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Silicon micro-ring resonator device design for optical interconnect systems
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Silicon micro-ring resonator device design for optical interconnect systems
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Silicon Micro-ring Resonator Device Design for Optical Interconnect Systems by Yunchu Li A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPY (ELECTRICAL ENGINEERING- EE PHYSICS) May 2013 Copyright 2013 Yunchu Li ii Dedication To my parents, Wei Li and Huiyuan Jiang the greatest supporters of mine with love, encourage, and trust iii Acknowledgements I would like to thank Professor Dapkus for his kindness to let me pursue my interests, to provide me support and to provide me the perspective when I needed. In my process of pursuing PhD, for several times I fell into very difficult situations due to multiple personal reasons. Dr. Dapkus always encouraged and supported me to insist on my study till I achieved enough results. Dr. Dapkus is one of the greatest persons in my life. I can never thank enough for the training and help provided by my CSL group members — Lawrence Stewart who took responsibility for training me, Hyung-Joon Chu who provided expertise in equipments, soldering and circuit, and Tingwei Yeh, who trained me with using multiple measurement methods. I would also like to thank members of the OCLAB, including Prof. Willner who allowed me to pursue my EE PhD in USC and recommended me to EE-physics when I decided to switch from communication system to device design, Lin Zhang, who trained me with simulations and Jengyuan Yang who provided me expertise in fiber optics experiments. I would like to thank Prof. O’Brien, Prof. Povinelli, Prof. Zhou, and Prof. Kalia, who participated on my qualifying and defense committees. I would like to thank those who supported my efforts toward science— my father and mother, who always supported and encouraged me when I was facing the most difficult situations. I would also like to recognize Angella Johnson's help in finding TA position in Physics Department. Finally, I would like to thank my friends— Bo Zhang, Prof. Song, Xiaoxia Wu, Yue Yang, Yan Yan, Huang Hao, Wang Xue, Teng Wu, Chenxi Lin, Jing (Maggie) Ma, Ningfeng Huang, Eric Jaquay, Mehmet Solmaz and L. J. Martí nez Rodrí guez. iv Table of Contents DEDICATION ................................................................................................ ii ACKNOWLEDGEMENTS ........................................................................... iii LIST OF FIGURES ........................................................................................ vi ABSTRACT .................................................................................................... ix CHAPTER 1 INTRODUCTION .............................................................. 1 1.1 Bottleneck of CPU speed................................................................... 1 1.2 Microring-resonator-based devices................................................... 2 1.3 Silicon and III/V material.................................. …………………… 2 1.4 Outline ............................................................................................... 3 1.5 References ......................................................................................... 3 CHAPTER 2 SILICON REFRACTIVE INDEX MODULATION ....... 5 2.1 Introduction............................................................................ ……... 5 2.2 MOS based E-O refractive index modulation …………………....... 5 2.3 Reverse-biased-PN-junction-based refractive index modulation....... 8 2.4 Summary............................................................................................ 11 2.5 References ......................................................................................... 11 CHAPTER 3 RESONANCE-SWITCH MODULATORS ...................... 14 3.1 Introduction ...................................................................................... 14 3.2 Dynamic of single-ring modulators: speed-linewidth trade-off ........ 15 3.3 Coupled-ring modulator: over-coupling and transient effect ............ 31 3.4 Summary ........................................................................................... 39 3.5 References ......................................................................................... 39 CHAPTER 4 COUPLING-SWITCH MODULATORS ……................. 45 4.1 Introduction........................................................................................ 45 4.2 Principle of compound coupler.......................................................... 49 4.3 Breaking the trade-off of speed-linewidth......................................... 