z(z, -p.)2]0'5 zm ax : highest pixel in the picture zmin ■ lowest pixel in the picture N : total number of pixels (sample points) Zj: height o f the ilh pixel p : mean height calculated using N sample points 158 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 Microdisk modulator in RF-optical link 3.1 Introduction In a RF-optical link, the data modulated RF carrier is up-converted to optical frequencies in an optical intensity modulator. Once the RF signal is up-converted to optical frequencies, it can be transmitted through optical fibers that are less lossy than conventional RF transmission lines and cables especially at mm-wave frequencies [1-5]. After transmission and distribution, the optical signal is typically down-converted to RF frequencies in a high-speed photodetector. The baseband information is then extracted from the detected RF signal by mixing with a local oscillator. Although by convention the RF carrier is referred to as the sub-carrier and the laser light (194 THz) as the carrier, in this chapter we will refer to them as the RF carrier and the optical carrier respectively. The performance o f a RF-optical link that uses the microdisk modulator for optical up-conversion is an indicator o f the quality o f the optical modulation in a microdisk. This chapter presents the results o f employing the microdisk modulator in a 8.7 GHz RF-optical link. We also present the design and fabrication o f patch antennas and 159 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. patch antenna arrays used to evaluate the performance of the modulator in a wireless RF-optical link. The noise performance o f the link is simulated based on the simple model that was explained in chapter 2 as well as the conventional noise models for other optical and electronic elements in the link. Furthermore the noise calculation demonstrates the sensitivity limits and the role o f different device parameters in overall signal-to-noise and bit error ratio (BER) o f the link. 3.2 RF-optical link Fig. 3.1(a) and (b) show the architecture o f the experimental RF-optical (a) and wireless RF-optical (b) links. In this section, we will specifically discuss RF-optical links based on intensity modulation and direct detection (IM-DD). The RF carrier is modulated by the baseband signal, data or video, using a conventional RF-mixer. The output RF signal has a double-sideband suppressed carrier modulation format. A tunable DFB laser generates the optical carrier around the communication wavelength kiaser = 1550 nm (v]ase, . = 194 THz). The intensity o f the laser light is modulated by the RF signal in an optical modulator. After transmission through an optical fiber the optical signal is detected in a high-speed photodetector. The baseband information is subsequently extracted from the received RF signal by mixing with a local oscillator. 160 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In a wireless link (Fig. 3.1(b)) the output signal of the first mixer is fed to an antenna and is transmitted through free space. On the receiver side, a second antenna feeds the received signal to the optical modulator. In both cases, depending on signal and noise levels at each stage amplifiers may be used to boost the signal power. ■ ; O /E converter E/O m odulator Data RF m ixer Laser Fiber RF m ixer LO Data RF signal LO ( a ) RF m ixer RF signal Data LO LO Data Laser ^>- Fiber RF m ixer O /E converter E/O m odulator ( b ) F ig u re 3.1 B a sic operation o f w ired (a) and w ireless (b ) R F -optical links. D ep en d in g on the sig n a l-to-n oise-ratio required at each stage, am plifiers m ay be used in so m e interfaces. Fig. 3.2 shows the details of signal flow through a RF-optical link that employs a microdisk optical modulator. The RF carrier frequency is limited to frequencies matched to modulation frequencies o f the microdisk modulator i.e. / « 0x A v Fs r . 161 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig.3.3 shows a schematic diagram of the experimental arrangement and the equipment used to build our microdisk based RF-optical links. RF carrier + data 8.7 GHz E lectric carrier field E lectric field 1 Data T im e, t Frequency, coR F RF electrode L iN b 0 3 m icrodisk O ptical fiber PIN detector o - D F B laser 2 0 0 THz carrier Electrici ^ field f 2 0 0 THz optical carrier E le c tr ic i I field U M icroprism s E lectric field 1 Frequency, Q op t Frequency, Q op t T im e, / F ig u re 3 .2 Schem atic diagram sh o w in g the signal flo w in an R F -optical link that uses the m icrodisk optical m odulator. The microdisk employed in our modulator has a diameter of 5.13 mm, a thickness o f 0.4 mm, and a FSR o f 8.7 GHz for a TE polarized WG resonance. The RF resonator is a semi-ring electrode side-coupled to an open microstrip line and its fundamental resonant frequency is tuned to 8.7 GHz. The RF carrier is modulated by a data stream or video signal using a double-balanced RF-mixer (l). For digital data transmission a non-return-to-zero pseudo-random bit stream (NRZ 27-l PRBS) from 162 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a pattern generator is fed to the IF port o f the RF mixer at different bit rates and for video transmission a VCR provides the baseband signal. The local oscillator signal at 8.7 GHz (power « 8 dBm) is provided by a RF-synthesizer. A RF amplifier (2 ) amplifies the signal and feeds it into the microdisk optical modulator, however in the wireless case the amplified RF-signal is fed to the transmitting antenna (dashed lines) and a similar antenna directly feeds the received signal to the microdisk modulator. A single mode tunable laser provides the optical carrier at X = 1550 nm with a line width o f less than 500 kHz. The optical output power from the microdisk is divided between two photodetectors by a single mode 10/90 optical power divider. The detector labeled as #1 is a low-speed photodetector with a bandwidth o f 1 kHz. This detector that receives 10% o f the optical output power monitors the location o f the laser wavelength relative to the WG resonant wavelength. It may also provide the feedback voltage required for wavelength locking circuit when active stabilization is required. 90% o f the modulated optical output power is transmitted through several meters o f optical fiber and at the end is detected by a high-speed photodetector (#2) that is a high-speed photodetector with a bandwidth o f 15 GHz (3). A RF amplifier (#2) amplifies the detected signal and feeds it into a RF mixer where it is mixed with a local oscillator (L02) to extract the baseband signal. The local oscillator signals in both the transmit and receive side are provided by the same signal generator and are phase matched. The down-converted baseband signal is amplified in a low-speed amplifier (4 ) (#3) and sent to a bit error ratio tester (BERT) 163 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for measurement or to a TV for display. The integrity o f the demodulated data is measured with the BERT and a digital oscilloscope. The laser wavelength is always tuned to one o f the high-Q TE-resonances o f the microdisk where optical modulation efficiency is maximized. Antenna Pattern Generator. Error Detector Amplifier (1) Attenuator Mixer Oscilloscope Monitor Locking circuit Microdisk modulator Detector (1) Detector (2) Mixer Amplifier (3) Amplifier (2) F ig u re 3 .3 S chem atic diagram o f the experim ental R F -optical link d esig n ed for in v estigatin g the LiNbC >3 m icrod isk m odulator perform ance. 164 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The bandwidth of a typical TE-resonance is about 150 MHz, corresponding to a Q - 3 x 106, which limits the data transmission rate to less than 150 Mb/s. As mentioned in chapter 2 the modulation bandwidth in a microdisk modulator is limited by the optical-g. The RF power in all experiments is defined as the measured power within 150 MHz bandwidth centered at 8.7 GHz. 3.3 Video and data transmission Fig. 3.4 shows a photograph of the 8.7 GHz microdisk modulator whose structure was described in section 2.6.3 (Fig. 39(d)). The mechanical stability o f this modulator is noticeably improved by the planar design. F ig u re 3 .4 P hotograph o f the 8.7 G H z L iN b 0 3 m icrodisk m odulator. (Z D = 5.13 m m , h = 0 .4 m m ) 165 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.5(a) shows the measured phase-margin o f the detected output at a data rate of 10 Mb/s (NRZ 27 - 1 PRBS) for the indicated modulated RF-power. The inset is representative o f the corresponding input and output eye-diagrams. Fig. 3.5(b) shows the spectrum o f the RF-signal before and after optical modulation. w m 1.0E-01 j I.0 E -0 2 ♦ A 1.0E -03 ♦ 4 1.0E -04 \i\ I.0 E -0 5 4 4 1.0E -06 i 4 4 1.0E -07 ♦ 1.0E -08 4 A 1.0E -09 t ' i 1 .0E -10 Output data CHI 1.00V “ CH2 s6.0mV M jS S iw ' A 10 A RF pow er = 4 m W ^ RF pow er = 10 m W A«! A* i 4 A f 4 4 A 4 h 4 A 4 20 30 40 5 0 60 Time (ns) 70 80 90 1 0 0 ( a ) RF spectrum before m icrodisk RF spectrum after m icrodisk -20 -25 5 -30 o -35 u. "p -40 ^ “ 45 T3 "O "45 § -50 S -55 Q -60 -65 -70 8640 8660 8680 8700 8720 8740 -30 -40 g. -45 v, I " 50 S * 5 5 4) Q -60 -65 -70 Frequency (MHz) 8680 8700 F re q u e n c y (M H z) ( b ) F ig u re 3 .5 (a) M easured phase m argin o f the output at 10 M b/s (N R Z 2 7 - 1 P R B S ) for 10 m W and 2 .5 m W m odu latin g RF pow er. T he inset sh o w s representative input and output eye-d iagram s. ( b ) M e a s u r e d R F s i g n a l s p e c t r u m b e f o r e a n d a f t e r m i c r o d i s k m o d u l a t o r u s i n g 2 .5 m W R F p o w e r . 166 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.6 shows the measured sensitivity of BER as a function o f RF power. The inset is the detected optical output power against input laser wavelength. The maximum optical output power (P0,m) for all of these measurements is in the range 18 pW to 27 |_iW wherein the laser wavelength is tuned close to the maximum slope o f the optical mode. Fig. 3.7 shows input and demodulated output eye-diagrams transmitted over the RF fiber-optic link at (a) 50 Mb/s and (b) 100 Mb/s NRZ 27 - 1 PRBS data rates. The critical factors for high-quality data transmission are the purity and (9-factor of the optical mode, the magnitude o f the rising or falling slope o f the optical mode in the vicinity of the laser wavelength, and the optical output power from the disk. ^ D efin e RF pow er w ithin 150 MHz B andw idth centered at 8 .6 8 5 GHz * A I.0E-02 I.0E-03 o p 1.0E-04 2 Q 6 O 1.0E-05 0 6 c 6 ui H 1 0E-06 5 o o 1 O E-07 -J 1.0E-08 1.0E-09 2 5 20 Av = 0.8 pm i o 0 Q 0 0 5 8 0 0 5 9 0 0 6 0 0 6 ! W a v e le n g th ! I 5 5 0 + .inn) ▲ 0 0.1 0.2 0.3 0.4 0.5 0,6 0.7 0.8 0.9 1 Total RF pow er (mW ) F ig u re 3 .6 M easured sen sitiv ity o f B E R to m odu latin g RF pow er (m easured RF pow er w ithin 150 M H z bandw idth centered at 8 .6 8 5 G H z). T he inset is the detected optical output pow er against input laser w avelen gth. By tuning the laser wavelength and RF carrier frequency it is possible to optimize the modulation quality and efficiency. Due to the presence o f high-62 (1 - 3 x 106) optical modes, and the sensitivity o f the modulation efficiency to the mode slope, 167 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. wavelength stability of the laser is an important issue. To ensure stable, high- quality, data transmission the wavelength stability should be less than 0.1 pm. RF pow er = 2 0 m W RF pow er = 4 0 m W CHI 1.00V CH2 50.dmV M M O ns 50 M b/s ( a ) CH1 1.00V CH2 50.0mV M 5.00ns 100 M b/s ( b ) F ig u re 3 .7 O ptical output eye-d iagram s at 50 M b/s (a) and 100 M b/s (b ) (N R Z 2 - 1 P R B S ). T he m odulating R F -pow er is 4 0 m W and 6 0 m W resp ectively. We use the same experimental arrangement for video transmission. The demodulated video signal is amplified by a video amplifier and fed to a monitor to compare the image quality with the original version. Original video After transmission (a) (b) F ig u re 3 .8 D em onstration o f v id eo transm ission through m icrodisk based R F -optical link, (a) T he original im age, (b) The transm itted im age. 168 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.8 shows the original image (left) and the transmitted image (right). The image quality hasn’t been distorted and is acceptable as a proof o f principle demonstration for the microdisk based RF-optical link. 3.4 Microstrip antenna and antenna arrays The antenna is an important component in a wireless RF-optical link or a photonic RF receiver. Its design and performance has a strong impact on the overall link or receiver sensitivity. In this section after a brief review o f patch antenna design issues, we present measurement results for planar antennas that have been designed and fabricated for microdisk based wireless links and photonic RF receivers. 3.4.1 Patch antenna Microstrip resonators can be classified into two main categories depending on their length-to-width ratio. A resonator with broad strip (length «width) is known as a microstrip patch. When the signal frequency is in the vicinity o f a resonance, a microstrip resonator radiates a relatively broad beam, broadside to the plane o f the structure. A significant part o f the input signal contributes to the radiation and the resonator behaves as an antenna. A patch antenna is just a rectangular resonator. The main dimensions o f the patch should be near one half-guided wavelength so the 169 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fundamental resonance o f the patch can be used for coupling to radiation field. At higher harmonic radiation pattern is more complicated and the energy might be radiated to unwanted directions. Fig. 3.9(a) shows the definition o f E and H radiation planes and Fig. 3.9(b) shows a typical example of the radiation patterns o f a rectangular microstrip patch antenna [6]. G round (d8)~30 -80 -10 0 ( a ) ( b ) F ig u re 3 .9 (a) T he definition o f E- and //-ra d ia tio n planes, (b ) A typical exam p le o f the radiation patterns o f a rectangular m icrostrip patch antenna [1], Typically a microstrip patch antenna has a gain within the 5-6 dB range, and exhibits a 3 dB beam width somewhere between 70 and 90 degrees. Fig. 3.10 provides a simple illustration of the operation of patch antenna in terms o f an array o f dipoles located at opposite edges o f the patch. 170 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u re 3 .1 0 T op v ie w and sid e v iew o f spatial distribution o f £ -fie ld in a rectangular m icrostrip patch resonator sh o w in g that the £ -fie ld lines e ffe c tiv e ly beh ave like tw o d ip o le arrays. The feed line breaks the symmetry o f the patch in y-direction resulting in a two set of parallel dipole arrays with the same phase where in x-direction the dipoles are out of phase and the radiation field is canceled out. The fundamental resonant frequency of the patch (f) is determined by the dielectric constant of the substrate and the patch where 8re is the effective dielectric constant, L is the dimension o f the patch parallel to dipole direction and Aloc is the equivalent length accounting for the fringing fields at the open ends of the patch antenna. sre and Alo c can be calculated using the following equations [2]: ( length L [2]: fr 2 ^ ( L + 2AlJ ( 3 - 1 ) (3.2) (3.3) 171 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Where hp and sr are the thickness and the relative dielectric constant of the dielectric substrate respectively. Different configurations have been developed to feed a patch antenna [6-10], Since for microphotonic receiver applications, integration of the antenna with the ring resonator is desired, we have chosen a microstrip line feed technique. The main difficulty o f feeding the patch antenna is the impedance mismatch between the feeding line and the antenna. The input impedance o f a patch is relatively high at the patch edge (200 Q - 400 Q) therefore a matching section is required between the 50 Q microstrip line and the patch antenna. We have investigated three approaches to solve the mismatch problem: (1) tapered line coupling, (2) quarter-wave matching section and (3) inset microstrip feed. ( a ) yo] ( b ) (c) F ig u r e 3 .1 1 D ifferen t tech niques used for feed in g the patch antenna: (a) T he tapered m icrostrip feed , (b ) M ultisection im pedance m atching, (c) Inset m icrostrip feed Fig. 3.11 shows a schematic diagram of each one o f these approaches. Among them the 3 rd method is much easier to implement and provides a very good impedance 172 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. matching between the feed line and the patch. The line is connected within an inset cut in the patch (see Fig. 3.11(c)). It is found experimentally that cutting such an inset does not significantly alter the resonant frequency [6]. The maximum input impedance occurs at the edge of the patch and decreases as the inset distance (yo) is increased toward the center o f the radiator. It has been shown that the functional behavior o f the impedance is very close to cos4(nyiyL) [9], The input impedance o f a rectangular patch in the middle o f the patch edge can be calculated from [7,10]: Z„, = 0.5/?,.< cos2(jSJV /2) + ( |^ ) + ( M , , ) 2 sin2(j8fV IT) - j3Alo c sin(2/3W /2 ) > (3.4) Where p = (27i/T0Vcrc), and Rt is the radiation resistance that can be calculated from the radiation pattern, more details can be found in Ref. 7. Using equation (3.4) we can calculate the impedance at center (Zm ) and then find by solving: Z = 50 = Zm cos4(ny(/L). Notice that the microstrip line is 50 Q and its width is determined by the dielectric thickness (hp ) and dielectric constant (ar) o f the substrate. Single patch experimental results Fig. 3.12(a) shows the photograph o f the fabricated patch antenna attached to a microdisk modulator. The transmit antenna is identical to the receive antenna. 173 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F requ en cy(G H z) S in g le patch antenna ( b ) w ith tapered line feed M icrod isk m odulator (w ith sem i-ring RF resonator and dou ble prism optical cou p lin g) -35 -25 -30 8.1 RF electrode 8.3 8.5 8.7 — Transm it antenna: R eceiv e antenna ■ 8.9 9.1 9.3 ( a ) F ig u r e 3 .1 2 (a) Photograph o f the patch antenna (w ith tapered line feed ) attached to m icrodisk m odulator, (b ) S n m easurem ent results for receiv e and transm it patch antennas as w ell as the sem i-ring resonator sh o w in g g o o d resonant frequency m atching. The antenna 0 -fa c to r is about 25 and the sem i-ring 0 -fa c to r is about 70. Since the optical FSR o f the microdisk modulator is 8.7 GHz, the patch antenna resonant frequency (fr) should also be 8.7 GHz. The patch antenna is fabricated on a substrate with a thickness o f 0.508 mm and a dielectric constant o f 2.94. Using equations 3.1-3.3 we can show that if L - 10 mm the fundamental frequency o f the patch is f r = 8.7 GHz. Although the width (W) o f the patch has a miniscule effect on the resonant frequency, it affects the radiation pattern. In our design W = L = 10 mm. First we use the tapered microsrtipline technique to feed the antenna. Fig. 3.12(b) shows the result of S\\ measurements for the receive antenna, transmit 174 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. antenna and the semi-ring resonator on top o f microdisk. The resonant frequencies are very close (+ 3 0 MHz) but the semi-ring has a larger Q. Fig. 3.13(a) shows the same patch (same dimensions on the same substrate) but with inset line feed. Using Equation 3.4 the input impedance o f the patch at the edge is Zm = 296 Q. An inset distance ( y o ) o f 3 mm satisfies the equation 50 = Zm cos4(7iyo/Z>) and matches the input impedance to the 50 Q line. Fig. 3.13(b) shows the S\ i measurement for this patch. As may be seen, the better match results in an increase in the coupling efficiency and S\ i is about 5 dB smaller at resonance. o 5 -10 15 -20 -25 7.5 8 8.5 9 9.5 1 0 1 cm 1 cm Frequency (G H z) ( a ) ( b ) F ig u r e 3 .1 3 (a) P hotograph o f the sin g le patch w ith in set lin e feed , (b) S t i m easurem ent result ( Q = 2 6 ,/ R F = 8 .73 G H z) 3.4.2 Patch antenna array As shown in Fig. 3.9, for 9s within 0-90 degrees the radiation pattern o f a single patch antenna is almost homogeneous and a large amount o f the radiated 175 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. electromagnetic energy is not received by the receive antenna. If the location o f the recei ver is fixed for a long period o f time it is reasonable to increase the efficiency o f the wireless link by limiting the radiation direction so that the radiated power mainly travels toward the receive antenna. This can be achieved by employing directional antenna-arrays where the wireless gain is highly dependent on the direction. By tuning the relative phase o f a series o f patch antennas it is possible to eliminate the radiated power along undesired directions by means o f destructive interference. It is evident that the degree o f directionality is directly proportional to the number o f patches employed in an array. In our first attempt we designed a four-patch antenna array. Each patch is similar to the one shown in Fig. 3.13. A microstrip power divider and phase shifter network feed the patches with the proper phase and power. Since the RF power is simultaneously distributed among all patches this feeding technique is called “corporate feeding”. The patches on the left-hand side are rotated 180 degree relative to the patches on the other side, therefore the input voltage to the right side must have a n phase shift so that all four dipoles oscillate synchronously. The spacing between the antennas is optimized for the best efficiency and directivity using CST electromagnetic simulation software (4). Fig. 3.14(a) shows the photograph o f the fabricated 4-patch antenna array with a resonant frequency o f 8.7 GHz. 176 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S;/(dB) / r = 8.6 G H z B W = 2 6 0 M H z Frequency (G H z) -10 -20 -30 C/2 -4 0 -5 0 8.2 8.4 8.6 9 F requency (G H z) ( b ) F ig u re 3 .1 4 (a) P hotograph o f the fabricated four-patch antenna array (m ade on a 0 .5 0 8 m m thick dielectric substrate w ith s = 2 .9 4 and loss tangent = 0 .0 0 1 1 9 ). (b) S M m easurem ent result sh o w in g a Q o f about 2 0 at 8 .6 8 G H z resonant frequency, (c) Sim ulated S n and 3 D radiation pattern o f the four-patch antenna u sin g C S T electrom agnetic sim ulation softw are. The dielectric substrate has a thickness o f 0.508 mm and a sr o f 2.94. Fig. 3 .14(b) is the S\ i measurement result for this array. The antenna has a Q o f about 20. We have quantified the directivity and effective range o f this antenna array by measuring the received RF power at different distances and directions using a similar patch antenna array for detection. 177 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ~2Q/4Bm 50 / / -30 dBm E -p la n e (x = 0,R = 5.5 ft) //- p la n e (y = 0 , R = 5.5 ft) * H~ plane 5.5 ft 90 90 180 270 ( b ) 270 ■ 5 S -10 15 -25 0 2 4 6 8 Z (ft) (c) F ig u r e 3 .1 5 (a) M easured radiation pattern o f the 4-patch antenna array and the d efin itio n o f radiation planes, (b) Sim ulated radiation pattern o f the 4-patch antenna, (c) R eceiv ed RF pow er as a fun ction o f the distance betw een receiv e and transm it antennae. T he R F -pow er injected to the transm it antenna is 10 dB m and the radiation is m easured along z-a x is (x=y = 0). 