Electro-optic and thermo -optic polymer micro-ring resonators and their applications

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Content ELECTRO-OPTIC AND THERMO-OPTIC POLYMER MICRO-RING RESONATORS AND THEIR APPLICATIONS Copyright 2002 by Payam Rabiei 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) Dec 2002 Payam Rabiei Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3093963 Copyright 2002 by Rabiei, Payam All rights reserved. ® UMI UMI Microform 3093963 Copyright 2003 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. UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-1695 This dissertation, written by Payam R a b ie i under the direction o f h i s dissertation committee, and approved by all its members, has been presented to and accepted by the Director o f Graduate and Professional Programs, in partial fulfillment o f the requirements fo r the degree of DOCTOR OF PHILOSOPHY Director Dissertation Committee llLv& Z- Chair Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments It was a great opportunity for me to work in the research group of Dr. Steier. Dr. Steier has been a very supportive advisor during the course of this work. His vision and patience has been all I need to succeed during my Ph.D. The scientific atmosphere he created in the group has thought me how to do the research and how to work. Also his nonlinear optics course was among the best courses I took in USC. I sincerely appreciate all his support. I am grateful of the members o f my thesis committee and guidance committee. I would like to thank Dr. R.W. Hellwarth (Chair), Dr. W. H. Steier, Dr. M. A. Gunderson, Dr. A. A. Sawchuk, and Dr. J. O'Brien for their time and their advises. I will never forget all the help and discussions with the members of our group during my work. There were all those discussions and help which resulted in the working devices. I would like to thank Ying-Hao Kuo, Dr. Atilla Szep, Dr. Seh-wan Ahn, Reem Song and Hidehisa Tazawa for all their help. I would also like to thank to the senior members of our group Dr. Hua Zhang and Dr. Min-Cheol Oh for all their experience, which helped me to leam the basic of polymer processing. Without the electro-optic polymers it is impossible to make any kind of useful device. I would like to thank Dr. Cheng Zhang and Chuanguang Wang from Dr. L.R. Dalton group at chemistry department. Their effort to make the polymers instantly for fabrication o f the device is greatly appreciated. I would also like to thank Dr. A.F. J. Levi, which I spend two years of my Ph.D. in his group. The ideas for making the devices demonstrated in this thesis were initiated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. during the work in his lab. I would like to thank Dr. David Cohen and Dr. Mani Thyagarajan, which were my first instructors on photonic and device processing. I would like to thank Betty Madrid for her kind discussions and for making purchase orders ready quickly and all her administrative support. Finally I would like to thank my family which all they have wished on the other side of the earth was my success and my joy in life. It was impossible to do anything without their support. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iv Table of Contents Acknowledgments...................................................................................................................... ii List of Tables ........................................................................................................................... vi List of Figures........................................................................................................................... vii Abstract...................................................................................................................................... xii Chapter 1: Introduction.......................................................................................................1 1.1 Functional optical com ponents.............................................................................. 1 1.2 Nonlinear optical m aterials..................................................................................... 2 1.3 Micro-ring resonators................................................................................................6 1.4 Photonic V L S I................................................. 8 1.5 References...................................................................................................................9 Chapter 2. Micro resonators coupled to waveguides...................................................10 2.1 Concept......................................................................................................................10 2.2 Analysis of loss mechanisms in micro-resonator............................................... 13 2.2.1 Bending Loss and effective index...............................................................13 2.2.2 Scattering loss................................................................................................ 21 2.2.3 Materials and material lo ss..........................................................................29 2.3 Waveguides coupled to the micro-resonator...................................................... 32 2.3.1 Beam propagation method for calculating the coupling........................ 33 2.3.2 Coupling optim ization..................................................................................35 2.4 Micro resonator transfer function.........................................................................38 2.5 References.................................................................................................................45 Chapter 3. Experimental results for passive M R ..........................................................49 3.1 Larger devices...........................................................................................................49 3.1.1 Device design..................................................................................................49 3.1.2 Fabrication...................................................................................................... 51 3.1.3 Device characterization................................................................................. 53 3.2 Smaller D evices........................................................................................................55 3.2.1 Device design..................................................................................................56 3.2.2 Device fabrication.......................................................................................... 56 3.2.3 Device characterization................................................................................. 58 3.3 Summary of passive devices.................................................................................. 60 3.4 Temperature Tuning of the filter........................................................................... 61 3.5 Resonance wavelength control..............................................................................61 3.6 References................................................................................................................. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4: Light modulation using micro-resonators................................................ 64 4.1 Introduction............................................................................................................ 64 4.2 Theory of micro-ring modulator.......................................................................... 64 4.3 Larger devices........................................................................................................ 71 4.3.1 Fabrication.....................................................................................................71 4.3.2 Low frequency characterization..................................................................73 4.3.3 High frequency characterization.................................................................74 4.4 Small devices......................................................................................................... 76 4.5 Multi-wavelength modulator...............................................................................79 4.5.1 Analysis of cross talk....................................................................................81 4.6 Reference................................................................................................................84 Chapter 5: Mode coupling in electro-optic ring resonators and its applications... 85 5.1 Introduction.............................................................................................................85 5.2 W avelength converter........................................................................................... 85 5.3 Comb Generation...................................................................................................89 5.4 Phase matching issues........................................................................................... 93 5.5 Conclusion..............................................................................................................96 5.6 References...............................................................................................................96 Chapter 6: Widely tunable external cavity DMR lasers.............................................97 6.1 Introduction.............................................................................................................97 6.2 Thermo-optic device............................................................................................. 99 6.2.1 Fabrication..................................................................................................... 99 6.2.2 Device characterization.............................................................................. 101 6.3 Electro-optic device............................................................................................ 105 6.4 Analysis of speed of tuning.................................................................................109 6.5 Conclusion............................................................................................................ 112 6.6 References............................................................................................................. 114 Chapter 7: Packaging and conclusion...........................................................................115 7.1 Introduction............................................................................................................115 7.2 The coupling......................................................................................................... 116 7.3 Packaging...............................................................................................................118 7.4 SION waveguide...................................................................................................119 7.5 Conclusion.............................................................................................................123 7.6 References..............................................................................................................125 Bibliography...........................................................................................................................126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vi List of Tables Table 2-1: The refractive index and the loss of the polymers used for device fabrication....................................................................................................................... 31 Table 4-1: The performance of three different devices at 1300nm................................ 79 Table 7-1: The measured mode size for different fibers in our lab.............................. 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures Figure l-l:Chem ical structures o f FTC and CLD-1........................................................... 3 Figure 1-2: Dynamic thermal stability of poled CLD-1/PMMA (solid square) and CLD-l/PC (triangle) films............................................................................................. 5 Figure 1-3: Photostability of the electrically poled CLD-1/APC ridge waveguide in air and in argon. (10 mW input, 1.55 pm ).................................................................. 6 Figure 2-1: Concept of a micro-resonator.........................................................................11 Figure 2-2:SEM picture of micro-disk laser fabricated in 1992 at Bell Labs 11 Figure 2-3: Channel waveguide coupled to resonator..................................................... 12 Figure 2-4: Geometry of curved cylindrical waveguide.................................................. 14 Figure 2-5: (a) Original refractive index profile for curved waveguide (b) Equivalent straight waveguide refractive index profile.............................................................. 15 Figure 2-6: Geometry o f the curved waveguide............................................................... 16 Figure 2-7: Refractive index profile of the original curved waveguide and refractive index profile o f the approximated waveguide for 3D case.....................................17 Figure 2-8: Field profile for TE and TM polarizations. (Notice that for TM for example TMY is one order of magnitude smaller than TMX and TMZ is 3 orders of magnitude smaller than TM X )...................................................................19 Figure 2-9: Minimum radius required to achieve ldB/cm loss and the corresponding FSR calculated for 1.55pm as a function of difference of index of refraction of core to cladding for the structure shown in figure...................................................20 Figure 2-10: Calculated effective index of the curved waveguide at 1.55pm for the fundamental mode assuming 1 dB/cm radiation loss for the structure shown as a function of refractive index difference between core and cladding.............. 21 Figure 2-11: (a) An ideal micro resonator (b) Practical micro-resonator......................22 Figure 2-12: Geometry for the surface roughness problem............................................ 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2-13: Wall roughness loss calculated at 1.55 pm as a function of index difference between core and cladding for 30nm roughness.................................. 29 Figure 2-14: (a) Side coupling to micro-resonator (b) Vertical coupling to the micro resonator........................................................................................................................32 Figure 2-15: The structure modeled for calculating the coupling to the resonator 34 Figure 2-16: Field profile for coupling between the waveguide and the resonator mode.............................................................................................................................. 34 Figure 2-17: Calculated dropped power due to coupling to the micro-resonator as a function of refractive index of waveguide for the structure shown. The minimum happens due to phase matching of the waveguide mode and resonator mode....................................................... ..................................................... 35 Figure 2-18: Geometry for mis-alignment of the resonator and waveguide............... 36 Figure 2-19:Calculated dropped power due to coupling to the micro-resonator as a function of mis-alignment of the resonator and waveguide..................................37 Figure 2-20 Calculated dropped power due to coupling to a micro-resonator at the optimum condition versus the vertical distance between the resonator and the waveguide.................................................................................................................... 38 Figure 2-21: Geometry o f single waveguide coupled to resonator.............................. 39 Figure 2-22: Transfer function of the resonator for different values of the loss of resonator w aveguide...................................................................................................40 Figure 2-23: Geometry of two waveguide to coupled to a micro-resonator...............41 Figure 2-24: Measurements required for characterizing M R........................................ 44 Figure 3-1: Large passive device, (a) Fabricated device picture..................................50 Figure 3-2: The fabrication procedure for large passive devices..................................52 Figure 3-3: Measurement setup......................................................................................... 54 Figure 3-4: Measured response of 220pm radius device as a function of the input frequency for both the drop and through port at 1.3pm.........................................54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IX Figure 3-5: Fabrication procedure for small passive device............................................57 Figure 3-6: Small passive devices cross-section schematic and the fabricated device picture.............................................................................................................................59 Figure 3-7: Measured power at drop port as a function of laser wavelength for 55pm diameter device..............................................................................................................59 Figure 3-8: Measured power at drop port as a function of laser wavelength for 64pm diameter device..............................................................................................................60 Figure 3-9: Temperature tuning of the micro-resonator filter....................................... 61 Figure 3-10: Array o f micro-resonators chip....................................................................62 Figure 3-11: Measured resonance wavelength as a function of device diam eter........ 62 Figure 4-1: Light modulators using M Rs.............................................................................66 Figure 4-2: Light modulation concept using a single M R................................................66 Figure 4-3: Light modulation using push pull MR in the arms of Mach-Zehnder interferometer.................................................................................................................67 Figure 4-4: Large electro-optic device layout and the cross section of the device...... 71 Figure 4-5: Large electro-optic device performance (a) Measured dropped power as a function of the input laser wavelength, (b) Measured dropped power and the applied signal to the device for a fixed laser wavelength.................................74 Figure 4-6: Eye diagram for data transmission at 1 Gb/sec using electro-optic M R...75 Figure 4-7: Small electro-optic devices. Fabricated device picture and the cross section............................................................................................................................. 76 Figure 4-8: Response of the electro-optic device as a function of laser wavelength... 78 Figure 4-9: The modulation performance for three different small electro-optic devices, (a) 150pm, (b) 70pm, (c) 50pm.(diameter). The applied voltage is 20Vpp.............................................................................................................................. 79 Figure 4-10: Typical WDM architecture............................................................................80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X Figure 4-11: Proposed architecture for the WDM system............................................... 81 Figure 5-1: Electro-optic ring-resonator wavelength converter.......................................86 Figure 5-2: Power in the two adjacent modes of the resonator as a function of the applied voltage............................................................................................................... 88 Figure 5-3: Frequency response of the wavelength converter......................................... 89 Figure 5-4: Calculated power in different modes as a function of applied voltage to the device.........................................................................................................................91 Figure 5-5: Structure of the device for suppression of unwanted m o d es.....................92 Figure 5-6: Small ring and the large ring transfer function. Only two adjacent modes couple to each other due to the electro-optic effect................................................. 92 Figure 5-7: The comparison between the phase matched case and the case where there is 0.1 index difference between the RF and light wave................................. 94 Figure 5-8: The multi-mode coupling in the phase mis-matched case with 0.1 index difference between the RF and optical fields.............................................................95 Figure 6-1: (a) The structure of the device. Micro-resonators, Waveguides and electrodes geometry, (b) The cross section of the device. The SU-8 is the MR and the NOA72 is the waveguide.............................................................................100 Figure 6-2:: The optical circuit for the laser. P: Polarizer, PC: Polarization controller, EDFA: Erbium doped amplifier.............................................................102 Figure 6-3: The filtered spontaneous emission of the device for different values of the current to the electrode heater and the EDFA spontaneous emission spectrum........................................................................................................................103 Figure 6-4: The lasing spectrum of the DMR thermo optic device..............................104 Figure 6-5: The tuning characteristic of the DMR device as a function of the current in the electrodes.............................................................................................. 