53 4.4 Model accuracy ………………………………................................ 60 4.5 Summary ............................................................................................ 61 4.6 References ......................................................................................... 62 v CHAPTER 5 DESIGN OF HIGH SPEED DPSK MODULATOR........ 70 5.1 Introduction …………………………………………....................... 70 5.2 Principle of DPSK modulator …………………………................... 71 5.3 Advantages to notch design ………….............................................. 78 5.4 Summary.. ......................................................................................... 86 5.5 References ......................................................................................... 86 CHAPTER 6 SYSTEMATIC ANALYSIS OF MICRORING FILTER 89 6.1 Introduction........................................................................................ 89 6.2 Concept of optical data timing skew ……......................................... 90 6.3 Characterization and link performance …......................................... 92 6.5 Summary ………………………………………………………… 97 6.6 References ……………………………………………………… 97 CHAPTER 7 CONCLUSION AND FUTURE WORK … ..................... 100 BIBLIOGRAPHY …………………………………………………………... 102 vi List of Figures Figure 2.1 Cross section of MOS-capacitor-based SOI optical modulator …...... 6 Figure 2.2 SEM image of the fabricated device and schematic cross section of the ring waveguide ……………………………………………………………. 9 Figure 2.3 The calculated effective index change over voltage and the fitted curve of the simulated reverse biased pn junction ……………………………….. 11 Figure 3.1 Single-ring modulators are divided into three types ……………………... 17 Figure 3.2 Pulse waveforms and signal spectra generated by the three types of the microring modulators ………………………………………………..... 21 Figure 3.3 Extinction ratio is increased by applying a large drive voltage ………….. 22 Figure 3.4 Pulse width is examined as a function of drive voltage …………………. 23 Figure 3.5 3-dB modulation bandwidth of the microring modulators ………………. 24 Figure 3.6 Signal quality is examined as the drive voltage increases ……………….. 26 Figure 3.7 Signal quality is examined as laser linewidth increases …………………. 26 Figure 3.8 Pulse waveforms (dotted line) and effective chirps (solid line) generated by the types I and II modulators …………………………………………. 28 Figure 3.9 Power penalty as a function of fiber transmission distance for types I and II modulators and a MZM ……………………………………………….. 29 Figure 3.10 Power penalty in signal transmission over 80-km fibers is examined as a function of drive voltage for types I and II modulators ………………… 30 Figure 3.11 Power penalty caused by detuning the type II modulator. ……………… 30 Figure 3.12 Single ring modulator and the proposed coupled-ring modulator scheme … 32 Figure 3.13 Comparison among the three examples of the modulation of a 60-Gb/s NRZ signal …………………………………………………………… 35 Figure 3.14 Modulation bandwidth and extinction ratio versus the ring-to-waveguide coupling coefficient …………………………………………………… 36 Figure 3.15 Extinction ratio versus the coupling coefficient and frequency chirp……… 37 Figure 3.16 Back-to-back BER curves and power penalty under different chromatic vii dispersion values …………………………………………………………… 38 Figure 4.1 Comparison between the notch design and drop design for coupling modulation ………………………………………………………... 48 Figure 4.2 Schematic diagram of the composite interferometer …………………… 49 Figure 4.3 The absolute coupling coefficient, intra-cavity energy amplitude output signal power, the ratio of max/min intracavity energy amplitude and the extinction ratio of the notch design and the proposed design ……………. 56 Figure 4.4 Bandwidth of the drop design coupling modulator and the coupled ring modulator over RC constant and intrinsic loss ………………… 57 Figure 4.5 BER curve and power penalty comparison of different designs ………... 59 Figure 4.6 Signal pulses of 40 Gb/s RZ signals obtained using the time dependent model and the dynamic equations model ……………………………… 61 Figure 5.1 Comparison between the traditional resonance-shifting-based DPSK modulator and he coupling-modulation-based one ……………….. 72 Figure 5.2 Schematic diagram of the composite interferometer …………………… 73 Figure 5.3 The calculated effective index change over voltage and the fitted curve of the simulated reverse biased pn junction ………………………………. 77 Figure 5.4 The original logic and the received signals after balanced detection ……… 80 Figure 5.5 The proposed modulator’s bandwidth versus RC constant and the phase change versus intrinsic loss in the ring phase shifter ……………………. 81 Figure 5.6 Total transmission loss and power penalty comparison between the proposed design and the traditional design ……………………………... 