178 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.15(a) shows the measured and simulated radiation patterns o f our 4-path antenna. The 3dB angular width in both planes (E and H) is about 30 degree. This corresponds to a directivity o f about 36. The simulated and measured results are in very good agreement. Fig. 3.15(b) illustrates the measured received power against the distance between the transmitting and receiving antennae (z). The RF-power injected to the transmitting antenna is 10 dBm and the measurement is done along z- axis (x = y = 0). As previously we mentioned, increasing the number o f patches improves the directionality o f the patch antenna array. In our second array design we have increased the number o f patches to 10. The major difficulty with large numbers o f patches is the complexity o f the feeding network and the associated loss. The electromagnetic field o f the feeding microstiplines can interfere with radiation fields and change the radiation pattern. In addition the power loss in the transmission lines reduces the power efficiency o f the antenna. To reduce the loss and interference effects, we used a serial feeding technique to feed to the 10-patch antenna array. Fig. 3.16(a) is a photograph o f a serially fed 10-patch antenna array. Fig 3.16 (b) is a schematic diagram o f the antenna and simulated angular distribution o f the radiated power for the main beam. 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X RF input ( a ) ( b ) F ig u re 3 .1 6 (a) Photograph o f a serially fed 10-patch antenna array, (b) Sch em atic diagram sh o w in g the sim ulated 3 dB angular w idth o f the m ain radiation lobe. Fig 3.17(a) illustrates the measured radiation pattern of the 10 patch antenna in the ft-plane and H-plane. Fig 3.17(b) shows the measured RF power as a function of distance between the receive and transmit antennae when 10 dBm RF power is fed to the transmit antenna at resonant frequency. 180 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -20 dBm -JO clt -20 dBm .. 40 d B m //- p la n e (y = 0 , R = 5 .5 ft) /T -plane (.v- = 0 , R = 5 .5 ft) 10ft H- plane 0 1 = 3 -5 | -10 O G . -a -15 > < L > O < D c 6 -20 -25 £ -p la n e (x = 0 ,y~ 0 , R = Z) Input pow er to transm itting antenna = 10 dB m o o O 10 patch series fed 4 patch corporate fed o o o o o o o 10 Z (ft) ( b ) F ig u re 3 .1 7 (a) M easured radiation pattern o f the 10-patch antenna array and the defin ition o f radiation planes, (b) R eceiv ed RF pow er as a function o f the distan ce betw een receiv e and transm it antenna. T he R F -pow er injected to the transm it antenna is 10 dB m and the radiation is m easured alo n g z-a x is (x = y = 0). We have also fabricated 4 and 10 patch antenna arrays with resonant frequencies around 15 GHz for the 3 mm diameter microdisk modulators. 181 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.5 Wireless video data and video transmission Using the patch antenna and patch antenna arrays we have demonstrated the first wireless RF-optical link based on microdisk modulator. Fig. 3.18 shows the schematic and photograph o f the experimental arrangement. In this experiment we have employed the single patch antenna shown in Fig. 3.12. Due to the low efficiency o f the single patch, the distance between the transmit and receive antenna is about 7 inch. This experiment is a proof o f principle experiment demonstrating the potential o f combining the patch antenna with a microdisk modulator in a wireless optical receiver. T ransm it antenna R F input R e ce iv e antenna «i9 F ig u r e 3 .1 8 S chem atic diagram and photograph o f the short w ireless-o p tica l link b a sed o n sin g le patch and m icrod isk m odulator. Data and video were successfully transmitted through this wireless link though the quality was inferior to the wired link. 182 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.19 (a) shows the BER measurement results at 10 Mb/s (NRZ 27 - 1 PRBS) as a function o f injected RF-power to the transmit antenna and Fig. 3.19(b) shows the measured eye-diagram when 18 dBm RF power is fed to the transmit antenna. I.00E-03 1.00E-04 5 j 1.00E-05 0Q I.00E-06 1.00E-07 A 14 15 16 17 18 19 RF input power to transm it antenna (dBm) 20 ( a ) O utput data Input data m sm m v ( b ) F ig u re 3 .1 9 (a) sh o w s the B E R m easurem ent results at 10 M b/s (N R Z 2 7 - 1 P R B S ) as a function o f injected R F -pow er to the transm it antenna, (b ) T he m easured eye-d iagram at 18 dB m RF input pow er. Fig. 3.20(a) is a schematic diagram of the wireless optical link with a 4-patch antenna. This link has been successfully tested for wireless data and video transmission over 7 ft. Fig. 3.20(b) presents the results of BER measurement, at 10 Mb/s (NRZ 27 - 1 PRBS), as a function of link length. 183 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ••• LO V id e o signal Ife Laser (a) l.E +00 l.E -02 l.E -04 i 13 9 5 7 25 ns/div D is ta n c e ( f t) ( b ) ( c ) F ig u re 3 .2 0 (a) W ireless R F -optical link u sin g patch antenna arrays and the m icrodisk m odulator, (b) T he m easured B E R (at 10 M b/s N R Z 2 7 - 1 P R B S ) as a function o f the distan ce betw een tw o antenna (receiv ed optical pow er = 100 pW , injected RF pow er to the transm it antenna = 1W ). (c) T he m easured eye-d iagram at z = 1 0 ft. T he average op tical output pow er is about 30 pW . 184 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.20(c) shows the measured eye-diagram at 10 ft. Using the patch antenna arrays we demonstrated wireless RF-optical links up to 12 ft. 3.6 Noise analysis Noise in the RF-optical receiver is usually ascribed to either optical or electrical sources. The optical sources are laser relative intensity noise (RIN) and detector noise (thermal and shot noise). The electrical sources are the microstripline, RF- resonator, and amplification stages used after photodetection. Fig. 3.21(a) shows a schematic diagram of signal and noise flow in the wireless RF-optical receiver. The signal-to-noise value at each stage is calculated using standard noise equations o f RF and optical devices that can be found in references 11-14. Fig. 3.21(b) presents the typical values of parameters that are required for calculating the overall signal-to- noise ratio o f the RF-optical receiver, the same values as used in our simulations. After calculating the final signal-to-noise ratio, Sd/Nd, the equivalent BER is calculated using [12]: probability and erfc is the complementary error function. Fig. 3.21(c) is a plot of BER against signal-to-noise ratio. We use BER and sensitivity as a measure o f link performance. Our simulations show that critical parameters strongly influencing (3.5) where s / / N . 2 1 /V is the analog signal-to-noise ratio, P(e) is the digital error 185 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BER are optical 0-factor, disk thickness, RF resonator voltage gain, and optical input amplitude fluctuations (laser RIN). The noise performance o f the microdisk modulator is calculated based on the simple model explained in section 2.6.1. antenna microdisk (P o,in> P o.R I n ) DFB Laser PIN detector RF electrode ( a ) G eneral assum ptions R I N - - 1 5 5 dBIHz Laser output = 5 m W D etector bandw idth = 100 MHz Stab ilized laser linew idth = 10 kHz A ntenna im pedance - 5 0 Q D etector R ~ 10 k£2 D etector resp on sivity = 0.8 A /W D etector am plifier n o ise figure = 3 Tem perature = 3 0 0 K A ntenna background tem perature = 2 0 0 K D etector dark current = 10 nA ( b ) S/N (dB) ( C ) 1.00E-01 1.00E-03 .00E-05 (0 1.00E-07 1.00E-09 1.00E-11 I.OOE-13 0 5 10 1 5 20 25 F ig u re 3 .21 (a) Schem atic diagram o f signal and n o ise flo w in m icrodisk R F -w ireless receiver. (b) V a lu es o f param eters required for n o ise calculation, (c) B E R against sig n a l-to - n o ise ratio [15] As shown in Fig. 3.21(a), the received signal (Sa) and noise (jVa) power are fed to an open terminated microstripline. The signal (SL ) and the noise power (A) ) at the 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coupling location (where the microstripline is coupled to the ring resonator) are related to the input values through: (a) SL = S J L j (b) jVl= N JL t + kBTB(LT-l) (3.6) where L j is the loss factor for the mictorstripline, k\i is the Boltzman factor, and B is the bandwidth. The bandwidth of the receiver is defined by the optical modulation bandwidth, which is limited by optical Q (BW~v\a s e r /Q ). The signal and noise power change throughout the microstripline due to attenuation and the thermal noise in the microstrip. Therefore the voltage amplitude o f the signal and noise voltage at the coupling zone can be written as: (a) V s = 2 ^ 2 Z 0S L {b)VN = 2 ^ 2 Z „N L (3.7) when Z0 is the characteristic impedance of the line (50 ohm). Now we can use equation (2.41) from chapter 2 to calculate the signal and noise optical power coming out o f the microdisk modulator by replacing Vm with Vs and Tn. (a) P 0,s= 2PsAXdcGv (Q / Kes)VsxPo m ax (b) Po n = 2 ps AXdcGv (Q / W K n x J W (3-8) If we define the optical coupling efficiency for an optical mode as p =P0,m ax / f ’ o .in and the electro-optical gain as Geo = 2/rpsAA[x:Gv (Q /Xrcs) : (a) Po,s— Geo x V % xP0j n (b )P 0,n = GEOxVNxPo :m (3.9) Equations 3.9(a) and 39(b) are the signal and noise optical powers. The electro- optical gain factor ( G e o ) relates the modulated optical power to the RF input voltage and input optical power. Equation 3.9(b) is not complete because the laser input 187 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. power Pojn has random intensity noise that contributes to the total optical power noise. The random intensity noise power can be written as: P0.m = (10 m 7 1 0 xA/)^P„,„„, (3.10) where R IN is the random intensity noise (dB/Hz) and Af is the equivalent noise bandwidth. P 0,0u t is the optical output power from the microdisk modulator at Aiascr. Since in most cases P o,0 U tis close to P D ,m ax for simplicity we assume P 0,out = pPo,in, so the total optical noise power is: P»,n = [Gli(, X VN + p { 10 R IN /l0 X A/ ) * > „ . „ , (3.11) Now we should calculate the signal and noise after photodetection. The photocurrent is related to optical power through the detector responsivity (R) so: (a) Tos = RP„,s (b) fas = (3.12) These are the photocurrents generated by the optical signal and noise power but there is also noise generated during the detection (shot noise and dark current noise) and the amplification process: A k T R F P N = 2 eB ( i p + id ) + — ^ (3.13) R /, where /c i is the photodetector dark current, F is the amplifier noise figure, R i is the load resistance and ip is the total photocurrent generated by the received optical power. The total received optical power consists of the modulated optical power and the DC optical power that is not modulated so ip = R(P0^ C + Pop- The average received DC optical power (P0,dc) may be written as P 0,ou t - Po,s/2 . The final signal to noise ratio is calculated using equations (3.12) and (3.13): 188 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.22 shows simulation results for a RF-optical-link with direct detection. The BER is calculated as a function of RF input power for different optical 0-factors, disk thickness, and voltage gain, Gv. In all cases the assumptions are 5.13 mm disk diameter, RIN = -150 dB/FIz, 15% optical coupling efficiency, 5 mW optical input power, 0.8 A/W detector responsivity, 10 nA detector dark current, 300 K temperature, 10 kQ detector impedance, and a 3 dB detector amplifier noise-figure. Sensitivity is defined as the RF-power at which the signal-to-noise ratio is unity (SNR =1). In Fig. 3.22(a) the effect of optical 0-factor on BER performance is demonstrated for h = 400 pm and Gv = 2. As may be seen, increasing optical 0 by a factor o f two improves sensitivity by a factor o f eight. Fig. 3.22(b) shows the effect of reducing the disk thickness for Gv = 2 and 0 = 1.5 x 106. In more advanced simulations Gv may be calculated as a function o f RF coupling factor, the geometry of the resonator and input RF power. Fig. 3.22(c) shows the effect of increasing Gv on BER performance for 0 = 1.5 x 106 and h - 400 pm. 189 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. l.E+OO l.E-02 l.E-04 w I.E-06 m l.E-08 l.E-10 l.E-12 h = 400 |xm , Gy = 2 Q — 2 x 1 0 , S en sitivity 4 .5 nW Q = 3 x 1 0 6, S en sitiv ity 1.36 nW Q — 4 x 10 , S en sitivity 0 .5 5 nW l.E+OO l.E-02 l.E-04 W l.E-06 C Q l.E-08 l.E-10 l.E-12 200 400 600 RF input power (nW) (a) .......... Gv 800 1000 2,Q=1.5 x 101 1 h = 3 0 0 \xm, Sen sitivity 6 nW h = 2 0 0 jit/??, S en sitivity 2.6 nW h = 1 0 0 \im, S en sitivity 0. 6 6 nW 200 400 600 RF input power (nW) ( b ) 800 1000 o i, U J C Q l.E + 0 1 l.E -01 l.E -0 3 l.E -0 5 l.E -0 7 I.E -0 9 l.E - 1 1 l.E -1 3 h = 400 \xm,Q=\.5 x 106 Gv Gy — 3 , Sen sitivity 4.5 nW Gy = 4, S en sitivity 2 .7 nW 6 , S en sitivity 1.2 nW 0 2 0 0 4 0 0 6 0 0 800 1000 RF input pow er (nW ) (c) F ig u r e 3 .2 2 B E R calcu lation s as a function o f RF input pow er for different optical ^ -fa cto rs, disk th ick n esses, and v o lta g e gain factor. In all ca ses optical cou p lin g effic ie n c y (p ) is 15%, RIN is - 150 d B /H z, optical input pow er is 5 m W , detector resp on sivity is 0 .8 A /W , detector dark current is 10 nA , tem perature is 3 0 0 K, detector im pedance is 10 kQ and detector am plifier n oise-fig u re is 3 dB . T he sen sitiv ity is defined as the R F -pow er at w h ich the S N R is unity, (a) E ffect o f op tical Q- factor on B E R perform ance, (b) E ffect o f disk thickness on B E R perform ance, (c ) E ffect o f RF resonator v o lta g e gain factor on B E R perform ance 190 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Calculations show nW sensitivity may be achieved by simply reducing disk thickness, increasing RF-resonator voltage gain, and reducing laser RIN. Fig. 3.23 (a) illustrates how laser RIN can influence BER. In this case Gv = 6, h = 200 pm and Q — 2 x 106. With a value o f RIN = — 140 dB/Hz and Gv = 6 it is possible to achieve a BER around 10'1 0 with 200 nW RF input power. oi w 03 l.E +01 l.E -01 l.E -03 l.E -05 I.E -07 l.E -0 9 I.E -1 1 l.E -1 3 450 ^ 400 1 350 ' s 300 o 250 a . 5 200 a .£ 150 £ too 50 0 -130 d B /H z, S en sitivity 12 nW -140 d B /H z, S en sitivity 12 nW -1 5 0 d B /H z S en sitivity 0 .1 3 nW 2 0 0 4 0 0 6 0 0 RF in p u t p o w e r ( n W ) C O .............. h = 4 0 0 p m h = 2 0 0 pm G v = 6 800 1000 -120 d B /H z -1 3 0 d B /H z -1 4 0 d B /H z 4 5 6 7 V oltage gain factor (Gv) (b) 10 F ig u re 3 .2 3 C alculated influence o f laser RIN on B E R and sen sitivity (Q = 2 x 106 and other param eters are the sam e as in Fig. 15). (a) B E R perform ance w ith different valu es o f RIN as a fun ction o f RF input pow er, (b) S en sitivity w ith different valu es o f R IN as a function o f G v. 191 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.23(b) shows that the impact on the sensitivity o f noise generated by laser RIN can be reduced by increasing voltage gain Gv in the system. The results shown in Fig. 3.23(b) are obtained using h = 400 pm and Q = 2 x 106. Increasing voltage gain by a factor o f five can be equivalent to reducing RIN by 10 dB/Hz. 3.7 Summary In this chapter the performance o f the microdisk modulator in wired and wireless RF-optical links has been demonstrated. The experimental results show that a microdisk modulator can provide high-quality modulation up to 100 Mb/s in a RF- optical subcarrier link with an 8.7 GHz RF-carrier frequency. The modulator is able to efficiently modulate an optical carrier at X = 1550 nm wavelength with a data modulated RF signal. By tuning the laser wavelength to a high-Q optical mode 10 Mb/s NRZ 27 - 1 PRBS, data was successfully transmitted through a RF fiber-optic link with a measured BER o f less than 10'9. We have shown that the microdisk modulator can directly receive signal from planar antennas. The preliminary results with home made patch antenna arrays demonstrate the potential o f employing the microdisk modulator in short distance indoor wireless links. Furtherm ore the results o f noise analysis show the im pact o f different link and modulator parameters on the overall signal-to-noise perfonnance and hence BER o f 192 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the wireless RF-optical link. By optimizing these critical parameters, microdisk based optical receivers with nW sensitivity are feasible. 193 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.8 References [1] J. Oreilly and P. Lane, “Remote delivery o f video services using mm-waves and optics,” IEEE journal o f lightwave technol., vol 12, no 2, pp. 369-375, Feb. 1994. [2] Hirata, M. Harada, K. Sato, and T. Nagtsuma, “Millimeter-wave photonic wireless link using low-cost generation and modulation techniques,” Microwave photonics international meeting, pp. 37-40, 2002. [3] H. Ogava, D. Polifko, and S. Banba, “Millimeter-wave fiber optic systems for personal radio communication,” IEEE Trans, on microwave theory and techniques, vol. 40, no. 12, pp. 2285-2293 Dec. 1992 [4] D. Novak, G. H. smith, C. Lim, H. F. Liu, R. B. Waterhouse, “Optically fed millimeter-wave wireless communication,” OFC ’ 98 technical digest, pp. 14. [5] G. H. Smith, D. Novak, C. Lim, “A millimeter-wave full-duplex W DM/SCM fiber-radio access network,” OFC technical digest, pp. 18. [6] J-F Zurcher and F. E. Gadiol, “Broadband patch antennas”. [7] P. Bhartin, K. V. S. Rao, and R. S. Tomar, “Millimeter-wave microstrip and printed circuit antennas” [8] W. S. T. Rowe and R. B. Waterhouse, “Efficient wide band printed antennas on lithium Niobate for OE1CS,” IEEE trans. on antennas ancl Propagation, vol. 51, no.6, pp. 1413-1415, June 2003. [9] L. I. Basilio, M. A. Khayat, J. T. Williams, and S. A. Long, “The dependence o f the input impedance on feed position o f probe and microstrip line-fed patch antennas,” IEEE trans. on Antenna and propagation, vol. 49, no. 1, pp. 45-47, Jan. 2001 [10] J. Bahl and P. Bhartia “Microstrip antennas,” 1980. [11] G. P. Agrawal, “Fiber-optic com m unication system s,” 1997. [12] J. M. Senior, “optical fiber communications principles and practice,” Prentice- Hall series in optoelectronics, 1985. 194 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [13] D. M. Pozar, “Microwave and RF design o f wireless systems,” John W iley and Sons, Inc. 2001 [14] L. Kazovsky, S. Benedetto, A. Willner, “Optical fiber communication systems,” Artech house publishers, 1996. Technical notes (1) Double balanced RF mixer from Pulsar Microwave Co. LO/RF 0.5- 10 GHz IF DC-2 GHz (2) RF amplifier manufactured by JCA Frequency range: 4-8 GHz Gain: 30 dB Noise figure: 1.9 dB (3) High-speed OE converter with a responsivity o f 300 V/W and a bandwidth o f 15 GHz. {Agilent 11982A) (4) Power amplifier manufactured by Sonoma Instruments. Frequency rang: 10 KHz-2.5 GHz Gain: 20 dB (5) CST MICROW AVE STUDIO: electromagnetic field simulation software based on FTDT, from Computer Simulation Technology. 195 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 Photonic RF receiver 4.1 Introduction In chapter 3 the performance o f the microdisk modulator in intensity modulation direct detection (IM-DD) RF optical links was has been investigated to demonstrate the potential o f employing it in RF sub-carrier fiber optic links such as LANs or fiber-feed back bone networks (section 1.1.2 and 1.1.3). In these applications, the microdisk performs linear optical intensity modulation similar to a conventional Mach-Zehnder (MZ) modulator but in a smaller volume and with less power consumption. On the receiver side, after converting the optical intensity modulation to an electric signal frequency mixing with a local oscillator in a RF mixer is used to down-convert the baseband information (video or data) from the received RF signal similar to a conventional homodyne RF receiver. In this chapter we investigate the possibility o f using the microdisk in a novel photonic RF receiver architecture without using high-speed electronic circuitry. One o f the key operations in microwave communication is frequency mixing. Several techniques have been proposed for RF mixing in the optical domain such as 196 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. nonlinear modulation in a Mach-Zehnder modulator [1-3] and nonlinear detection in a photodiode [4-6]. After a brief review o f the conventional nonlinear photodetection method, we will introduce an alternative technique for self-mixing that is based on optical filtering prior to photodetection. Nonlinear optical modulation is the next technique described as a more efficient alternative to nonlinear photodetection. Previously this technique has been used in a photonic heterodyne receiver where the M Z-modulator was used as a photonic RF mixer to mix the local oscillator and the received signal [2]. Here we show that by utilizing transmitted carrier RF format combined with optical filtering prior to detection or nonlinear modulation in the modulator it is possible to down-convert the baseband signal without using a local oscillator, a RF mixer or any high speed electronic or optoelectronic devices. 4.2 Nonlinear photodetection A photodiode is effectively a square-law detector for the optical F-field (ipx P0ccE2). Linear photodetection, used in conventional AM-DD optical links, is basically m ixing the 194 TH z (k = 1550 nm ) optical carrier w ith the side bands 194THz ± Avb MHz (Avb: baseband signal) to generate the baseband photocurrent. In RF sub carrier optical links, since the baseband signal is replaced with a data modulated RF 197 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carrier, the photodetector output needs to be mixed with a local oscillator in order to extract the baseband data. If the photodiode operates in the nonlinear regime where ■ j . /p Q c P0 , it can function as an optical RF mixer similar to a conventional electronic diode mixer. The bias voltage on the photodiode may be used as the third terminal to mix the RF signal with a local oscillator in the optical domain. This technique has been employed in several photonic RF mixer designs for receiver and transmitter applications [4-6], By using the transmitted RF carrier modulation format it may be possible to use this technique for passive down-conversion in RF subcarrier microwave-optical links. Physics of nonlincarities in photodiode Recently there has been an increasing amount o f work concerning the nonlinearities in photodetectors (PD ’s) because it can be an important limiting factor in high- fidelity analog and digital communication systems [7]. The nonlinearities in P D ’s have been measured and modeled by numerical solutions o f coupled differential equations governing the flow o f carriers and distribution o f the electric field along the PD. The main nonlinear mechanisms have been identified as: (a) Space-charge fields that change the electron velocity and the diffusion constants (b) PD potential drop from current flow in the external load resistance which lowers the internal electric field, (c) Carrier trapping effect and (d) The current flow in the p-contacts [7-11]. So far all efforts have been concentrated on improving the PD design to reduce 198 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. nonlinearities in the photodetection especially at larger photocurrents. Operation at large photocurrent is desired because it increases the dynamic range and reduces the loss and noise figure in externally-modulated links [7], Conversely for photonic RF mixing applications the question is ‘How can we modify the design o f a regular p-i-n photodiode to enhance the second-order nonlinearities?’ The answer to this question requires a deep understanding o f the physics o f nonlinearities in a p-i-n photodiode. This subject has been briefly discussed in Appendix (A). We can understand the basic mechanism behind nonlinear photodetection by focusing on nonlinearity generated by the space-charge effect. The photocurrent density can be estimated as: ./photo = exMphoto-*ve (e : electron charge, ^photo- photo-generated electron density, ve: electron velocity). In a standard configuration, where highly linear operation is desired, the photodiode is reverse biased in such a way that electron velocities are saturated and therefore v is not a function o f « p hot<>. By decreasing the reverse bias voltage below the threshold required for carrier velocity saturation, v becomes a function o f /?photo. Knowing «photo is proportional to incident optical power (P0) and assuming v?/;p|lo lo ) cc «p|U )t0 then TP hotoccT’ 0 2. Experimentally it has been demonstrated that changing the reverse bias voltage from 8 Volt to 1 Volt increases the detected second-harmonic power by 20 dB [7]. Through the same mechanism second-harmonic nonlinearity increases by increasing the optical power incident to photodiode. So low-bias voltage and high photocurrent seem to be the trivial answer to our question. For a conventional p-i-n diode (the one used in [7]) at its best bias point and modulation frequency (5 GHz), 199 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the second-harmonic power is 24.5 dB below the fundamental power, and is thus very inefficient for real applications. However the large magnitude of the linearly modulated photocurrent at RF frequencies doesn’t interfere with the minuscule baseband photocurrent and can be filtered out using a low pass filter. This may result in an acceptable signal-to-noise ratio for certain applications. Ideally we need a specialized design for strengthening the nonlinear behavior. 4.3 Down-conversion through optical filtering In this section we demonstrate that by tailoring the optical spectrum after modulation and prior to detection it is possible to extract the baseband information from the RF signal using only a slow-photodiode operating in the linear regime. 4.3.1 Introduction Let’s assume the baseband signal is a pure sinusoidal signal so the received RF voltage is written as: Vrf = HjO + mi cos(eoht))cos(fi}l{ l,t) (4.1) 200 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where C D b is the baseband frequency, ©rf is the RF carrier frequency, mi is the RF modulation index and Vo is the RF voltage amplitude. If this signal modulates the optical carrier (©opt: THz regime), then the optical electric field will have the form: where Eo is the amplitude of the optical carrier and M is the optical modulation index. Fig. 4.1 shows the frequency spectrum o f the optical signal. In the frequency domain the optical modulation process adds two sidebands to the optical carrier where each sideband is a baseband modulated RF carrier. We call these RF-optical sidebands because they are RF signals up-converted to optical frequencies. F ig u re 4.1 Schem atic diagram o f the frequency spectrum o f an optical carrier m odulated w ith an RF signal. T he RF signal is an RF sub-carrier m odulated by a sin gle-ton e baseband. T he am plitude o f each frequency com p on en t is w ritten as a function o f optical .E-field and the m odulation ind exes. By expanding equation (4.2) we can calculate the amplitude of each frequency component as shown in Fig. 4.1. The amplitude o f the RF sub-carrier (black lines) and up-converted baseband components (light gray lines) is determined by RF and optical modulation indices. If the optical carrier and the upper RF-optical sideband are filtered out the modified optical E-field can be written as: Eopl(t) = E 0[l + M (\ + m l cos(Q}ht))cos(coR I,t)]cos(£0olJ ) (4.2) it-field ...■ ® o p t • Eq ^ ® o p t ± C 0 R F + ® b : EoMm/2 ./•■ ® opt + ® r f : E()M/2 + ■ ■ ■ ■ A* £ ; , ( 0 = Re 2 2 201 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This can be easily done using a band-pass optical filter with proper band width and Using equation (4.3) we can calculate the spectrum o f the modified optical intensity The optical intensity spectrum consists of a DC component, the baseband frequency and its second-harmonic. So if we use a photodetector we can generate the baseband current and its second-harmonic. Notice that using this approach we can extract the baseband information from the RF signal by means of linear optical modulation, optical filtering and linear photodetection. Also the speed of the photodetector is determined by the bandwidth of the baseband signal and not the RF carrier. Fig. 4.2 shows a schematic diagram o f the signal flow in a RF-subcarrier optical-link that uses optical filtering for optical down-conversion. The RF-carrier is modulated by the baseband signal in a regular double-balanced RF mixer which generates a double sideband suppressed carrier (DSB) modulation signal (mj > 2). The mixer output is fed into a MZ modulator to modulate the optical carrier generated by a single mode DFB laser (194 TFIz). The modulated laser light then passes through a FBG filter that rejects the optical carrier and the upper RF-optical sideband. Finally, the filtered light is detected by a p-i-n detector that directly generates the baseband current. A simple explanation for down-conversion in the photodetector is based on the fact that the p-i-n photodiode is a square-law .E-field detector, meaning the output role-off. 1(0: m = E ' opl(t) 2 M 2E 02 , m 2 = — 1 + — + 2m , cos(coht) h — - c o s ( 2 coht) 2 4 2 202 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. current is proportional to the intensity o f the oscillating E-field o f the incident optical signal. W ithout filtering, the photodiode is effectively mixing the optical carrier frequency with the RF-optical sidebands to generate the RF signals. When only one RF-optical sideband is detected, the photodiode mixes the up-converted RF-carrier with up-converted basebands and therefore generates the baseband signal. L ow er R F -optical-sid eb and O ptical carrier R F -sideban ds is-field M Z optical m odulator FBG ; o / e converter | D F B Laser; f u , ■ = RF carrier L ow pass filter r - 0 D S B supp ressed carrier m ixin g B aseband am plifier f h = baseband LO B aseband F ig u re 4 .2 S chem atic diagram o f a R F-subcarrier optical-lin k that uses optical filtering for optical d ow n -con version . In our proof o f principle experiment we use a single-frequency baseband at 100 MHz to modulate a 7.6 GHz RF-carrier. The optical filter is a custom made FBG filter with transmission characteristics shown in Fig. 4.3. The filter has a very fast role-off of about 1 dB/pm around X = 1553.15 nm. The photodetector is an amplified p-i-n detector with a 3 dB bandwidth o f 15 GHz. A RF spectrum analyzer is used to measure the RF frequency spectrum of the photodetector output. The laser source is a tunable single mode laser with a linewidth o f 20 MHz, so we can tune the 203 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. wavelength to different regions o f the FBG transmission spectrum. The MZ modulator has a V% o f 4.5 V and optical insertion loss of 5 dB. Fig. 4.4 shows: (a) the FBG transmission and the modulated optical signal spectrum, (b) The measured RF-spectrum o f the photodetector output and (c) The simulated RF spectrum o f the detected signal. These are shown for two different cases: (1) A ,|aser = 1553.16 nm where only the upper RF-optical sideband is rejected (2) A ,|aser = 1553.23 nm where the upper RF-optical sideband and the optical carrier are rejected. -o a j C ? 03 O is ft. O h o o z 1 « -25 1 5 53.2 1553.3 1 5 5 3 .4 1553.5 W avelength (nm ) 0 — 1553.13 1553.43 1553.23 1553.33 1553.53 Wavelength(nm) F ig u re 4 .3 T he transm ission spectrum o f the Fiber B ragg G rating (F B G ) em p lo y ed in the optical d o w n -co n v ersio n experim ent. (C enter w avelength: 1 553.3 nm , Slope: 1 dB /p m , R eflectio n Band width: 0 .2 6 nm ) In the first case the spectrum o f the detected RF-signal is similar to the spectrum of the original RF-signal fed to the modulator and nothing is observed at baseband frequencies (no down-conversion). If the upper RF-optical sideband is also transmitted, only the amplitude o f the detected RF signal becomes larger. In the 204 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. second case a small peak is observed at 100 MHz (baseband frequency), a large peak is observed at 200 MHz and the detected RF-signal is suppressed. ( 1 ) ( 2 ) 1 5 5 3 .1 6 nm = 1 5 5 3 .2 3 nm o Z 0 Vw v/m„. + 7 ,5 G H z S + 7 .7 G H z , / v , + 7 .6 G H z 1553.13 1553.23 1553.33 1553.43 W a v e le n g th (n m ) 1553.53 > o 0 0.5 1 7 7.5 8 Frequency (G H z) Cl 0 z 1553.13 1553.23 1553.33 1553.43 1553.53 (a) ( b ) W a v e le n g th (m n ) 0.5 - //- 7 7.5 Frequency (G H z) 0 0 ( x lO " H z) Frequency 0.2 Frequency ( C ) F ig u re 4 .4 RF d o w n -con version by optical filtering (a) T he m easured spectrum o f the FB G t r a n s m i s s i o n a n d t h e m o d u l a t e d o p t i c a l s ig n a l , ( b ) R F - s p e c t r u m o f t h e d e t e c t e d s i g n a l ( c ) T h e sim ulated spectrum o f the detected signal. In this the sim ulation the RF carrier freq uency is o n ly ten tim es sm aller than the optical frequency and the baseband signal is ten tim es sm aller than the RF- carrier frequency, to m ake the FFT calculations faster. 205 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. So the signal is down-converted but there is more energy at the second-harmonic o f the baseband compared to the baseband frequency. This is because the RF modulation format is a suppressed carrier and the RF carrier is about 16 dB smaller than the sidebands. So the second-harmonic o f the baseband signal generated by beating between two RF-sidebands at 7600 MHz ± 100 MHz, is larger than the baseband signal generated by beating between the RF-carrier and each RF-sideband. Equation (4.4) shows that ratio between the baseband component and its second harmonic in the modified optical spectrum is Iub/hmb = 2/mi so if m\ > 2, Im i, < hub and if ni\ < 2 then Im b > hub. Linearity is one o f the important requirements o f a RF receiver so it is evident that hub has to be smaller than /< „ b. Employing a transmitted carrier RF modulation format {ni\ < 2) where the carrier amplitude is larger than the sideband amplitudes can solve this problem. Although sending a large amount o f energy in the RF carrier frequency is inefficient for long distance communications but it may be practical for short distance indoor wireless links. In the next section we show employing transmitted carrier format can solve the linearity issue. 4.3.2 Self-homodyne RF down-conversion In a conventional super-heterodyne RF receiver architecture a local oscillator (LO) and mixer are used to down-convert the signal to IF frequencies (1.2.5). Baseband 206 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. information is subsequently extracted from the IF signal in a detector/demodulator. Alternatively, in a direct-conversion (homodyne) radio receiver, baseband information is obtained by mixing the received signal and the LO without using an IF frequency [11], In addition to such approaches, self-heterodyne techniques have been proposed to reduce the number o f components as well as size, weight, and power consumption in high-carrier frequency (mm-wave), short distance applications [ 12]. In a self-heterodyne transmission system, the transmitter broadcasts a RF signal (carrier + sidebands) and LO so the IF signal can be down-converted by mixing the received LO and modulated RF signal in a nonlinear device called a self-mixer. The receiver power consumption, phase noise, and complexity are reduced as a result o f eliminating the conventional LO and mixer. Although such an approach suffers from reduced power efficiency, it has been shown that it can lower the overall cost and complexity in mm-wave local area networks and indoor wireless transmission systems [12]. One may eliminate the down-conversion to IF frequencies in a self heterodyne receiver, by using a transmitted carrier RF format. So the baseband signal can be directly down-converted by mixing the received carrier and sidebands in the self-mixer. We call this receiver architecture self-homodyne (self = mixing the transmitted carrier and sidebands, homodyne = no IF stage involved). The concept o f self-homodyne down-conversion o f a transmitted carrier RF signal may be used to design a photonic RF receiver where the electronic self-mixing is replaced by photonic self-mixing using optical signal processing techniques. 207 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Here we demonstrate baseband down-conversion from a transmitted carrier RF signal using optical fdtering technique (introduced in the previous section). Experimental results In our experimental demonstration we use the arrangement shown in Fig. 4.2. In order to generate the transmitted carrier RF format we apply a DC voltage on the IF port o f the double-balanced mixer so by tuning the voltage we can control m[. Similar to the previous experiment by aligning the laser wavelength (optical carrier frequency) relative to the center frequency o f the FBG, we reject the optical carrier and one o f the RF-optical sidebands. Fig. 4.5(a) shows the FBG transmission spectrum and the wavelength components o f the modulated optical carrier for three different optical carrier wavelengths (lines with diamond tip). Fig. 4.5(b) shows the spectrum of the received RF signal. The RF carrier frequency is 7.6 GHz and the baseband is a 300 MHz single tone. The RF modulation format is suppressed carrier (,m/< 2) so the magnitude o f the sidebands (8.7GHz ± 300MHz) are smaller than the carrier. We study three different cases, first the lower RF-optical sideband is rejected but the optical carrier is not completely suppressed (the signal shown by gray dashed in Fig 4.5 (a)). This results in the optical output intensity spectrum shown in Fig. 4.5(c). Fig. 4.5(d) shows the optical output intensity spectrum where one o f the RF-optical sidebands and the optical carrier are completely rejected (optical spectrum shown by solid black lines in Fig. 4.5(a)). 208 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 -5 S ' -10 -a « -1 5 •i -20 1 -25 -30 -35 -40 -45 0 G L - H * O ptical carrier • R F -optical sidebands 21 0 .2 4 0 .2 7 0.3 0 .3 3 0 .3 6 0 .3 9 0 .4 2 0 .4 5 0 .4 8 0.51 0 .5 4 W avelength (nm ) (a) CL O < D £ o CL 100 50 a o * o < D 3 -a O o O- ill 2000 4000 6000 8000 Frequency (M H z) ( b ) 6 % o Cl " c S * + 2 Cl O " O < D □ -a o 2000 4000 6000 8000 F requency (M H z) ( O 0 2000 4000 6000 8000 Frequency (M Hz) (d) F ig u re 4 .5 (a) T he transm ission spectrum o f the F B G filter and the location o f the w avelen gth com p on en ts o f the m odulated optical carrier, (b ) Frequency spectrum o f the transm itted carrier RF signal fed into the M Z m odulator, (c) T he spectrum o f the detected signal after filterin g for the optical spectrum sh ow n by dashed gray lines in (a), (d) T he spectrum o f the detected signal after filterin g for the optical spectrum sh ow n by so lid black lines in (a). As we expected the down-conversion is more linear and the second-harmonic o f the baseband is now suppressed relative to the baseband itself. To study the effect o f the modulation index (mf) on the down-conversion efficiency and linearity, we have 209 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measured the magnitude of the down-converted signal and its second-harmonic as a function o f RF modulation index. Fig. 4.6 shows the measured and calculated baseband power and its second-harmonic against m\. As may be seen at m \= 1.2 the magnitude o f the baseband signal is maximized but the magnitude o f its second- harmonic increases monotonically by in creasing m\. The solid lines are calculated using equation (4.4). Notice that highly linear down-conversion (very small second-harmonic) is accompanied by a low efficiency. At m\ = 1 we can have a second-harmonic suppression of 7 dB (15 dB electrical) and an efficiency close to maximum. } - l £ o 13 o o T3 < u q—* o < D Q 120 100 0 6 2 4 8 RF modulation index (m ( ) F ig u re 4 .6 T he m agnitude o f the detected baseband signal (black trian gles) and its secon d -h arm on ic (gray d iam ond s) against RF m odulation index. T he solid lin es are the calculated usin g equation (4 .4 ). In order to evaluate the performance o f this photonic down-conversion technique we replaced the 300 MHz single tone with a 10 Mb/s 27-l PRBS NRZ data stream. 210 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o w a a l.E-O l l.E -0 2 I.E-03 l.E -0 4 l.E -05 1.E-06 l.E -0 7 l.E -0 8 -1 3 .0 0 O o o o o o 11.00 -9 .0 0 -7.00 R F input pow er (dB m ) O -5 .0 0 F ig u re 4 .7 T he m easured B E R perform ance o f the self-h o m o d y n e receiver that em p lo y s pre detection op tical fdterin g for p h otonic d ow n -con version . We used a digital photoreceiver with a sensitivity o f -41 dBm and bandwidth o f 50 Mb/s to detect the down-converted signal. Fig. 4.7 shows the BER measurement results against the total received RF power. The sensitivity o f the receiver can be improved by employing a MZ modulator with smaller VK and better insertion loss. We repeated the same experiment using our 14.6 GFIz microdisk modulator. Fig. 4.8 shows the BER measurement results of the FBG based self-homodyne receiver using the microdisk modulator. 211 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. w l.E-02 l.E-03 l.E-04 l.E-05 l.E-06 l.E-07 l.E-08 l.E-09 -22 -21 -20 -19 8 17 RF input power (dBm) F ig u r e 4 .8 M easured B E R o f the dow n-con verted data against received RF pow er. T he RF carrier is 14.6 G H z and the transm itted data is 10 M b/S 2 7- l N R Z P R B S. T he ph otonic d o w n -co n v ersio n is a ch iev ed usin g a linear m odulation in a m icrodisk m odulator and FB G fdter. T he m icrod isk has an F SR o f 14.6 G H z and a K H m m o f 0 .6 V . The baseband signal is again a 10 Mb/s 27-l PRBS NRZ data stream while the carrier frequency is 14.6 GHz. The microdisk modulator has a H hmm o f about 1.2 V and an optical insertion loss o f 10 dB. As may be seen although we have doubled the RF carrier frequency the sensitivity o f receiver is improved. Fig. 4.9 shows the measured eye-diagrams for 10 Mb/s, 50 Mb/s and 100 Mb/s at -18 dBm received RF power. 50 M b/s 10 M b/s 100 M b/s 50 ns/d iv 10 ns/d iv 5 ns/d iv F ig u re 4 .9 M easured eye diagram s o f the dow n-converted data from 14.6 G H z RF carrier usin g m icrodisk m odulator and FBG 212 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The efficiency o f this down-conversion mechanism is low because a large amount of optical energy is filtered out passing through the FBG and hence does not contribute to the down-conversion process as opposed to the conventional intensity detection where almost all the available optical energy contributes to the down-conversion process. Therefore reducing the transmitted optical power at optical carrier and the upper RF-optical sideband should improve the power efficiency o f this passive down-conversion process. In conclusion efficient RF down-conversion using optical filtering prior to photodetection requires both transmitted carrier RF modulation format and suppressed carrier single sideband optical modulation format. 4.3.3 Optical heterodyning An alternative solution to improve the low down-converted power in the optical filtering technique is using a second laser to boost the baseband modulated optical power. In this approach the modulated optical signal is mixed with a laser that has an optical frequency equal to the up-converted RF-carrier in the lower RF-optical sideband. This is the optical equivalent o f mixing the received RF signal with a local oscillator in conventional RF-receivers. We refer to the second laser as the optical local oscillator. So if we filter out the optical carrier frequency and the upper RF- optical side band, the baseband photocurrent is generated as a result o f mixing the lower RF-optical sideband and the optical local oscillator in the photodetector. Note 213 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. that the photodetector is still working as a linear optical intensity detector and the mixing is hidden in the square-law nature o f optical detection (ip< x.E 2) and not in any nonlinearities in the photodiode. In effect the RF mixer and local oscillator o f a conventional system are replaced with their photonic counter parts: a laser and a photodetector. Clearly the first laser and the optical modulator function as the optical up-conversion stage and play no role in the down-conversion process. We call this process optical heterodyning because the optical carrier frequency and the optical local oscillator frequency are not equal. Fig. 4.10(a) shows a schematic diagram o f the receiver architecture based on optical heterodyning and filtering. The output power o f the local oscillator laser is the same power as the main laser but with a shifted wavelength Av = f R F ( f m : the RF carrier frequency ). The optical local oscillator and the optical modulator output are combined in a 50/50 optical power combiner. Fig. 4.10(b) and (c) show the simulated output spectrum with and without optical heterodyning (mixing the second laser). Indeed when the local optical oscillator is used the detected baseband signal becomes larger. In this case the RF signal has a transmitted carrier modulation format to show that by changing the modulation format even without the second laser we can suppress the second-harmonic o f the baseband. 