105 Figure 6-6: (a) The electro-optic device picture. The waveguides and the electrodes can be seen. The MR is under the electrode, (b) The cross section of the E -0 DMR device................................................................................................................. 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X I Figure 6-7: The filtered spontaneous emission of the device for different values of the voltage applied to the electrodes of the device........................................... 107 Figure 6-8:The lasing spectrum for four different voltages applied to the electrodes of the device................................................................................................................ 108 Figure 6-9: The geometry of the DMR with SOA gain region....................................109 Figure 6-10: The simulation results for the laser power and the carrier density for a DMR laser................................................................................................................I l l Figure 6-11: The simulation results for the DMR laser the laser power with a 0.4nsec pulse for depletion of the cavity from the lasing m ode.........................112 Figure 7-1: The coupling loss for two Gaussian modes with different mode size.... 117 Figure 7-2; The semi-packaging used for device. The fibers, strip line and other components can be seen in the figure......................................................................119 Figure 7-3: The proposed device for the integration of SION technology with active polymer M R................................................................................................................ 121 Figure 7-4: The refractive index and deposition rate for SiON film using different values for 0 2 flow rate.(NH3(SCCM)=10(SCCM),N2=5(SCCM), Si 114=50 (SCCM), Pressure=300mT, Temp=310)............................................................... 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract This thesis presents some novel devices using electro-optic polymers. The electro-optic polymer is used in a micro-ring resonator to make different devices. First the micro resonator characteristics are analyzed. The bending loss is calculated using computer program for polymer material to obtain the minimum-bending radius. It is shown that using polymers it is possible to achieve bending radius as small as 5 pm. An analytical formula is obtained for scattering loss from the rough sidewalls. The scattering loss is calculated for practical polymer devices. It is shown that the wall roughness is the dominant loss mechanism. The coupling to the resonator is calculated using beam propagation method. The optimization of coupling is discussed. Some passive polymer micro-resonators are fabricated. The novel fabrication method is described. Filters with a finesse of 141 and free spectral range of 5nm at 1300 nm and finesse of 117 with a free spectral range of 8nm at 1550nm are demonstrated. Ring resonators with a Q as high as 1.3xl05 at 1300 nm are demonstrated. The filters can be temperature tuned at the rate of 14GHz/°C. The control of resonance wavelength by changing the size of the micro-resonator is demonstrated experimentally. It is shown that resonance wavelength can be controlled with less than lnm accuracy at 1550nm. Resonant ring modulators, which use an electro-optic polymer, are demonstrated. The performance of these devices is analyzed theoretically. For one set of devices with relatively large diameter the resonance wavelength voltage tunes at the rate of 0.82GHz/V. The modulators have a bandwidth larger than 2 GHz. Using the resonant modulator, and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xiii open eye diagram at 1 Gb/s is demonstrated. Polymer microring modulators with FSR larger than IThz, modulation bandwidth of 15GHz and the full with half maximum voltage of 20V are demonstrated at 1300nm by using Teflon AF cladding. Multi wavelength modulation with a total bandwidth of 400Gb/s is practical. The theory o f mode coupling using electro-optic micro-resonators is presented. It is shown that these devices can be used as a wavelength converter or a comb generator. Widely tunable double micro-ring filters by thermo-optic effect and electro-optic effect are demonstrated. The tuning range is more than 40nm. The required electrical power to achieve 40 nm using thermo-optic effect is less than 20 mW. The elctro-optic tuning is also demonstrated for the first time. 16V is required for lnm tuning. A widely tunable laser using this filter and EDFA gain is demonstrated. The side mode suppression ratio is greater than 30dB and the tuning range is 40nm. The coupling using small core fibers and packaging of the device are presented. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1: Introduction 1.1 Functional optical components It is more than 40 years since the invention of the first gas lasers. During this period the filed of opto-electronic has seen many inventions. Optical fibers, semiconductor lasers, erbium doped amplifier and planner lightwave circuits are a few o f the many achievements in this field. However the complexity of optical circuits used today are far beyond what have been reached in electronic world. Most of the components are discrete and the functionality is very limited. This limited functionality has limited the photonic applications to long distance communication. Even in long distance communication very simple modulation schemes have been used. Future optical communication systems require more advanced opto-electronic components. Other modulation schemes such as frequency shift keying (FSK) or code division multiple access (CDMA) might be required. Interconnects are a major issue in the computer industry. The limited bandwidth of electrical interconnects has made the achievable speed of CPU useless. The main issue for achieving higher performance in computers is the low speed interconnects Optical methods are considered for interconnects in computers [1]. In this thesis an effort has been made to solve some of the problems mentioned above. The goal is to achieve lightwave circuits, which are very functional for processing of lightwave signals. The micro-resonators are used as the building blocks Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 for these functional circuits. Nonlinear optical materials have been used to achieve the signal processing ability. Advanced semiconductor processing methods have been used to make these circuits and devices. 1.2 Nonlinear optical materials Materials with nonlinear optical properties are the steels of the future integrated optical circuits. There are two major classes of nonlinear optical materials. Inorganic ferroelectric crystals have been used for practical devices such as modulators so far. To date inorganic ferroelectric crystals have superior performance in terms of loss and large nonlinear coefficient to any other material. As it will become more clear in the following chapters to achieve the functional devices we are are going to fabricate we would require large index contrast between the core and cladding. The available technology in the ferroelectric crystals allows very small index difference between core and cladding of waveguides. Hence it is not useful for these devices. However recently thin film ferreoelectric crystals have been made using epitaxial growth [2]. Using these thin films it may be possible to make the devices we are going to discuss in this thesis. The second group of the materials is the inorganic materials. The inorganic materials are particularly interesting since in principle one can engineer the molecules to achieve the desired optical properties. Very large nonlinear coefficient may be achieved in this way. In fact recent results have shown materials with nonlinear Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coefficient higher than ferroelectric crystals. Figure 1-1 shows the structure of the CLD1 chromophore, which has been used in all the devices made in this thesis. AcO AcO NC NC TBDMSO FTC TBDMSO CLD-1 trans isomer TBDMSO TBDMSO CLD-1 c/s isomer CN Figure l-l:Chem ical structures of FTC and CLD-1. The basic idea for the nonlinear response is the have a donor molecule connected to an accepter molecule through a conjugated n bridge. The movement of electrons Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. from the donor to the acceptor creates a polarized molecule with a large dipole moment. Hence large electro-optic effect is obtained. [3] The CLD1 is based on structural design of chromophores to reduce the large dipole-dipole interactions between chromophores, which prevent alignment during polling and thereby increase the EO coefficient. The chromophores are a ring-locked phenyltetraene, which is labeled CLD1. The material is in the guest host form with APC (amorphous polycarbonate) as the host material. Electro-optic coefficient of CLD1/APC polymer in Mach-Zehnder devices is measured to be 36pm/V at 1550nm. Since these polymers can easily form thin films they are suitable for the devices that I will discuss in this thesis. However there are several disadvantages to the polymers for micro-resonators. First the refractive index of the polymers is not very large. The largest refractive index that has been achieved in our lab is 1.8 . This limits the device size to 1 Opm in diameter, which might not be good enough for future devices. The ferro-electric crystals have higher refractive index, which is probably enough for many generations of devices. It is noticeable that if the inorganic materials can be made in the form of crystal [4] large refractive indexes can be obtained. Second major problem is the extremely unstable properties of the polymers. Several different instabilities exist in the polymer devices. First is the thermal stability. The chromophores in the polymer matrix are polled and the system is in a meta-stable condition. By heating the device one can move to the minimum energy point and the electro-optic coefficient is reduced. This problem has been solved and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. relatively stable condition has been achieved. Figure 1-2 shows some data for the thermal stability of the polymers, which we have used. As it is clear heating the film more than 120 °C reduces the electro-optic coefficient. ' i » W W ! ) * K \ 0.4 0 w 0.2 20 70 0 120 Temperature ( C) Figure 1-2: Dynamic thermal stability of poled CLD-1/PMMA (solid square) and CLD-1/PC (triangle) films. The second problem with the polymer thin films is the photo-stability. The designed chromophores can react with oxygen in the presence of light. This problem can be avoided using an oxygen free environment as shown in Figure 1-3. However making this kind of environment is not easy. The ferroelectric or organic crystals do not have these kinds of stability problems. However making thin film devices and etching is probably more difficult. Perhaps the reason that the devices we have demonstrated for the first time using polymers will be demonstrated very soon using crystals. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 m- Argon Q. o T R 0.4- Air 0.0 20 40 60 80 100 120 0 Time [hour] Figure 1-3: Photostability of the electrically poled CLD-1/APC ridge waveguide in air and in argon. (10 mW input, 1.55 pm) 1.3 Micro-ring resonators Micro-resonators that have been used in this thesis for all the demonstrated devices are perhaps as important for photonics as transistors in electronics. Almost any device you can imagine can be fabricated using micro-ring resonators. Using gain medium lasers can be made. Using electro-optic materials modulators can be made. Filters, and dispersion compensator are other devices, which can be made. In addition it is possible to make functional devices such as widely tunable lasers using MRs. Wavelength converters and comb frequency generators can be made using the MRs. The idea of micro-resonator waveguides has been considered as early as 1969. [5] However only recently working devices have been demonstrated. The main topic for Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 this thesis is different devices, which can be made using micro-resonators. In chapter 2 I will discuss the micro-resonator properties. I will calculate the bending loss and scattering loss for a MR. The required values for index difference between core to cladding and surface roughness to achieve a useful device are calculated. The coupling to the MR is discussed. Simulation results are presented for the coupling to the MR. Transfer function of MR is calculated and some useful formula are calculated to evaluate the performance of resonators based on the measurement. In chapter 3 experimental results for passive micro-resonators are discussed. It is shown that using polymers high Q resonators can be obtained. Perhaps the most important chapter in this thesis is chapter 4. Using electro-optic polymers in a micro-resonator one can make very small electro-optic switches and modulators. The performance of these devices is analyzed and some experimental results are provided. These devices might be used in computer interconnects in future due to their exceptional functionality. Chapter 5 is a theoretical calculation for a wavelength converter and frequency comb generator using electro-optic ring resonators. It is possible to make a widely tunable laser using electro-optic effect in micro-resonator. In chapter 6 widely tunable lasers using electro-optic MR is discussed and demonstrated experimentally. This might open the door for more sophisticated modulation schemes in optical communication systems. Widely tunable lasers with sub-nano second tuning range might be made using this technology. Chapter 7 discusses the packaging issue and some problems, which need to be solved for future devices and concludes the thesis. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 1.4 Photonic VLSI As it was mentioned previously this thesis demonstrates for the first time several different very functional devices. These devices are probably the building blocks for future photonic circuits, which are very functional and integrated in a small cheap. For example using electro-optic MR one can modulate several different wavelengths is a small cheap which is only a few mm long. As it was mentioned before the electrical interconnects is a major bottleneck for higher performance computers. The idea is to use optics to communicate between the elements in a computer. This could be achieved using polymer micro-ring modulator. One special feature of the polymers is the ease of integration. The polymer layers can directly be spin coated on top of an integrated circuit. Since the micro-ring modulator can be fabricated in an area as small as 10pm many modulators can be fabricated on a small integrated circuit. Also since the modulator is basically a lumped element one does not need to worry about the impedance matching. This is compatible with CMOS transistors, in which have a large output impedance. The modulator would behave simply as a capacitive load. Consider that using a single fiber with this technology it is possible to obtain Terabit/sec data rate out o f an integrated circuit. (You can compare this with a maximum of 100 Mb/sec possible with one copper wires). This kind of technology can significantly improve the data rates between different components in a digital electronic system. This is probably the beginning of the photonic VLSI industry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 1.5 References [1] Miller, D.A.B., “Rationale and challenges for optical interconnects to electronic chips”, Proceedings of the IEEE vol. 88, no. 6, pp 728-49, June 2000 [2] Gill, D.M. ; Block, B.A. ; Conrad, C.W. ; Wessels, B.W. ; Ho, S.T., “Thin film channel waveguides fabricated in metalorganic chemical vapor deposition grown BaTiO/sub 3/ on MgO”, Applied Physics Letters, vol 69, no. 20, pp 2968-70, Nov. 1996 [3] C.Zhang, L.R. Dalton, M.-C. Oh, H. Zhang, W.H. Steier, “Low VgElectro- optic modulators from CLD-1: Chromophore design and synthesis, Material processing and characterization, “ Chem. Mater., vol 13, p. 3043-3050, (2001) [4] Meier, U., Bosch, M., Bosshard, C., Gunter, P. “DAST a high optical nonlinearity organic crystal”, Synthetic Metals vol. 109, no. 1-3, pp 19-22, March 2000 [5] E.A.J. Marcatili, “Bends in optical dielectric waveguides”, The Bell System Technical Journal, Vol 48, pp.2103-2132,1969 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Chapter 2. Micro resonators coupled to waveguides 2.1 Concept Figure 2-1 shows a typical micro-resonator. The light is confined in a ring shaped dielectric waveguide. By total internal reflection the light is reflected from the surface of dielectric-dielectric interface. The term “micro” refers to the size of these structures. Usually the diameters of these structures are in the range of a few microns. Depending on the wavelength of the light the reflected waves can be constructively or destructively interfering. Hence these kinds of structures are highly wavelength selective. Marcatilli [1] first suggested the idea of curved waveguides and ring resonators as early as 1969. The first opto-electronic devices based on these structures were semiconductor lasers based on GaAs. Micro-ring and micro-disk lasers were demonstrated in 1977 [2]. Either a complete disk or ring or a half ring with cleaved facets formed the cavity of the laser. Later on in 1992 McCall and A. Levi [3] demonstrated lasing in much smaller devices. Figure 2-2 shows SEM image of a fabricated micro-disk laser. These devices are as small as 1pm in radius. The very small size of the cavity formed by very small disk size ensures single mode operation of the laser. Very low threshold currents were demonstrated due to strong coupling of spontaneous emission to a single mode of the cavity. Although very interesting in concept except for some pure physics studies micro disk lasers have not found any application. One problem associated with these lasers is the light is radiated in all directions. So although the emission is single mode it Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 nci nc o <nci Figure 2-1: Concept of a micro-resonator is not possible to obtain large amount of power, which is critical for any good laser. Other structures are suggested to improve directionality to radiation [4]. To improve the coupling efficiency one can introduce waveguides coupled to resonator to collect the light. Figure 2-3 shows a structure in which two waveguides are coupled to a resonator. In this structure the light can couple from the channel waveguides to the resonator and vice-versa. However it is not very easy to achieve coupling between the Figure 2-2:SEM picture of micro-disk laser fabricated in 1992 at Bell Labs Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 Figure 2-3: Channel waveguide coupled to resonator waveguide and the resonator. As I will describe in the following sections many conditions should be satisfied to achieve a good coupling between the resonator and the waveguide. Ring resonator coupled to channel waveguide with sizes as large as a few centimeters were demonstrated in 1980’s [5][6], Little [7] and Rafizadeh [8] demonstrated the coupling from the waveguide to small micro-resonator for the first time in 1997. It is noticeable that ring lasers have similar structure however ring lasers are usually many centimeters or even meters long. Notice that it is required to make devices as small as 10pm if it is going to be used in communications. There are two bottlenecks to this problem. The first one is due to the complicated geometry of the micro-resonator it is impossible to solve the Maxwell equations analytically to design Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. an optimal structure. Simulation methods have been used for calculation of the resonator and coupling properties. The second problem is due to fabrication of these structures. As we will show in the following sections the micro-resonator requires nano-meter scale fabrication capability. The progress in micro-fabrication now makes it possible to fabricate these devises. 2.2 Analysis of loss mechanisms in micro-resonator In this section we will analyze the micro-ring resonator problem. First the mode profde, effective index of whispering gallery modes and bending loss are calculated. In the next part we will discuss the scattering loss due to surface roughness. Finally we will discuss the material loss. In next sections we will calculate the coupling to the micro-resonator and we use coupled mode theory to calculate the transfer function of micro-resonators. We will derive simple formulas to describe the quality of a micro resonator. 2.2.1 Bending Loss and effective index There are a large number of papers on calculation of the curved dielectric waveguides. This problem is in particular interesting for bending of optical fibers for example. Marcatilli [1] first analyzed the problem. Here we describe simple yet accurate methods, which uses computers to calculate the bending loss. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 Figure 2-4: Geometry of curved cylindrical waveguide Consider a curved dielectric interface as shown in structure in the Figure 2-4. The Maxwell equation is written as (Assuming no z variation and TE): V%E, (x, y) + k(x, y ) 2 Ez (x, y) = 0 (2-1) Because of the curved geometry the solution to Maxwell equations is complicated. One approach for solving this problem is using the conformal transformation [9]: W = R0 ln(“ -) (2-2) -W Where: Z = x + iy W - u + iv (2-3) The Maxwell equation is rewritten: V 2 uvEz ( u , v ) + k 2e2ulR°Ez{u,v) = 0 (2-4) It can be easily shown that: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 Guided mode effective indexes Figure 2-5: (a) Original refractive index profile for curved waveguide (b) Equivalent straight waveguide refractive index profile Therefore the edge of guiding layer at r=Ro is the u=0 line in the W plane and the other edge at r=R0 -a is at u-Rq ln(Ro~a)/Ro. As it can be seen the curved structure is transformed to a straight structure. However the index is not constant anymore. Figure 2-5 shows the original index profile and the transformed index profile. To solve the Maxwell equation one can use standard numerical techniques to obtain the modes for this index profile. One o f the techniques is the finite difference method. Notice that because of the exponential variation of the refractive index there is no pure guided mode. All the modes for this structure are leaky. This problem is very similar to tunneling of electrons in a finite barrier. By introducing absorbing boundary conditions one can calculate the bending loss using finite difference method. The actual structure in our experiment is a ring shown in Figure 2-6. Conformal mapping cannot be applied for 3D case. To solve this problem Thyagarajan [10] has suggested the following method for the solution of the problem. Assuming the u = R 0 ln(-p-) Aq v = Rne (2-5) (2-6) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 Figure 2-6: Geometry of the curved waveguide scalar case the electric fielc) can be written as: Ez (r, r or dr oz r Assuming that index can be written as: n2(r,z) = n;{r) + n2 z(z) Where: ni \ n l - n l , l 2 (R0 - a )< r < (R0) r I n]t l 2 O.W. (2-8) (2-9) (2-10) And: 2 | nlo ~ nd ! 2 — t / 2 < z < t / 2 O.W. One can use method of separation of variables. E(r,z) = R(r)Z(z) (2- 11) (2-12) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 And obtain the solution: r Sr dr ~ T " (r ^ + (k°n''w - + & )R = 0 r or dr r (2-13) And (2-14) The above Equation can be further simplified by taking R(r) = r m u{r) and Finally the last two equations are discretized and numerically solved. n(g)is very similar to the index profile obtained by conformal mapping. Notice that there are two approximations in this method. First we assume the scalar wave equation. This is a good approximation even with relatively large index contrast between core and cladding. The second approximation is the assumption of separation o f index profile. Based on this assumption the index profile of the original problem is replaced by the index profile shown in Figure 2-7. This is a good approximation since the field energy is small in the regions that index is changed. £ = r - R 0 : (2-15) Where: »(£)2 =«,2(r) + {- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 nc nci -nC o 2)0'5 nci (2nc,2 nci W o nci nc o 2)0'5 W i (2nc,2- 2 x 0 .5 2 x 0 .5 Figure 2-7: Refractive index profile of the original curved waveguide and refractive index profile of the approximated waveguide for 3D case Besides the index change is fairly small for small index difference between core and cladding. We have used TempSelene, which is commercially available package to do the bending loss calculation. This software uses semi-vectorial finite difference method in cylindrical coordinates with absorbing boundary conditions to calculate the mode profile and the loss of a curved waveguide. Figure 2-8 shows the result of the calculations for a 50pm diameter micro ring with 1pm thickness. As it can be seen from these figures the modes are hybrid. However for the case of TE for example the value of TEY is an order of magnitude larger than TEX and 3 orders of magnitude larger than TEZ. It is also important to know that for the calculation of loss one requires perfect absorbing boundary conditions in the implementation of numerical value. One can refer to [12] for detailed explanation of the absorbing boundary condition implementation. Figure 2-9 shows the minimum radius required to achieve 1 dB/cm loss as a ftmction of the index contrast between the core and cladding for a structure shown in the figure. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TMZ TEZ Figure 2-8: Field profile for TE and TM polarizations. (Notice that for TM for example TMY is one order of magnitude smaller than TMX and TMZ is 3 orders of magnitude smaller than TMX) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 45 - 40 - 35 - 350 300 _ 30 i - 250 E - 200 3 100 K 10 - 5 - - 50 0 -r------------------------- , -----------, -------------------------- , ----- ■ ■ _ 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Index contrast (nco-nC |) Figure 2-9: Minimum radius required to achieve ldB/cm loss and the corresponding FSR calculated for 1.55pm as a function of difference of index o f refraction of core to Figure 2-9 also shows the calculated Free Spectral Range (FSR) for the micro resonator. As it is clear from this figure large FSR is possible with relatively small index contrast. For a typical communication system the available bandwidth of Erbium doped fiber amplifier is 40nm. Flence a single micro-resonator should have FSR comparable to 40nm if it is going to be used for WDM applications. Based on this calculations an index contrast of 0.55 is enough to achieve 40nm FSR. It is very important to minimize the index contrast since, as we will see in the following section the high index contrast results in a very large wall roughness scattering loss. Another important parameter obtained from these calculations is the effective index. We define the effective index as the following: cladding for the structure shown in figure A B n < f f ~ D (2-17) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 Here Rm ax is the radius in which the field amplitude is largest. Figure 2-10 shows the calculated effective index for the same conditions as Figure 7. The effective index is important when considering the coupling to the micro-resonator. 1.54 1.52 - nco=T.57 nci X O T 3 C 1.5 pm < D > 1.46 - 1.44 U J 1.42 - 0.6 0.7 0.3 0.4 0.5 0 0.1 0.2 Index contrast (nco-ncl) Figure 2-10: Calculated effective index of the curved waveguide at 1,55pm for the fundamental mode assuming 1 dB/cm radiation loss for the structure shown as a function of refractive index difference between core and cladding. 2.2.2 Scattering loss In the previous section we discussed the calculation of the whispering gallery mode and defined the effective index and the loss due to bending. As it was shown for 0.6 index contrast it is possible to confine light in an area as small as a 10 microns in diameter. With larger dielectric discontinuity (e.g. semiconductor air) it is possible to make the bending loss very small. However there is another dominant loss mechanism in micro-resonators. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 During the fabrication, which includes lithography and etching, there would be some roughness introduced in the structure. Figure 2-11 shows an ideal and a practical micro-resonator Figure 2-11: (a) An ideal micro resonator (b) Practical micro-resonator. In this section we will analyze this problem and obtain an analytical formula, which describes the loss due to wall roughness. To calculate the amount of the radiation Marcusa [13-14] developed a technique for the calculation of the radiation loss based on the coupling between the radiation modes and the guided modes of the waveguide. Here we provide a simpler approach, which is very similar to calculation of radiation from a series of antennas. To solve this problem we assume a random wall variation in the perimeter of the micro-resonator. Previously Lacey and Payne [15] have calculated the scattering loss due to this kind of roughness for straight waveguide. Here we provide a similar approach for the micro-resonator. The micro resonator has an outer radius of Ro and a thickness of l. The approach is basically considering the roughness as small antennas radiating the energy out of the waveguide. We consider the simpler 2D case to simplify the problem. The roughness Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 Figure 2-12: Geometry for the surface roughness problem Can be considered random variation of radius as a function of (p. First consider that we can write the index as: Notice that this is slightly different than the ring index. This is in fact describes a disk index. However since the energy is confined in the edge of the ring it does not matter whether to consider a ring or a disk. Also the roughness in the inner edge is not important since the filed is very small in the inner edge. So we can write the wave equation as: n2 = n] - (n;0 - n2 ,)U[R0 + f{(p) - r] (2-18) Where U[Ro+f((p)-r] is a unit step function i.e.: a < 0 a > 0 (2-19) so that: n2 =n2 C 0 r< R 0+f(<p) n2 = n2 c l r > R0+ f(<p) (2-20) V 2Ez (r, ) = k 2 (n2 - n2 C 0 M * 0 + f{cp) - r]Ez (r, < p ) (2-21) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 and kl = 1 0 2 s0 J u0 (2-22) Although (2-21) is an exact expression of the problem however it can not be solved analytically. To solve this problem we consider that U[Ro+f(cp)-r] is zero outside the waveguide region. Hence the right hand side of the equation (2-21) is only dependent on the filed inside the waveguide. The perturbation due to roughness is assumed to be small enough so that it does not affect the field inside the waveguide. So we can replace the field inside the waveguide by the unperturbed solution of the problem, which was obtained in the previous section. Ez (r, (r) e x p ( - z ^ ) (2-24) This approximation has been used before [17]. The equation (2-24) is an inhomogeneous differential equation. This is very similar to radiation problem. To solve this equation we use the green function method. The solution to (2-24) is given by: 2 k a : Ez (r, ' dr ' (2-25) 0 0 Because the U[Ro+f((p)~r]=0 for r>Ro+f(<p) we can write: 2?r RQ+f((p) Ez{r,(p) = {n2 cl- n 2 co)kl fd<p' J 0 ( r ■ )exp(-z/fy’ )G(r,r',(p,(p')r'dr'(2-26) 0 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 Next we can divide the integration from r=0 to r=R0 and from r=Ro to r-Ro+f(<p). The part from r=0 to r=Ro does not contribute to the scattering loss. So we only need to consider the integration in the section r=R0 to r=Ro+f(<p). Next consider that f(<p)«R0 so we can write: Rq +/(<P) | p(r ')dr' = p(R0)f(<p) (2-27) * 0 So we can simplify the double integral to: In Ez (r,<p) = (n2 cl- n 2 J k l $d<p'®(R0)exp(-ifi<p')G(r,R(l,<p,<p')R0f(<p') (2-28) o Next we consider the roughness function f(<p). This is a random function. We can measure this roughness using atomic force microscopy [16], The best way to describe this random function is using the statistical approach. To solve (2-27) we can replace thQf(<p) by its Fourier transform: f((p) = J Fm exp(inup) (2-29) m = -co So we can rewrite (2-27) as: c o Ez(r,<p) = (n2 cl- n 2 co)kfo(R 0) Fm jd<p'exp(-i/3<p')R0G(r,R0,(p,<p')exip(im<p')(2-30) m = -co o Finally we have to replace the green function. The green function has been calculated for cylindrical coordinates with no z variation and is given by [18]: G(r, r > , (p ') = - H {2 \ n dk0 \r-r'\) (2-31) 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 where H ( 02 ) is the Hankel function of the second kind. Since we are only interested in calculating the radiated power we can replace the Hankel function with its asymptotic form given by: lim H f y{r) = , I— exp(-/(r - n 14)) (2-32) So we can write: E, <r,9) = («c/ - n D k l ^ i R . ) (2-33) 2 7 1 x lL Fm fd<p'exp(i(m-fl)<p’ ) _ , exp (~i(nclk0 \r - R0 \ - n / 4)) m = - c o o V Y * 0 1 Since we are interested to calculate the radiated power we can make r arbitrarily large. Since we have: lim \r - I = lim J r 2 + i ?0 2 - 2ri?0 cos(<p - ^ ') = r + f?0 cos(^ - ^7') (2-34) » • i . r / 1 ' ' f " Notice that we can replace\r - R 01 by r in the term j— — r but we have to keep \hi\r - Rn o the R( l cos((p -cp') in the exponent term. So finally we get this integral: E: (r,<p) = (n2 c I - f72 o)k2R0O(R0) ----- — exp(-inclk0r) (2-35) 7ZnclK r c c x X \d(p'exp(i(m- f3)cp')exp(-i(nclk0R^ cos(< p-(p')-n!4)) m --o o o Now using the following identity [19]: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 2 . 7 1 We can simplify (2-34) to obtain: , - n Jn (x) = — J exp(zx cos($>') + inq) ')d(p' (2-36) Ez (r,<p) = (n2 d - n;o)^0 2i?0O(i?0) — exp(-inclkQ r) (2-37) TrnclkQ r n 2n ■ A x ( - e x p 0 ) ? - - ) ) - ^ ^ X J fi-n,(-nclKRi>)Fm * 1 m = — co Next we calculate the power radiated out of the disk. We obtain: I O = ~ , P L(«;, ( 2 * f £ (2-38) 2 \/* 0 »=-» Notice that we have assumed that f(q>) can be described by a wide sense stationary random process so that: \ y m = n E{Fm K ) = \ : (2*39) 0 m ^ n Where: _ 2 n 1 2n — J /?(<!>) exp(-/mO)rf<D (2-40) and: Assuming R(z) is given by: , Rn O R(z) = Sp2Qx p(— i) (2-42) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 We can approximate ym by: Tn, 5p2k 1 ftR^ . L2m2 o 1 + . c (2-43) R 2 Finally dividing the radiated power to the length of the device and the guided mode power we can obtain the wall roughness scattering loss per unit length as: p ~ n co I £ 0 2 Jd>(r)2<ir (2-44) 4 n„ (n2 cl- n 2 J ~ k X O(i?0)2(2 O V J l m(ndk0R0)ym (2-45) P - m-~ o o Assuming the guided power is normalized such that: J® (r)2 dr = 1 Equation (2-44) is exact and can be easily calculated. To get a feeling on the dependence of the loss on the parameters of the resonator we provide a simple approximation to the above formula. Notice that we have approximately: nnclk{ ,R0 \/3-m\< nclk0R0 OW. (2-46) And assuming yn 5 p % XRn which basically means that the Lc is much smaller than the wavelength we obtain: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 a w= ^ - ( 4 - n i ) 2kl®(R0f S p 2Lc (2-47) ™co Notice that a*, is a square function of the index difference between the core and cladding. Figure 2-13 shows this function plotted for Sp=30nm and Lc=0.1/.mi [16] for different core to cladding index difference. It is interesting to note that if we need a 40nm FSR then we need a minimum index difference of 0.6 (Figure 2-9) then we would get at least 70dB/cm surface roughness loss. Scattering Loss (db/cm) as a function of delta 70.00 T — _ 60.00 | 50.00 - m 40.00 - ~ 30.00 - o 20.00 "J 10.00 - 0.00 — 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Index difference (nC 0 -nC |) Figure 2-13: Wall roughness loss calculated at 1.55 pm as a function of index difference between core and cladding for 30nm roughness 2.2.3 Materials and material loss In the past two kinds of materials have been considered for the fabrication of micro-resonators and optical waveguides. Semiconductors versions include Si and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 InGaAs/InP (for 1.55(am) and Glass. The semiconductors are fabricated by epitaxy and dry etching. The waveguides are rather small due to high index. This makes coupling to these devices particularly difficult. Also for the case of micro-resonator with very large index contrast (assuming air cladding) significant wall scattering loss will be obtained. Glass or Silica has been considered for the fabrication of photonic integrated circuits. In fact the most successful technology to date has been the Silica waveguides fabricated by flame hydrolysis deposition (FHD) on a substrate (usually silicon). The glass system is not very attractive for micro-resonators due to relatively small index contrast possible between core and cladding. In fact practical micro resonator devices use air as cladding. The unsymmetrical structure obtained in this way with air on top and a substrate on bottom is not very attractive. There is a third class of materials, which is in fact is a huge class of materials. Polymers have shown a wide range of refractive index (from 1.3 to 1.8) and are very flexible for processing. A very important feature for polymers is that small pattern can be defined optically. Usually in other technology to fabricate a waveguide one needs to use a polymer to define a pattern and do etching to transfer the pattern to the material. However polymers can be made in the form of photo-resist and waveguides can directly be defined using optical exposure. This is extremely important since the micro-resonators fabricated are limited by scattering loss due to rough surface after etching. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 Recently very low loss polymers have been engineered for telecommunication wavelength [20][21]. The loss in these polymers is less than O.ldB/cm. However these polymers are not commercially available. We have used some standard polymers, which in fact have been used for other purposes to fabricate our devices. The losses of these polymers are summarized in Table 2-1. The polymer loss is measured by spin coating a thin layer of polymer on low index SiCL layer. Light is coupled to the slab waveguide made in this way by prism coupling. Next the slab waveguide is immersed into a liquid with high refractive index and the light is coupled out. Table 2-1 :The refractive index and the loss of the polymers used for device fabrication Material Index 1300nm Loss (dB/cm) 1300nm Index 1550 nm Loss (dB/cm) 1550nm SU-8 1.567 0.53 1.565 4 NOA61 1.545 0.33 1.541 1.1 UFC170 1.49 0.53 1.49 3 UV15 1.51 0.89 1.5 4.2 Teflon AF 1601 1.3 " 1.3 - By moving the slab waveguide into liquid one can measure the loss accurately [22]. Also the refractive indexes of the polymers are measured using Ellipsometer. One of the beauties of polymers is ability to engineer the material to achieve desired optical properties. Engineered polymers have demonstrated superior nonlinear properties compared to other materials [24]. Also it is possible to introduce gain to the polymers [26] [27]. Finally one can make the polymers conductive while they are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 still optically transparent. These properties will open the door to fabrication of very functional devices in the future. As a part of this thesis we will fabricate micro resonators employing nonlinear polymers. 2.3 Waveguides coupled to the micro-resonator Coupling to micro-resonators is extremely critical to achieve practical devices. Because of the small evanescent tail of the electromagnetic mode in the resonator it is very difficult to achieve efficient coupling. The situation gets worse with small devices since the interaction length between the channel waveguide and the micro resonator is very short. Two schemes have been suggested for the coupling. The easiest scheme is the side coupling to the resonator shown in Figure 2-14(a). The second scheme is the vertical coupling to the resonator (Figure 2-14(b)). The side coupling method requires one-step lithography. However the gap between the resonator and the waveguide must be extremely small, (about 0.1pm). This makes the fabrication very difficult. In the vertical coupling the resonator and the waveguides are in different layers. To fabricate a vertical coupling using semiconductors one Figure 2-14:(a) Side coupling to micro-resonator (b) Vertical coupling to the micro resonator Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 requires wafer bonding [28]. However using polymers one can easily fabricate these devices. The gap in the vertical coupling can be controlled easily. Since the interaction length between the channel waveguide and the micro resonator is very small and since the index contrast between the core to cladding is large for small radius devices one requires a very efficient design to achieve the desired amount of coupling. It is almost impossible to achieve a good coupling between the resonator and side coupled channel waveguide. Hence one requires changing the shape of the resonator to a racetrack shape to achieve coupling. However in the racetrack design because of the transition of mode between the curved waveguide and straight waveguide some coupling loss will occur. So the best design is the vertical coupling. 2.3.1 Beam propagation method for calculating the coupling To analyze the vertical coupling problem analytically some methods have been introduced in the past [30] [31]. We have used computer simulation for the calculation of the coupling. One method, which has been used very efficiently in the past to calculate the coupling of the modes, is the beam propagation method. Using the 3D beam propagation method and defining a structure as shown in Figure 2-15 and by monitoring the power transmitted through the channel waveguide we can estimate the amount of the power which is coupled to the micro-resonator. It is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 important to note that the coupled power to the curved waveguide be lost in the absorbing boundaries defined as the boundaries for the beam propagation method. Figure 2-15: The structure modeled for calculating the coupling to the resonator The method has proved to be accurate for the calculation of the coupling. Figure 2-16 shows a typical result in which the channel waveguide is excited and the resonance mode is coupled. Notice that the shape of the mode matches the result calculated before. Figure 2-16: Field profile for coupling between the waveguide and the resonator mode Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 2.3.2 Coupling optimization To optimize the coupling we consider the effect o f different parameters on the coupled power. First consider the effect of channel waveguide refractive index. 