82 Figure 5.7 The energy amplitude variation depth comparison ……………………… 84 Figure 5.8 BER curves of the coupling-switching-based DPSK modulator………… 84 Figure 5.9 The power penalty comparison between the proposed design, the notch design and the OOK signals of the previous design.…………… ……….. 85 Figure 6.1 (a) Micro-ring modulator, isolated-type and coupled-type cascaded ring resonator filters. (b) Cavity Q and linewidth non-uniformities in the ring-resonator-based devices can lead to differences in the delays. (c) Timing skew between channels resulting from the delay difference ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 viii Figure 6.2 (a) Linewidth of the microring modulator and filter versus gap width variation. (b) timing skew of the modulator and filter versus linewidth. (c) power loss of the isolated and coupled type filters …… 94 Figure 6.3 (a) pattern dependence induced by gap width variation; (b) the level ratio vs. variation in gap width of isolated and coupled ring resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................ 95 Figure 6.4 (a) Eye-opening penalty induced by power loss and signal distortion. (b) Eye-opening penalty induced by timing skew…………………………... 96 Figure 6.5 Maximum eye-opening penalty versus the ratio of the filter linewidth to the bitrate of the NRZ signal……………………………………………..... 96 ix Abstract Optical interconnect systems is one of the most promising solutions to surpass the speed bottleneck of CPU from the electrical interconnects. To realize this idea, one of the key topics is to design compact photonic devices suitable for building the optical interconnects The use of silicon microring resonators is an attractive technology for the integrated photonics pursuing optical interconnect applications, highly exciting due to the high integration density, low power consumption, and versatile functionalities. The platform technologies available for silicon microring resonators can be categorized by their structures, functions in optical interconnect systems, etc. Specific designs are in great needed to break off some critical tradeoffs in these silicon microring-based devices performances. In this dissertation, the design and simulations of silicon microring based photonic devices for optical interconnects are presented. Utilizing the proposed technologies, various types of optical elements such as resonance-switching/coupling-switching OOK modulators, DPSK modulators and filters are designed. The systematic performance is studied as well. The data have shown that, by employing our unique designs critical tradeoffs in the device performance can be successfully broken and great data quality at ultra-high data transmission speed can be obtained. 1 Chapter 1 Introduction 1.1 Bottleneck of CPU speed As described in [1], the current CPU speed is facing a severe bottleneck from the interconnection. People can continue to increase the clock speeds and wiring density inside CPU but not the interconnection through metal wires [2]–[7]. For on-chip electrical interconnects there is a tradeoff between propagation delay and the interconnect bandwidth density. The electrical interconnect delay can be reduced by increasing the interconnect width at the expense of a smaller bandwidth density, or vice versa. In another words, there is always a tradeoff between low interconnect delay and large bandwidth density. To break this tradeoff and overcome the bottleneck of the electrical interconnects, the optical interconnect systems have been advocated through improved architectures enabled by silicon and III/V devices [8], [9]. The differences in physics lead to three specific major possible practical advantages for optical interconnects. 1) Propagation Loss: optics use dielectric waveguides instead of metal wires to guide the waves and hence resistive loss in metal wires for the radio frequency signals is avoided which is the critical issue in electrical interconnect. 2) Interconnect Density: because the carrier frequency is so high, there is a very large amount of available spectrum allowing wavelength-division multiplexing (WDM) that could increase the aggregate bit rate of a given optical beam well beyond the modulation rate possible on any one channel. 