214 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R F sig n al L a se r d io d e (o p tic a l ca rrier) I O p tic a l m o d u la to r V la s l= 194 THz B aseband output D e te c to r W ith optical local oscillator ) L a se r d io d e (lo c al o sc illa to r) V/os-2= V /a s / - J r f F B G filte r ( a ) B aseband RF carrier o ^ ------ 1 -------- U0 0.5 1 1.5 2 2.5 W ithout local oscillator 1 B aseband RF carrier o ^ — 1 --------r u 0 0.5 1 1.5 2 2.5 Frequency (x lO JI Hz) ( b ) Frequency (x IO 1 1 Hz) ( C ) F ig u re 4.10 A ctive dow n-conversion using optical filtering and local oscillator, (a) Schem atic diagram o f the system architecture. A second laser w ith the sam e pow er as the m ain laser but w ith a shifted w avelength (Av = / r f , / r f : the RF carrier frequency) is com bined (50/50) w ith the m odulator output before passing through the FB G filter, (b) T he sim ulated optical output intensity spectrum . T he RF signal has a transm itted carrier m odulation form at (R F-carrier is not suppressed). By using the optical local oscillator the baseband signal becom es larger (by a factor o f 5). In o rder to reduce the calculation com plexity o f the FFT, in this sim ulation the RF carrier frequency is only ten tim es sm aller than the optical frequency and the baseband signal is ten tim es sm aller than the R F -carrier frequency. But when we use the optical heterodyning technique the transmitted carrier RF modulation format is no longer required and we can also use a DSC RF-modulation format. In this way the available RF power is dedicated to the efficient transmission 215 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of data and the carrier power needed for down-conversion is provided, optically, in the receiver. This approach seems to be very promising since it solves the problems associated with passive down-conversion using a FBG. It relaxes the restriction we had on the RF-modulation format that was limiting the application o f the photonic receiver to indoor wireless systems and also it increases the efficiency o f the optical down- conversion process by providing power at the proper frequency. The main difficulty of this method is the high-sensitivity o f the system performance to relative power, frequency and polarization variations o f the two lasers. To address this issue we have performed a homodyne detection experiment. In this experiment the output o f a single-mode laser is divided between two optical paths. 90% o f the laser power is transmitted through a passive arm and 10% is modulated by digital data in a MZ modulator. All optical fibers, the splitter and the combiner are polarization maintaining (PM) to avoid fluctuations caused by random polarization rotations. Fig. 4.11(a) illustrates a schematic diagram o f the experimental arrangement. The CW and the modulated signals are combined in a 50/50 optical power combiner and then mixed in a photodetector. The amplitude o f the output signal is measured with an oscilloscope. 216 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Pattern generator 0 M > A (2 7 -1 P R B S ) P2 ! P x = 6 0 0 pW-715 iiW = 4 0 M Z m odulator 10% Laser 5 0 /5 0 P hotodetector mW 90% % 95 %5 H eating elem en t Control circuit RF pow er detector O sc illo sc o p e D irect detection 25 ns/div T, : 0 .9 « iV | j i : t . 1 atm i ! ( a ) ( b ) H om odyne detection P2 JP \ = 4 0 25 ns/d iv F ig u re 4 .11 (a) Schem atic diagram o f the experim ental arrangem ent to test the feed back loop therm al phase control in a hom od yn e detection sch em e. 90% o f the laser pow er g o e s to the p a ssiv e arm and 10% g o e s to the a ctive arm. D ue to optical insertion lo ss in M Z m odulator P2 /P\ is about 4 0 . 5% o f the detected signal is fed to a R F -pow er detector (that generates a voltage proportional to the received RF pow er). T he output v o lta g e from the pow er detector is used as the reference in a control circuit to drive the appropriate current through the heating elem en t and change the phase accordingly, (b ) T he m easured ey e diagram s w ith and w ithout the p a ssive arm. D ata am plitude is am plified by a factor o f 5.8 that is in very g o o d agreem ent w ith the calculated gain Although both arms are fed by a single laser the detected data amplitude is very unstable due to relative phase fluctuations during transmission. To solve this problem we have designed a feedback loop that uses 5% o f output electrical power 217 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. as a reference and controls the optical phase in CW arm accordingly to stabilize the detected data amplitude. The phase is controlled by thermal tuning o f the passive arm using a thin gold wire around a small length o f the fiber as the heating element. Fig. 4.11(b) shows the measured eye diagrams with and without the passive arm when the power ratio between the passive and active arm (P2 /P 1) is 40. Using the passive arm amplifies the detected amplitude by a factor o f 5.8 as compared to a direct detection configuration. This shows very good agreement with the calculated gain o f 6 (for P^Py — 40). This experiment demonstrates that by accurate control of relative phase fluctuation, a homodyne detection system (within a very short link) is achievable. The heterodyne system discussed earlier is similar to our homodyne experiment in the sense that they are both sensitive to relative phase o f optical waves mixed in the photodiode. But in heterodyne system, the use o f two lasers demands more advanced feedback loops and locking techniques must be used. The possible approaches are the electronic control o f the lasers or the optical injection locking of two lasers. We should point out that in all photonic down-conversion methods based on linear or non-linear mixing in a photodetector, the detector bandwidth must be at least equal to the RF carrier frequency. In the next section we will describe a different technique for implementing a photonic self-homodyne receiver that doesn’t require the optical filter. 218 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4 Down-conversion through nonlinear optical modulation The nonlinearities o f a Mach-Zehnder modulator have been used for signal processing in some RF-photonic systems [1-3]. It has been shown a MZ modulator biased at its quadrature point can be used to mix the LO and the RF signal in optical domain and generate the IF signal. In this section we demonstrate, both Mach-Zehnder and microdisk modulators can perform second-order nonlinear modulation when biased at their maximum or minimum transmission points. Then the combination o f second-order nonlinear modulation and transmitted RF format is used to implement a photonic self homodyne receiver. 4.4.1 Introduction In a photonic self-homodyne RF-receiver we can replace the function o f a single ended diode or FET mixer in a transmitted carrier wireless link with a sensitive optical modulator that performs down-conversion in the optical domain. In this approach the nonlinear dependence o f the m odulator’s transmitted optical power (Po.out) on applied RF voltage ( F r f ) is the source o f nonlinearity in the system. Fig. 4.12 illustrates the photonic self-homodyne RF receiver architecture. The received RF signal contains both sidebands and the center frequency (transmitted- 219 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carrier double-sideband modulation format) and is fed to an optical modulator biased at its nonlinear operating point. The carrier and sidebands are mixed through the second-order nonlinearity (P0,out x T r f 2 ) , hence the optical output intensity spectrum contains the baseband and high-frequency products around the second-harmonic of the carrier frequency. A photoreceiver with a bandwidth matched to the baseband signal generates the baseband photocurrent (zp) and automatically filters out the high- frequency components. Antenna N J / RF input ( O r f Nonlinear optical „ T. 2 , , + . P q .o u io c F rf modulation Laser light, A ,|a sc i = 1550 nm Optical waveguide Low speed photodiode and TIA Optical output Optical to electrical conversion Baseband > y M b > 2 o > b A t t 2 w b 2 ( 0 r f F ig u re 4 .1 2 S chem atic diagram o f the photonic self-h o m o d y n e RF receiver. T he transm itted carrier RF signal is received by the antenna and is directly fed to a square-law optical intensity m odulator. T hrough nonlinear optical m odulation the optical output intensity spectrum contains the baseband and high frequency com ponents that are filtered out by the response o f the lo w -sp eed photodetector. 220 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The bandwidth o f all electronic circuitry used in the system is no greater than that of the baseband signal. The electro-optic transfer function of an optical intensity modulator /no( Frf) can be expanded around Frf = 0 to give p„,„ = p™+ C + + - - W . + W m + Y V " " + - (4-5) Here, N t (i > 0) is the zth Taylor expansion coefficient of Frf) at Frf = 0 and jV q is the transmitted optical power at Frf = 0. At a fixed wavelength the magnitude of Ni depends on modulator properties and the chosen bias point. The first-order term in equation (4.5) generates linear optical intensity modulation OPo.om^RF) while other terms contribute nonlinear frequency components. Usually, such nonlinearities are minimized in conventional direct detection (DD) optical communication links. If the RF voltage amplitude is small enough and the modulator is biased at its extreme transmission point (where dP0 fix A /dVwe = 0) the second-order term P 0(2 ) dominates the behavior o f the modulator and the optical output power (P0 out) dependence on voltage around Frf = 0 will be similar to an ideal square-law mixer with: (4.6) If the baseband is a pure sinusoidal signal, the received RF voltage can be written as: VR I, - F0(l + m, cos(coht))cos(col(l,.t) (4.7) where m .\ is the RF modulation index, © /, is the baseband frequency and corf =2nfRF is the RF carrier frequency. The second-order term can be written as P(2 ) - F/ f 2 ,. = ^ V 0 2(] +m, c o sK O )2 cos2{coR ,t) (4.8) 221 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Expanding the right hand side o f equation (4.8), one obtains a DC term equal to 2 2 • (NiVt) /4 )(1 + m\ 12), h ig h frequency com ponents centered around 2cdrf given by ((1 + m ,2 12 ) cos{2com,t) + (m2 / 4)cos2(2Q)ht)cos(2coR I,t) + m , cos(a)h()cos(2a>R I,t)) (4.9) and the tw o d o w n -co n v erted low -frequency term s at co/, and 2cob are given by N V 2m 2 M V 2 ——-— —cos(2a>ht) H — ^ - m , cos(coht) (4.10) 8 2 T he o scillatio n am plitude o f the to tal second-order m o d u lated o ptical p o w er is C » = ( l + » , ! + 2 ' » , ) Y r »2 <4 J 1 > w hich is ju s t the m ax im u m am plitude in equ atio n (4.8). I f w e use a slo w speed p h o to d etecto r w ith a responsivity R, the optical pow er m o d u lated at oi/, generates baseb an d p h o to cu rren t im b th at carries the received inform ation: N V2 L„ = R ~ Y L m i C0SM (4.12) T he efficiency o f this d o w n -co n v ersio n p rocess m ay be defin ed as the ratio b etw een the am p litu d e o f the optical p o w er m o d u lated at co/, and T his efficien cy is lim ited by th e generation o f und esired frequency co m ponents at 20%, 2 c o r f ± 2ce>b, and 2 ©rf± oi|, as w ell as the DC com ponent. T he linearity o f the d o w n -co n v ersio n is also an im p o rtan t p aram eter in receiv er op eratio n and is defined as the ratio o f the optical p o w er am p litu d e m o d u lated at ©b and 2c0b (first and second term s in eq u atio n 4.10). H ere w e assum e that the strength o f the seco n d -o rd er n onlinearity d o m in ates hig h er o rder term s in equation (4.5) so the generation o f hig h er harm onics o f the baseband (3coi„ 4cob, etc.) can be ignored. 222 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. E lectrical O ptical 0 0.5 1.5 2 0 0.5 1.5 2 RF m odulation index (m ,) RF m odulation index ( m ,) F ig u re 4 .1 3 (a) C alculated d ow n -co n v ersio n e ffic ic ien cy (/\>,Mb/T0,m ax(2)) versus RF m odu lation index (m). (b) S econd-h arm on ic su pp ression ratio against m x . T he electrical (after d etectio n ) and optical supp ression ratios are related through Pe, J P ^ h = ^ J h ^ ^ { P 0 ,iJ P a >.A: f The down-conversion efficiency and its linearity are determined by the RF modulation index (m\). In Fig. 4.13 the down-conversion efficiency (a) and second- harmonic suppression ratio (b) are calculated against m\. The second-harmonic baseband term (2cob) can be suppressed relative to the baseband (©b) by employing a transmitted carrier RF modulation format {m\ < 2) and the down-conversion efficiency reaches its maximum value of 25% around m x = 1. By choosing m\ = 0.8, an efficiency of about 25% and a second-harmonic suppression o f 7 dB optical (14 dB electrical, Pcx ip 2x P 00l]2) can be achieved. The sensitivity of a photonic RF receiver strongly depends on the magnitude o f the second-order nonlinearity (A^) in equation (4.5) and thus is determined by the modulator sensitivity and the transfer function /fo- Given that most wireless links only require a limited bandwidth around a high frequency carrier, a microdisk resonant optical modulator is a suitable choice for this application. In chapter 2 we 223 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. showed that tuning the laser wavelength we can maximized the efficiency o f linear modulation and suppressed second order nonlinearity. Conversely for down- conversion in the optical domain, large second-order nonlinearity is a requirement. This can be achieved by tuning the laser wavelength to a maximum or minimum optical transmission of a high-Q whispering gallery (WG) resonance. The large value o f N j at resonance in Fig. 2.38 supports our argument. It is useful to compare a conventional electronic diode and the microdisk optical modulator as second-order mixers. In both cases the aim is to generate a current proportional to Frf2. When the RF voltage is applied across a diode, the current may be expanded as: * M - t . * r m0 , + Z f O l + ~ (4.13) where (7 < i is the dynamic conductance o f the diode and the G ’< j' = a Gt|, (a = q/nkgT). If Vrf has the same form as equation (4.7) the baseband current is: I I I , 7 lio b =^ GjVrf (4.14) This equation is equivalent to equation (4.12) for the photonic mixer where RNi in equation (4.12) is replaced by G&'. In order to compete with an electronic diode mixer we need large second-order nonlinearity and a very sensitive low speed photodiode. Fig. 4.14 shows the typical P0,0ut-F and I-V curves for a microdisk mixer and an electronic diode and also the frequency spectrum o f their output current (with an input voltage similar to equation 4.7). As opposed to the microdisk mixer, the frequency spectrum o f the electronic diode contains the linear terms around c o r f . This is because there is no pure nonlinear bias 224 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. point in the I-V curve o f a diode while at A,ascr = Xre s the microdisk has a purely nonlinear response. Since the only useful frequency component is the baseband modulated current, the amount o f wasted energy, energy pumped to undesired frequencies, is larger in a diode mixer. V r f O (^"laser ^res^ V r f 1 DC term D C term (a) (b ) F ig u re 4 .1 4 (a) T he output optical pow er o f a m icrodisk m odulator against the input v o lta g e and the frequency spectrum o f the photocurrent generated by the v o ltage in equation 4 .7 . (b ) T he current across a co n v en tion al d iod e against the input v o lta g e and the frequency spectrum o f the current generated by the v o lta g e in equation 4.7 . 225 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4.2 Nonlinear optical modulation using MZ modulator Fig. 4.15(a) shows the typical response o f a MZ-modulator. The output optical power can be written as: Po,out= ^ [ lW e /a A p Z ) ] (4.15) P o,o u t o ,m ax P o.m in ( a ) ^ 500 400 u 300 & a 200 100 0 3 6 9 12 15 Voltage (V) ( b ) F ig u re 4 .1 5 (a) P0M lt versus ApZ,/7i characteristic o f a M ach-Z ehnder m odulator, (b ) T he DC response o f the M Z m odulator used in our experim ents. T he circles are the m easured data points w h ile the so lid line is the calculated response u sin g equation 4 .1 6 assum ing P0 ,m iK = 4 6 8 pW , < ) > = 2 .3 7 5 rad and = 5.2 V . T he dashed curve is the parabola defined by N2V2 /2 w here N2 is the seco n d d erivative o f the equation 4 .1 6 . Ap is the propagation constant variation in the active arm created by the electro- optical effect (2nAnc /X, o c F r f ) , and L is the interaction length in the active arm. 226 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The main parameter that quantifies the modulation sensitivity o f a MZ modulator is Vn or the voltage required to create a 71 optical phase shift in the active arm (ApL = %). W hen A p/fn is an integer number the optical output power is maximum or minimum so dPlK m il/dVi{\. = 0 and Ap =d2 P0,ou/dVRF 2 has its maximum value. If a MZ modulator is biased at any o f these extreme transmission points it can be used as a square-law RF mixer. We can rewrite equation (4.15) in terms o f the input voltage (F) and the n phase shift voltage (Vn): P o .o u t = W ,/™ a[co s((|> + 7 i V/2 Vn) f (4.16) Fig. 4.15(b) shows the DC response o f the MZ modulator used in our experiments. The circles are the measured values o f the optical output power as a function o f the input voltage. The solid curve is generated using equation 4.16 and the proper values o f Pn,m ax, < ( > and VK to fit the experimental data: P 0,m ax = 468 pW, < j > = 2.375 rad and Vn = 5.2 V. The optical input power is 1500 pW and the optical insertion loss is 5 dB. The dashed curve is the parabola defined by Ay Vl!2 where Nj is the second derivative o f the equation 4.16. As may be seen V < 0.25 Vn can be considered as small signal regime because in this range the parabola perfectly overlaps with the actual response. So as mentioned in the previous section at this regime the MZ modulator behaves like an ideal second-order intensity modulator and the simple formulation developed for down-conversion can be used to estimate the down converted optical power. 227 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RF mixer V ariable B andpass RF attenuator filter LO = 7.6 GHz A m p lifier DC pow er supply B aseband = 3 0 0 M H z P hotodetector 5 5 0 nm RF spectrum analyzer L rN b 0 3 M Z m odulator Laser F ig u re 4 .1 6 E xperim ental arrangem ent for stu dying ph otonic d ow n -con version through nonlinear m odulation in an M Z m odulator. In order to validate theoretical prediction o f our simple model we used the experimental setup shown in Fig. 4.16. In this experiment the baseband is a 300 MHz single tone and the RF carrier frequency is 7.6 GHz. Mixing the baseband with the local oscillator in a biased RF-mixer generates the transmitted carrier RF signal (equation 4.7) where the RF modulation index can be controlled by varying the bias voltage. A band pass RF filter removes all intermodulation products at baseband and the higher harmonics of the carrier so that the output only contains the double sideband (DSB) modulated RF-carrier. The MZ modulator is biased at its minimum transmission operating point. The modulator parameters and maximum optical output power are the same as Fig. 4.15(b) and the photodetector responsivity is 270 pV/pW . Fig. 4.17(a) shows the calculated and detected rms voltage at baseband (V\) and the second-harm onic o f the baseband (Vi) as a function o f m\. The calculation is based on square-law optical modulator model (equation 4.6) where N 2 is calculated using equation 4.16 and the measured values o f MZ modulator parameters. One can 228 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. calculate the detected voltage amplitude at mi, and 2(0b using equation 4.10 and the photodetector responsivity. Fig. 4.17(b) shows the calculated and measured rms voltage at baseband (V/) and the second-harmonic o f the baseband (V 2) as a function of the total received RF power at m\ = 1.2. 90 80 > 70 < D 60 b /) c d 50 o > 40 " S o 30 O J u Q 20 10 0 > 55. b i) 0 3 O > 7 3 < D U < u ♦ ♦o O ♦ t * ♦o f a a z ♦ VI (m easured) o V I(calcu lated ) V2(m easured) A V 2(calculated) 0.00 140 120 100 80 60 40 20 1.00 2.00 3.00 RF m odulation ind ex (/» /) ( a ) ♦ VI (m easured) VI (calculated ) O V 2(m easured) V 2(calculated) . 0 ' ♦ a ' ♦ . 0 ’ ♦ 0 - 12.00 - 10.00 - 8.00 - 6.00 RF input pow er (dBm) ( b ) 4.00 5.00 ,0 ♦ ♦ -4.00 - 2.00 F ig u re 4 .1 7 (a) C alculated and detected rms v o lta g e at baseband and the secon d -h arm on ic o f the baseband as a function o f ni\. T he calculation is based on square-law optical m odulator m od el, (b) C alculated and m easured rms v o lta g e at baseband and the second-h arm on ic o f the baseband (V2) as a function o f the total received RF pow er at m ] = 1.2. 229 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The received RF power is related to m\ and V0 through P R F = F02( 1 + ‘ 72)/100 so again we can use equation 4.10 and photodetector responsivity to calculate the detected voltage amplitude at co b and 2cob as a function of Rrf. The calculated and measured results are in good agreement showing that at small signal regime the modulator is effectively a square-law modulator We have also demonstrated direct data down-conversion at data rates up to 100 Mb/s from a transmitted carrier RF signal (carrier frequency =7.6 GHz) by replacing the signal generator in the experimental arrangement of Fig. 4.16, with a pattern generator and the photodetector with a digital photoreceiver. The patterns are NRZ 27 -l PRBS and the sensitivity of the photoreceiver is -41 dBm for a BER of 1 O ’9. Fig. 4.18 shows the measured eye diagrams at 10, 50 and 100 Mb/s. The respective BER results are 10'9, 10’6 and 10’5 at -1 0 dBm total received RF power 10 M b/s D ow n -con verted data O riginal data M i m m 50 ns/div 50 M b/s 10 ns/d iv 100 M b/s r .. T T — 7 r.. n x z 5 ns/d iv F ig u re 4 .1 8 M easured eye-d iagram s at 10, 50 and 100 M b /s (P R B S N R Z 2 7- 1). T he data is dow n - converted from a 7 .6 G H z RF carrier through nonlinear optical m odulation in an M Z m odulator. 230 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4.3 Nonlinear optical modulation using microdisk modulator In chapter 2 (2.6.1) we introduced the electro-optic transfer function ./no that governs the behavior of the modulator. We showed that at a given RF voltage depending on the laser input wavelength, / eo can be a linear or nonlinear function of input voltage. This section explores the nonlinear operation regime for RF down-conversion applications. Fig. 4.19 shows how the location of the laser wavelength relative to the resonant wavelength can change the linearity o f the optical modulation in a microdisk modulator. O ptical output pow er O ptical output intensity — ^ L ^- W avelength ( a ) -H 1 ----- 0 0.5 1 1.5 2 G H z Frequency O ptical output pow er l- W avelength - + ■ ( b ) — i----------- 1- 0.5 I 1.5 2 G H z F requency F ig u re 4 .1 9 Sim ulated optical output pow er spectrum o f m icrodisk m odulator at linear (a) and nonlinear (b ) operation regim e. T he RF input pow er is a 1 G H z RF carrier m odulated by a 100 M H z (sin g le freq uency) baseband signal 231 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Two cases were simulated: (a) the laser wavelength is tuned to the middle o f the mode slope where P 0,mod F r f (b) the laser wavelength is tuned to a resonant wavelength where P 0,mod rf- ( F r f )2. The RF input voltage has a form similar to equation (4.7). The simulation clearly shows that when X ,]aser = Are s the spectrum of the optical output power is similar to what is shown in Fig. 4.14(a). To demonstrate nonlinear modulation with a microdisk electro-optic modulator, we have performed a single frequency modulation experiment. Fig. 4.17 shows the experimental results of switching between linear and nonlinear operation by changing the laser wavelength. > 6 .E -0 5 jjf 5 .E -0 5 o 4 .E -0 5 a 3 .E -0 5 O 2 .E -0 5 S l.E -0 5 > 2 .E -0 4 m 2 .E -0 4 | 1 .E -0 4 | 5 .E -0 5 B 0 .E + 0 0 F requ en cy (G H z) F requ en cy (G H z) D. O 0 .0 5 5 0 . 0 5 6 0 . 0 5 7 0 .0 5 8 0 . 