1 0.95 5 0.9 0 0.85 1 0-8 £ 0.75 g 0.7 0.65 0.6 L wg 5 jam 1.5pm 1.535 1.54 1.545 1.55 1.555 1.56 Channel waveguide refractive index 1.565 Figure 2-17: Calculated dropped power due to coupling to the micro-resonator as a function of refractive index of waveguide for the structure shown. The minimum happens due to phase matching of the waveguide mode and resonator mode. Figure 2-17 shows the amount of dropped power for a structure shown in the Figure as a function of the refractive index of the channel waveguide. It is clear that for a given refractive index of the channel waveguide the coupling is maximum and there is a minimum in the transmitted power. By calculation the effective index of the WGM mode as defined in the previous sections and the effective refractive index of the channel waveguide we observe that the minimum occurs when these effective indexes are equal. This is basically the phase matching condition. Also it is clear that the coupling is not as sensitive to the effective index mismatch compared to straight waveguide coupling for example [31]. This is due to the circular geometry of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 resonator, which provides a range of effective indexes since the phase front of the waves travel with different speeds depending on their distance from the center of the resonator. It is possible by adjusting the refractive index of the channel waveguide to excite higher order modes in the micro-resonator. (This will appear as another minima in lower values o f refractive index in Figure 2-17). We can also observe that one needs to control the to refractive index on the order of 0.001. If one cannot change the index very accurately, one can change the waveguide geometry to achieve the required effective index matching. Next we consider the effect of mis-alignment of the waveguides and the resonator. In this case we assume that the effective index of WGM mode is matched to the effective index of the channel waveguide. Figure 2-19 shows the dropped power as a function of the alignment mis-match d shown in the Figure 2-18. It is interesting to note that the maximum coupling occurs when d=-ljum. This is probably due to the fact that for negative d there is a larger interaction length between the WGM mode and the channel waveguide mode. Also this calculation shows that the alignment accuracy must by as good as 0.1pm so that the dropped power does not Figure 2-18: Geometry for mis-alignment of the resonator and waveguide Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 _ 0.95- 0 1 °'9 ~ Q . I 0.85- Q , O 0 .8 - 0.75- 0.74 3 1 5 7 d(nm ) Figure 2-19:Calculated dropped power due to coupling to the micro-resonator as a function of mis-alignment of the resonator and waveguide change significantly. This is easily possible with the aligners made for semiconductor manufacturing Next we calculate the amount of dropped power as a function of the distance between the channel waveguide and the micro-resonator. This is shown in Figure 2- 20. We assume optimal conditions (i.e. index matched and d=-l). For this example the index of the cladding is 1.3 and the core index is 1.57. The radius of the device simulated in this case is 40 pm. As it is clear the distance between the two waveguide must be less than 1pm to achieve significant coupling. Also it is interesting to note that complete power transfer happens at a distance of 0.2 pm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 | 0.9- 1 0 .8- Q - 0.7- " § 0 .6 - £ 0 .5 < > a o.4- Q 0.3- 0 .2 - 1.0pm n=1.3 1.54 5 pm 1 1.4 0.6 0.8 1.2 0 0.2 0.4 d(pm) Figure 2-20: Calculated dropped power due to coupling to a micro-resonator at the optimum condition versus the vertical distance between the resonator and the waveguide 2.4 Micro resonator transfer function Now that we have talked about all sorts of loss mechanisms and the coupling to the micro-resonator we are ready to calculate the transfer function of the resonator. For this purpose consider the model provided below: Consider the geometry shown in Figure 2-21. Using the coupled mode theory [32] we can relate the field in the coupling region as: E3 ~ rEx + itE2 Ea ~ itEx + rE2 (2-48) Where \t‘ is the amount of coupling calculated using beam propagation method in the previous section and: I |2 I |2 m +\r\ =1 Also we can write: E2 =exp(-cmR)exp(i/3(p)E4 = aexp(i27tfJ)E4 (2-49) (2-50) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 E, Figure 2-21: Geometry of single waveguide coupled to resonator Where [i is the mode number calculated in the previous section and a is the total loss in the ring given by: a = a m+ab + aw (2‘51) a m : The material loss ott,: Radiation loss due to bending a w : radiation loss due to wall roughness By replacing E 2 from (2-50) to (2-48) and solving the equation for E4 we obtain: E4 ita exp(/2/r/?) (2-52) Ex 1 - ra exp(/2/T/?) Or: 2 \ 2 / 4 (1 - r )a (2-53) I x l-2racos(2;r/?) + r 2a 2 This function is plotted in Figure 2-22. As it is clear there are peaks which correspond to the condition (5-m (m an integer) the resonance. Notice that at the resonance cos(2n[i)=0. Also we can obtain: A = exp(/(?r + 2 m g z r g PH M ) (2-54) Ex l- r a e x p ( i 2 ^ ) Or: 2 / 3 _ a -2racos(2n;/3) + r~ /, l - 2 r a c o s ( 2 ^ ) + r 2a 2 (2-55) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 20.00 18.00 16.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 -3 ..~~ -a=0.98 -a=0.95 a=0.9 -a=0.8 0.86 1.86 2.86 Figure 2-22: Transfer function of the resonator for different values of the loss of resonator waveguide It is important to note that at resonance: h _ ( a ~ r)2 /, (1 - rd f 3 - ' ' (2-56) if a = r then all the power is extracted and lost in the resonator. This condition is critical coupling and has been demonstrated experimentally [33]. Consider that our fabricated devices have a second coupler to couple the power out of the resonator as shown in Figure 2-23. For this case one can calculated the coupled power from the input waveguide to the output waveguide simply by: Ei = itE4 cxp(ifi(p2 ) (2-57) To obtain: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 I I 2 I I 2 n r2 /, \- 2 r x r2acos(2n:^) + r^r2a2 (2-58) Ei Figure 2-23: Geometry of two waveguide to coupled to a micro-resonator Where ti and t2 are the coupling of the two couplers. It is noticeable that critical coupling in this case is given by: rx = r2a (2-59) Assuming this condition is satisfied it is easy to show that the transmitted power at resonance is given by: L 1 - k (— ) = V j /m a x A l - k 1 i i2 ~ 1 i i2 l - r 2 l - r 2a (2-60) Next let’s define and calculate some parameters, which are important for micro resonators. The first parameter is the Q of the micro-resonator, which is defined by: Q- An (2-61) A /^/2 A v1/2 where A /L,/2 is the full width half maximum of the dropped power or transmitted power. To calculate Av1 /2 we can re write (2-58) as: I I 2 I I 2 ri r 2 (1 - r x r2a) +4rx r2a sin infi) (2-62) Now the FWHM happens when we have: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 2 In the first order approximation we will get: sm(n/Sv2,) = ± (l / ' V ) (2-63) ^4rx r0a A Now since we can write: (2-64) rx r2a A ,21= 7 L - " ,W ,I1) i (2-65) \ l 2 ± Where L is the length of the resonator (2nr). We can obtain: = = < *225H l (2-66J ■ s jrx r2aLnng where ng is the group index given by: dne (A) ng{A) = ne( A ) - A - ^ - (2-67) dA So we obtain: Jr,r0aLn;nr , Q = t t 2 — r f (2' 6 8 ) (1 - r x r2a ) \ Equation (2-68) specifies the loaded Q of the resonator. If we are considering the unloaded Q we can replace rj and r^by 1. Also since we have: 1 - a = 1 - exp(-aZ / 2 )« aZ, / 2 (2-69) We can obtain this equation for unloaded Q: 2 7tn„ Q = — r (2-70) aA0 For practical purposes where a is specified in dB/cm and Xo is specified in microns we obtain: 2.73x10V Q = - ----- :----- L (2-71) aA0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 It is important to note that the Q is not a function of the length o f the device. Also it is interesting to know that with ldB/cm loss a Q of more than 105 is possible. Next we consider free spectral range (FSR), which is basically the distance between the peaks in the resonator. To calculate the FSR we consider that the resonance frequency of the mode number j5 can be specified by: 0 = , /? +1 = (2-72) ^ m + 1 So the free spectral range is simply: FSR = A + 1 - 1 = (2-73) m + l m ng(A)L Finally another important parameter for the micro-resonator is the finesse. The finesse is defined as: f = m . ^ = ± (2-74) A A 1/2 ol L aR This parameter together with FSR is the most important parameters for a micro resonator. Again for practical purposes one can use this formula for Finesse: / = (2-75) aR where a is in dB/cm and R is in microns. To characterize and obtain the coupling and the loss of the resonator it is enough to measure the through port response. Since the through port response is given by (2- 55) one can solve this for r and a if one knows A, A and Af as shown in the figure and the FSR. Notice that Af is measured at the point in the middle of A and A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 C Frequency Figure 2-24: Measurements required for characterizing MR. One can then easily obtain: ra 1 . ,?rA/\ (2 --------------) ==cos(_Z _) 2 2 ra FSR (2-80) Using this together with (2-56) one can calculate r and a with a simple measurement. If the resonator is coupled to a second waveguide, one need to simply replace a by ar in the above formulas. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 2.5 References [1] E.A.J. Marcatili, “Bends in optical dielectric waveguides”, The Bell System Technical Journal, Vol 48, pp.2103-2132,1969 [2] Matsumoto, N.; Kumabe, K., AlGaAs-GaAs Semiconductor ring Lasers, NTT, Japan, Japanese Journal of Applied Physics, Vol. 16, No. 8, 1395-1398, (1977) [3] S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan," Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60,no. 3, pp 289-291,1992 [4] Gmachl, C.; Capasso, F.; Narimanov, E.E.; Noclcel, J.U.; Stone, A.D.; Faist, J.; Sivco, D.L.; Cho, A.Y.,” High-power directional emission from microlasers with chaotic resonators”, Science, vol.280, no.5369 p. 1556-64, 5 June 1998 [5] Haavisto, J.; Pajer, G.A., “Resonance effects in low-loss ring waveguides”, Optics Letters, vol.5, no.12 p. 510-12, Dec. 1980 [6] Honda, K.; Garmire, E.M.; Wilson, K.E.” Characteristics of an integrated optics ring resonator fabricated in glass”, Journal of Lightwave Technology, vol.LT-2, no.5 p. 714-19, Oct. 1984 [7] B.E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P.Laine, “ Microring resonator channel dropping filters,” J. Lightwave Technol. 15,no6. pp 998- 1005 ,1997. [8] D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S.T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett., vol. 22, no. 16, pp. 1244-1226, 1997. [9] S. Ramo, J.R. Whinnery, T.V. Duzer, “Fields and waves in communication electronics”, John Wiley & Sons, NY. 1984 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 [10] Thyagarajan, K.; Shenoy, M.R.; Ghatak, A.K., “Accurate numerical method for the calculation of bending loss in optical waveguides using a matrix approach”, Optics Letters, vol.12, no.4 p. 296-8, April 1987 [11] Ghatak, A.K.; Thyagarajan, K.; Shenoy, M.R., “Numerical analysis of planar optical waveguides using matrix approach”, Journal of Lightwave Technology, vol.LT-5, no.5 p. 660-7, May 1987 [12] Teixeira, F.L.; Chew, W.C. “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates”, IEEE Microwave and Guided Wave Letters, Vol 7 , no 11 p. 371 - 373 , Nov 1997 [13] Marcuse, D. “Mode conversion caused by surface imperfections of a dielectric slab waveguide”, Bell System Technical Journal, vol.48, no.10 p. 3187-215, Dec. 1969 [14] Marcuse, D. “Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function”, Bell System Technical Journal, vol.48, no.10 p. 3233-42, Dec. 1969 [15] Lacey, J.P.R.; Payne, F.P.” Radiation loss from planar waveguides with random wall imperfections”, IEE Proceedings J (Optoelectronics), vol. 137, no.4 p. 282-8, Aug. 1990 [16] F. Ladouceur, J.D. Love, T.J. Senden,” Effect of side wall roughness in buried channel waveguides”, IEE Proc-optoelectronics, IEE Proceedings- Optoelectronics, vol.141, no.4 p. 242-8 Aug 1994 [17] Snyder, A.W., and Love, “Optical waveguide theory” Chapman and Hall 1983 [18] Balanis, C. A. “ Advanced Engineering Electromagnetics”, John Wiley & Sons, 1989 [19] Arfken, G. “ Mathematical methods for physicists”, Academic Press, 1985 [20] L. Eldada, S. Yin, R. A. Norwood, and J. T. Yardley, “Affordable WDM components: The polymer solution,” Proc. SPIE, vol. 3234, pp. 161-174, 1997. [21] S.I. Najafi, T. Touam, R. Sara, M.P. Andrews, M.A. Fardad, “ Sol-Gel Glass Waveguides and Grating on Silicon”, IEEE J. Lightwave Tech. Vol 16, no 9, 1640-1646, 1998 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 [22] Chia-Chi Teng Precision measurements of the optical attenuation profile along the propagation path in thin-film waveguides”, Applied Optics, vol.32, no.7 p. 1051-4, 1 March 1993 [23] Gamer, S.M., Sang-Shin Lee, Chuyanov, V., Chen, A., Yacoubian, A., Steier, W.H., Dalton, L.R., “Three-dimensional integrated optics using polymers,” Quantum Electronics, IEEE Journal of , Vol. 35 No 8 ,pp 1146-1155, Aug. 1999 [24] Yongqiang Shi; Cheng Zhang; Hua Zhang; Bechtel, J.H.; Dalton, L.R.; Robinson, B.H.; Steier, W.H.,” Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape”, Science, vol.288, no.5463 p. 119-22, April 2000 [25] Min-Cheol Oh; Hua Zhang; Szep, A.; Chuyanov, V.; Steier, W.H.; Cheng Zhang; Dalton, L.R.; Erlig, H.; Tsap, B.; Fetterman, H.R., “Electro-optic polymer modulators for 1.55 mu m wavelength using phenyltetraene bridged chromophore in polycarbonate ”, Applied Physics Letters, vol.76, no.24 p. 3525-7, June 2000 [26] Schon, H.; Kloc, C.; Dodabalapur, A.; Batlogg, B. , “An organic solid state injection laser”, Science, vol.289, no.5479 p. 599-601, July 2000 [27] Riechel, S.; Lemmer, U.; Feldmann, J.; Berleb, S.; Muckl, A.G.; Bmtting, W.; Gombert, A.; Wittwer, V.,” Very compact tunable solid-state laser utilizing a thin-film organic semiconductor”, Optics Letters, vol.26, no.9 p. 593-5, 1 May 2001 [28] Tishinin, D.V.; Dapkus, P.D.; Bond, A.E.; Kim, I.; Lin, C.K.; O'Brien, J.” Vertical resonant couplers with precise coupling efficiency control fabricated by wafer bonding”, IEEE Photonics Technology Letters, vol.l 1, no.8 p. 1003- 5, Aug. 1999 [29] Rowland, D.R.; Love, J.D.” Evanescent wave coupling of whispering gallery modes of a dielectric cylinder”, IEE Proceedings J (Optoelectronics), vol. 140, no.3 p. 177-88, June 1993 [30] Rowland, D.R.” Analysis of optical directional couplers composed of asymmetrically curved waveguides”, IEE Proceedings-Optoelectronics, vol. 142, no.6 p. 305-12, Dec. 1995 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 [31] Ulrich, R.” Theory of the prism-film coupler by plane-wave analysis”, Journal of the Optical Society of America, vol.60, no. 10 p. 1337-50, Oct. 1970 [32] Reinhard Marz, “Optical Waveguide Theory”, Artech House, Bostonl995 [33] Cai, M.; Painter, 0.; Vahala, K.J.,” Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system”, Physical Review Letters, vol.85, no.l p. 74-7, 3 July 2000 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 Chapter 3. Experimental results for passive MR In this section we will describe the fabrication of micro-resonator. Two different micro-resonators are fabricated using polymer materials. In one design a relatively large devices is demonstrated. Next using a larger index contrast a smaller device with a larger FSR is demonstrated. The design, fabrication and experimental measurements are presented. 3.1 Larger devices 3.1.1 Device design To investigate the micro-ring resonators using polymer materials we started with relatively large devices. The schematic cross section of the device as well as the fabricated device layout is shown in Figure 3-1. A micro ring is coupled vertically to the input and output channel waveguides. SU-8 [1] is used for the micro-ring. SU-8 is a relatively low loss material, which can be patterned using photolithography. The optical properties of the materials used in this device were measured in our lab and are summarized in Table 2-1. As it can be seen from the figure the cladding is chosen to be UFC170A. The index difference between the core and cladding is 0.07. So we are limited to 220pm minimum radius for 1300nm and 330pm for 1550nm (look at Figure 2-9) if we required ldB/cm-bending loss for the device. Next we consider the material loss. The loss for SU-8 was measured and is 4 dB/cm for 1550 nm and 0.5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UFC 170A i . 2 pm N 0 A 6 1 2 p m ---------- pC 170D SU-8 Vsum V UV15 __ SU-8 l|am (a) Figure 3-1: Large passive device, (a) Fabricated device picture (b) Schematic cross section dB/cm in 1300 nm (Table 2-1). If we assume 2dB/cm scattering loss (Figure 2-13) and 1 dB/cm radiation loss, the total ring waveguide loss is approximately 7 dB/cm for 1550 nm and 3.5 dB/cm for 1300nm. Hence critical coupling into a 330pm radius resonator without a drop port at 1550nm requires 18% coupling. To make an efficient coupling first we have to make sure that the effective index of the whispering gallery mode matches the effective index of the waveguide. Based on the calculations, the effective index of whispering gallery mode for a 1pm thick SU-8 ring with a radius of 330pm is 1.54. Using NOA 61 [1] as the channel waveguide material with UFC 170 as the cladding we can achieve the effective index of 1.54, which matches the ring mode. Next we have to vertically couple the ring to the waveguide. Based on our calculations with a vertical distance of 2pm between the channel waveguide and the ring it is possible to achieve the critical coupling (Assuming there is no drop port). It Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 is important to note that all our devices are single mode. The single mode operation is achieved since the fundamental mode is close to radiation loss limit. So higher order modes have high radiation loss and radiate out and single mode operation is achieved. 3.1.2 Fabrication The fabrication is as shown in Figure3-2. First a UV15 [1] lower cladding is spin coated at 6krpm for 30 sec. Using this condition 2.6pm thickness is obtained. Next the UV 15 layer is cured using UV light in a Fusion UV using a F300 UV lamp for 30 sec. Next the sample is baked for lhour at 160°C. This will fully cure the sample. Next a 1pm layer SU-8 negative tone photo-resist is spin coated and patterned using Carl-Suss mask aligner to form the micro ring resonator. It is important to note that no etching is required to form the ring structure. SU-8 is a kind o f photo-resist designed for thick MEMS structures [1], To achieve 1pm thickness we used 4.8 Krpm spin coating for 30 sec. The sample was baked for lhour at 160°C. Next the ring structure is covered with 5 pm UFC-170D. This layer will be the layer between the micro-ring and the channel waveguide. It is important to note that the sample is planarized after coating this layer. To achieve 5 pm thickness 5Krpm for 30 sec was used. The sample was cured in the UV light for 10 sec and was baked for 1 hour at 160°C. The UFC-170D layer was patterned and etched to form the channel waveguides. These channel waveguide were aligned to the ring-resonator. Since the polymers are all transparent in the visible light the alignment is very easy. Two- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 Si Spin co a tin g , B akin g, RIE ______________U V 1 5 Si Spin co a tin g 1 I S U -8 U V 1 5 Si P attering, U V I E xposure S U -8 ______________ U V I 5 Si Spin co a tin g , B aking, RIE S U -8 U V I 5 S U -8 1 S U -8 U V I 5 Si Patterning RIE E tching U F C 1 7 0 L S U -8 S U -8 U V I 5 Si Spin c o a tin g , U V cure. ' I N O A 6 1 U F C 1 7 0 S U -8 S U -8 U V I 5 Si R IE etch in g i U F C 1 7 0 N O A " 6 1 ------- S U -8 S U -8 U V I 5 Si Spin c o a tin g , U V cure I U F C 1 7 0 U F C 1 70 S U -8 N O A " 6 1 ------- S U -8 U V I 5 Si Figure 3-2: The fabrication procedure for large passive devices micron trenches were made in the UFC-170D material and hence the required distance of 2pm between the channel waveguide and the ring is achieved. Spin Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 coating NOA61 optical adhesive filled the trenches. For this layer lOkrpm spinning for 30 sec was used. This resulted in a ridge waveguide with a ridge height of 2pm and a slab height of 2pm. The slab region was etched away using reactive ion etching. It is important to note that the slab layer will couple the light out of the micro resonator. A 3pm upper cladding of UFC-170A was spin coated on NOA61. Finally the device was cut using dicing saw. 3.1.3 Device characterization Using single mode cleaved fiber or lensed fiber the input port of the device is excited. The two output are measured with objective lens and cleaved fiber as shown in Figure 3-3. A New Focus tunable laser with a line-width of less than 300kHz is used as the source. Applying a voltage to the piezo of the laser changes the laser wavelength. Figure 3-4 shows the response of the two port of the device for 1300nm. As it can be seen a nice Lorenzian response is obtained. Also there is a drop in the throughput port of the device. The bandwidth of the filter is measured to be 2GHz and 3 GHz for TM and TE polarization respectively (TE polarization is defined as the polarization in which the E vector is perpendicular to the ring plane). This bandwidth corresponds to O.Olnm and 0.015nm and a Q of 1.3*105 and 0.9*105 respectively. The free spectral range of the device is 0.8nm for 220pm radius device. And hence the finesse of the device is 80 (TE). The response shown in Figure 3-4 indicates the device is under-coupled. The total power out of the device at resonance (drop and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 Polarization controller T un able laser sou rce generator Fiber D etecto r A D etecto r O s c illo s c o p e D e te c to r unit Figure 3-3: Measurement setup Figure 3-4: Measured response of 220pm radius device as a function of the input frequency for both the drop and through port at 1.3 pm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 through ports) is 1.8 dB less than the power out off resonance (throughput port), which is a measure of the loss in the ring resonator. The device performance of the 330pm radius device for 1550 nm is also measured. The bandwidth of this device is 5 GHz and 10GHz for TM and TE polarization corresponding to 0.0375 nm and 0.075nm bandwidth and Q of 0.34*105 (TE). The FSR is 0.74 nm and hence the finesse for this wavelength is 19 (TE). Based on these values for Q the loss of the ring waveguide must be 3.3 dB/cm for 1300 nm and 10 dB/cm for 1550nm. This is in agreement with our calculation. The reason for the difference in Q between TE and TM is due to the difference in coupling of the TE and TM modes. For the TE mode the coupling is larger and hence the Q is smaller. 