3) Interconnect Energy: Optics may be able to save energy in interconnection because it is not necessary to charge the line to the operating voltage of the link. 2 1.2 Microring-resonator-based devices As discussed in [10], passive dielectric waveguide structures are shown to enable revolutionary reduction in footprint of waveguides, and especially wavelength selective devices. Ring resonators play an important role in the success of photonics integration, because high refractive index dielectric material enables ring resonators of an unprecedented small size. Typically, a ring resonator is an optical waveguide which is looped back on itself. When the optical path length of the ring resonator is exactly multiple times of the wavelengths, a resonance occurs. The spacing between these resonances is called the free spectral range (FSR), and people preferred large FSR (several nm) to enable channels as many as possible. Till now, many compact optical devices based on ring resonators, such as modulators, filters, switches, and detectors, have been demonstrated. 1.3 Silicon and III/V material Compared to the silicon material systems, the III/V material system has a few unique advantages [11]. The compound semiconductors InP and GaAs have direct band-gaps and much stronger electro-optical properties, which makes them attractive in making lasers and receivers. GaAs and AlAs have nearly the same lattice constant. AlAs can be selectively oxidized to quickly form low index cladding layers, experimentally very low loss waveguide structures have been demonstrated in GaAs. Similarly, InP, InGaAsP and InAlAsP are lattice matched to each other [11]. Silicon as a photonic material is attractive because of its low cost and the availability of advanced fabrication technology [11], although it is not ideal for active devices nor is it able to efficiently emit light. In part because of the massive demand of the microelectronics industry, silicon is several orders of magnitude cheaper than InP or GaAs or other optical 3 materials such as lithium niobate. Also thanks to the microelectronics industry silicon processing is very well understood and tools are readily available. Photonic structures are on the micron size scale and are readily achievable with even modest silicon processing technology. One exception to micron scale features is narrow coupling gaps in evanescently coupled resonators, but even these devices are accessible with state of the art silicon processing tools. Silicon photonics has become one of the most promising photonic integration platforms in the last years. This can be mainly attributed to the combination of a very high index contrast and the availability of CMOS fabrication technology[11], which allows the use of electronics fabrication facilities to make photonic circuitry [11]. 1.4. Outline This dissertation is organized as follows. Chapter 2 describes the analysis of the electro-optic modulation schemes specifically for silicon. The modeling method of the MOS structure and reversely-biased pn junction are discussed. Chapter 3 and 4 present the study of resonance- switching-based and the coupling-switching-based silicon microring modulator for on-off- keying (OOK) modulation. The designs for breaking the speed limitation from the ring resonator’s linewidth are presented and characterized. Chapter 5 proposes a differential phase shift keying modulator design bat speed beyond 100 Gb/s by referring to the design in chapter 4. Chapter 6 presents silicon microring filter design and its influence on the system data timing in studied. 1.5. References [1] David A. B. Miller, "Device requirements for optical interconnects to silicon chips", Proceedings of the IEEE, 97, pp 1166-1185 (2009). [2] R. Ho, K. W. Mai, and M. A. Horowitz, "The future of wires," Proc. IEEE, 89 490–504 (2001). 4 [3] J. A. Davis, R. Venkatesan, A. Kaloyeros, M. Beylansky, S. J. Souri, K. Banerjee, K. C. Saraswat, A. Rahman, R. Reif, and J. D. Meindl, "Interconnect limits on gigascale integration (GSI) in the 21st century," Proc. IEEE, 89 305–324 (2001). [4] J. D. Meindl, BInterconnect opportunities for gigascale integration,[ IEEE Micro, 23 28– 35, (2003). [5] D. A. B. Miller and H. M. Ozaktas, "Limit to the bit-rate capacity of electrical interconnects from the aspect ratio of the system architecture," J. Parallel Distrib. Comput., 41 4252, (1997). [6] K. C. Saraswat and F.Mohammadi, "Effect of scaling of interconnections on the time delay of VLSI circuits," IEEE Trans. Electron Devices, ED-29, 645–650, (1982). [7] M. Haurylau, C. Q. Chen, H. Chen, J. D. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, "On-chip optical interconnect roadmap: Challenges and critical directions," IEEE J. Sel. Topics Quantum Electron., 12 1699–1705, (2007). [8] R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S.-Y. Wang, and R. S. Williams, "Nanoelectronic and nanophotonic interconnect," Proc. IEEE, 96 230–247 (2008). [9] A. Shacham, K. Bergman, and L. P. Carloni, BPhotonic networks-on-chip for future generations of chip multiprocessors,[ IEEE Trans. Comput., 57 1246–1260 (2008). [10] W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. V. Thourhout, and R. Baets, "Silicon microring resonators, " Laser Photonics Rev. 6, 47–73 (2012). [11] Lawrence S. Stewart, “Tunable microdisk and microring resonators in compound semiconductors and silicon,” Dissertation published in 2012. 