0 5 9 W a v e l e n g t h ( 1 5 5 0 + .. u r n ) F ig u re 4 .2 0 N on lin ear m odulation w ith m icrodisk m odulator. T he m icrodisk is fed by a 0 dB m sin g le freq uency RF signal (fR F = 8.7 G H z = optical free spectral range o f the disk). W hen the laser w avelen gth is set to the m iddle o f the optical m ode slo p e the m odulation is linear and is o n ly observed at 8.7 G H z (right). If the laser w avelen gth is tuned to the W G resonant freq uency, m odulation b eco m es nonlinear and a second-h arm on ic o f the input RF frequency (1 7 .4 G H z) is generated w h ile the linear com p o n en t d ecreases (left). 232 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. W hen the laser wavelength is set to the middle o f the optical mode slope, the modulation is linear. But if we tune the laser wavelength to the WG resonant frequency, modulation becomes nonlinear and generates the second-harmonic of input RF frequency is generated. The calculations in section 4.4 show that for small signal RF down-conversion the critical parameter is N 2 or the second order derivative of the electro-optical transfer function (fE o). Basically N 2 is equivalent to the mode slope (S) for linear modulation. In chapter 2 we calculated f E o for a microdisk modulator using the optical transfer function and electro-optically modulated optical refractive index. We can use the same approach to calculate f E o while the microdisk is biased to its extreme nonlinear operating regime (Ajascr = Arcs). Fig. 4.21 shows the simulated transmitted optical output power (P0,ou t) o f a typical microdisk modulator as a function o f wavelength and input RF voltage amplitude. In our simulation the modulator parameters are chosen to be representative o f the experimental values with Q = 3 .5 x l0 6 (corresponding to a = 0.0075 cm '1 and K o = 0.095), h = 400 pm, and Gv = 6. The optical input power is 50 jaW and W |asc, - ~ 1550 nm. The DC-shift is set to the measured value o f A7.D C = 0.13 pm/V (corresponding to Peo = 0.5) for our optimized 14.55 GHz microdisk modulator. 233 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -3 -2 - 1 0 1 2 3 RF voltage (V) F ig u re 4 .2 1 C alculated optical output intensity o f an ideal m icrodisk m odulator as a fun ction o f RF input v o lta g e (G v = 6). T he dashed and the dotted lines are generated as the first (V ,) and seco n d (N 2) T aylor co efficie n ts in an ex p an sion o f the optical transfer function (so lid line). T he laser is biased to the extrem e nonlinear operating regim e /V iaser = kres- At small signal RF input powers, the simulated value of N 2 can be directly used in Equation (8 ) to calculate the down-converted baseband current as a function o f input RF voltage amplitude. To define what constitutes small signal it is useful to quantify the sensitivity of the modulator by a voltage amplitude F h m m that modulates half of the optical mode power ( P o d = P 0 ,m a x - P u W - F i m m is determined by the optical Q, h, rj3, and Gv. Typically the F h m m for our LiNbCF microdisk modulators is between 0.4 V and 0.6 V. N2 is directly proportional to F h m m and maximum (Po niax). Note that if the optical coupling process is lossless, Po n iax is equal to the optical input power (P o.in)- Fig. 4.21 shows that a F Hm m of 0.54 V and optical input power o f 50 pW result in N 2 = 0.032 mW /V2. We have calculated the down-converted optical 234 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. power (at M b) with two different methods. First by using the electro-optic transfer function (/eo) and measuring the amplitude o f (O b in the Fourier transform of P 0,o u t and then by substituting the estimated N 2 in equation (8) for different values o f Gv. The calculation shows that if F r f < 0 . 2 5 x F Hm m the microdisk modulator is effectively operating as a square law optical intensity modulator (N, ~ 0, / > 2) and the baseband modulated optical power is equal to m xNjV^l. Basically this means for input voltage amplitudes \ V q \ < 0.25 Fhmm the parabola defined by A A V r > 2 /2 perfectly matches with P 0,out = ./eo ( F r f ) . This approximation provides a powerful tool for calculating the baseband current as a function of the received RF power. Fig. 4.22(a) shows the calculated baseband modulated optical power against RF input power for a microdisk modulator with an electro-optic transfer function similar to the one shown in Fig. 4.21. If we use a PIN diode with a responsivity R in series with a transimpedance amplifier the baseband voltage can be written as: N V 2 Vh = RZr 0 mI cos(coh t) (4.17) where Zt is the transimpedance. Fig. 4.22(b) shows the down-converted voltage amplitude and power gain ( F /F 0 and Pmi/Pin) against received RF power for a microdisk photonic RF receiver with the following parameters: R = 0.9 (A/W), Z t = 700KX2, Q - 4 .8 x l0 6, V h m m ^0.4 Volt. 235 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -25 /ir» Pow er V o lta g e -70 -50 -40 -30 -20 RF input pow er (dBm) -10 -30 -20 RF input power (dBm) -10 0 (a) ( b ) F ig u re 4 .2 2 (a) C alculated baseband m odulated optical pow er against RF input pow er for a m icrodisk m odulator w ith an electro-op tic transfer function sim ilar to Fig. 4 .2 1 . (b ) T he dow n - converted v o lta g e and pow er gain against receiv ed RF pow er for a m icrodisk optical RF receiver (R = 0.9 (A /W ), Z T = 7 0 0 K Q , Q = 4 .8 x 1 0 s, K H m m = 0 .4 V o lt) 4.4.4 Comparison We have shown both MZ modulator and microdisk modulator can be used for nonlinear optical modulation and RF mixing in optical domain. Fig. 4.23(a) and (b) shows the calculated optical output power against the applied RF voltage for a MZ and a microdisk modulator respectively (solid lines). The dashed curves are the parabolas defined by (AyA?) V2. At small signal regime (defined by the dotted boxes) where VR F < 0.25 Fhmm (< 0.25 VK for MZ modulator) the parabolas perfectly match the actual response, hence the strength o f the second-order nonlinear modulation can be estimated simply by calculating JV 2. So we can use the magnitude o f Ay to 236 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compare the performance o f MZ and microdisk modulator as nonlinear modulators at small signal regime. The received RF signal for wireless communications is bellow -3 0 dBm corresponding to a voltage amplitude o f less than 0.01 V. Knowing the typical value o f F h m m is between 0.2 V and 0.6 V and typical value o f VK is between 1 V and 5 V, our comparison is valid for all wireless applications. Fig. 4.23(c) shows the calculated value o f N 2 versus F h m m and assuming the MZ has an insertion loss o f 4 dB and microdisk modulator has an insertion loss o f 10 dB. One may see that the state-of-the-art LiNbOs MZ modulator with a Vn o f 1 V [14] has the same nonlinear modulation efficiency as a LiNb0 3 microdisk modulator with a Fhmm of about 0.4 V that can be easily made using a 200 pm LiNb0 3 thick microdisk. More importantly the insertion loss o f the microdisk modulator can be improved without affecting its sensitivity while in a MZ modulator generally enhanced sensitivity is accompanied by extra loss. So the 4 dB insertion loss for a MZ modulator with a VK o f 1 V is a very optimistic assumption while the 10 dB insertion loss and F H mm o f 0-5 V for a LiNbC>3 microdisk modulator is easily achievable by reducing the disk thickness to a 2 0 0 pm. 237 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. & a O 2 0 -0.5 0.5 RF voltage (V) ( a ) % o $ g . 0.8 0.6 J L o r t O G. ° 0.2 RF voltage (V) ( b ) 6.0E-03 M Z m odulator 5.0E-03 47) 4.0E-03 ^ 3.0E-03 ^ 2.0E-03 — M icrodisk m odulator 1.0E-03 0.0E+00 6 7 2 3 4 5 0 Vn ,10VHMM(V) ( c ) F ig u re 4 .2 3 (a) C alculated optical output p o w er against the RF v o ltage for a M Z m odulator w ith a V% o f 1V and insertion lo ss o f 4 d B . T he gray line is the approxim ated hyp erbola (N2/2)V2. T he dotted block s sh o w s the sm all signal region, (b) C alculated optical output pow er against RF v o lta g e. T he m icrodisk has a Fhmm o f 0 .5 5 V and insertion lo ss o f 10 dB . T he optical input pow er is 1 m W . (c) C alculated value o f N2 versus Fhmm and F„ assum ing the M Z has an insertion loss o f 4 dB and m icrodisk m odulator has an insertion lo ss o f 10 dB Although in most of our experiments the optical insertion loss was around 10 dB but insertion losses as low as 3 dB has been already demonstrated. Fig. 4.24 shows N 2 versus Fhmm for the LiNbCh microdisk modulator in Fig 4.23(b) and for three different values o f insertion losses. 238 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8.E-02 7.E -02 6.E-02 “ Inssloss = -1 0 dB Insloss = -7dB Insloss = -3dB 5.E-02 ^ 4.E -02 ^ 3.E -02 2.E -02 l.E -02 0 . E + 0 0 -------------------- ■ ■ ■ ■ .i... ..................................... - 0.1 0.2 0.3 0.4 0.5 0.6 F HMM ( V ) F ig u re 4 .2 4 T he sim ulated m agnitude o f N2 as a function o f FH M M for different va lu es o f insertion loss. T he optical input pow er is 1 m W . Currently a commercial 10 GHz MZ modulator has a Hr o f 4.5 V and an optical insertion loss o f about 4 dB [13] resulting in a N 2 of 9x10' 5 W /V2 at 1 mW optical input power. Our 14.6 GHz LiNb0 3 microdisk modulator has a F h m m of 0.6 Y and insertion loss o f 10 dB. Resulting in a JV 2 of 7x10‘4 W/V2 (at 1 mW optical input power) that is 8 times larger. 4.5 Microdisk photonic self-homodyne RF receiver 4.5.1 Modeling The calculation for the single tone baseband signal can be extended to more general baseband signals such as video and data. For an arbitrary baseband signal the received RF voltage may be written as: Vrf = j / o (1 + mIB{tj)cos(G)R Ft) (4.18) 239 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Bit) is an arbitrary baseband signal. The optical output power fed to the detector can be calculated using equation (4.7) in the electro-optic transfer function ( / h o ) . Given the frequency dependent photodetector responsivity (R(co)) the photocurrent can be calculated as follows: Po,ou,(co) = <F{P0,0U t(t)} = < E ^ E o iV n fim (4-19) ip(t) = < F "' {R((o)xPo out (co)} (4.20) We have simulated the signal flow in the photonic RF receiver to show details o f the down-conversion process in both the frequency and time domain. Fig. 4.25(a) shows the modulated transfer function when the laser emission wavelength (X|ascl) is centered at one o f the microdisk optical resonant wavelengths and the modulator is fed by the data modulated RF carrier. AXRF is the maximum shift in resonant wavelength due to the applied RF voltage (this shift is exaggerated to show the down-conversion mechanism). In the simulation, the RF carrier frequency/«/.- = 1 0 GHz is modulated by a 62.5 Mb/s non-retum-to-zero (NRZ) data stream with a modulation index o f m = 0.8. Fig 4.25(b) shows the RF spectrum of the transmitted- carrier input signal and the inset shows the original data stream in a 640 ns time interval. Fig 4.35(c) shows the calculated spectrum of the optical output intensity. Nonlinear modulation generates the baseband signal and high-frequency components around 20 GHz. 240 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. O ptical output pow er, a.u. J o,max G laser W avelength , X ■ I I I . , , 0 180 (a ) T im e, t (n s) Input data Detected baseband optical pow er a.u. > 10' 640 Tim e, t (ns) 0 Tim e, / (ns) 640 x IO 0.95 1.05 0.9 0.5 2.5 Frequency (GHz) Frequency (GHz) x IO ( b ) ( c ) F ig u re 4 .2 5 Sim ulated signal flo w in a self-h o m o d y n e RF receiver, (a) M odulated optical transfer function w h en the laser em issio n w a velen gth (A,|aser) is centered at on e o f the m icrod isk optical resonant w avelen g th s and the m odulator is fed by the data m odulated RF carrier. T he RF carrier frequency is 10 G H z and is m odulated by a 6 2 .5 M b/s data stream w ith a m odulation index o f nij = 0.8. T he m odulation am plitude is exaggerated to sh ow the d o w n -con version m ech anism , (b) Spectrum o f the transm itted-carrier RF input signal. T he inset sh ow s the original data stream in a short tim e interval (6 4 0 ns). (c) C alculated spectrum o f the optical output intensity. N o n lin ea r m odu lation generates the baseband signal and high -frequency com ponents around 2 0 G H z. T he p h o t o d e t e c t o r b a n d w i d t h o f 0.1 G H z ( d a s h e d l in e ) fdters o u t t h e high -frequency c o m p o n e n t s a n d on ly the baseband is converted to an electric signal. T he inset sh o w s the detected data stream again in a 6 4 0 ns tim e interval 241 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The photodetector bandwidth o f 150 MHz (dashed line) filters out the high- frequency components and only the baseband is converted to an electric signal. The inset shows the detected data stream once again in a 640 ns time interval. 4.5.2 Experimental results Single tone down-conversion: In our initial experiments we used a single tone baseband signal to study the effect o f RF modulation index (ni\) and RF power on down-conversion efficiency and its linearity. Fig. 4.26(a) and (b) are photographs o f the 14.6 GHz microdisk modulator. Fig. 4.26(c) is a schematic diagram o f the experimental arrangement. The modulator uses a 400 pm thick LiNb0 3 microdisk o f 3 mm diameter and a free spectral range o f A v f s r = 14.6 GHz. The laser source is a tunable single mode laser with 0.05 pm wavelength resolution and a linewidth o f less than 0.5 MHz. The laser wavelength is always tuned to the minimum o f the chosen transmission dip to maximize the second-order nonlinear modulation strength (N2). The RF signal is a 10 MHz single tone baseband signal mixed with a 14.6 GHz RF-carrier in a double-balanced RF- mixer. By DC-biasing the IF port o f the mixer we can control the modulation index (in/) and hence the magnitude o f the transmitted power at the carrier frequency. 242 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) ( b ) RF m ixer V ariable attenuator S ign al generator (L O ) A m plifier D C pow er supply Signal/pattern generator P hotodetector = 1550 nm B aseban d output T unable laser L iN b 0 3 m icrodisk m odulator (c) F ig u re 4 .2 6 (a) Photograph o f the L iN b 0 3 m icrod isk m odulator, (b ) A clo se-u p v iew o f the m odulator sh o w in g the m icrostripline, L iN b 0 3 m icrodisk , m icroprism , m icroring RF resonator and the output fiber, (c ) Schem atic diagram o f the experim ental arrangem ent used for ph oton ic RF d ow n -co n v ersio n m easurem ents. T he RF m odulation index (/W[) is tuned usin g the DC bias on the m ixer. T he l a s e r is a t u n a b l e s i n g l e m o d e l a s e r w i t h a r e s o l u t i o n o f 0.1 p m a n d l i n e w i d t h o f le s s than 0.5 M H z. T he RF filter elim inates any lo w frequency com p on en t generated due to nonlinearities in RF d ev ices. T he loca l oscillator frequency is 14.6 G H z that is equal to the optical free spectral range o f the m icrodisk m odulator. 243 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The RF signal is fed to the microdisk modulator through a bandpass RF filter with 1 GFIz bandwidth around 14.5 GHz, to make sure that all of the nonlinear products generated in the RF components are filtered out. The optical output is detected in an amplified photodetector with a bandwidth o f 150 MHz and responsivity o f 3 mV/pW . Fig. 4.27 shows the down-converted optical power against the total RF input power when m\ = 0.8. The black circles are the experimental data and the white circles and dashed line are the simulated data. The inset shows the optical resonance selected for nonlinear modulation. £ o o. ^ 13 £ •a m 0 T 3 jy v, i £ ° ° u ta 1 o Q -37 -39 -41 -43 -45 -47 -49 -51 -53 O Sim ulation • M easurem ent O' -20 9 a ' ,0 j a 50 40 o s 30 -0.4 -0.2 0 0.2 0.4{ W a v e le n g th d e tu n in g (p m ) • -16 -14 -12 -10 Total RF power (dBm) -6 F ig u re 4 .2 7 T he m easured and calculated baseband m odulated optical pow er versus total RF input pow er. T he inset sh o w s the optical spectrum o f the W G resonance ch osen for d o w n -co n v ersio n (Q = 2 .7 x 106, Ni = 2 .2 3 x 1 O'2 m W /V 2). The arrow indicates the location of the laser wavelength, k|aser- The optical resonance has a Q o f 2.7x106 and a JV 2 coefficient o f 0.023 mW /V2 (Fhmm = 0.7 V). 244 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The simulated data in Fig. 4.28 are calculated using m\ N 2 Vo /2 and knowing that the total average RF power of a single tone modulated RF carrier (Equation 3) is given 2 ^ by P R F = Vq (1 + m\ '/ 2 )/l 0 0 (this can be easily calculated by integrating the average power o f the RF signal). Fig. 4.28(a) shows the variation o f the down-converted optical power at 10 MHz as a function o f the modulation m and for three resonances with different quality factors. The modulation index is tuned to the desired values by changing the DC bias applied to the mixer, h 1.2 ^ > < D > ' O 1 8 O h I S 0 - 8 -T -t * -G u ft 0 6 N O U’U | g 0.4 H ^ 8 1 0.2 a z * ♦ g = 4 x 10° c 3 . 5 4 X I 0 6 C = 3 .1 5 x 10° 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Modulation index (m t ) 03 50 40 (a) o £ 30 o o "55 2 h 8 u 20 S. ffl & T3 tZ 3 10 □ A A Second-harmonic . □ Third-harmonic 'A - . . • ■ - □ ' - -A 0.40 0.60 0.80 1.00 1.20 RF modulation index (m ,) (b) 1.40 F ig u re 4 .2 8 (a) M easured baseband m odulated (1 0 M H z) optical output pow er against m for three optical m od es w ith different optical quality factors, (b) M easured secon d and third H arm onic su pp ression ratios (electrica l) against m. 245 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The total received RF power is about -15 dBm that corresponds to F 0 = 0.05 V (3). Since for the optical resonance used F h m m is around 0.8 V, so F 0 < 0.1 F h m m guarantees device operation in the small-signal regime (section III). As may be seen in Fig. 4.28(a), down-conversion efficiency is maximized around m/ - 0.8, in very good agreement with the simulated curve for an ideal square law mixer. Also, as anticipated, the amount o f down-converted power increases as we increase the optical Q (a larger Q results in a larger F h m m and therefore a larger A h ) . To evaluate the linearity o f the down-conversion process we have measured the detected power at the second and third harmonic o f the baseband signal (20 MHz and 30 MHz respectively). In a perfect square law modulator the third harmonic should be absent but the chosen optical resonance lacks an ideal symmetric shape and so generates odd harmonics. Fig. 4.28(b) shows the harmonic suppression ratio against m. As predicted (Fig. 4.11(b)) the suppression ratio decreases as m\ increases. At m\ = 0.8 the second- harmonic suppression ratio is about 17 dB (electrical). Down-conversion of digital data To demonstrate data transmission we use the arrangement in Fig. 4.26(c) but replace the signal generator with a NRZ pattern generator and the photodetector with a digital photoreceiver. The photoreceiver has a -3 dB frequency bandwidth o f 120 MHz and a sensitivity of -34.5 dBm. Fig. 4.29(a) shows the measured frequency spectrum o f the input RF signal and the down-converted signal after detection. The 246 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carrier frequency is 14.62 GHz and the baseband data is a 10 Mb/s NRZ 27-l pseudo-random bit stream (PRBS). Fig. 4.29(b) shows the measured bit error ratio (BER) against the total RF input power. Input RF signal D ow n -con verted data P -10 5 -4 0 n. -5 0 14 .5 8 14.6 14 .6 2 1 4 .6 4 F req u en cy (G H z) 1 4 .6 6 0 10 2 0 3 0 4 0 50 F req u en cy (M H z) (a) l.E-01 1 .E-02 l.E-03 l.E-04 pi l.E-05 l.E-06 l.E-07 l.E-08 l.E-09 l.E-10 D ow n-converted data 25 20 15 10 5 0 •0.6 -0.4 -0.2 0 0.2 0.4 0.6 Input data ▲ m um - W avelength detuning (pm ) -22 -21 -20 -19 -18 -17 -16 -15 -14 Received RF power (dBm) (b) F ig u r e 4 .2 9 M easurem ent results o f photonic data d o w n -con version in L iN bO j m icrodisk m odulator, (a) T he frequency spectrum o f the input RF signal and dow n-con verted signal. T he RF carrier freq uency is 14.6 G H z and it is m odulated by a 10 M b/s 2 7- l N R Z P R B S bit stream , (b) T he B E R sen sitiv ity o f the ph otonic RF receiver. T he RF pow er is the m easured RF pow er w ithin 10 M H z bandw idth centered around 14.6 G H z. T he right inset sh ow s the input and detected data in tim e dom ain. T he left inset sh ow s the optical spectrum o f the selected W G resonance. 247 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The received RF power is defined as the measured RF power within 10 M Hz bandwidth centered around 14.6 GHz. The left inset shows the spectrum o f the optical resonance with Q = 2 x l0 6. The inset on the right shows the input and down- converted data in the time domain. In Fig. 4.30 the measured eye diagrams at 10 Mb/s, 50 Mb/s and 100 Mb/s are shown. The received RF power is -15 dBm. The maximum data rate is limited by the optical Q to approximately 100 Mb/s. We note that the down-conversion efficiency can be increased by reducing the disk thickness (h) and employing a high- Q RF ring resonator (both these factors lead to a larger W coefficient). 10 M b/s 50 M b/s 100 M b/s D o w n -con verted [ eye | ■ O riginal ey e | T im e, t (2 5 ns/d iv) T im e, 1 (1 0 n s/d iv) T im e, t (5 n s/d iv) F ig u re 4 .3 0 M easured eye diagram s at 10 M b/s, 50 M b /s and 100 M b/s (receiv ed RF pow er = -15 dB m ). 4.5.3 Noise in microdisk photonic self-homodyne RF receiver A precise analysis of the noise performance of the photonic self-homodyne RF receiver is a very difficult task due to the variety of noise sources in the system. Here we just want to identify these noise sources and derive a simple analytic 248 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. expression for the overall signal to noise ratio o f the receiver as function o f the device parameters. Fig. 4.31 is a schematic diagram o f the signal and noise flow in the receiver. \ | / a , (Sr, N.) antenna C ou pling p o i n t ^ ^ ^ ^ RF ring resonator o (Sa, N a) (VS,VN) ^ ^ ( VRs , VKN) L iN bO j m icrodisk (S.i.NJ) Photoreeeiver 1 DFB Laser (Po.s , P o.n) (Po.in ' P o.W n) F ig u re 4.31 S chem atic diagram sh o w in g the signal and n o ise flo w in the ph otonic self-h o m o d y n e receiver For simplicity we assume that the baseband signal is a single tone with the frequency oib. The received signal (.S 'a) and noise (7 V a) power from the antenna are fed to an open terminated microstripline. The microstripline attenuates the signal and adds some thermal noise. The voltage amplitude o f the signal and noise at the coupling zone can be written as: (a) Vs = 2 j 2 Z 0Sa/L r (b) VN = 2 p Z 0[Na / Lr + k J B ( L r -l)\ (4.21) where Lj is the loss factor for the mictorstripline, kB is the Boltzman factor and B is the bandwidth defined by the optical modulation bandwidth, which is limited by optical Q (BW~viase,/Q). 