3.2 Smaller Devices In the previous section we demonstrated a relatively large device. The FSR of those devices were on the order of lnm. However for a commercial WDM system the FSR should be larger than this. To make FSR larger one requires making the core to cladding index difference higher. To demonstrate a smaller device we used a Teflon [1] material for the cladding. Teflon has a refractive index of 1.3. So it makes the index difference between the core and cladding 0.3. Hence based on this index difference we should obtain a FSR around lOnm. In this section we describe the fabrication of the Teflon device and the experimental results. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 3.2.1 Device design Since the refractive index difference in this case is 0.275 (1.575-1.3) we are limited by devices as small as 50pm in diameter (Figure 2-9). Next let’s estimate the amount of loss in the resonator. For 1300nm assuming 0.5 dB/cm material loss, ldB/cm bending loss and 14dB/cm scattering (see Figure 2-13) loss we would have a total of 15.5-dB/cm loss. This corresponds to a round trip loss of 0.055 for a 55pm device. Hence we require around 5% coupling. Hence the distance between the waveguide and resonator must be 0.8 pm. (Figure 2-20) 3.2.2 Device fabrication The fabrication procedure is shown in Figure 3-5. The fabrication of the device starts with spin coating Teflon on silicon substrate. Using 11% solution of Teflon AF 1600 in 3M FC-40 solvents we spin coat 2.8 pm Teflon. For this purpose we need 2Krpm and 30 sec. Next we etch this layer using RIE for 2 minutes in oxygen. This etching is required to change the surface properties of Teflon since the adhesion to Teflon is very poor. Next a 0.5 pm protection layer is spin coated on Teflon. This layer is a 25% UVI 5 solution in Methanol. Next this layer is etched down to 0.1 pm so that it does not affect the properties o f the micro-ring. (Thick layer will couple the light out of the micro-ring resonator.) In the next step a 1.5 pm SU-8 layer is spin coated on the substrate. This thickness is achieved by 3.5 krpm and 30 sec spin Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 coating. Next The SU-8 layer is patterned to form the micro-ring. In the next step a 4.5 pm Teflon layer is spin coated on the device. Using 11% solution one requires Si Spin coating, Baking, RIE Teflon Si I Spin coating, UV Cure, Baking, RIE UV 15 Protection Layer Teflon Si Spin coating T eflon Teflon SU-8 SU-8 UV 15 Protection Layer T eflon Si I Patterning RIE ” Etching SU-8 SU-8 UV 15 Protect b n Layer Teflon Si 1 Spin coating, U V cure, Baking SU-8 UV 15 Protectbn Layer Teflon Si Pattering, U V Exposure UFC 170 Teflon SU-8 SU-8 SU-8 UV 15 Protectbn Layer Teflon Si Teflon ▼ Spin coating, Baking, RIE SU-8 UV 15 Protection Layer Teflon Si 1 RIE Etching UFC170 SU-8 SU-8 UV 15 Protection Layer Teflon Figure 3-5: Fabrication procedure for small passive device Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 l.K rpm for 30 sec to achieve this thickness. The Teflon layer is etched for 2 minutes to improve the adhesion for the following step of the process. In the next step the Teflon layer is patterned using photo-resist and etched to form trenches for the channel waveguide. Next a UFC 170 A layer is spin coated on the device and cured using UV exposure and baking to fill out the trenches formed in the previous step. In the next step the slab part of UFC 170 layer is removed using RIE etching. Finally the device is cut using dicing saw. Figure 3-6 shows the device cross-section and the top picture of the fabricated device. 3.2.3 Device characterization The characterization of the device is similar to the larger device except that in this case. To achieve a large wavelength range for the characterization of the device we use a computer in this case to collect the data. So the detector is connected to the computer. Also computer is used to change and read the wavelength and control the tunable laser. Figure 3-7 shows the measured power for a 55pm diameter device in the drop port. The FSR is close to lOnm for 1550 and also for 1300 (With a smaller device). The bandwidth of the device is 12GHz for 1550nm and 10.3GHz for 1300nm. Hence a Finesse of 84 for 1550nm and 92 for 1300nm is obtained. In the throughput port small drop is observed. This is because the coupling is not optimized so the amount of power coupled to the resonator is small. Figure 3-8 shows the response for a 64 pm diameter device. In this case the Q is higher. However the device is not single mode in this case. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dropped Power(mW ) 59 t UFC 2|a.m .5nm fT E FL O N f 4 SU-8 SU-8 1.5|am Tef 4 Si Figure 3-6: Small passive devices cross-section schematic and the fabricated device picture 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000 1530 1540 1550 1560 1570 1580 1590 W avelength (nm) Figure 3-7: Measured power at drop port as a function of laser wavelength for 55pm diameter device - ------ , -- J J |i r ’— J L --------------- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 1.2 y 1550 1555 1560 1565 1570 1575 1580 W avelength (nm) Figure 3-8: Measured power at drop port as a function of laser wavelength for 64pm diameter device 3.3 Summary of passive devices Table 3-1 summarizes the performances of the fabricated devices. As it can be seen the smaller devices have much larger scattering loss. Also it can be seen that the longer wavelength has smaller scattering loss. A maximum finesse of 141 is achieved for a 64 pm device at 1.3 pm. Table 3-1: The measured FSR and Finesse for different devices In dex d ifferen ce D e v ic e D iam eter B W (G H z) 1 30 0 n m F in esse 1 3 00n m L o ss* (d B /cm ) B W (G H z) 1 5 5 0 n m F in esse 1 5 50n m L o ss* (d B /cm ) 0.3 6 4 pm 6.2 141 8.0 8 117 6.9 0.3 55 pm 10.3 92 1 3 .5 5 12 84 12.3 0.1 4 4 0 p m 1.7 80 1.8 0.1 6 6 0 p m 5 20 2 .8 2 * E x clu d in g m aterial lo ss Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 3.4 Temperature Tuning of the filter Refractive indexes of polymers have a large thermal dependence. Hence one can use this to tune the resonant wavelength of micro-resonators made out of polymers. Figure 3-9 shows the thermal tuning of the micro-resonators we have fabricated. As it is seen from the figure the resonance wavelength can be tuned around 5nm by 40°C. It is possible with a larger temperature range to achieve more than 10 nm tuning. Temprature Tuning of SU-8 C □ J Z O ) I I -2-5 1 > -3 i (8 5 -3.5 ' c ra c o W 0 ) O C 20 30 40 50 60 Temparature Figure 3-9: Temperature tuning of the micro-resonator filter 3.5 Resonance wavelength control To make a practical system one would need to make ring resonators with slightly different radius. To see the practicality of this I have made an array of MR with slightly different radiuses. Notice that if we need 25GHz channel spacing for example Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 the radius difference between adjacent micro-resonators must be about 4nm for a device with a diameter of 40jam at 1550nm. It is not obvious if the lithographically defined structures can achieve this kind of resolution. Hence we tried to fabricate a passive device and monitor the resonance wavelength. Figure 3-10 shows the picture of the device, which has been fabricated. An array of micro-resonators, which are only lOnm different in the radius, is fabricated. The diameter of the devices are 70pm. Figure 3-10: Array of micro-resonators chip SU-8 is used as the core material and Teflon is used as the cladding. Figure 3-11 shows the measured resonance wavelength for different devices on the cheap. 1308 - _ 1307 JC u > I 1306 5 1305 - = 1304 1303 - i 1302 4- 70 70.05 70.1 70.15 70.2 Device diam eter Figure 3-11: Measured resonance wavelength as a function of device diameter Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 As it is clear from this graph the resonance wavelength can be controlled accurately by changing the radius of the device. It is noticeable to consider the tuning property as a function of the radius of the device. The resonance wavelength shift is given by: SA _ ne Sne SR A ng ne R Where 8ne is the change in the effective index, SR is the change in the radius of the device and ng is the group index defined in (2-67). Based on the measurement the Sn slope of tuning is 0.00042. Since the 8R/R is 0.00028 we conclude that — - is equal ne to 0.00013 for two adjacent devices. Hence the effective index of the device increases rapidly which the change in the diameter of the device. Based on the simulation results this change is much smaller than this result. This shows that perhaps the confinement of the light is lower than what is calculated using Kymata software and Sn the effective index is lower than what is calculated using this software. Since — - n e changes very rapidly probably the devices are close to the radius, which the confinment is lost, and the mode radiates to the cladding. 3.6 References [1] NOA 61 is supplied by Norland Products INC, UV 15 is supplied by MasterBond Co., UFC-XXX is supplied by URAY Co., Korea, Teflon AF 1600 is supplied by Dupont, SU-8 is supplied by MicroChem Co. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 Chapter 4: Light modulation using micro-resonators 4.1 Introduction In the previous sections we demonstrated efficient filters using polymer micro resonator. However polymers are famous for good electro-optic modulators. In the next step we would introduce electro-optic polymers into the device. In this way we can modulate the light in the output ports of the device by applying electrical signals. In this section first we consider some geometries that have been considered for light modulation using micro-resonator or ring resonators. Next we will discuss some theoretical issues describing these modulators. In the next section we will discus the fabrication of a micro-ring modulator. Finally we will present some experimental results. 4.2 Theory of micro-ring modulator Electro-optic polymers demonstrating large values for electro-optic coefficient have been studied extensively in the past two decades. Recently very efficient devices using polymers have been demonstrated [ 1 ] [2]. The electro-optic coefficient of poled polymers can be written as [3]: 0 0 r \3 0 0 r n 0 0 r3 3 0 r A l 0 Ei 0 0 0 0 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 Where : and: r i3 r 2J ~ ~ r 42 — r 51 r 33 = 3 ^13 (4-2) (4-3) The change in the refractive index of the polymer as a function of applied voltage can be written as: A(-^-)y = (r^.E . Assuming the electric field is given by: n (4-4) one would obtain: and: A n2 = ~ n 3 r3 3 Ez 1 An — An,, — — An 3 (4-5) (4-5) Assuming that the light polarization is along the z axis then the index modulation for this polarization is given by: 1 3 V n, = nn + — n — z 0 2 3 3 d (4-6) Where Y is the applied voltage to the device. Now if the waveguide is in the form of a ring the change in the refractive index causes the resonance wavelength of the ring to change. Hence the transmitted amplitude at the drop port and throughput port will Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 change. Also the phase of the transmitted light will change in the throughput port. Based on this observation one can think about the structures shown in Figure 4-1 as a modulator structure. In the first structure simply by changing the refractive index of the core waveguide the resonance frequency of the resonator changes and hence the output changes as shown in Figure 4-2. In the second structure close to the resonance the phase of the transmitted light changes rapidly. Hence by making a structure as shown in Fig 4-1(a) and by polling the micro-resonators in a push pull fashion one can modulate the transmitted light. Notice that this is very similar to a Mach-Zender modulator however this structure is wavelength sensitive. The light wavelength must Figure 4-1: Light modulators using MRs. Drop Input T h ro u g h Wavelength Figure 4-2: Light modulation concept using a single MR. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 & t / > 1.00 0.90 c < 1 > 0.80 c 0.70 4 — < J C 0.60 ra 0.50 T S H 0.40 E 0.30 in c 0.20 2 H 0.10 0.00 J - 2.0 - 1.0 0.0 Applied Voltage 1.0 2.0 Figure 4-3: Light modulation using push pull MR in the arms of Mach-Zehnder interferometer be close to the resonance wavelength of the resonator. The transmission for this modulator as a function of applied voltage is shown in Figure 4-3. Consider the single resonator coupled to channel waveguides. Let’s consider the through put port. Based on (2-55) we have: / 3 _ a2 - 2ra cos(2?r/?) + r2 /, l-2racos(27rj3) + r 2 a2 This can be rewritten as (assuming a=r): 4 r2 sin2(7r/3) /[ (1 — r ) + 4 r sin (tt/5) This is approximated close to resonance frequency c c > o as: - ( ^ - w 0) v r l y r Lnr , x 2 L 2 \2 ( l ~ r ) 1 ( 1 - r 2) (4-7) (4-8) (4-9) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Or: 68 A (a -c o o)2 I x (A © /2)2 +(co-co0)2 (4-10) A co _ c ( l - r 2) 2 rLn (4-11) To find the maximum sensitivity to the index change we have 0 ^ ( u - u o) a/3 A u 3 2 (4-12) Notice that this point is the maximum sensitivity point and also the linear point at the same time. In other words if the modulator is biased at this point the variation of the output intensity will be linear function of the index change. At this point we have: U x /3 a (4-13) and: 8 (7 -) dn V3 to U J 2 Aw/2 n Acu F W H M V 3 Q (4-14) or: 8 ( v ) 11' yflQn'r, dV 33 (4-15) Hence the sensitivity of the modulator is directly proportional to Q. For a typical resonator with a Q of 105 and index change of 10'5 will significantly change the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 transmitted intensity. It is important to note that to work in the optimal point one can either change the frequency of the input laser or if it is not possible to tune the laser one can apply a dc bias voltage or some other method to bring the resonance wavelength in the right position. In fact in our experiments we change the temperature to obtain the maximum sensitivity point. Next let’s consider the frequency response of the modulator. As a simple method consider the group delay of the signal in the resonator. For a given transfer function Il(ioj) the group delay is given by: In this equation arg(H(co)) is the phase response of the resonator. The group delay is basically the time it takes for a photon to pass through the resonator. This can be considered as the time the photons spend in the resonator. Consider the phase of the transmission in single pole resonator (equation (4-10)) T „ = ^ - ( a r g h QUO (4-16) A uj! 2 (4-17) 1 + i ^ A uj/ 2 1 r Auj 12 (4-18) A uj2 / 4 At the maximum sensitivity point this group delay is given by: 3 (4-19) T, W 2Auu Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 Next consider that the micro-resonator is basically a lumped element by the electrical signal viewpoint. Consider a 100GHz signal the wavelength for this signal is 3mm. This is much larger than the size of the modulator. Hence we can consider the applied voltage constant over the micro-resonator. By this argument the photon will average the electrical signal inside the modulator in a time given by the group delay. The average value for a sinusoidal electrical signal can be written as: — 1 ‘+ r sin(cu ,r ) V — — — I V sm(uj,J)dt « — ---/—* — V sm {u t) (4-20) T, , ^ r g Hence one can obtain the frequency response for the micro-resonator modulator as a sine function. It is clear that the bandwidth of the modulator is inversely proportional to the group delay and hence the Q. It is interesting to note that the product of sensitivity and the bandwidth is not related to the Q and is constant: f,mdByS = A 3 1 ^ ^ (4-21) one can improve the sensitivity but this will cost bandwidth. The only way to improve the sensitivity (keeping bandwidth constant) is to improve the electro-optic coefficient. Finally consider the loss for this kind of modulator. It is interesting to note that the through-port loss is negligible if the waveguides are low loss. This is a very interesting feature of this modulator. If one supply enough voltage to move the modulator far from resonance the transmission is equal to 1 and the modulator is loss Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 less. Notice that in practice one will bias the modulator at maximum sensitivity point. Hence 3dB loss will appear on the on state for a digital modulation. 4.3 Larger devices 4.3.1 Fabrication The schematic of fabricated device is shown in Figure 4-4. As can be seen from the figure a micro-ring waveguide vertically coupled to the input and output waveguides is fabricated. Gold is used for electrodes. The refractive indexes of the GND m Au Au Throughput Input 3 pm 4 .5 |im CLD1 C L D l SU- Sam CLD1/APC GND Au Drop Figure 4-4: Large electro-optic device layout and the cross section of the device materials used in the device are summarized in Table (2-1). CLD1/APC [1][2] is used as the material for the micro-ring. The device fabrication starts with Au coated Si substrate. A 5pm UV-curable epoxy UV15 (from master bond Co.) is used as the lower cladding. 5pm thickness is required to ensure negligible plasmon loss due to the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. bottom Au electrode. A lpm CLD1/APC layer is coated and etched using RIE in Oxygen to form a channel waveguide in the form of a micro-ring. The width of the ring waveguide is 5(am. Different radius rings are fabricated on the same substrate. Based on the calculation and measurement the radiation loss is negligible for devices larger than 300|um in diameter for 1.55(am and 200|um for 1.3(am. Next a middle cladding of UFC-170 is spin coated on the device. The thickness of this layer ,which determines the distance between the ring and channel waveguides is 4.5 pm. This also planarized the device. Two channel waveguides are made on top of the micro-ring as the input and output channel waveguides. To do this first the UFC-170 layer is patterned in the form of a waveguide. Next the required depth is etched into the UFC- 170. On the next step SU-8 is used as the material for the channel waveguide. The effective refractive index of SU-8 waveguide matches the effective refractive index of the whispering gallery mode of the CLD1/APC micro-ring. Hence efficient coupling is achieved. By spin coating SU-8 an inverted ridge waveguide is formed. The slab region of the ridge waveguide is removed by RIE etching. Next a 3 pm upper cladding is spin coated on the device. In the next step the device is polled using corona polling. The polling temperature was 145 °C and the applied voltage is lOkV. The sample was polled for 30 minutes. An upper gold cladding is patterned on the device to cover the micro-ring. The device is cut using dicing saw. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 4.3.2 Low frequency characterization The device was tested using cleaved fiber as the input and output waveguide. A tunable New Focus laser at 1.3pm was used as the source. Figure 4-5(a) shows the drop port power as a function of change of the input laser frequency for a 1500pm diameter device. As can be seen from this figure for 1300nm the FWHM (Full width half maximum) bandwidth of the device is approximately 4GHz for TE and 3 GHz for TM. (TE is defined as the Electric field perpendicular to the device surface). Hence the Q of the device is 6.2* 104 and 7.6* 104 for TE and TM respectively. The calculated loss based on the measured Q for this device is 5.2 and 4.2 dB/cm for TE and TM respectively. The Q of the device for 1.55pm is almost half the values at 1.3pm. Next a low frequency saw-tooth voltage is applied to the electrodes of the device. Figure 4-5(b) shows the modulated signal at the drop port of the device. It is important to note that there is no V n for this device. Equivalently we can define the equivalent voltage to cover FWHM. This is measured to be 4.86 volt for 1300nm. This corresponds to an r33 of 33pm/V. It is noticeable that the measured r33 for Mach- Zehnder devices in our group is 50pm/V at 1300nm. The FWHM voltage for 1.55pm for this device is 16V. Similar results for smaller devices are obtained. For a 300pm device the FWHM voltage is measured to be 9 V. This voltage is higher partly because the device Q is slightly lower (4.7X104 and 5.8X104 for TE and TM respectively) and also because Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 (a) (b) Figure 4-5: Large electro-optic device performance (a) Measured dropped power as a function of the input laser wavelength, (b) Measured dropped power and the applied signal to the device for a fixed laser wavelength the confinement of the mode is smaller in the micro-ring due to larger curvature. The FSR for this device is 0.9nm. 4.3.3 High frequency characterization The high-speed characteristic of one of the fabricated devices is measured in our laboratory. Normally high-speed polymer electro-optic modulators are limited by the micro-strip RF waveguide loss. Flowever in micro-ring modulator since the device is much smaller that the microwave wavelength (even up to lOOGFlz) the device high speed behavior is mainly capacitive. Flence one does not need to worry about the microwave loss, provided that the electrode capacitance is small enough which does not limit the modulation. Based on the calculations for devices smaller than 500pm in diameter the electrodes can be designed such that the device capacitance be very small. However there is an optical limit for high-speed modulation as it was discussed before. This limit comes from the fact that there is a limited time for the optical signal Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to build up or decay in the resonance tank. The time constant for this is related to the optical bandwidth of the device. Hence for our device since the FWHM optical bandwidth is 4GHz the maximum modulation bandwidth must be around 4GHz. However it is noticeable that first this can be improved by compromising voltage applied to the device. In other word higher bandwidth devices can be fabricated but they would require higher driving voltage to achieve the same modulation depth. Only by using materials with higher r33 coefficient it is possible to achieve higher bandwidth and maintain the same voltage. Figure 4-6: Eye diagram for data transmission at 1 Gb/sec using electro-optic MR Also we have done some high frequency measurement for one of the fabricated devices. A relatively clear eye diagram up to IGB/sec is obtained for this device as shown in the Figure 4-6 by applying IV data stream. The extra noise is due to bleaching of the unpackaged device and instability in the setup. The bandwidth of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 device is measured to be 2GHz. This is the maximum we could measure with our setup. So the bandwidth of the device is higher than 2GHz. 4.4 Small devices As I will describe in the next section the micro-ring devices can be used as a multi wavelength modulator. The number of channels, which can be modulated, is directly proportional to the FSR of the micro-resonator. To increase the FSR we have fabricated devices with a lower cladding index. The index difference between the core and cladding is increased and hence the device is much smaller. Figure 4-7 is the schematic cross section of the device which is fabricated. The Teflon is used as the cladding of the device and the CLD1/APC is used as the core material. Au Au 1 ellon Cl.D 2 u r n $ SI 1 . 