5 Chapter 2 Silicon Refractive Index Modulation 2.1 Introduction To electrically change the silicon refractive index through free carrier plasma dispersion effect, forward biased p-i-n junctions, reverse biased p-n junctions, and MOS structures have been employed to vary electron and hole distribution within the material. The carrier- injection-based p-i-n modulator suffers from low speed since it relies on the slower diffusion of minority carriers, as opposed to the faster motion of majority carriers. Reverse biased p-n junction and having a bandwidth around 20 GHz has been demonstrated [1-5] but the modulation efficiency of the modulators employing a reversely biased p-n junction is relatively lower than p-i-n’ s and MOS structure’s. Sub-micrometer MOS modulators permit us to achieve both high modulation efficiency, and high speed [6]. 2.2 MOS based E-O refractive index modulation A sub-micrometer MOS structure is shown in Fig.2-1. In a MOS structure, the gate and substrate form the plates of a capacitor with the SiO 2 as a dielectric. As a positive voltage is applied on the gate, the positive charge accumulates on the gate and negative charge accumulates in the substrate. The charge density on the plate follows the equation. (2-1-a) (2-1-b) where V(t) is the voltage on the capacitor, R is the resistance, C is the capacitor’s capacitance, Essentially, the MOS structure acts the same as a capacitor. 6 Fig. 2-1. Cross section of MOS-capacitor-based SOI optical modulator, as in [7]. Typically, as analyzed in [7], electron and hole distribution dependences on either applied voltage (static analysis) or time (dynamic analysis) is calculated using a 2-D drift- diffusion model, solved by finite element method(FEM). It consists of three-coupled partial differential equations (PDEs)written as [7] (2-2-a) (2-2-b) (2-2-c) where R SHR is the Shockley–Hall–Read recombination rate, ε 0 is the vacuum permittivity, ε r is the relative permittivity, q is the elementary electron charge, N e is the electron distribution, N h is the hole distribution, N i is the silicon free-carrier intrinsic concentration, C is the doping profile, μ n is the electron mobility, μ p is the hole mobility, v T is the thermal voltage, ψ is the electric potential, and τ n and τ p are the electron and hole lifetimes in silicon, respectively. Electron and hole mobility dependence on impurity concentration and electric field has been taken into account by an empirical model, as in [8]. 7 For boundaries in contact with dielectric materials, normal components of electric displacement and current density vectors are imposed to be equal to 0[7]. At boundaries in contact with a metal, neutrality condition and action mass law have been considered. Then, hole and electron concentrations and electric potential have been imposed as[7] (2-3-a) (2-3-b) (2-3-c) where V a is the voltage applied to electrodes. Starting from the 2-D free-carrier distribution, silicon refractive index and absorption coefficient changes due to applied voltage are calculated using the well-known Soref–Bennett relationships [9]. Once the 2-D distribution of refractive index n(x, y) and absorption coefficient α(x, y) is known, field distributions and complex effective indexes of optical modes propagating within the device are calculated as the eigen-functions and eigen-values of the electromagnetic wave equation (solved again by FEM). However, this method is not suitable for dynamic modeling when the applied voltage changes with a long pseudo random binary sequence used as the logic signal. To address a simplified model, variation in carrier density is simulated as a charging process following the applied voltage, which is believed to be a good fit to real behavior in MOS capacitors [10]. The carrier transit time, defined as the duration for carrier density to increase from 10% to 90% of its peak value when a voltage step is applied, is considered here from 12 to 50 ps [2, 10]. Then the effective index change of an optical guided mode [6- 7,11-13] due to the free carrier dispersion effect [14] is obtained by the spatial integration and average. The refractive index and loss are calculated according to Dr. Soref Bennett’s well-know equations [15] 8 (2-4-a) (2-4-b) in which N is the electron concentration change in cm −3 and P is the hole concentration change in cm −3 . Since our research mainly focuses on the structure design in the optical domain, we care more about the average effective index change instead of the transverse optical field distribution. Hence a spatially averaged carrier density with its