249 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Since the fundamental resonance o f the RF ring resonator has a voltage gain Gv, the amplitude o f the voltage oscillation on the ring resonator is Frs = GvV,s while the amplitude o f the voltage noise induced on the ring resonator is not necessary Gv Fy because the noise isn’t coherent and can not build a resonant field on the resonator similar to a coherent signal. So we assume that the induced noise on the ring resonator is related to the noise on the microstripline with unknown coefficient G vn- The ring resonator also adds extra thermal noise to the signal due to its resistance and temperature. Since the temperature o f the ring resonator is a function o f RF input power, one may expect that the thermal noise power is proportional to V % so the total voltage noise across the microdisk is: v „ = G„V„ + j4 R rm sk„BT(V>) (4 .22) where Rring is the resistance o f the ring resonator and T( V / ) is the ring temperature as a function o f RF power at the coupling point. Now we need to calculate the optical output power modulated at baseband frequency co b and the output optical noise within the bandwidth between DC and co b that is approximately the same as B. The baseband modulated optical power can be easily N 7 7 calculated P0 s = m , V~h . using while the calculation of the output optical noise is much more difficult. The baseband optical output noise power consists o f three major components: (1) P 0 , r i n : Laser RIN, (2) P0jmx- The optical noise generated as a result o f electro-optical mixing of the resonator voltage noise around RF carrier frequency ( FrnJ and the RF signal frequency components, and (3) P 0,bb: The optical 250 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. noise generated by the resonator voltage noise ( F r n ) at frequencies smaller than cob (baseband frequencies). The first component can be easily calculated using equation 2 . 1 0 and replacing P0,0u t with P 0,s : P».*ni = ( 1 0 ^ 710 x A/ ) * > „ . , (4.23) The second component is more complex since it involves down-conversion and mixing. If we add a single frequency noise component to the RF signal, the RF voltage at the coupling point will have the following form: VR F =Ks(1 + m i cos(6)ht)]cos(a)m, t) + cos(aNt + < p N) (4.24) where co/v is an arbitrary frequency within a bandwidth B around c o r f - N o w knowing 'y Bo,out = N jV r f / 2 (equation 4.6), we can derive all the noisy baseband frequency terms by calculating ( F r f ) ■ If we just keep the first order noise terms it can be shown that only three mixed terms will have frequencies smaller than B: (a) VNVS cos(conFt - coNt-<pN) m V V , (b) " , s cos(coht + coR , t - mNt - < pN) (c) m iVNVs cos(cot t - com ,t + coNt + (pN) (4.25) So if the we have a uniform noise distribution within a bandwidth B round c o r f then the total optical intensity noise amplitude can be written as the summation o f the optical intensity modulation generated by each one o f these terms multiplied by the bandwidth: (4.26) 251 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The third optical noise component is the linear modulation generated by the second term in equation 4.22 and can be approximated using equation 2.8(b) but with Gv = 1 (since the voltage gain doesn’t amplifies the thermal noise): P,,tl = 2 /S A Z x P,,m (Q /Z r j j 4 R „ J , B T ( V , 2) (4.27) Now we can use the detector responsivity to calculate the signal and noise currents: (a) h)S ~ RP n,S (b) i()N ~ P ( P n , lilN + P n .m ix + P o ,hh ) (4.28) Equation 4.28(b) is the photocurrent generated by the optical noise power but the photodetector also adds the shot noise and dark current noise to the total photocurrent. The total noise current generated in photodetector is given by equation P N = 2 eB(ip + id)+ A k J B F - R,. here ip = R(P0.s +P( 2 > 0,m ax) where P (2 )0;m ax can be derived using equation 4.11. So the final signal-to-noise-ratio may be written as: S d _ PS _ RPo.S 2 i ~2 T2 , D / D , D , D \ (4.29) N d *N + i()N *N + R(P<>, KIN + Pn.ma + P o ,hh ) The equivalent BER may be calculated using equation 3.5. 4.6 Summary Four possible approaches for all-optical down-conversion from a RF signal have been presented: nonlinear photodetection, optical filtering prior to detection, 252 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. combination o f optical filtering and optical heterodyning, and nonlinear optical modulation. Preliminary simulations and experimental results shows that by improving the sensitivity o f the microdisk modulator each one o f these approaches has the potential to take over the task o f direct optical down-conversion and eliminate the local oscillator and RF-mixer in conventional electronic wireless receivers for short- distance communication. The limitation on distance is due to a transmitted carrier modulation format that is required for self-homodyne down-conversion. The main challenge here is to choose the best approach and to improve it to a level that can compete with electronic receivers by providing lower power consumption in a smaller volume. Our photonic self-homodyne architecture combines direct-conversion, self- heterodyning, and microdisk modulator technology to directly extract baseband information from the received signal by the self-mixing o f the transmitted carrier and the sidebands in the optical domain. We have shown that the second-order nonlinearity in the transfer function o f a LiNb0 3 microdisk optical modulator when biased at its minimum transmission point may be used to realize the self-mixing process. Since the optical output power is baseband modulated, the optical-to- electrical conversion is performed in a photoreceiver with a bandwidth limited to that o f the baseband. Receiver operation is demonstrated experimentally by demodulating digital data from a 14.6 GHz RF carrier frequency. The microdisk modulator and the photonic 253 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. self-homodyne architecture have the potential to be incorporated into a photonic integrated circuit by using alternative electro-optic materials (such as polymers and compound semiconductors). Reducing the disk diameter will extend the carrier frequency into the mm-wave regime so that this receiver architecture has the potential to be used in future indoor mm-wave wireless systems. 254 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.7 References [1] J. Marti, V. Polo, F. Ramos, and J. M. Fuster, “Single Mach-Zehnder modulator electro-optical harmonic mixer for broadband microwave/millimeter-wave applications,” Wireless personal communications, vol. 15, no. 1, Oct. 2000. [2] G. K. Gopalakrishnan, W. K. Bums, and Catherine H. Buhner, “Microwave- optical mixing in LiNbOs modulators,” IEEE Trans. Microwave Theory and Tech., vol. 41, pp. 2383-2391, Dec 1993. [3] A. Narasimba, and E. Yablonovitch, “Code-selective frequency shifting by RF photonic mixing in a dual-electrode Mach-Zehnder modulator,” Electron. Lett., vol. 39, pp. 619-620, April 2003. [4] J. K. Piotrowski, B. A. Galwas, S. A. Malyshev, and V. F. Andrievski, “Investigation o f InGaAs P-I-N photodiode for optical-microwave mixing process,” Micriowave and radar, 1998. M IKON’98, 12th international conference, pp. 171-175 [5] M. Tsuchiya, T. Hoshida, “Nonlinear photodetection scheme and its system applications to fiber-optic millimeter-wave wireless down-links,” IEEE Trans. On Microwave theory and techniques, vol. 47, pp. 1342, 1999. [6 ] T. Hoshida, Tsuchiya, “Broad-band millimeter-wave up-conversion by nonlinear photodetection using a waveguide p-i-n photodiode,” IEEE Photon. Technol. Lett., vol 10, pp.860, 1998. [7] K.J. Williams, R.D.Esman, and M. Degenais, “Nonlinearities in p-i-n microwave photodetectors,” /. Lightwave Technol., vol 14, p.84, 1996. [8 ] R.R.Hayes and D.L.Persechini, “Nonlinearity o f p-i-n photodetectors,” IEEE Photon. Technol. Lett., vol. 5, pp. 70, 1993. [9] M. Dentan and B. de Cremous, “Numerical simulation o f the nonlinear response o f a p-i-n photodiode under high illumination,” J. Lightwave Technol. vol. 8 , pp.1137, 1990. [10] K.J.W illiams, R. D. Esman and M. Dagenais, “Effects o f high space-charge fields on the response o f the microwave photodetectors,” IEEE Photon. Technol. Lett., vol. 6 , pp.639, 1994. 255 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [11] A. A. Abidi, “Direct-conversion radio transceivers for digital communications,” IEEE J. Solid-State Circuits, vol. 30, pp 1399-1410, Dec 1995. [12] Y. Shoji, K. Hamaguchi, H. Ogawa, “Millimeter-wave remote self-heterodyne system for extremely stable and low cost broad-band signal transmission”, IEEE Trans. Microwave. Theory and Tech, vol. 50, ppl458-1468, June 2002. [13] www.fcsi.fuiitsu.com/products/LW CharacteristicsTables/linb03.htm [14] M. Sugiyama, M. Doi, S. Taniguchi, T. Nakazawa, and H. Onaka, “Low-drive voltage LiNbCL 40-Gb/s modulator”, IEEE Leos news letter, vol. 17, no. 1, pp. 12-13, Feb 2003. 256 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5 Conclusion and future work 5.1 Introduction In the previous chapter the key aspects o f a self-homodyne photonic RF receiver based on LiNb0 3 microdisk modulator technology was described. The proof-of- principle experiments and analytical studies show the feasibility o f employing this type o f receiver in indoor wireless links or short distance fiber-feed backbone networks. In this final chapter we explore future research challenges toward building a practical photonic RF wireless link. We start with the receiver side and show that by adding extra features to our design and employing alternative electro-optic materials, a fully integrated RF-photonic receiver with adequate sensitivity is possible. Next we review the state-of-the-art in RF/mm-wave generation using optical heterodyning. We discuss the possibility o f building a photonic RF-mm wave transmitter that, when combined with our receiver design, can result in an all-optical wireless link. In principle the carrier frequency o f this link can be extended to the mm-wave domain without any major complication because the signal processing is performed at optical frequencies. 257 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2 Self-homodyne photonic RF receiver In Chapter 4 we proposed two different techniques for direct down-conversion o f the baseband information from a transmitted carrier RF signal in the optical domain: 1) Modifying the spectrum o f the modulated optical carrier prior to detection. 2) Nonlinear optical modulation. We refer to these techniques as DOF (down-conversion through optical filtering) and DNOM (down-conversion through nonlinear optical modulation) respectively. A self-homodyne photonic RF receiver can employ either one o f these techniques to eliminate the high-speed electronic circuitry from the receiver side. The efficiency o f both techniques depends on the sensitivity o f the optical modulator and the photoreceiver. Although both a traveling wave MZ modulator and a resonant microdisk modulator can be used for linear or nonlinear optical modulation in the photonic receiver, we showed that in both situations LiNbCb microdisk outperforms the MZ modulators. The DOF technique requires a very sensitive linear optical modulator and a band- stop optical filter while the DNOM technique only requires a very sensitive second- order nonlinear optical modulator. On the other hand the DNOM technique is more sensitive to wavelength fluctuations as well as thermal and mechanical perturbations. This may be explained by observing the behavior o f the first and second derivatives o f the electro-optic transfer function o f the microdisk. As may be seen in Fig. 4.21, N2 is more sensitive to the bias point than N\. For the modulator simulated in Fig. 258 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.21 N 2 is 5 times more sensitive to the difference between the resonant wavelength and the laser wavelength compared to N\. Since the down-conversion efficiency of DOF and DNOM techniques directly depends on N\ and N 2 respectively, therefore DOF is more stable. Another difference between the two techniques is the amount o f DC optical power received by the photoreceiver that affects the detector shot noise. In DOF the laser wavelength is biased to the middle o f the optical resonance so given the small magnitude o f the received RF power a relatively large amount o f optical output power is not modulated. This DC optical power cannot be filtered out without affecting the baseband modulated optical power. Assuming the total modulated optical power is 0.01/Jo,m ax and the laser wavelength is biased at 0 .2 5 /J().max, the DC optical power is 25 times larger than the total modulated optical power. In DNOM technique part o f the down-converted optical power is DC and since the photodetector speed is limited by the baseband, the up-converted optical power (around 2coR F ) is also seen as DC optical power by the photodetector. If the optical resonance is critically coupled, these are the only DC components in the optical power spectrum. As shown in the previous chapter at m\ = 0.8, 25% o f the nonlinearly modulated optical power is baseband modulated so the DC optical power received by the detector is about 75% o f the total modulated optical power. In conclusion the shot noise in DNOM case is about 25 times smaller than in the DOF case. As explained in Section 4.5.3 a detailed analysis o f the noise performance of the photonic receiver is quite complicated therefore depending on what mechanism 259 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dominates the signal-to-noise ratio o f DNOM technique may or may not be larger than that o f DOF. In the next section we address the potential modifications that can solve some o f the problems associated with these techniques and improve the over all sensitivity o f the receiver. 5.3 Microdisk photonic receiver: potential improvements Regardless o f the chosen photonic down-conversion technique the performance of the photonic self-homodyne RF receiver is determined by three major factors (1) Power and wavelength stability o f the laser. (2) Sensitivity and stability o f the microdisk modulator. (3) Responsivity and noise performance o f the photoreceiver. The laser performance is independent o f the other components and directly affects the signal-to-noise ratio o f the down-converted signal. It is trivial that the laser source in a photonic receiver should have very low RIN, narrow linewidth and very stable wavelength. Although for a given sensitivity, improvement o f the modulator and receiver reduces some o f the constraints on laser performance, here our goal is to reach the best sensitivity using a commercial high-quality laser. For this reason we will only address the possible improvements in the second and third issues mentioned above. 260 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.3.1 Microdisk modulator As shown in Chapter 2 the sensitivity o f the microdisk modulator is mainly determined by the optical quality factor and the intensity o f the modulating /Afield. The unloaded optical-g is limited by the surface quality o f the LiNbO,} microdisk and the presence o f the external particles on the sidewall. So a high quality polishing and a clean surface can improve the optical-^. Recently advanced polishing techniques have been developed that can result in optical-Qs as high as 1010 [1]. But we should keep in mind that the required bandwidth puts a fundamental limitation on the Q (Fig. 1.10). So ideally we want to reach the bandwidth-limited regime, where the required bandwidth limits the Q, as opposed to surface-quality limited case. Optical coupling is also an important issue that affects the loaded optical-Q o f the resonator as well as the unidirectional nature o f the WG resonance. An ideal optical coupling mechanism should be lossless and have a negligible perturbing effect on the optical resonance. The intensity o f the modulating A-field inside the microdisk is proportional to the voltage gain factor (Gv) o f the ring resonator and increases as the microdisk thickness (h) decreases. The voltage gain factor can be improved by employing high quality RF-ring resonators but it will be limited by the RF loss in the ring and LiNbO;, as well as the radiation losses. The simulation and experimental results show that by optimizing the surface quality o f the ring resonator loaded R F-0s o f larger than 100 are 261 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. achievable. The thinnest LiNb0 3 microdisk modulator reported so far has a thickness o f 150 pm [2] but given the WG mode size and the possibility of fabricating toroidal LiNb0 3 microresonators, a thickness of 50 pm seems feasible. Reducing the microdisk thickness from 400 pm (the standard microdisk thickness used in most o f our experiments) to 50 pm can increase the E-field intensity by a factor o f 8 . As we mentioned in Chapter 4, the sensitivity o f the microdisk modulator is adequately expressed in terms of F Hm m - Fig- 5.1 shows the simulated value o f F h m m as a function o f Gv, Q and h using the microdisk electro-optic transfer function (fE0). 2 Q = 3 x 1 0 h = 400p.m 1.5 1 0.5 0 2 3 4 5 6 7 8 9 10 2 1.5 1 ^ 0.5 0 h = 400(.im G v = 6 (a) 1.2 1 S5 0.8 S 0.6 J 0.4 ^ 0.2 0 l.E+06 3.E+06 5.E+06 7.E+06 0 ( b ) O = 3 x l 0 6 G v = 6 100 200 300 400 500 600 700 Microdisk thickness (pm) ( c ) F ig u r e 5.1 Sim ulated valu e o f F H M m as a function o f (a) G v , (b) Q and (c ) h usin g the electro -o p tic transfer fun ction ). 262 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stability is one o f the most important issues o f the microdisk modulator that requires special attention. The linear or nonlinear modulation efficiency o f the microdisk is very sensitive to the location o f the laser wavelength relative to the resonant wavelength o f the WG mode. The high quality factor of the W G modes makes the modulator extremely susceptible to thermal and mechanical fluctuations as well as the laser wavelength shift. In Chapter 2 we explained how applying a DC voltage on the ring resonator might be used to control the W G resonant wavelength through a feedback loop. The proof-of-concept experiment with a very basic feedback circuit shows that one can lock the laser wavelength to a specific location o f the WG slope. This was achieved by comparing the photodetector output with a reference voltage and changing the DC bias voltage accordingly. A feedback loop that can guarantee steady sate operation over a long period o f time requires a more sophisticated circuit design. As shown in Fig. 5.2 depending on desired operation regime o f the microdisk modulator, the laser wavelength can be locked to different offset wavelengths relative to A ,res. In the case o f nonlinear modulation, where the laser wavelength should be locked to kres (zero offset), the feed back loop should be able to determine the sign o f the slope because deviation from Xies to both directions generates the same amount o f variation in optical output power. This will increase the complexity o f the control circuit compared to what is shown in Fig. 2.55. 263 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o,mm (A * re s) Nonlinear operation ^ p 0 out Linear operation 2 h res h o ►Wavelength (k) F ig u re 5 .2 R elative alignm ent o f the laser w a velen gth and W G resonant w avelen gth for linear and nonlinear m odulation. We can summarize the future challenges toward a more sensitive and stable microdisk modulator as follows: 1) Improved optical coupling. 2) Fabrication of very thin microdisks with high quality sidewalls. 3) High quality microring resonators. 4) Feed back circuit for wavelength locking. 5.3.2 Photoreceiver The final step in the photonic self-homodyne RF receiver is the detection of baseband modulated optical power with a slow-speed photoreceiver. The sensitivity and noise performance of the photoreceiver directly contributes to the overall sensitivity of the receiver. The minimum detectable optical power for a 264 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. photoreceiver is limited by the photodiode responsivity and the transimpedance of the amplifier. State-of-the-art photodetectors can detect optical signals as small as -50 dBm (3). As we mentioned in Chapter 3 the shot noise in the photodetector is equal to 2eB{Iv+I&). / p is the total amount o f the total photocurrent (generated by the baseband modulated optical power and the DC optical power). We can write the mean square value o f the noise photocurrents as: if? = 2cB[IP+ R( P 0 M C + Po.dc)] (5.1) where P 0 ,dc and P 0 ,ac are the received DC and AC optical powers respectively. As mentioned before, if we use DNM down-conversion technique, due to low speed response o f the photodetector the high-frequency components in the frequency spectrum o f the optical output power (around 2 /rf) do not contribute in the AC photocurrent. But these components can still generate shot noise. Therefore P 0 ,dc is the sum o f /J0,m in, the DC optical power and the modulated optical power at frequencies around 2 /rf (both generated through nonlinear modulation). For a critically coupled WG mode P 0,m m is zero but the DC and high-frequency components generated through mixing are always present. Although the DC component cannot be eliminated, a band pass optical filter with a bandwidth less than 4 /rf can eliminate the high frequency optical components around 194 THz ± 2 /rf and cancel modulated optical power at 2/R F . Fig. 5.3 demonstrates the frequency domain signal flow in the presence o f the optical filter. 265 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 194 T H z 2/w 2fu; 194 T H z — /A M icrodisk m odulator. Data O ptical filter P hotodetector F ig u re 5 .3 Schem atic diagram o f freq uency signal flo w in the photonic RF receiver in the presence o f the optical filter. In conclusion, if DNOM technique is used, employing a high sensitivity photoreceiver and post modulation optical filtering can increase the sensitivity o f the photonic self-homodyne RF receiver. In DOF technique there is no high-frequency component in the optical intensity spectrum and filtering cann’t remove the large DC component so the only possible modification is to enhance the performance o f the photoreceiver. 