5 i m £ | 1. i .. * J / l * l 1 ' 5 l i» T Au 3 pm 4 pm 1 5 pm "g n d Figure 4-7: Small electro-optic devices. Fabricated device picture and the cross section Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 The fabrication o f the device is similar to previous structures. The structure is fabricated on silicon substrate gold electrodes are used as the lower and upper cladding. ZPU13[4] is used as the lower cladding this material has a low (1.42) refractive index in telecommunication wavelengths. CLD1/APC is used as the core material for the micro-ring structure. Next a Teflon layer is used as the middle cladding. For the waveguide SU- 8 is used. The effective refractive index of SU8 waveguide matches to the effective refractive index of the CLD1/APC micro-ring hence efficient coupling is obtained. Finally a UFC170A upper cladding is used. The device is polled using corona polling at 145°C for 30min before the Teflon layer is coated. It is noticeable that Teflon layer has very low conductivity, which makes polling inefficient. 0.5pm of the CLD1/APC layer is etched to reduce the lower cladding radiation loss. Finally the device is cut using dicing saw. To characterize the device first we consider a 50pm device. Figure 4-8 shows the power in drop port of the device as a function of the input laser wavelength. The device is characterized at 1300nm. As it can be seen from the figure single mode operation is obtained The FSR of the device is more than ITHz. The bandwidth of the device is 16GHz. The finesse of the device is 67. Hence roughly speaking this device is able to modulate 40 WDM channels with channel spacing of 25GHz and lOGb/s for each channel, which is a total bandwidth of 400Gb/sec. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 _ 4.00 - 5 3.50 ~ 3.00 | 2.50 E. 2.00 ■ § 1.50 - 6 1.00 2 0.50 - 0.00 - 1290 1295 1300 1305 1310 wavlength(nm) Figure 4-8: Response of the electro-optic device as a function o f laser wavelength Next we consider the modulation properties of the device. For this purpose the input laser wavelength is adjusted close to one of the resonance peak of the device. Next a saw tooth voltage is applied to the electrodes of the device. Figure 4-9 shows the modulated light intensity at the drop port of the device. The modulation response for 3 different devices with different radiuses is plotted in Figure 4-9. As it can be seen from the figure the required voltage increases for smaller devices. This is due to decrease of the Q of the resonator for the smaller devices due to higher scattering loss and also the reduction of the confinement of the light in the core of the modulator. For a 150pm device 1.2GHz/v resonance frequency shift is observed. For 50pm device this value drops to 0.5GHz/v (Table (4-1)). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 (c) Figure 4-9: The modulation performance for three different small electro-optic devices, (a) 150pm, (b) 70pm, (c) 50pm.(diameter). The applied voltage is 2QVpp. Table 4-1: The performance of three different devices at 1300nm Device Diameter (pm) F S R (G H z) Bandwidt h (GHz) VFWH M (V) Tuning (GHz/V) 150 300 1 2 1 0 1 . 2 70 770 16 2 0 0 . 8 50 1 1 0 0 18 36 0.5 4.5 Multi-wavelength modulator Perhaps the most interesting application of micro-resonators is a multi wavelength modulator. Figure 4-11 shows the structure of a multi-wavelength modulator. In this structure a periodic series of electro-optic micro-resonators is used. Each micro-resonator diameter is slightly different than the adjacent one. In this way Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 each MR resonance wavelength is slightly shifted. Hence each resonator will modulate a different wavelength. Figure 4-10 shows the architecture o f a typical WDM system. Different laser source with different wavelengths are modulated. The obtained signals are multiplexed and are sent through the fiber. On the receiver side different wavelengths are separated using a demultiplexer (filter). Finally the signals are detected using high-speed detectors. Current WDM systems are 16-64 channels with 50 or 100GHz channel spacing and the signal rate in each channel is 2.5 or 10 GB/sec. Although the system looks simple in practice it requires precise control of the wavelength of the lasers and also the filters. Using the system shown in Figure 4-11 the system can be simplified significantly. The integration of the lasers is relatively straightforward. Multi-mode lasers can be made in several different ways [5]. Next each individual channel should be Modulators Multiplexer Filters Detectors DFB Lasers Figure 4-10: Typical WDM architecture x\ X I X 3 X n X \ X I X 3 X n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 modulated using a modulator. For this purpose one can use the modulator shown in Figure 4-11. In this modulator each micro ring will modulate one wavelength while it will not change any other wavelength. On the receiver side micro-ring resonators Detectors input Data Electrodes Multi- mode laser X1 A hn O M M M u O i n ------ 1 Electro-optic polymer Figure 4-11: Proposed architecture for the WDM system are used to filter each individual wavelength. Finally one needs integrated detectors, which can be made using Silicon detectors. Also one can make the system bi-directional and use the same device as modulator and filter. Hence a very compact communication system with tara bit capability can be made on a silicon micro-chip. 4.5.1 Analysis of cross talk The limitation for the multi-wavelength modulator (MWM) comes from the cross talk between adjacent MR modulators. There are several reasons that the cross talk can be created in this system. One of the sources of the cross talk is the inter-symbol interference. This happens since the adjacent channels overlap in the frequency domain. This kind of cross talk is very similar to any multi-channel system. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 There is another source for cross talk in this system. This happens because when each modulator is working it will not only modulate the wavelength at resonance but also it will modulate the adjacent channels as well. To analyze this problem consider the following model (equation 4-10): O ~ ® o ) 2 P = P0 (A o /2 ) 2 +(<y- ® 0 ) 2 ^4_ 22^ where Po is the input power, ©o is the resonance wavelength and A co is the FWHM bandwidth of the device. P is the transmitted power to the through port of the MR and c o is the laser frequency. Here If we assume that the MR modulator is biased at the half maximum point for the “ 1 ” bit and at resonance for the “0 ” bit the amount of signal power is given by: P = P / 2 r (4-23) Next consider the adjacent MR. When this modulator is working it will affect and change the power in the first modulator. Here we calculate the amount of signal power, which is created by applying voltage to the adjacent modulator. Assume that the adjacent modulator resonance wavelength is 5<n away from the original modulator. The signal power is given by: p _ P W 2 2 0 (5ca)2 + {Aco 11)2 (4_ 24) When this modulator is working the amount of power coupled to the original signal is given by: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 dP A R = ^ -(A < b /2 ) dco (4-25) If we assume that 5co=nAca/2 then one can easily obtain the power change due to adjacent modulator as: 2 n AP (4-26) (n2+l) 2 This power can be considered as noise for the channel 1. Based on this formula the to achieve a SNR of 20dB one would need to have n=6 . So For example for a 2.5Gb/S one cannot put the resonance wavelengths for adjacent channels closer than 15GHz. This kind of noise appears on the high level of the signal only. Hence it might be possible to remove this noise using limiter. This is a very simple model and more research is required for system issues, which might exist using this modulator. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 4.6 Reference [1] Yongqiang Shi, Cheng Zhang, Hua Zhang, Bechtel, J.H., Dalton, L.R., Robinson, B.H., Steier, W.H., “ Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape”, Science, 288,119-122, (2000) [2] Min-Cheol Oh; Hua Zhang; Szep, A.; Chuyanov, V.; Steier, W.H.; Cheng Zhang; Dalton, L.R.; Erlig, H.; Tsap, B.; Fetterman, H.R., “Electro-optic polymer modulators for 1.55 mu m wavelength using phenyltetraene bridged chromophore in polycarbonate ”, Applied Physics Letters, vol.76, no.24 p. 3525-7, June 2000 [3] Singer, K.D. ; Kuzyk, M.G. ; Sohn, J.E., “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties” Journal o f the Optical Society o f America B (Optical Physics) vol. 4, no. 6 ,PP. 968-76, June 1987 [4] ZPU13 is available from Zen Photonics, Korea, Teflon AF is available from Dupont [5] Yamada, E. ; Takara, H .; Ohara, T. ; Sato, K. ; Morioka, T. ; Jinguji, K .; Itoh, M. ; Ishii, M., “150 channel supercontinuum CW optical source with high SNR and precise 25 GHz spacing for 10 Gbit/s DWDM systems” Electronics Letters vol. 37, no. 5, pp 304-6, March 2001 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 Chapter 5: Mode coupling in electro-optic ring resonators and its applications 5.1 Introduction In the previous chapter I introduced the idea of light modulators based on the electro optic micro-resonators. Lumped element modulators were demonstrated and analyzed. There is a second method for light modulation using micro-resonators. In this method the light is propagated along with RF field and new frequency component are generated. The size of these devices is larger than the devices discussed before. In this case the size of the device is comparable to the applied signal wavelength. In this chapter I provide an analysis for this kind of modulator. We also show that this kind of device can be used as a wavelength converter or as a optical frequency comb generator. I was not able to demonstrate these devices experimentally. Hopefully they will be demonstrated in future. 5.2 Wavelength converter Wavelength conversion is required for future WDM networks. In this section we present a new method for wavelength conversion. The idea is to directly mix the optical signal with the RF signal to generate new wavelength. Figure 5-1 is the schematic proposed device. A ring-resonator is used which uses an electro-optic material as the core material. An RF signal is applied to the electrodes of the device. Figure5-1 is the schematic picture of the device. In this picture the RF signal is mixed with the optical signal and it generates the new wavelength (X2), Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which is 25GHz (one WDM channel) away from the original wavelength. Due to the special geometry in this device the wavelength 5 G is completely removed in the output and no filter is required. In the following we will analyze this structure. X 25GHz Figure 5-1: Electro-optic ring-resonator wavelength converter First we consider the interaction of the light with the RF signal. Since both the light and the RF signal are traveling waves one can use the envelope approximation[ 1 ]: 'In/Xnz! Xpj? (5-1) ^ = - t o ClZ Z V £ q Where Eri, Er2 and E rf are the electric field amplitude of the optical wave in the resonator at X\, %2 and RF respectively, a is the loss of the ring, d33 is the d coefficient of the nonlinear polymer. The last term is basically the phase matching condition. An d E r l _ a F dz 2 r p p M 3 3 £'WC ';-2 e Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 is the index difference between the RF and optical signal, coi and co2 is the frequency of the light corresponding to A -i and By replacing the variables as: 4 i = J — Erl,Ar ] & r„ g = 2 (j y n s0 (5-2) we obtain: AArl dz dA, t2 dz ■ | Arl- f A r2e - ^ (5-3) Solving the above equation assuming Ak=0 one will obtain: cos(gjvr) - i e a" sin(gxr) Ar\ -le Arl A, r 2 (5-4) sin(g^r) e a7tr'2 cos(g^r) r is the radius for the resonator. This is very similar to frequency up-conversion [1], Next we consider the resonator. One can relate the fields in the resonator and the coupled waveguide as: 'A ,,' r o ' ' ilrurlt a e a r j + it 1 n 1 ° r iln r k a _ R2 _ A ,., (5-5) where r and t are the coupling terms and k is the wave vector in the resonator. Notice that since the (5-4) does not carry the phase information the phase term is added in (5- 5). Using the above two equations one can obtain: ( rr< yr\ AC,n 9.( irc rr\ A, 1 I ‘ rei2,crke a ic r cos{ngr) -ireil7trke anr sin {ngr) 1 _ _ J + ite K a r cos(^gr) 1 -irel2nrke anr sin(;rgr) ren*rke-a*r gr) _ 1 to 1 sin(^gr) (5-6) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 Finally one will obtain the solution as: > __ 1 = ite anr ~\-reil1trke~anr cos(gxr) irei2nrke anr sin{gnr) " -i cos(g^rr) A -d ~ R 2 _ _ irei2*rke anr sin (gnr) 1 - rei2m k e~a 7 T r cos(g;rr)_ sin(gTZ-r) I (5-7) The output fields are given by: 4a it 0 1 > 1 + r — .4,2. 0 it 2 _ Figure 5-2 is the output power in each mode plotted for a device with ldB/cm loss, 10pm electrode spacing and an r coefficient of 50pm/V for 25GHz mode spacing. The device is over-coupled with the coupling of 40%. (The round trip loss is 15%). As it can be seen from the figure with zero voltage there is some power in the output port in the A .i mode. By applying RF signal to the device the power in mode one is decreased and finally reaches zero. This is due to “critical coupling”. The 1.00 0.80 0.60 0.40 0.20 0.00 0.00 5.00 10.00 15.00 20.00 A pplied V oltage (v) Figure 5-2: Power in the two adjacent modes o f the resonator as a function of the applied voltage Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 0.60 0.50 0.40 I o Q . 0.30 0.20 0.10 0.00 4 6 •4 ■ 2 0 2 •6 Frequecy (GHz) Figure 5-3: Frequency response of the wavelength converter. conversion of power from mode one to mode 2 behaves as an extra loss and it will cause the complete power transfer from mode one to mode 2. It is also important to note that relatively small value of voltage (RF power) is required to achieve critical coupling and better than 50% conversion is achieved with 2 Volts applied to the device electrodes. By increasing the coupling to 70% and the voltage to 5V one can improve the conversion efficiency to 80%. Next we consider the frequency response of the device. Figure 5- 3 shows the frequency response of the device. As it can be seen the device bandwidth is about 1GHz. By increasing the coupling to 70% one can achieve a bandwidth of 3GHz. 5.3 Comb Generation So far we considered that there are only 2 modes interacting with each other. However in a real device many modes exist and they will all interact with each other. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 To obtain the behavior of the device in the multi-mode case consider the following model for the device: d dz 4(-m) - a ! 2 - ig /2 0 0 4(0) = -ig /2 - a l l -ig /2 A(m) 0 -ig /2 - a 12 A, 'r(-m ) M o) r(m) (5-9) t > 1 ] ' A r(-m ) Aftr 4(m = e Am In this case each mode is coupled to two adjacent modes in the device. To solve this problem we can simply replace the transition matrix by: (5-10) where A is the matrix in (5-9). The transition matrix eAnr can be easily calculated using numerical techniques (Using Matlab for example). Following the same as above we can finally obtain for each mode: ^ 0 " A R{-m) 1 > 0 = [ 1 - A - * (" 0 _ 0 ik„,7ir re m gA nr n-1 it 0 (5-11) And the output of the device can be written as: A(-m) it 0 A 'o ' = + r A _ o (m ) _ 0 it A _ R(m) _ 0 (5-12) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 Notice that we assume the mode 0 is the excited mode. Figure 5-4 shows the power for different modes, which are generated. It is interesting to note that the power in higher order modes decreases exponentially. As it is clear from this figure the device is used as a comb generator. The generated powers in different modes are not constant and decrease exponentially. There is a n/2 phase difference between each adjacent mode. This means the modes actually tend to lock together and create a pulse of light. However if the device application is a wavelength converter then some mechanism should be used to suppress the higher order modes. One approach is to use a second ring with FSR 3 times the original ring as shown in Figure 5-5. In this case since the small ring has a FSR 3 times larger than the large ring and assuming that the modes of the small ring align with the modes of the larger ring (Figure 5-6) then only two modes will be supported in the large ring and the wavelength conversion without -10 I -15 J m o n ^ -o -20 V . I I -30 i -35 - ! -40 j -45 - i -50 - i 4.00 0.00 2.00 6.00 8.00 10.00 Applied voltage (V) Figure 5-4: Calculated power in different modes as a function of applied voltage to the device. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 Mode selection ring Electro optic polymer Electrodes o f the device 25GHz Figure 5-5: Structure of the device for suppression of unwanted modes Smaller ring Large ring modes , ■ • b b transmission 0.9 p 0 .8 r 0.7 0 0.6 W 0.5 e 0.4 r 0.3 0.2 Wavelength Figure 5-6: Small ring and the large ring transfer function. Only two adjacent modes couple to each other due to the electro-optic effect generation of higher order modes can be achieved. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 5.4 Phase matching issues So far we assumed that the RF wave and optical wave are phase matched. In this section we analyze the problem when there is a phase mis-match. Similar to the approach for parametric oscillator [ 1 ] one can use the change of variables: A i = Ane -iA k zl2 ikkz/2 One will obtain: Ar2 = A^e' dAr, . a . Ak ~ ig —J± = (---- + i ) A - dz 2 2 2 (5-13) dz 2 2 2 One can easily show that eigen values of the solution in this case are: (5-14) X - ~ — ±ib 2 (5-15) (5-16) The transition matrix in this case will be written as: A R \ A ■ R 2 - a n r 2b jK J r ' [cos(h;zr) ------- sin(6 ;rr)] 2b _ie-axr J _ sin(g^r) g-aitrl2 [cos(g^Tr) — — Sm (g7ZT ) 2b 2b A, A r 2 (5-17) After obtaining the transition matrix one can follow the same method as above to obtain the output as a function of the input for different modes of the structure. It is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 noticeable that if b » g then the phase mismatching is considerable. Hence one requires to have Ak « g Hence one requires that: An « — g (5-18) 1.00 - 0.90 0.80 0.70 - 0 0.60 | 0.50 o- 0.40 - 0.30 0.20 0.10 0.00 0.00 5.00 10.00 15.00 20.00 Applied voltage Figure 5-7: The comparison between the phase matched case and the case where there is 0.1 index difference between the RF and light wave. So for a 25GHz mode spacing using the numbers given above one requires A n«0.2. This index matching can be achieved by using appropriate materials (such as polymers) and also careful design of the micro-strip lines used for the device. Figure 5-7 shows the result of simulation for the case where there is an index difference of 0.1 between the optical wave and the RF wave. For the mis-matched case the critical coupling is not obtained. For an index difference of 0.02 no major change is observed. For the multi-mode case also the phase mis-matched case can be solved. By changing the variable as: Phase matched Not phase matched Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 A — A p < 2 A fe W - ( - 2 ) ~ r(-2) 4 (-d = 4 (- i / Ah A o = A o A x = A i^ A i A i^ i&kz i2&kz one will obtain the matrix: (5-19) d d z A -a 1 2 + i m t S k ~ ig ! 2 0 0 A ( 0 ) = -ig/2 -a 1 2 -ig / 2 : ^r(m) 0 -ig 1 2 -a 12- im i\k r(~m) M o) r(m) (5-20) o -5 -10 S T ' 1 5 C Q S "2 0 s ’ -25 | -30 -35 -40 -45 -50 0.00 2.00 4.00 6.00 8.00 10.00 Applied voltage (v) Figure 5-8: The multi-mode coupling in the phase mis-matched case with 0.1 index difference between the RF and optical fields. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 The transition matrix can be calculated in the same way as described above. Figure 5-8 shows the generated power in different modes for 0.1 index mis-match. It is clear that this case is very sensitive to index mist-mach. Even an index mis-match of 0.01 causes the power in different modes to decrease significantly. Hence for a comb generation a very accurate phase matching is required. By increasing the RF power and hence the gain one can achieve a flatter response for different modes of the structure. 5.5 Conclusion We have analyzed the problem of mode coupling between different resonance modes of a resonator. The device can be used as a comb generator or as a wavelength converter or as a pass band modulator. With currently available technology a 15dBm RF power is sufficient for wavelength conversion or comb generation. 