5.3.3 Integration and final design Fig. 5.4 shows the block diagrams of the microdisk photonic self-homodyne RF receiver based on DNOM technique (a) and DOF technique (b). Flere we summarize the desired specifications o f each stage: Laser: The laser should be a DFB laser with a very narrow linewidth and low RIM. Although a larger laser power results in a more efficient down-conversion but due to 266 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the small mode volume of WG resonances a high power density can cause thermal and nonlinear instabilities. Laser RF signal from antenna Laser RF signal from antenna A A i B andpass i ■ ■ . optical filter r - -R- - - ■ * » - ph olodetector . E lectro-op tic m icrodisk (nonlinear nodulation) C ontrol circuit ( a ) B andstop optical filter H igh-speed ph otodetcclor E lectro-op tic m icrodisk " (linear m odu lation ) ■ " Control circuit D SP Data D SP Data ( b ) F ig u re 5 .4 S chem atic diagram o f tw o m icrodisk photonic self-h o m o d y n e RF receiver architectures: (a) D N O M , w here the m icrodisk is biased at nonlinear m odulation regim e and (b) D O F w here the m icrodisk is biased at linear operating regim e. The power threshold at which the modulator becomes unstable depends on the absorption and nonlinear characteristics o f the electro-optic material used to fabricate the microdisk. Optical waveguides'. Low loss optical waveguides with the potential for integration with other photonic components is desired. Optical filte r: If we use DNOM technique, a bandpass optical filter with a bandwidth of less than 4 /rf helps the shot noise reduction (Fig. 5.5(a)). For DOF technique a band-stop filter with a bandwidth larger than /rf is a requirement for photonic down- 267 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. conversion (Fig. 5.5(b)). In both cases the filter role-off is determined by the RF carrier frequency ( / r f ) and the bandwidth o f the baseband signal. T ransm ission T ransm ission a b F ig u re 5 .5 (a) Band pass filter in a D N O M p h otonic RF receiver decrea ses the sh ot n o ise by elim inating the high frequency com ponents, (b) B and stop filter in a D O F ph otonic RF receiver elim inates the optical carrier and on e o f the R F -optical sidebands. Recently multipole ring resonator based filter have been demonstrated with a very low loss and narrow passbands [3]. The role off of these filters can be increased by increasing the number of ring resonators (poles). Fig. 5.6(a) shows a photograph o f a three-pole ring resonator filter and Fig. 5.6(b) shows the spectral response o f multipole filters up to 6 poles [3]. a- •10 I D rop port Input - 120 urn ( a ) ( b ) Thru port F ig u re 5 .6 (a) Spectral response o f op tical filters w ith different num ber o f ring resonator, (b ) T he m ulti ring resonator bandpass optical filter fabricated on hydex m aterial system [3] 268 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The microring based filter can be used in both DNOM and DOF photonic receiver architecture because its thru port is a banstop filter and its drop port is a bandpass filter. Since these filters are fabricated on a new optical material called hydex the main challenge is the integration o f the filter with other photonic and electronics components in the receiver. Integration Due to versatility o f the material and techniques used for fabricating different components in a photonic RF receiver, currently the most feasible approach for building an integrated system is hybrid integration on a silicon bench. Various silicon micromachining techniques that are originally developed for IC industry and MEMS devices can be employed to build features such as V-grooves and steps for mounting the photonic components. Fig. 5.7(a) shows schematic diagram an integrated LiNbCb microdisk photonic receiver based on hybrid integration technique. The LiNbCb microdisk, laser and the detector are mounted on pedestals with the proper height. The miniature ball lenses are aligned in a V-groove while the microprism is etched off the silicon substrate. Since silicon has a refractive index larger than LiNbCfi (3.5 > 2.14) it can be used for evanescent optical coupling to the microdisk. Potentially the electronic circuitry including the signal processing and the control circuit can be fabricated directly on the silicon substrate. Hybrid integration o f optical and electronic elements on silicon bench is the subject of current research [20], 269 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M icro len ses L iN b 0 3 m icrodisk RF signal S ilico n m icroprism S en sitive lo w -sp eed ph otod iod e Signal p rocessin g Data C ontrol circuit V -g ro o v e O ptical w a v eg u id e M icrostripline ( a ) Laser O ptical w av eg u id e M ulti-ring filter RF signal o S en sitiv e low -sp eed p h otodiode Data M icrostripline Se'm iconductor/polym er m icrodisk ( b ) F ig u re 5 .7 (a) Hybrid integration o f a L iN b 0 3 m icrodisk p h otonic RF receiver on a silico n bench, (b) M on olith ic integration o f a sem icon ductor m icrodisk photonic RF receiver based on com p ou n d sem icon d u ctor m aterial system . In the future a monolithic fabrication process may be developed to build a fully integrated photonic receiver. For example lasers, detectors, waveguides, microring filters and also microdisk modulator have been already made based on compound semiconductor technology so in principle one may design a process sequence that allow s m onolithic integration o f all these elem ents on the sam e substrate (Fig. 5.7(b)). 270 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sensitivity In order to clarify the benefits o f using photonic technology in wireless receiver design here we make a crude comparison between a photonic receiver and an electronic receiver. A state-of-the-art 60 GHz superhetrodyne electronic receiver with a sensitivity of 10 pW (-20 dBm), consumes about 400 mW power [20], This receiver is built based on 0.15 pm N-AlGaAs/InGaAs HJFET MMIC technology and has a volume o f 900 mm3. The receiver consists o f a low-noise amplifier (LNA), mixer and Local oscillator (LO). The local oscillator employs a dielectric resonator oscillator (DRO) that is co-integrated with a single-stage wide-band amplifier. Fig. 5.8 is the schematic diagram o f a 60 GHz photonic self-homodyne receiver indicating the specification o f each section and estimated power consumption. E le c tr o -o p tic m icrodisk ( V h m m 0 .0 5 dB /pm B E R o f 10 ' 1 a t - 4 0 d B m Baseband © - Total power » 130 mW Power < 100 mW (CMOS) Power w 6 mW Power « 56 mW Power < 5 0 mW (BiCMOS) F ig u re 5 .8 E stim ated pow er consu m ption using com m ercia lly availab le tech n o lo g y (gray b lo ck s), and co stu m e d esig n tech n o lo g y (dotted line). 271 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Using a low cost laser source (about 3% power efficiency) and digital photoreceiver (based on CMOS technology) the estimated power consumption for a sensitivity o f -30 dBm is about 130 mW. If we replace the laser with a more efficient laser (20%) and employ a low power photoreceiver based on BiCMOS technology the total power consumption is reduce to 56 mW. So photonic self-homodyne architecture can improve the receiver sensitivity by a factor o f 10 while reducing the power consumption by a factor o f 4 compared to an electronic receiver. Beside low power consumption and better sensitivity the photonic receiver will benefit from the reduced size and complexity as well as low cost fabrication due to the absence o f high-speed electronic components. The estimated value o f photonic receiver sensitivity (-30 dB) is based on the current LiNbCb microdisk modulator technology, commercially available photoreceivers and a moderate input optical power (1 mW). It is very useful to explore the sensitivity limit o f the receiver in the absence o f current limitations on device technology. In Chapter 4 it has been shown that the efficiency o f down-conversion in a photonic mixer is directly proportional to N 2. For a microdisk modulator N 2 is determined by the maximum optical output power (B o ,m a x ) and F h m m - Since B „ ,max = optical insertion loss x B0jn , Optical insertion loss, optical input power and Fhmm are the determining factors for the down-conversion efficiency o f the microdisk photonic mixer. So the overall sensitivity o f the self-homodyne microdisk receiver is a function o f all of the above-mentioned parameters plus the sensitivity of the digital photoreceiver. 272 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If the sensitivity o f the digital photoreceiver and the wireless RF receiver are defined based on the same bit error ratio (BER), we can estimate the overall sensitive o f the microdisk photonic self-homodyne receiver using the formalism developed in Chapter 4. In this case the total RF input power that results in a baseband modulated optical power equal to the sensitivity o f the digital photoreceiver is the minimum received power or sensitivity o f the wireless receiver. This definition is equivalent to equation 1.6 for the sensitivity o f photonic RF receiver discussed in section 1.5. Here we assume a single frequency baseband and an optimized RF modulation index o f m\ = 0.8. Fig. 5.9(a) shows the calculated receiver sensitivity against Fhmm flo r 3 different values o f optical insertion loss. The optical input power (P0,m ) is 1 mW and the sensitivity o f the photoreceiver is -40 dBm. Fig. 5.9(b) shows the calculated receiver sensitivity against optical input power {P0,m ) for two microdisk modulators with Fhmm o f 0.45 V and 0.1 V. Again the sensitivity of the digital photoreceiver is - 40 dBm. Fig.5.9(c) shows the calculated receiver sensitivity against sensitivity of the digital photoreceiver. The optical input power (P0,in) is 1 mW and Fhmm is 0.1 V. As may be seen a combination o f low insertion loss (< 3dB), sensitive digital photoreceiver (<-65 dB) and efficient photonic mixing ( F Hm m < 0.2 V) results in a dramatic improvement in wireless receiver sensitivity (< -70 dBm). With this sensitivity the microdisk photonic wireless receiver may be employed in high frequency carrier links such as LMDS(2). For example EtherAir (3 ) that is a transceiver for LMDS has a sensitivity o f -7 2 dBm at 26 GHz carrier frequency and -7 0 dBm at 38 GHz carrier frequency. 273 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. s C O ’ > a > > ’5 o i> C d A I n s .lo s s = -1 0 d B V h m m ( V ) O ) c < l> CD .> "S o C L ) P 4 -30 -35 -40 -45 -50 -55 -60 o V H M M = 0 . 4 5 V □ V H M M = 0 .1 V 0 2 4 6 8 10 12 C/5 s 0 ) C/5 • — u .> 'S 0 < 0 01 m -a -40 -50 -60 -70 -80 O p tic a l input p o w e r (m W ) ( b ) -75 -65 -55 -45 -35 Photodetector sensitivity (dBm) (c) Fig. 5 .9 (a) C alculated receiver sen sitiv ity against K H M m for 3 different va lu es o f optical insertion loss (-1 0 d B , -5 dB and -1 0 dB ). T he optical input pow er (P0 -in ) is 1 m W and the sen sitiv ity o f the ph otoreceiver is -4 0 dB m . (b) C alculated receiver sen sitiv ity against optical input pow er ( / 5 0j n ) for tw o m icrod isk m odulators w ith Fhmm o f 0 .4 5 V and 0.1 V . T he insertion loss is - 3 dB . A gain the sen sitiv ity o f the digital ph otoreceiver is -4 0 dB m . (c) C alculated receiver sen sitiv ity against sen sitiv ity o f the digital p h otoreceiver for an optical input pow er ( P 0 ,m ) o f 1 m W , insertion lo ss o f - 3 dB and F H m m o f 0.1 V. 274 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We should mention these estimations are all for a DNM based photonic receiver. If we use DOF technique for photonic down-conversion we may achieve very high sensitivity by means o f optical heterodyning (see section 4.3.3). In this approach heterodyne generation o f the RF carrier in the receiver enhances the signal-to-noise ratio and may also relax the restriction o f using transmitted carrier format. 5.4 Alternative electro-optic materials Although, based on its electro-optic and mechanical properties L iN b03 seems to be an excellent material for micro resonator fabrication, but it suffers from incompatibility with the standard integrated optic fabrication processes. The sidewalls o f LiNbC>3 microdisk are mechanically polished and LiNbCb cannot be grown and etched on a semiconductor substrate. Investigating the alternative material systems that can provide the same functionality may result in a fully integrated photonic receiver with higher sensitivity. The important parameters that have to be considered in selecting a material system for photonic receiver applications are: 1) Electro-optic activity. 2) RF and optical loss. 3) Optical and RF refractive index. 4) Compatibility with the standard integrated fabrication process. 275 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.4.1 Electro-optic polymers Electro-optic polymers are special polymers that if their molecules are aligned by applying an .E-field (poling), they can have large electro-optic coefficient. Recently These materials have been used to fabricate numerous electro-optical devices including electro-optic modulators [4-6]. There has been significant advances in the synthesis o f molecules with large optical nonlinearity that has been sterically designed to prevent the large dipole-dipole interactions between the molecules during electric field poling. One o f the most promising o f these is a ring-locked phenyltetraene bridged chromophore [4], which has been labeled CLD by chemists. The electro-optic molecule needs a host polymer that is thermally stable and also has small optical loss at the wavelength o f interest. For example amorphous polycarbonate (APC) has been identified as a promising host material for CLD and the electro-optic polymer is labeled as APC/CLD. The measured electro-optic coefficient (r^) o f this material is about 90 pm/V at a wavelength o f 1060 nm that corresponds to r ?3 o f 65 pm/V and 55 pm/V at 1300 nm and 1550 nm respectively [4], At 1550 nm the measured value o f propagation loss in a ridge waveguide fabricated from APC/CLD polymer is about 1.7 dB/cm for TM polarized mode and 1.65 dB/cm for TE polarized mode. Although APC/LCD material is difficult to process using standard photolithography, it has been shown that by adding some additional stages to the standard processing sequence high quality polymer structures can be created. APC/CLD has a refractive 276 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. index o f 1.6 at 1550 nm and its microwave refractive index is about 1.5 [5], APC/CLD has been used to monolithically fabricate a polymer micro-ring modulator with a Q o f 1.3xl05 on a silicon substrate [5], This device has been fabricated monolithically on a silicon substrate. The long-term thermal and photo stability o f the polymer devices is a serious system issue. Currently the polymer devices have to be packaged in an inert atmosphere to maintain their electro-optical properties. Research on various aspects o f polymer electro-optic devices continues and with further improvement o f the polymer electro-optic materials may become a very good candidates for monolithic fabrication o f a self-homodyne receiver on a small chip. Electro-optic microdisk and optical waveguides are the only parts o f the photonic receiver that can be fabricated based on polymer materials. This may raise difficulties for the monolithic fabrication process because the laser, the detector and the electronic circuitry are fabricated based on semiconductor materials. Some o f the critical technologies required for the monolithic integration o f polymer electrooptic modulators and VLSI circuitry has been discussed in [6], 5.4.2 Semiconductors Semiconductor materials offer the obvious advantage o f monolithic integration of active/passive photonic and electronic devices. Semiconductor photonic is a very mature field and it is as old as laser itself. The main disadvantages o f using the 277 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. semiconductor materials in electro-optic devices is the fact that the field effect electro-optic mechanisms are weak in semiconductors and other electro-optic mechanisms are accompanied with loss and are wavelength sensitive. Compound semiconductors Various waveguide structures and optoelectronic devices and circuits have been fabricated based on compound semiconductors [7-14], The compound semiconductor materials commonly used in optoelectronics are GaAs and InP as substrate and alloys, which can be lattice, matched to these substrates GaAlAs for GaAs and GalnAsP or InGaAlAs for InP. These materials are zincblend type semiconductors and belong to 43m symmetry group so their linear electro-optic tensor has only 3 nonzero equal elements that are equal (r$\ = rsi = r( ) 3). For GaAs r 4 1 = 1.43 pm/V that is much smaller than that o f the LiNb0 3 or electro-optic polymers. But unlike polymers and electro-optic crystals, linear electro-optic effect (Pokels effect) is not the only mechanism for electro-optic activity in semiconductor materials. The subject o f electro-optic activity in bulk and heterostructure semiconductor materials is very complicated and has been under investigation for many years [7,8], The electro-optic mechanisms in compound semiconductors can be summarized as: 1) Pokels effect 2) Kerr effect 3) Franz-Keldysh effect (electrorefractive effect) 278 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4) Quantum confined Franz-Keldysh effect 5) Quantum confined Stark effect 6) Wannier-Stark localization 7) Plasma effect 8) Band-filling effect These electro-optic effects can be divided into two main categories: carrier and field effects. Also since the quantum confined effects as well as W annier-Stark effect are exclusively observed in quantum-well structures, electro-optic semiconductor devices can be designed either based on quantum-wells or depletion edge translation. We should mention that except the first two effects that directly change the refractive index, the other effects change the absorption coefficient that is related to refractive index change through Kramers-Kroning dispersion relation. So the electo-optic effects in the semiconductors are mainly accompanied with a change o f loss and also they are highly sensitive to the wavelength due to sensitivity o f the absorption processes to wavelength. These properties are disadvantageous for designing electro-optic devices based on semiconductors especially resonant devices. For example if the absorption and refractive index change simultaneously in a resonant modulator (such a s microdisk), the spectral profile o f resonant mode changes during modulation that can cause problem in both linear and nonlinear modulation performance. So ideally absorption related electrooptic mechanisms should be avoided as much as possible in the semiconductor modulators. Unfortunately even the field effect mechanisms such as Franz-Keldysh effect or quantum confined stark 279 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. effect that have beneficial effect on the highly efficient refractive index change degrade the performance, wavelength insensitivity and optical insertion loss. Recently a microdisk modulator with a bandwidth of 8 GHz and sub-volt drive voltage has been demonstrated [14]. The electrooptic mechanism employed in this device is depletion width translation in a pn-based junction based on InGaAs. The microdisk has a Q o f 8500 the bandwidth is limited by the capacitance o f the device. It has been shown that depletion-edge-translation lightwave modulators work based on two electric field related and two carrier-related effects: linear electrooptic, electrorefractive (Franz-Keldysh), plasma and band filling. The sum o f the refractive index variations produced by each one o f these effects, taking into account the waveguide geometry, accounts quantitatively for the experimental phase shifts measured in the devices [7]. Fig. 5.10 shows the voltage dependence o f the effective refractive index variation and the corresponding phase shift for a N-AlGaAs/n- GaAs/P-AlGaAs waveguide modulator with length o f 800 pm at X = 1.06 pm. Lines correspond to the theoretical calculations [7]. The dots are the experimental data for TE mode and triangles for TM mode. As may be seen the summation o f LEO, ER, PL and BF effect (indicated by total (TE) and total (TM)) is in good agreement with the experimental data. The fastest Mach-Zehnder semiconductor optical modulator reported is a 40 Gb/S InP Mach-Zehnder modulator with a Vn - 2.2 V [9]. This modulator uses a n-i-n heterostructure on a InP substrate. The length o f the active ami is 3 mm. In this modulator, the optical modulation is achieved due to Pockels effect. 280 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 1 1 1 1 1 ----- N -A lG o A s /n - G a A s /P - A I Go As ‘ N d :3*101 7 , 8 - \ = l.06p.m t* 8 0 0 /nm REVERSE BIAS VOLTAGE, Va {VOLTS) F ig u r e 5 .1 0 T he v o ltage d ep en d en ce o f the effe c tiv e refractive index variation and the correspon ding phase shift for a N -A lG a A s/n -G a A s/P -A lG a A s w a v egu id e m odulator w ith length o f 8 0 0 pm at X= 1.06 pm [7], L ines correspond to the theoretical calcu lation s. T he d ots are the experim ental data for TE m ode and triangles for T M m ode Neither the Franz-Keldysh effect nor the quantum confined Stark effect (QCSE) plays any part in the operation of this modulator. An extintion ratio of 20 dB was obtained for voltage of 2.2 at a wavelength o f 1550 nm. Between 1530 and 1570 nm, the extintion ratio was still maintained at 13 dB in a fixed voltage swing o f 2 V. This modulator can be directly employed in a 30 GHz photonic self-homodyne receiver. Silicon Silicon photonic is a relatively young field o f research and it is attractive because most o f the current electronic integrated circuits are silicon based therefore silicon processing is a very mature technology and is capable of fabrication very small and complicated features and structures. Since photonic devices still need the electronic 281 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. circuitry for control and processing, it is very useful to have the ability o f manufacturing both electronic and photonic devices on the same platform. Sources and detectors in silicon have not been reported with sufficient efficiency to make them commercially viable as yet, but this is a current active research topic [15- 19], One significant technological issue is associated with the possibility o f optical phase and amplitude modulation in silicon. Pockels effect cannot be observed in silicon owing to centro-symmetric nature o f the crystal structure. Refractive index change is possible via Kerr effect, Franz-Keldysh effect and free carrier injection. Although it is widely accepted that free carrier injection (free carrier plasma dispersion effect) is the most efficient o f these, this mechanism is not a fast modulation mechanism when compared to field-effect mechanisms. Fig. 5.11 shows the calculated refractive index change generated by Kerr effect (a) and Franz-Keldysh (b) effect in silicon [19]. Recently a silicon-based modulator has been reported that overcomes the speed limitation due to slow carrier generation and/or recombination process, by using a metal-oxide-semiconductor (MOS) capacitor [17]. This modulator has a bandwidth o f 1 GHz and a low speed Vn o f 12V for a 8mm device and its fabrication process in compatible with conventional CMOS processing. So its efficiency and speed is very low compared to current modulators fabricated based on L iN b03 or even compound semiconductors. 282 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10-4 < i i<r5 ltr6 i F ig u re 5.11 C alculated refractive index change generated by Kerr (a) and F ranz-K eldysh e ffe c t in silico n [19]. Silicon still has a long way to go before it can be considered as a candidate electro optic material for microwave-photonic applications. , * / " t i f / / a = : -07 / / / im / / / 3 / / f / k=\X / > 9 (im • / < / i p / / • / / / / / ; / • i • ✓ • * / /. , . f 60 80 100 200 400 E (kV /cm ) ( a ) 104 A pplied field (V /cm ) ( b ) 5.4.3 SBN Strontium Barium Niobate is a well-known photorefractive material that has a high electro-optical coefficient and fast response time. SBN crystals come in a variety of Strontium/Barium atomic combinations. The 60% / 40% ratio, or SBN:60, is well 283 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. suited for fabricating microdisk modulators because o f its relatively high Curie temperature (75 C). At an optical wavelength o f A , = 633 nm, SBN 60 has an extraordinary refractive index ne o f 2.2817 and n0 o f 2.3103. We estimate ne = 2.28 at X = 1550 nm by measuring the FSR o f a 3 mm diameter SBN:60 microdisk. SBN:60 has a r 33 o f 235 pm/V which is about 8 times larger than that o f LiNbCb. So a SBN:60 microdisk modulator has a DC-shift 8 times larger than a LiNbCh microdisk with the same size. The main difficulty o f using SBN in a resonant microdisk modulator is the RF- optical frequency matching. The value o f the relative permittivity for SBN: 60 differs greatly from that o f LiNbCb along the optical axis. The measured value for LiNbCb is sr = 26, which contrasts with sr = 880, the listed value for SBN:60 [20], In Chapter 2 we showed that even for LiNbCh, matching the effective RF refractive index with the optical refractive index is a very challenging task. So it is evident that simultaneous RF-optical resonance in a SBN microdisk requires major modifications in the RF ring design. To address this issue we made a 3 mm diameter SBN:60 microdisk optical resonator with a thickness o f 300 pm was studied. Similar to a LiNbCh microdisk modulator, diamond microprism was used to couple laser light into and out o f the microdisk. WG modes at 1550 nm with Q factors in the order o f 10° to 5 x l0 6 have been m easured for this m icrodisk [30]. To achieve RF resonance we used a regular ring resonator on top o f the microdisk that was slightly elevated from the microdisk surface using very thin gold wires to create an air gap underneath the ring. By 284 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. controlling the size o f the air gap between the ring and the microdisk surface we were able to match the RF resonant frequency with the optical FSR frequency (13.5 GHz) and observe optical modulation [30]. This proof o f concept experiment demonstrates that further modification o f the ring resonator may result in a resonant electro-optic microdisk modulator that is, in principle, 8 times more sensitive than an identical LiNbCF microdisk modulator. 5.5 mm-wave photonic transceiver Pushing carrier frequency in the wireless links to mm-wave frequencies is major challenge for the transmitter design as well as the receiver. Electronic devices lose their efficiency and transmission lines become extremely lossy at these frequencies. Photonic generation o f millimeter and sub-millimeter wave signal is a promising technique because it provides several advantages; such as extremely wideband afforded by the characteristics o f optical components, and can use low-loss fibers for transmission o f very high-frequency signals. A photonic local oscillator is based on mixing two optical signals separated by the required local oscillator frequency in a high-speed photodiode that its bandwidth is at least equal to the oscillator frequency [25]. So narrow line high power tunable lasers and high-speed photodetectors are the key elements in a photonic mm-wave oscillator. Fortunately tunable high-power lasers with linewidths o f less than 1 GHz 285 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are commercially available. But conventional p-i-n photodiodes lose their efficiency at frequencies above 60 GHz. To address this issue two novel photodiode designs have been proposed: 1) Traveling-wave photodetectors (TWPD) [22] and 2) Unitraveling-carrier photodiode (UTC-PD) [23], So far unitraveling-carrier photodiode has offered the highest output power and speed compared to other technologies. The primary feature o f the UTC-PD is that only electrons are the active carriers. This is o f great benefit to high-speed and high-output operations. In addition, in the UTC-PD structure, the depletion layer thickness can be designed independently from the neutral absorption layer thickness. Therefore, the carrier transit time can be reduced by narrowing absorption layer thickness without decreasing the CR charging time [23]. Recently a compact UTC-PD module with a WR-8 rectangular waveguide output port for operation in the F-band (90-140 GHz) has been demonstrated [26]. This module generates 17 mW mm-wave power at 120 GHz with a 3 dB o f 55 GHz. Fig. 5.12(a) shows a photograph o f the module and Fig. 5.12(b) is micrograph o f the transformer connecting the UTC-PD and the rectangular waveguide. Fig. 5.12(c) shows the relationship between the measured mm-wave output power and input optical power at 120 GHz for several bias voltages. The UTC-PD has been also used for sub-millimeter wave generation up to 800 GHz [29]. In this case the sub-millimeter wave emitter uses a log-periodic antenna and a unit-traveling carrier photodiode that have been monolithically fabricated on A InP substrate. 286 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mm-wave output < # - W R-8 w aveguide 10 100 Input Optical Power (mW) m peciance iransforimor UTC-PD ; optical inpul ( b ) F ig u re 5 .1 2 (a) Photograph o f the w avegu id e-ou tp u t and the rectangular w av eg u id e, o f the ph otonic 1 20G H z o scillator [26 ]. (b ) M icrograph o f the transform er con n ectin g the U T C -P D and the rectangular w a v egu id e, (c ) R elationship b etw een the m easured m m -w ave output pow er and input optical pow er at 120 G H z for several bias v o lta g es [26], The log-periodic antenna has the features of frequency-independent real impedance from 150 GHz to 2.4 THz. The radiation from the antenna is collimated using a silicon lens. Fig. 5.13 shows a schematic diagram of a mm-wave emitter that employs a UTC-PD, a log-periodic antenna and two lasers that are fabricated on the same substrate. Although this structure seems too idealistic, given the current advancem ent in sem iconductor processing and laser fabrication it may not be too far from reality. 287 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. U T C -P D MMW Si lens L og-p eriod ic antenna F ig u re 5 .1 3 Schem atic diagram o f a ph oton ic m m -w ave transm itter. So employing UTC-PD and photonic mixing technique can open a new horizon in high-frequency LO generation for wireless applications. A combination o f photonic microwave generation and photonic wireless receiver can result in a photonic wireless link where microwave is only used to transmit the signal and signal processing is performed in optical domain. An example o f a mm-wave wireless link that uses mm-wave photonic techniques has been recently demonstrated [28]. The carrier frequency o f this link is 120 GHz. The photonic transmitter consists o f a 120 GHz mm-wave generator, and optical modulator, and a UTC-PD photonic emitter. On the receiver side a mm-wave detector (Schottky Barrier diode) is used as receiver that also demodulates the signal by means of envelop detection. Finally an E/O converter converts the demodulated signal back into the original optical signal and output it to an optical fiber. Fig. 5.14 is the schematic diagram of the photonic wireless link demonstrated by employing UTC-PD [28] 288 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120-GHz MMW 120 GHz Optical M M W Source Intensity M odulator Optical Amp. ; CUTC YHV'Y T -PD M M W Detector —I — V 1000 Base-SX PC O/E Photonic Em itter E/O Converter Converter V ideo Camera PC 1000 Base SX Electrical Signal o p tica l Signal F ig u re 5.14 S chem atic o f the ph oton ic w ireless lin k.[28] The idea o f a photonic wireless link can be implemented using the microdisk photonic self-homodyne receiver. Basically we just need to replace the electronic transmitter with its photonic counterpart. Fig. 5.15 shows how the photomixing technique may be used to generate the transmitted carrier RF signal. Two lasers generate optical carriers (v2 and V|) with an offset frequency equal to the RF carrier frequency (/« /•■ = v2-vi). The intensity o f one o f the optical carriers (v2 ) is intensity modulated (in a MZ or microdisk modulator) with the baseband frequency (ft) and then the both optical carriers are combined and mixed in a photodetector that generates the RF signal. Since one of the carriers was already data modulated the resulting RF signal is also data modulated. By proper adjustment o f the power ratio between the optical carriers (P i/P 2) and the modulation depth it is possible to generate any desired RF modulation index (mi). 289 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 . 3 O ptical pow er (norm alized to Pi) mj = 0.73 K ,/ ^ = 0 . 3 3 f h= 1 G H z 0.1 ( V | - v 2) = 5 G H z ' P2 = 0 .0 4P, i i Laser-2 :/.L2 - < r m 7, \ I ■ -A - i ____ 1 2 3 4 . 3 6 7 8 9 Frequency (G H z) RF filter lock in g circuit L aser 1 P, v. F ig u re 5 .1 5 P hotonic generation o f the transm itted carrier signal by m eans o f optical m odulation and p h otom ixin g. Let’s assume that the baseband frequency is 1 GHz and we want to generate a transmitted carrier RF signal with a carrier frequency of 5 GHz and m\ - 0.7. The simulation results show that if P % = 0.04/h and the optical modulation depth is 0.33 the optical intensity spectrum o f the resulting signal is similar to a transmitted carrier RF signal with m\ = 0.7 and / r f = 5 GHz. The main challenge in the photonic transmitter design is frequency locking of the two lasers. This can be done using optical frequency locked loop (OFLL) or optical phased-locked loop (OFLL) [27]. A detailed description o f frequency locking methods and desired specifications o f the laser sources is beyond the scope of this thesis. Here we just demonstrated that implementation of a photonic self-homodyne wireless link based on microdisk receiver and photomixing technique is a feasible task. 290 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.6 Summary By improving the key components o f the proposed photonic self-homodyne architectures, a stable, low power and small volume photonic receiver can be realized. Employing alternative electro-optic materials such as compound semiconductors may result in a fully integrated photonic receiver that is less complex than its electronic counterparts and consumes less power. Using the high-speed and high efficiency offered by uni-traveling carrier photodiodes, we can generate the transmitted carrier RF/mm-wave signal photonically and implement a photonic wireless link. 291 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.7 References [1] A. A. Savchencov, “Ultrahigh-Q crystalline optical whispering gallery mode resonators,” IEEE LEO S summer topicals meeting on WGM microcavities, TuC1.2, 2004. [2] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Sub microwatt photonic microwave receiver”, IEEE Photonics Technol., vol 14, no. 11, pp. 1602-1604, Nov 2002. [3] Little optics (http://www.littleoptics.com) [4] M-C Oh, H. Zhang, A. Szep, V. Chuyanov, and W. H. Steier, C. Zhang, L. Dalton, H. Erlig, B. Tsap, H. R. Fetterman, “Electro-optic polymer modulators for 1.55 pm wavelength using phenyltetraene bridged chromophore in polycarbonate,” AppliedPhys Lett., vol. 76, no. 24, pp. 3525-3527, June 2000. [5] P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters and modulators,” J. o f Lightwave Technol., vol. 20, no. 11, pp. 1968- 1975, Nov. 2002. [6] S. Kalluri, M. Ziari, A. Chen, V. Chuyanov, W. H. Steier, D. Chen, B. Jalali, H. Fetterman, and L. R. Dalton, “Monolithic integration o f waveguide polymer electro-optic modulators on VLSI circuitry,” IEEE photon. Technol lett., vol. 8, no.5, pp. 644-646, May 1996. [7] J. G. M endoza-Alvarez, L. A. Coldren, A. Alping, R. H. Yan, T. Hausken, K. Lee, and K. Pedrotti, “Analysis o f depletion edge translation lightwave modulators,” /, o f Lightwave Technol., vol. 6, no. 6, pp.793-808, June 1988. [8] K. Wakita, “Semiconductor optical modulators,” Kluwer academic publishers, 1998. [9] K. Tsuzuki, T. Ishibashi, T. Ito, S. Oku, Y. Shibata, R. Iga, Y. Kondo, and Y. Tohmori, “40Gb/s n-I-n InP Mach-Zehnder modulator with a n voltage o f 2.2 V,” Electron. Lett., vol. 39, no. 20, pp. 1464-1466, Oct 2003. [10] M. Feterman, C.-P Chao, and S. R. Forrest, “Fabrication and analysis o f high- contrast InGaAsP-InP Mach-Zehnder modulators for use at 1.55-pm wavelength,” IEEE photon. Technol lett., vol. 8, no.l, pp. 69-71, Jan 1996. 292 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [11] R. G. Walker, “High-speed III-V semiconductor intensity modulators,” IEEE J. o f Quantum Electron., vol 27, no. 3, pp. 654-666, March 1991. [12] N. Shaw, W. J. Stewart, J. Heaton, and D. R. Wight, “Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators,” Electron. Lett., vol. 35, no. 18, pp. 1557-1558, Sept 1999. [13] Kostadin Djordjev; Seung June Choi, Sang Jun Choi, and P. Daniel Dapkus, “Active semiconductor microdisk devices”, IEEE J. o f Lightwave Technology, vol. 20, n o .l, January 2002, pp.105-113. [14] T. Sadagopan, S. J. Choi, S. J. Choi, and P. D. Dapkus, “High-speed, low- voltage modulation in circular WGM microresonator,” IEEE/LEOS, summer topical meetings, 2004, MC2-3. [15] B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Redina, and F. Coppinger, “Advances in silicon-on-insulator optoelectronics,’ IEEEI.J. o f selected topics in quantum electron., vol. 4, no. 6, pp. 938-947, Nov 1998. [16] B. Jalali, L. Naval, and A.F.J Levi, “Si-based receivers for optical data links,” J. o f lightwave technology, vol. 12, no. 6, pp. 930-934, June 1994. [17] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaesu, and M. Paniccla, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature, vol. 427, Feb 2004, pp. 615- 618. [18] C. A. Barrios, U. R. Almeida, R. R. Panepucci, B.S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry-Perot resonator with low power consumption,” IEEE Photonic Technol. Lett., vol. 16, no. 2, pp. 56-508, Feb. 2004 [19] G. T. Reed and A. P. Knights, “Silicon photonics an introduction,” Wiley, 2004. [20] T. Takashi, S. Higashiyama, H. Takemori, and Koizmi, “A silicon optical bench incorporating a tantalum-nitride thin-film resistor,” J. o f Micromech. AndM icroeng., vol. 14, pp. 283-289, 2004. [21] K. Ohata, T. Inoue, M. Funabashi, A. Inoue, Y. Takimoto, T. Kuwabara, S. Shinozaki, K. Maryhashi, K. Hosaya, and H. Nagai, “Sixty-GHz-Band ultra- miniature monolithic T/R modules for multimedia wireless communication systems”, IEEE trans. on microwave theory and tech., vol. 11, no. 12, pp. 2354-2360, Dec. 1996. 293 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [22] A. Stohr, A. Malcoci, A. Sauerwald, I. C. Mayorga, R. Gusten, and D. S. Jager, “Ultra wide-band traveling-wave photodetectors for photonic local oscillators,” J. ofLightw>ave Technol., vol. 21, no. 12, pp.3062-3070, Dec 2003. [23] H. Ito, T. Furuta, S. Kodama and T. Ishibashi, “InP/InGaAs uni-travelling- carrier photodiode with 310 GHz,” Electron. Lett., vol. 36, no. 21, pp. 1809- 1810, Oct 2000. [24] Y. Muramoto, Y. Hirota, K. Yoshino, H. Ito, and T. Ishibashi, “Uni-travelling- carrier photodiode module with bandwidth o f 80 GHz,” Electron. Lett., vol. 39, no. 25, Dec 2003. [25] P. G. Huggard, B. N. Ellison, P. Shen, N. J. Gomes, P. A. Davies, W. Shillue, A. Vaccari, and J.M. Payne, “Generation o f millimeter and sub-millimetre waves by photomixing un 1.55 pm wavelength photodiode,” J. Lightwave Technol., vol. 21, no. 12, pp. 3062-3070, Dec. 2003. [26] H. Ito, T. Ito, Y. Muramoto, T. Furuta, and T. Ishibashi, “Rectangular waveguide output unitraveling-carrier module for high-power photonic millimeter-wave generation in the F-band,” J. Lightwave Technol., vol. 21, no. 12, pp. 3456-3462, Dec. 2003. [27] J. O ’ Reily and P. Lane, “Remote deliver o f video services using mm-waves and optics,” J. Lightwave Technol., vol. 12, no. 2, pp. 369-375, Feb. 1994. [28] A. Hirata, M. Harada, and T. Nagatsuma, “ 120-GHz wireless link using photonic techniques for generation, modulation, and emission o f millimeter- wave signals,” J. Lightwave Technol., vol. 21, pp. 2145-2153, Oct. 2003. [29] A. Hirata, T. Nagatsuma, R. Yano, H. Ito, T. Furuta, Y. Hirota, T. Ishibashi, H. Matsuo, A. Ueda, T. Noguchi, Y. Sekimoto, M. Ishiguro, and S. Matsuura, “Output power measurement of photonic millimeter-wave and sub-millimetter wave emitter at 100-800 GHz,” Electron Lett., vol 38, no. 15, pp. 798-800, July 2002. [30] Unpublished data, Experiment done by Fernando Harriague, Advanced Network Technology Lab, USC. Technical notes (1) PINFET optical receiver from Laser Diode Incorporated (www.lasrdiode.com) LDPF 0012 (Bandwidth 12 MHz, Sensitivity-53 dBm) LDPF 0024 (Bandwidth 24 MHz, Sensitivity -5 0 dBm) 294 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2) LMDS (Local M ultipoint Distribution Service) is a fixed wireless technology that operates in the 26 - 32 GHz band and offers line-of-sight coverage over distances up to 3-5 Kim. (3) EtherAir 1500: is a digital radio system made by Ceragon networks that supports wireless fast Ethernet applications for the ISP carrier, corporate access and campus environments. This system operates in the 18,23,26,28 and 38 GHz frequency bands with a bandwidth o f 155 Mbps, (www.ceragon.com). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Glossary a Optical circulation factor in the microdisk c Speed o f light D Microdisk diameter e Electron charge E in Input E-field Et transmitted E-field ./RF,ni mth resonant frequency o f the RF ring resonator / r f RF carrier frequency f Resonant frequency o f the patch antenna (single and array) / e o Electro-optic transfer function o f the microdisk resonator / o Optical transfer function o f the microdisk resonator (frequency domain) Ge„ Electro-optic gain factor G r f,OB Baseband modulated optical power at 1 W received RF power Gtot Total gain in the wireless photonic receiver g Gap size between the ring resonator and the microstripline go Evanescent optical coupling gap size h M icrodisk thickness h s Dielectric substrate thickness (microstripline) K Dielectric substrate thickness (patch antenna) ip Total output photocurrent generated in the photodetector ^ o )b Baseband photocurrent ^2 cob Photocurrent at the second-harmonic o f the baseband signal k Dark current o f the photodetector io,s Signal photocurrent h>,N Noise photocurrent ■/hoto Photocurrent density k Wave vector o f the optical W G resonance k ]$ Boltzman factor I Polar WG mode order L j Transmission line loss factor E e f f Average length that photon travels before escaping from the resonator m Azimuthal WG mode order m0 Optical modulation order m r RF resonance order m\ RF modulation index M Optical modulation index n Optical refractive index (general) n0 Ordinary bulk optical refractive index o f LiNb0 3 (zero electric field) ne Extraordinary bulk optical refractive index ne' Electro-optically modulated extraordinary bulk optical refractive index «RF RF refractive index ^RF,e Effective RF refractive index 296 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ^ p lio to Density o f photo-generated electrons Na Received noise power Ee f f Effective electric field intensity P o ,R !N Laser RIN power P o .o u t Output (transmitted) optical power P o .m in Minimum optical power o f a WG resonance P o ,m a x Maximum optical power o f a W G resonance P o ,in Optical input power P o .m o d Modulated optical power Po ,d Available optical power in a dip Po,b Baseband modulated optical power Pb Down-converted baseband power (electrical) P o.ojb Optical power modulated at c o i, P o ,2cob Optical power modulated at 2 © b P e ,<ob Electrical power modulated at o)b P e ,2 m b Electrical power modulated at 2cob P 1 o ,s Instantaneous signal optical power Po,n Instantaneous noise optical power P o ,S Total signal optical power Po,N Total noise optical power P o ,d c DC optical power F„,, Transmitted optical power P 1 o ,m ix Down-converted optical noise power Po b b Optical noise power in baseband regime ■Pr f RF input power (received RF power) q Radial WG mode order Q Loaded optical quality factor o f a W G resonance Q u Unloaded optical quality factor o f a W G resonance Qrf,\ j Unloaded RF quality factor o f a W G resonance Q rf loaded RF quality factor o f a W G resonance R Photodetector responsivity Ro Outer radius o f the RF ring resonator R\ Inner radius o f the RF ring resonator P-ring Resistance o f the ring resonator S, Received signal power 5 d Sensitivity o f the digital photoreceiver t Optical transmission coefficient t Time T r f RF period V DC voltage across the microdisk Vfb Feedback voltage (peak-to-peak) Vrf Input RF voltage to the microdisk modulator V rf Noisy input RF voltage to the microdisk modulator vm Amplitude o f the voltage oscillation on the ring resonator 297 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vm, Vo Amplitude o f the input RF voltage ( F r f ) VRN Noise voltage on the ring resonator VRS Signal voltage on the ring resonator F n Amplitude Vh Amplitude W\ Width o f the microstripline w v Width o f the RF ring resonator 2 a The height o f air cylinder for tuning the RF resonant frequency Z m Impedance o f a rectangular patch in the middle a Distributed optical loss factor for W G modes (absorption+scattering) P e o Electro-optic correction factor (microdisk modulator) P ' e o Electro-optic correction factor (MZ modulator) P c Ring capacitance correction factor P s E’ -field oscillation correction factor Pqlm Wave vector o f the W G mode K Optical coupling factor 5 Optical skin depth 50F W H M Angular full width half max o f the WG resonance SrpWHM Radial full width half max o f the W G resonance A v f s r Optical free spectral range frequency AVpwtlM Full width half max frequency o f the W G resonance A L f w h m Full width half max wavelength o f the WG resonance AA-d c DC shift Aloe Effective length o f the patch antenna A-lascr Laser wavelength Vlaser Laser frequency X r f RF wavelength A-res Resonant wavelength o f WG resonance v res Frequency o f WG resonance (general) V lq Frequency o f WG resonance Ve Electron velocity v,„ mth resonant frequency o f an optical resonator P Optical coupling efficiency T p Photon lifetime in the microdisk resonator X r t Photon roundtrip time in the microdisk resonator © r f RF angular frequency © b Baseband angular frequency E re Effective dielectric constant Er Dielectric constant (relative permittivity) Ss relative permittivity o f the microstripline substrate Se,RF RF permittivity along c-axis 298 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix A Bibliography Abeles, J. H., “Resonant enhanced modulator development,” DARPA/MTO R-FLICs program: K ickoff meeting, August 2000. Armani, D. K., Kippenberg, T. J., Spillane, S. M., and Vahala, K. J., “U ltra-high-0 microcavity 011 a chip,” Nature, vol. 421, pp. 925-928, Feb. 2003. Agrawal, G. P., “Fiber-optic communication systems”, 1997. Abidi, A. , “Direct-conversion radio transceivers for digital communications,” IEEE J. Solid-State Circuits, vol. 30, pp 1399-1410, Dec 1995. Bernard, P. A., and Gautray, J. M., “Measurment of dielectric constant using a microstrip ring resonator,” IEEE Trans, on Microwave Theory and Tech., vol. MTT- 39, no 3, pp 592-594, March 1991. Bahl, J., and Bhartia, P., “Microstrip antennas”, 1980. Basilio, L. I., Khayat, M. A., Williams, J. T., and Long, S. 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Asset Metadata

Creator Hossein-Zadeh, Mani (author)

Core Title Electro -optic microdisk RF -wireless receiver

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, electronics and electrical,OAI-PMH Harvest,physics, optics

Language English

Advisor Levi, Anthony (committee chair), Cohen, David (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-572034

Unique identifier UC11335738

Identifier 3155423.pdf (filename),usctheses-c16-572034 (legacy record id)

Legacy Identifier 3155423.pdf

Dmrecord 572034

Document Type Dissertation

Rights Hossein-Zadeh, Mani

Type texts

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

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