5.6 References [1] Amnon Yariv, Pochi Yeh, “Optical Waves in Crystals: Propagation and Control of Laser Radiation”, John Wiley & Sons, November 2002 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 Chapter 6: Widely tunable external cavity DMR lasers 6.1 Introduction Widely tunable laser are highly required for the wavelength division multiplexing (WDM) systems. Previously widely tunable lasers were demonstrated using vernier effect and Bragg gratings [1][2], These structure use semiconductor Bragg gratings and tune by injecting current to the Bragg section of the device. Sampled grating DBR is used to achieve periodic reflections. Widely tunable lasers are demonstrated using this technology. Recently Bin Liu et.al [3] introduced the idea of using micro-resonator (MR) instead of Bragg gratings to fabricate widely tunable lasers. This idea is very similar to the sampled grating DBR laser. However instead of a Bragg reflector a micro resonator is used for mode selection. Figure 6-1 shows a double micro-ring structure. In this structure two micro-resonators are used. The radius of the two micro-ring resonators is slightly different. Hence the free spectral range (FSR) of the two resonators is slightly different. The lasing will happen only at the wavelength which the two- micro-ring resonators resonance at the same time. Note that by slightly changing the refractive index of one of the resonators one can change the resonance wavelength significantly due to vernier effect. The change in the lasing wavelength is directly proportional to refractive index change in a single resonator and is given by: Sn = (6-1) n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 To achieve 40nm tuning around 1550nm one would require a refractive index to change as high as 0.04. This is very high and is impossible to achieve using any index change mechanism. In a DMR laser there is an enhancement factor in the tuning range, M, which is due to vernier effect given by [3]: M = — 1 — (6-2) 1 - r j r 2 Notice that M can be arbitrary large if the two micro-resonators radiuses are arbitrary close to each other. Similar idea can be considered for SG-DBR devices. However there are many advantages to DMR devices. First the frequency response of M R is periodic and the transmission is equal for all the wavelengths. However the SG frequency response is not constant and the peak reflection decreases far from the Bragg condition. This limits the enhancement factor practically to 10 for SG-DBR structure [3], However in a MR structure provided that Q is high enough the enhancement factor can be very large. Also for the tuning mechanism carrier injection is used. However carrier injection changes the absorption and changes the threshold of the laser. Previously it was proposed to use electro optic effect to change the refractive index of the resonator. Using electro-optic effect it is possible to change the lasing wavelength very rapidly. However since the change in the refractive index is very small only DMR structure with very high M can be used to achieve a widely tunable laser using electro-optic effect. The DMR device has narrow linewidth due to the long cavity formed by MR Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 [4] and also there is not fundamentally time limitation on the speed of tuning since the index change mechanism is due to electro-optic effect. This might result in ultra-fast tunable devices, which might open the door to optical frequency shift keying (OFSK) or optical code division multiplexing (OCDMA) systems. Polymers can be used to make micro-resonator with very high Q. Also electro optic polymers with very large electro-optic coefficient can be used to make micro resonators as was shown in previous sections. In this section we have demonstrated for the first time the DMR laser. Single mode operation was demonstrated. For tuning either thermo-optic effect or electro-optic effect are used. We have demonstrated tuning using both these effects in this section. Finally we provide an analysis for the tuning and discuss limitations to the speed of tuning. 6.2 Thermo-optic device 6.2.1 Fabrication The fabrication of the device is very similar to previous structures we have fabricated. The cross section and top view of the device is shown in Figure 6-1. The fabrication of thermo-optic devices starts with spin coating a lower cladding of UV15 epoxy. The lower cladding is chosen to be 15 pm to behave as a thermal isolator between the thin film heater and the bottom substrate. Next a 1.8pm layer of SU- 8 is spin coated on the device. This layer forms the MRs. Two micro-resonators with 240pm and 246pm radiuses are fabricated. Next a middle cladding of UFC170A is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 Port3 Micro resonator 492jam 480|am Port2 Portl Heater electrodes Current Au 2 0 (am Au 1 Sum i U C I70 M ▼ 1.8jim 1 .B 8 9 I si ^ h ^ ___ £ lOOnm GND Figure 6-1: (a) The structure of the device. Micro-resonators, Waveguides and electrodes geometry, (b) The cross section of the device. The SU- 8 is the MR and the NOA72 is the waveguide Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. spin coated and the waveguides are etched into this layer. The thickness of this layer is chosen such that the distance between the waveguide and the MR is approximately lpm. This distance is very critical and determines the coupling to the resonators. This distance is chosen so that 10% coupling is achieved to the MR. Next waveguide pattern are etched to this cladding layer. The waveguides core layer (NOA72) is spin coated on the device. The refractive index of his layer matches the effective refractive index of the MR. The slab part of this waveguide is removed by RIE and the upper cladding is spin coated on the device. Finally gold electrodes (heaters) are deposited. The thickness of gold electrode is lOOnm. The width of the gold electrode is 20pm. The radius of the MR is chosen to be 240pm and 246pm. Hence the FSR of MR is approximately 120GHz. The tuning enhancement factor is 40. Based on this design one would get discrete tuning with 120GHz spacing. Notice that one can easily modify these dimensions to achieve ITU standards. Finally the devices are cut using dicing saw. This will result in optical quality facets. 6.2.2 Device characterization To characterize the device first we use a tunable laser to obtain the Q and the coupling to the device. The light is coupled through port 1 and is collected in port 2 while the laser wavelength is changed. Using the transmission in the through port (port2) it is possible to calculate the loss of the cavity and the coupling to the cavity. Based on this measurement at 1550 nm the r is measured to be 0.966. Hence the coupling of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 “power” to cavity is 6 %. The round trip power loss of the cavity is 30%. This corresponds to a waveguide loss of lOdB/cm. SU- 8 has a material loss of 4dB/cm in. O Q O EDFA Output PC Figure 6-2:: The optical circuit for the laser. P: Polarizer, PC: Polarization controller, EDFA: Erbium doped amplifier this wavelength. The rest of the loss is probably due to the scattering. Next we use a wideband source to characterize the device tuning performance. Figure 6-2 shows the experimental setup used for testing the device. A Newport EDFA (FPA-35) is used as the spontaneous emission source and gain region. The EDFA has a small signal gain of 40dB. A polrizer and a polarization controller is used to ensure single mode operation. For the testing of the device the light is butt coupled through small core fibers to the port 1 of the device and the output of port 2 is coupled to a second small core fiber and is sent to optical spectrum analyzer (OSA). Figure 6-3 shows the filtered spontaneous emission and the EDFA spectrum. Also it is clear how the spontaneous emission changes by changing the temperature. By passing current through the electrodes of the device the temperature of one of the ring changes. This change in temperature causes a change in refractive index. The change in refractive Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 index is 1.11X10'4/°C. It is interesting to see that only 5°C is enough to move the peak transmission wavelength 2 0 nm while the resonance wavelength of the single Filtered spontanous emission 9.00E-09 8.00E-09 - 7.00E-09 - 6.00E-09 - | 5.00E-09 - £ 4.00E-09 3.00E-09 - 2.00E-09 1.00E-09 O .O O E +O O i. e Wavelength (mm) Figure 6-3: The filtered spontaneous emission of the device for different values of the current to the electrode heater and the EDFA spontaneous emission spectrum MR is only moved 0.5nm. This is of course due to tuning enhancement factor of 40. As it is can be seen from the figure there is a very small difference in transmission between the maximum and the adjacent mode. The total insertion loss of DMR device is 20dB. The coupling loss from the fiber to the input and output waveguides is negligible using small core fibers. Next the output of the device is fed back to the input of the EDFA. Figure 6-4 shows the spectrum of the device output at port 3. The device lases with side mode suppression better than 30dB. It is noticeable that the gain of EDFA is very large 0mA 22mA 33mA 1.570 1.560 1.550 1.540 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 (40dB) and lasing is obtained easily. Also due to the large EDFA gain good side mode suppression is obtained. Finally Figure 6-5 shows the tuning characteristic of the laser. The lasing wavelength can be tuned by heating. However it does not lase at some region in the tuning range Lasing spectrum 1.00E-03 y 1.00E-04 1.00E-05 - | 1.00E-06 - £ 1.00E-07 1.00E-08 - S 1.00E-09 1.00E-10 1.5 Figure 6-4: The lasing spectrum of the DMR thermo optic device This is due to the shape of the gain of EDFA. As it is clear from the tuning curve lasing is not achieved in the 1544 to 1550 and 1530 to 1536 region. Using semiconductor optical amplifier (SOA) one can probably obtain lasing in the whole range since there is less features in the gain shape of SOA. The switching time for the wavelength is also measured. The device would require 1msec to increase the temperature and 2msec to decrease the temperature. So a few msec is required for the output light to stablize. 1.570 1.560 1.550 1.540 W avelength (pm) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 Notice that by heating only one of the electrodes one will obtain a discrete tuning. This is possibly ideal for some WDM networks which one only requires lasing on the ITU wavelengths. However one can achieve a continuous tuning by changing the refractive index of both micro-resonators. 1565 1560 _ 1555 | 1550 ■ 5 1545 O ) I 1540 a > | 1535 1530 1525 1520 37 ♦ ♦ 42 47 52 57 Current (mA) 62 Figure 6-5: The tuning characteristic of the DMR device as a function of the current in the electrodes. 6.3 Electro-optic device Although the thermo-optic device described above is interesting as a widely tunable source however the speed is limited to a few milliseconds. It is possible to use the electro-optic effect to achieve the tuning. Very rapid tuning (in less than 1 nsec) is possible using electro-optic effect. This is important not only as a tunable laser but also using very rapid tuning one can in principle transmit data using FSK scheme and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 also using CDMA scheme. The optical communication has used amplitude modulation so far since there are not any devices available to achieve rapid tuning of the wavelength. However using a DMR laser it might be possible to fabricate a low voltage and very fast tunable laser. We have fabricated and demonstrated for the first time a widely tunable source using electro-optic polymers. Details of device fabrication are described in chapter 4. All the dimensions and the cross section of the device are shown in Figure 6 -6 . CLD1/APC [5] is the nonlinear polymer which is used for the fabrication of this Au Au 1 K I 70 ] Spin £ * ipm ^ I J g ly J g V l \ 15 5 pm Au B- 3 pm i 4.5 pm 5 pm GND Figure 6 -6 : (a) The electro-optic device picture. The waveguides and the electrodes can be seen. The MR is under the electrode, (b) The cross section of the E -0 DMR device device. Top and bottom Au electrodes are used in the device. The device is polled using electrode polling. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 The performance of the ring waveguide and the coupling is very similar to the temperature tuned device describe above. The measured coupling is 6 % and the loss of the waveguide is 1 ldB/cm. The device is tested using an optical circuit as shown in V=90V 2.5E-09 V=-72V 2.0E-09 1.5E-09 W V=-180 o 1.0E-09 O - 5.0E-10 J ilil 1.54 0.0E+00 1.56 1.57 1.55 1.53 W avelength (pm) Figure 6-7: The filtered spontaneous emission of the device for different values of the voltage applied to the electrodes of the device. Figure 6-2. Figure 6-7 shows the filtered spontaneous emission for three different voltages for TE (E perpendicular to the surface of waveguide plane) polarization. As it can be seen from the figure the peak transmission moves by applying voltage to the device due to electro-optic index change effect. The required voltage is 16V/nm. Since M=40 Each rings tunes by applying voltage as high as 0.25GFIz/V. Next the laser cavity is closed by feeding the output of port 3 to the input of SOA. Single mode lasing with side mode suppression ratio of 30dB is demonstrated. Also the tuning of lasing wavelength by applying voltage is demonstrated as shown in Figure 6 -8 . As it Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 is clear from this figure 15V is required to change the wavelength lnm . The required voltage is relatively high for high speed wavelength switching. However by increasing M and also by using electro-optic material with higher r coefficient it is possible to achieve lower voltage. Based on our measurement the effective r coefficient for this device is around 12pm/V. However using other materials [6 ] an improvement o f effective index change of a factor of 10 might be possible. Also one can increase M by a factor of 10 by increasing the Q of the resonator and optimizing the device. Hence overall a factor of 100 improvement is expected for future devices. This will result in devices, which will require 0.1 V for each lnm for tuning. I 1.0E-06 146V 103V 157V 1 .QE-07 1.0E-08 1.0E-09 1.0E-10 1.0E-11 1.55 1.56 1.53 1.54 1.57 W avelength (pm) Figure 6 -8 :The lasing spectrum for four different voltages applied to the electrodes of the device. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 6.4 Analysis of speed of tuning As it was described before the EO-DMR might be used in future OFSK or OCDMA systems. In such kind of system one would require tuning speed in sub-nano second regime to be able to transmit more data. Here we analyze the problem and discuss some limitations to this problem. Consider the geometry as shown in Figure6-9. In this case the light is coupled from the MR(B) to the waveguide and next it is amplified using SOA. Next the light is coupled to a second MR(A). We assume that there is some mechanism for the unidirectional light propagation as shown in Fig. Also we assume that an SOA (semiconductor optical amplifier) is used as the gain medium. The dynamics of the total system can be described by: r,t Gain r,t r,t r,t Figure 6-9: The geometry o f the DMR with SOA gain region ,2 -all2+i<p\ (6-3) 2 - a l f 2+ i< p', Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 where N is the total carrier numbers in the SOA, Em a b is the field value in the MRs, G ( k) is the gain (loss), fi is the spontaneous emission factor, ye is the carrier recombination rate, and e is the charge of an electron. Rsp accounts for spontaneous emission into all optical modes, r an t are the coupling factor o f the waveguide to the rings and vg is the speed of light in the waveguides. / is the length of MR, la is the length of SOA and (fh n a ’ b is the round-trip phase which can be adjusted by applying voltage to the electrodes of e-o MR. a is the loss of the MR. A linear model of optical gain, G = r g si0p e( N /o - Ntr/u), is used with gain slope gsiope = 5.0X1 O ' 16 cm2, transparency carrier density Ntr/o = 1.0X1018 cm"3, mode confinement factor F =0.1, photon group velocity vg= 8.1X109 cm/s and lasing wavelength X = 1300 nm. Internal loss is 10 cm"1 , ye N=Rsp=BN2 /o where the radiative recombination coefficient B= 1 X 1 0 "'° cm V 1 , and the spontaneous emission factor ( 3 = 10"4. The dimensions of SOA are chosen to be u = 300X2X0.05 pm3. These values are typical of InGaAsP lasers [7], The diameter of ring cavities are chosen to be 450pm. The loss of the electro-optic MR is assumed to be ldB/cm and the coupling value r=0.95. We assume that 100mA is injected into the SOA. Also we assume that there are only two competing modes in the cavity. For 0<t<100X10"9 it is assumed that the phases for the first mode is zero and for the second mode is 2tc/M. (M=40). At t=100nsec the phase for the first mode is changed to 27i/M and the phase of the second mode is changed to zero. Figure 6-10 shows the result of the simulation for the rate equation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I l l above. As it is clear from this figure at t=100nsec the first mode power decreases. This is due to higher loss in the cavity due to the introduced phase. Also the carrier number increases to compensate for the loss in the cavity. The device will continue lasing for about 60nsec until finally the second mode increases and it will 10.00 - — ------------------------- -------------------------------------- - 5.E+07 / _ _ . 5.E+07 5.00 - 4.E+07 £ o no - 4.E+07 -® 3.E+07 3 -5.00 A 3.E+07 o \\ 2.E+07 « -10.00 - / \ 2.E+07 E / \ 3 -15.00 - / \ - 1.E+07 Z \ - 5.E+06 -20.00 - - ------ --------t -------L \ .-T- - L 0.E+00 90 140 190 240 time (nsec) Figure 6-10: The simulation results for the laser power and the carrier density for a DMR laser switch. As it is clear it take relatively long time for the switching to occur. This mainly is due to the fact that the cavity is at transparency and it will take a long time to switch. One way to make the switching faster is to introduce loss for a short time in the cavity to bring down the number of photons in the first mode. This can be achieved by introducing a large phase difference in the cavities for a short time. Fig 11 shows the result of the simulation for this case. In this case for 100ns<t< 100.4ns a 7i phase shift is introduced for mode 1 in the cavity. In this case the switching happens much faster. However it still requires about 10 nsec to stabilize. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. These time scales are probably not sufficient for the high bit rate OFSK or OCDMA. As it is clear the very high Q of the cavity due to lasing limits the switching time. Other techniques should be invented to achieve much faster tuning speed. 10.00 5.00 - E 0.00 - m r -5.oo - < u 5 £ - 10.00 -15.00 - - 20.00 109.00 114.00 119.00 104.00 99.00 time (nsec) Figure 6-11: The simulation results for the DMR laser the laser power with a 0.4nsec pulse for depletion of the cavity from the lasing mode We have measured the time response for our DMR laser with EDFA gain region. The time response shows oscillation with period of 32psec and it settles in about 200psec. These numbers of typical numbers are typical for a long cavity laser with large decay rate constant for spontaneous emission. 6.5 Conclusion We have demonstrated for the first time control of laser wavelength using two micro-ring structure. The lasing wavelength can be tuned over 35 nm and possibly larger provided enough gain bandwidth. The tuning can be either discrete or continuous. It is fairly easy to achieve tuning with 50GFIz or 100GHz spacing. (ITU Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 standard). The cost for making these kinds o f devices is very low compared to Bragg structures and semiconductors. The tuning speed for the thermo-optic version is in msec range and for the electro-optic can be very fast. The measured output power for this un-optimized device is lmW. The side mode suppression ratio of better than 30dB is demonstrated. To achieve a practical device one probably need to obtain better coupling control between the waveguides and ring structure to minimize the device loss. Also one should integrate these devices with SOA to achieve a compact cheap tunable laser. Further research is also required to achieve higher Q for the resonators using low loss materials. Analysis shows that the tuning speed is about a few nano-second. Some new techniques need to be considered to achieve faster tuning. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 6.6 References [1] Y. Jayaraman, Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron., 29, 1824-1834 (1993) [2] L. Zhang and J. C. Cartledge, “Fast wavelength switching of three-section DBR lasers,” IEEE J. Quantum Electron., 31, 75-81, (1995) [3] Bin Liu; Shakouri, A.; Bowers, J.E., “Wide tunable double ring resonator coupled lasers”, IEEE Photonics Technology Letters , 14, 600-602, (2002) [4] Bin Liu, Ali Shakouri and John E. Bowers, “Passive microring-resonator- coupled lasers”, Applied Physics Letters, 79, 3561-3563, (2001) [5] C.Zhang, L.R. Dalton, M.-C. Oh, H. Zhang, W.H. Steier, “Low VpElectro- optic modulators from CLD-1: Chromophore design and synthesis, Material processing and characterization, “ Chem. Mater., vol 13, p. 3043-3050, (2001) [6 ] D. M. Gill, C. W. Conrad, G. Ford, B. W. Wessels, and S. T. Ho, “.Thin-film channel waveguide electro-optic modulator in epitaxial BaTiOs”, Appl. Phys. Lett. 71, 1783 (1997) [7] G. P. Agrawal and N. K. Dutta, “Semiconductor Lasers”, 2nd edn., Van Nostrand Reinhold, New York, 1993. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 Chapter 7: Packaging and conclusion 7.1 Introduction Electro-optic polymers are sensitive materials. The optical properties of the material changes due to different processes. One major problem is the photo-bleaching in air. Due to presence of oxygen in air the oxygen reacts with the chromophore and change the molecule. However if the device operates in oxygen free environment this problem can be solved. Also the refractive index of the polymer waveguide is a function of temperature. For a micro-resonator the resonance frequency changes as high as 14 GHz/°C. This is much larger than the electro-optic tuning, which is about lGHz/V. Hence to operate the temperature should be controlled accurately. Another issue with the micro-resonators is relatively small size for the micro resonator and waveguides. lpm X lpm waveguides are required to achieve single mode operation. Hence one would require a good coupling mechanism to the device. Standard single mode fibers have a very large mode size, which results in significant coupling loss. Finally for high-speed operation one requires the correct impedance matching to the device. In this section I describe the approaches that has been used to package the device. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 7.2 The coupling The waveguide size for the MR devices must be as small as lp m X lp m to achieve single mode operation. The standard telecommunication fibers mode size is about lOpmXIOpm. If we assume that the mode in the fiber and in the waveguide can be described by Gaussian function: ( 7 . 1} ■sJ2k<7x 2 Where a is the mode size and indices 1,2 correspond to the mode size in the waveguide and the fiber one can easily obtain the coupling loss in dB given by: Loss = 10 log(2 1----------) 2 (7-2) cr, / (J2 + (J2 / < T , Notice that if the mode size is the same (i.e. cr^c^) then the loss would be zero. Figure 7-1 shows a plot of this function for different ration of cri/cj2- As it can be seen if the ratio of mode size is 6 the coupling loss is about lOdB. However if the mode size ratio is 2 the coupling loss is a reasonable value. To achieve a small mode size one can use either lensed fiber or small core fiber. A lensed fiber can create a small mode size. However a lensed fiber is very expensive and also the packaging is very difficult. We have used a small core fiber for the coupling. By fusion splicing a small core fiber to a standard fiber it is possible to get very low loss. Next the small core fiber is used to couple light into the device. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 0 ■ 2 ■ 4 ■ 6 ■ 8 -10 6 4 5 3 2 1 Mode size ratio Figure 7-1: The coupling loss for two Gaussian modes with different mode size The small core fiber used is UHNA3 available from Thor Labs. The mode size for this fiber together with the mode size for different fibers is summarized in Table 7-1: Table 7-1: The measured mode size for different fibers in our lab Fiber 1300nm (pmXpm) 155 0nm(pmX(pm) UHNA3 3.1X3.3 3.9X3.9 Orange SMF28 5.85X6.24 6.24X6.82 Lensed 3.1X3.3 3.5X3.5 SMF 8 .1X8.1 9X9 As it can be seen from the table the mode size of small core fiber is as small as lensed fiber. We have used Erricson fusion splicer to splice SMF28 to UHNA3. Based on the Butt coupling calculation the loss should be as high as 3.5dB. Flowever we Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 could achieve 0.5 dB loss. This is because during the splicing the core of two fibers melt together and a taper like profile is created. Finally the light is coupled from the small core fiber to the device. The waveguide size is 3pmX2.5pm. Using standard SMF28 fiber a coupling loss of 4.5dB is measured in each facet. Using small core fiber the coupling loss is very small (almost 0.5dB which is due to small core fiber to SMF fiber). Finally the small core fiber can be attached permanently to the device using standard packaging techniques. Notice that similar technique can be used for coupling to even smaller devices. For example using photonic-crystal fiber a mode size as small as 0.5umX0.5pm can be achieved. So in principle it is possible to couple light efficiently to device with sub-micron dimensions. 7.3 Packaging To be able to characterize high speed device performance for long time one has to do the packaging and put the device in oxygen free environment. To be able to do this the following semi-packaging technique was used. First a small piece of Brass was used as shown in the Figure 7-3. On this piece the device was mounted using standard glue. The small core fibers were aligned and using NOA epoxy were glued to the device. Two piece of glass were used as a support for the fiber. A temperature sensor (lOkQ Thermistor) was used to monitor the temperature. The electrical signal is fed through a standard SMA connector to a transmission line made by a piece of Alumina, which is gold coated on both sides and cut using dicing saw. Finally the signals are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 transferred to the device using gold wire bonding. Also a 50 Q cheap resistor was used to terminate the signal. The piece is attached on a Thermo-electric cooler. This controls the temperature and keeps the temperature constant. Finally the whole thing was put inside a box, which is purged with nitrogen. Fiber optic connectors were used on the sides to couple the light to the fibers. Fiber support Small core fiber Device o 50£! chip resistor Wire B onding Transmission line SMA connector Figure 7-2: The semi-packaging used for device. The fibers, strip line and other components can be seen in the figure. The device demonstrates much better stability inside the box however it is still not quiet stable. It took about 1 hour until the resonance wavelength stabilized and did not move. This is probably due to residual oxygen in the polymer matrix. After 1 hour the resonance wavelength became stable. The device was tested in about 5 hours and the resonance wavelength remained stable. 7.4 SION waveguide As the simulations in Chapter 2 demonstrated the coupling to the resonator is very sensitive to the refractive index matching between the resonator and the waveguide. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 Refractive index matching as good as 0.001 is required. Also the distance between the waveguide and the resonator is very critical. lOnm accuracy in this distance is required to achieve the desired value o f coupling. The polymers that we have used for fabrication have a fixed refractive index. It is not easy for us to control the refractive index accurately. Also the distance between the waveguide and the MR is very difficult to control. This is because first the thickness can not be controlled very accurately using spin coating. Also the etching rate using RIE changes significantly from one run to another run. Hence it is almost impossible to control the distance better than 0.1pm in our current method. This is very far from the desired lnm accuracy. Another problem arises from the fact that the refractive index of electro-optic polymer can be made very high. We have measured the refractive index as high as 1.8 using CLD75 chromophore with 50% loading in APC. This is very desirable to make even smaller devices. However the passive polymer refractive index can not be much higher than 1.6. So it is much desirable to use another material for the waveguide and using the active polymer for the resonator. SION has been used recently for optical waveguides [1], It has very good properties. First it can be deposited using standard PECVD. Also the refractive index can be controlled accurately by changing the ratio of oxygen to nitrogen in the film between 1.46 (SiOi) to 2 (Si3N4). Figure 7-3 shows the hybrid proposed device using SiON. The proposed device uses a SiON waveguide with S i0 2 claddings. There are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 several advantages to this structure. First the right gas mixture in the CVD can control the refractive index of SiON very accurately. Also the distance between the SiON A U A U T eflon CLD CLD SiO N S I 0 2 S I 0 2 Si Figure 7-3: The proposed device for the integration of SION technology with active polymer MR. waveguide and the polymer MR can be very accurately controlled using the following method. First the Si0 2 and the SiON layer are deposited using CVD. Next the SiON layer is patterned and etched to form the waveguide. In the next step the middle Si0 2 layer is deposited. After this step there will be a bump over the SiON waveguides. This bump can be removed using Chemical Mechanical Polishing machine. The polishing is done such that the SiON layer exposes to the air. Next another Si0 2 layer is deposited which controls the distance between the polymer and the waveguide. Since the deposition rate can be in the order of a few nano-meter/ minute this distance can be accurately controlled to within a few nanometers. Finally the polymer layers are deposited and the rest of process is very similar to standard processing. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 To achieve this goal I have tried to grow SiON waveguides. However at this stage only the refractive index is characterized for different conditions of the CVD. Figure 7-4 shows the result of the experiment. The gasses used were O 2, N 2, N 20 and Sillane. As it can be seen from the figure the refractive index changes between 2 to 1.46. However the control of the refractive index is not good. This is mainly because of the bad controller for the oxygen line. Presence of small amount o f oxygen in the chamber causes the film to become S i02. Hence a very good flow controller is required to achieve the desired ration between 0 2 and N2. The Si3N 4 waveguide fabricated in this way are very lossy. One requires to anneal the waveguide to reduce the loss [2]. However it is found that for the waveguide with refractive index higher than 1 . 6 annealing at high temperature causes a lot of crack on the waveguide. This is probably due to thermal expansion of Si substrate and may be avoided using Quartz substrate. 45 | 1-75 - ■ £ 1.7 * 1.65 - w 1.6 - ® 1.55 - 1.45 3 6 0 1 2 4 5 0 2 Flow rate (SCCM) Figure 7-4: The refractive index and deposition rate for SiON film using different values for 0 2 flow rate.(NH3(SCCM)=10(SCCM),N2=5(SCCM), SiH4=50(SCCM), Pressure=3 OOmT, Temp=310) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 In one experiment the Si3N 4 film was annealed at 1100°C and many small cracks were obtained. The development of this structure requires further work. 7.5 Conclusion This thesis has demonstrated several different functional devices. Some of the devices in this thesis have been demonstrated for the first time. The idea of confining the light in a micro-resonator to make functional devices is practically working. Passive micro-resonators will be used in future optical systems as filter. Active micro resonators can be used for modulation and switching of light and enable very functional devices such as multi-wavelength modulators. Other devices such as widely tunable lasers using electro-optic effect can be used for new modulation schemes. Finally wavelength converters and comb generators might be made using this technology. The passive micro-resonators are very interesting as filters for WDM systems. The micro-resonators should be combined to achieve desirable filter characteristics with large roll off in outside the pass band. The electro-optic micro-ring device is perhaps the most important device, which is demonstrated in this thesis. Due to its special characteristic it will probably be used in many systems in future. There are many thing need to be done before these modulator devices can be really commercialized and used practically. The stability of polymers is the main issue Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 which must be solved. If the stability problem can not be solved one have to use other materials such as organic crystals or ferro-electric crystals instead of polymer materials. The FSR of devices must be improved. This is only possible with larger index contrast between the core to cladding which result in large scattering loss. The wall roughness still remains the main challenge for improving the Q o f these resonators and new techniques are required to get rid of this roughness. Finally the coupling must be controlled very well to achieve modulators with very large extinction ratio. New techniques such as the hybrid device described above are required. The wavelength converters were analyzed in this thesis and they need to be demonstrated in future. Also these devices can be considered as modulators for analog signals with multi-GHz frequencies. The widely tunable lasers also need further research. The concept was demonstrated however one has to integrated these devices with SOA to make compact tunable lasers. New techniques are required to achieve ultra fast tuning. Most of the devices demonstrated in this thesis are on the level of proof of concept and need much more work to be available commercially. The story of Micro resonators continues and it will bring new devices for opto-electronic world. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 7.6 References [1] Worhoff, K .; Lambeck, P.V. ; Driessen, A., “Design, tolerance analysis, and fabrication of silicon oxynitride based planar optical waveguides for communication devices” , Journal o f Lightwave Technology 17, no. 8 , (Aug. 1999) : 1401-7 [2] Ay, F. ; Aydmli, A. ; Roeloffzen, C. ; Driessen, A, “Structural and loss characterization of SiON layers for optical waveguide applications”, LEOS 2000, vol. xxiii+898 p. 760-1 vol.2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 Bibliography Agrawal G. P., and N. K. Dutta, “Semiconductor Lasers”, 2nd edn., Van Nostrand Reinhold, New York, 1993. Arfken, G. “ Mathematical methods for physicists”, Academic Press, 1985 Ay, F. ; Aydmli, A. ; Roeloffzen, C. ; Driessen, A, “Structural and loss characterization of SiON layers for optical waveguide applications”, LEOS 2000, vol. xxiii+898 p. 760-1 vol.2 Balanis, C.A. “ Advanced Engineering Electromagnetics”, John Wiley & Sons, 1989 Cai, M.; Painter, O.; Vahala, K.J.,” Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system”, Physical Review Letters, vol.85, no.l p. 74-7, 3 July 2000 Eldada L., S. Yin, R. A. Norwood, and J. T. Yardley, “Affordable WDM components: The polymer solution,” Proc. SPIE, vol. 3234, pp. 161-174, 1997. Gamer S.M., Sang-Shin Lee, Chuyanov, V., Chen, A., Yacoubian, A., Steier, W.H., Dalton, L.R., “Three-dimensional integrated optics using polymers,” Quantum Electronics, IEEE Journal o f , Vol. 35 No 8 ,pp 1146-1155, Aug. 1999 Ghatak, A.K.; Thyagarajan, K.; Shenoy, M.R., “Numerical analysis of planar optical waveguides using matrix approach”, Journal of Lightwave Technology, vol.LT-5, no.5 p. 660-7, May 1987 Gill D.M, C. W. Conrad, G. Ford, B. W. Wessels, and S. T. Ho, “.Thin-film channel waveguide electro-optic modulator in epitaxial BaTRA”, Appl. Phys. Lett. 71, 1783 (1997) Gill D.M. ; Block, B.A. ; Conrad, C .W .; Wessels, B.W. ; Ho, S.T., “Thin film channel waveguides fabricated in metalorganic chemical vapor deposition grown BaTiO/sub 3/ on MgO”, Applied Physics Letters, vol 69, no. 20, pp 2968-70, Nov. 1996 Gmachl, C.; Capasso, F.; Narimanov, E.E.; Nockel, J.U.; Stone, A.D.; Faist, J.; Sivco, D.L.; Cho, A.Y.,” High-power directional emission from microlasers with chaotic resonators”, Science, vol.280, no.5369 p. 1556-64, 5 June 1998 Haavisto, J.; Pajer, G.A., “Resonance effects in low-loss ring waveguides”, Optics Letters, vol.5, no. 12 p. 510-12, Dec. 1980 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 Honda, K.; Garmire, E.M.; Wilson, K.E.” Characteristics of an integrated optics ring resonator fabricated in glass”, Journal of Lightwave Technology, vol.LT-2, no.5 p. 714-19, Oct. 1984 Jayaraman V., Z. M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron., 29, 1824-1834 (1993) Lacey, J.P.R.; Payne, F.P.” Radiation loss from planar waveguides with random wall imperfections”, IEE Proceedings J (Optoelectronics), vol. 137, no.4 p. 282-8, Aug. 1990 Ladouceur F., J.D. Love, T.J. Senden,” Effect of side wall roughness in buried channel waveguides”, IEE Proc-optoelectronics, IEE Proceedings-Optoelectronics, vol.141, no.4p. 242-8 Aug 1994 Little B.E., S. T. Chu, H. A. Haus, J. Foresi, and J.-P.Laine, “ Microring resonator channel dropping filters,” J. Lightwave Technol. 15,no6. pp 998-1005 ,1997. Liu B.; Ali Shakouri and John E. Bowers, “Passive microring-resonator-coupled lasers”, Applied Physics Letters, 79, 3561-3563, (2001) Liu B.; Shakouri, A.; Bowers, J.E., “Wide tunable double ring resonator coupled lasers”, IEEE Photonics Technology Letters , 14, 600-602, (2002) Marcatili E.A.J., “Bends in optical dielectric waveguides”, The Bell System Technical Journal, Vol 48, pp.2103-2132,1969 Marcuse D. “Mode conversion caused by surface imperfections of a dielectric slab waveguide”, Bell System Technical Journal, vol.48, no. 10 p. 3187-215, Dec. 1969 Marcuse D. “Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function”, Bell System Technical Journal, vol.48, no.10 p. 3233- 42, Dec. 1969 Marz R., “Optical Waveguide Theory”, Artech House, Boston 1995 Matsumoto N.; Kumabe, K., AlGaAs-GaAs Semiconductor ring Lasers, NTT, Japan, Japanese Journal of Applied Physics, Vol. 16, No. 8 , 1395-1398, (1977) McCall S.L., A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan," Whispering- gallery mode microdisk lasers," Appl. Phys. Lett. 60,no. 3, pp 289-291,1992 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 Meier, U., Bosch, M., Bosshard, C., Gunter, P. “DAST a high optical nonlinearity organic crystal”, Synthetic Metals vol. 109, no. 1-3, pp 19-22, March 2000 Miller, D.A.B., “Rationale and challenges for optical interconnects to electronic chips”, Proceedings of the IEEE vol. 8 8 , no. 6 , pp 728-49, June 2000 Najafi S.I., T. Touam, R. Sara, M.P. Andrews, M.A. Fardad, “ Sol-Gel Glass Waveguides and Grating on Silicon”, IEEE J. Lightwave Tech. Vol 16, no 9, 1640- 1646,1998 Oh, Min-Cheol; Hua Zhang; Szep, A.; Chuyanov, V.; Steier, W.H.; Cheng Zhang; Dalton, L.R.; Erlig, H.; Tsap, B.; Fetterman, H.R., “Electro-optic polymer modulators for 1.55 mu m wavelength using phenyltetraene bridged chromophore in polycarbonate ”, Applied Physics Letters, vol.76, no.24 p. 3525-7, June 2000 Rafizadeh D. , J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S.T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett., vol. 22, no. 16, pp. 1244-1226, 1997. Ramo S., J.R. Whinnery, T.V. Duzer, “Fields and waves in communication electronics”, John Wiley & Sons, NY. 1984 Riechel, S.; Lemmer, U.; Feldmann, J.; Berleb, S.; Muckl, A.G.; Brutting, W.; Gombert, A.; Wittwer, V.,” Very compact tunable solid-state laser utilizing a thin-film organic semiconductor”, Optics Letters, vol.26, no.9 p. 593-5, 1 M ay 2001 Rowland, D.R.; Love, J.D.” Evanescent wave coupling of whispering gallery modes of a dielectric cylinder”, IEE Proceedings J (Optoelectronics), vol. 140, no.3 p. 177-88, June 1993 Rowland, D.R.” Analysis of optical directional couplers composed of asymmetrically curved waveguides”, IEE Proceedings-Optoelectronics, vol. 142, no . 6 p. 305-12, Dec. 1995 Schon, H.; Kloc, C.; Dodabalapur, A.; Batlogg, B. , “An organic solid state injection laser”, Science, vol.289, no.5479 p. 599-601, July 2000 Shi, Yongqiang, Cheng Zhang, Hua Zhang, Bechtel, J.H., Dalton, L.R., Robinson, B.H., Steier, W.H., “ Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape”, Science, 288,119-122, (2000) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 Singer, K.D. ; Kuzyk, M.G. ; Sohn, J.E., “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties” Journal o f the Optical Society o f America B (Optical Physics) vol. 4, no. 6 ,PP. 968-76, June 1987 Snyder, A.W., and Love, “Optical waveguide theory” Chapman and Hall 1983 Teixeira, F.L.; Chew, W.C. “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates”, IEEE Microwave and Guided Wave Letters, Vol 7 , no 11 p. 371 - 373 , Nov 1997 Teng, C.-C.,” Precision measurements of the optical attenuation profile along the propagation path in thin-film waveguides”, Applied Optics, vol.32, no.7 p. 1051-4, 1 March 1993 Thyagarajan, K.; Shenoy, M.R.; Ghatak, A.K., “Accurate numerical method for the calculation of bending loss in optical waveguides using a matrix approach”, Optics Letters, vol. 12, no.4 p. 296-8, April 1987 Tishinin, D.V.; Dapkus, P.D.; Bond, A.E.; Kim, I.; Lin, C.K.; O'Brien, J.” Vertical resonant couplers with precise coupling efficiency control fabricated by wafer bonding”, IEEE Photonics Technology Letters, vol. 11, no . 8 p. 1003-5, Aug. 1999 Ulrich, R.” Theory of the prism-film coupler by plane-wave analysis”, Journal of the Optical Society of America, vol.60, no. 10 p. 1337-50, Oct. 1970 Worhoff, K. ; Lambeck, P.V. ; Driessen, A., “Design, tolerance analysis, and fabrication of silicon oxynitride based planar optical waveguides for communication devices” , Journal o f Lightwave Technology 17, no. 8 , (Aug. 1999): 1401-7 Yamada, E. ; Takara, H. ; Ohara, T. ; Sato, K. ; Morioka, T. ; Jinguji, K. ; Itoh, M. ; Ishii, M., “ 150 channel supercontinuum CW optical source with high SNR and precise 25 GHz spacing for 10 Gbit/s DWDM systems” Electronics Letters vol. 37, no. 5, pp 304-6, March 2001 Yariv, A., Pochi Yeh, “Optical Waves in Crystals: Propagation and Control of Laser Radiation”, John Wiley & Sons, November 2002 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 Zhang, C., L.R. Dalton, M.-C. Oh, H. Zhang, W.H. Steier, “Low V^Electro-optic modulators from CLD-1: Chromophore design and synthesis, Material processing and characterization, “ Chem. Mater., vol 13, p. 3043-3050, (2001) Zhang L. and J. C. Cartledge, “Fast wavelength switching of three-section DBR lasers,” IEEE J. Quantum Electron., 31, 75-81, (1995) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Rabiei, Payam (author)

Core Title Electro-optic and thermo -optic polymer micro-ring resonators and their applications

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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

Language English

Advisor Steier, William H. (committee chair), Hellwarth, Robert (committee member), O'Brien, John (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-270503

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