steady-state value linearly proportional to the peak-to-peak value of drive voltage is used. The effective index change is set at 2.4 × 10 −4 at 5 V, which can be obtained using several proposed electrode designs [7]. Dynamic loss due to the varied carrier density is calculated [14], which results in a dynamic cavity Q. 2.3 Reversely Biased PN junction Although MOS structure has so many advantages, it turns out to be difficult to utilize this design on ring resonators. There has been much interest in reversely biased pn junction since the device speed for a reverse biased pn junction is only limited by the RC constant[16]. Recently, it is demonstrated that the electro-optic modulation efficiency V π L of reversely biased pn junction can significantly improved to 1.5 cm∙V[17] on a ring resonator. To model a reversely biased pn step junction, we follow the specific structure which is reported in [17], as shown in Fig.2-2. 9 Fig.2-2 SEM image of the fabricated device and schematic cross section of the ring waveguide. a, Top-view SEM image of the fully fabricated device The ring and waveguide are clad by a 1.2-μm- thick oxide, followed by contact area etch. The metal covers the contact area and links to pad areas. b, schematic cross section of the ring waveguide. The white line indicates the middle line of the waveguide. Traditionally, to evaluate modulator's modulation efficiency, people have to work in 3 steps: i) use various software to calculate carrier density in the diode as a function of the bias voltage; ii) use an optical mode solver to obtain the optical field across the section; iii) calculate the refractive index over cross-section by using Soref Bennett's equation [9] and then integrate it over the optical field to calculate the effective index. To calculate the effective propagation loss, people also have to work in the similar way. This method is both time and computation consuming. To simplify the modeling work, we utilize 2 out of 3 assumption by referring to [16], which could save a lot of time and resources. 10 In silicon depletion-based modulators the effective index and effective loss variation and is low. They can be approximated by where || 2 is the normalized optical intensity of the fundamental guided mode, Δn (x, y) the local variation of the refractive index in silicon and Δα (x, y) the local variation of the loss in silicon. The 1 st assumption is that we consider the problem uniform along one specific direction, i.e. y direction because of the diode orientation (Fig. 2-2(b)). The 2 nd assumption is that we approximate hole and electron distribution variations with uniform regions, whose widths are and (widths of the space charge extension variation in the P and N regions which are calculated using the Poisson equation in 1D problem). Hole and electron concentration variations are assumed to be N A and N D in these depleted regions. The equation of depletion width is derived in [18] The optical mode distribution was simulated and obtained by Olympios software. The calculated effective index change and the fitted curve (n(v)) is shown in Fig. 2-3. Here the positive voltages are the voltages applied in the reverse-bias direction. When phase shifter is reversely biased at 1V, the V π L is calculated to be 1.5 cm∙V, which agrees exactly with the experimental results in [16]. The loss change is also calculated and fitted in the same way. 11 Fig.2-3 The calculated effective index change over voltage and the fitted curve of the simulated reverse biased pn junction In dynamic model, the reversely biased pn junction can be considered as a capacitor whose capacitance varies slightly with the drive voltage. In our dynamic model, we assume that the capacitance variation speed is far higher than the drive signal speed. In another word, the dynamic model is quasi-static [18]. 2.4 Summary In conclusion, both MOS and reversely biased pn junction can enable high speed modulation. The reported effective index change of a MOS is essentially linear over voltage because the optical field is mostly contained in the n layer and the refractive index changes linearly over electron density. This is one advantage over reversely biased pn junction as high linearity is required for a silicon analog modulator. Compared to MOS, pn junction is more easily fabricated, which implies potentially lower cost. 2.5 References [1] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, "A high-speed silicon optical modulator based on a metal–oxide–semiconductor capacitor," Nature, 427, pp. 615–618 (2004). 12 [2] C. A. Barrios and M. Lipson, "Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration," J. Appl. Phys., 96, pp. 6008–6010 (2004). [3] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature, 435, pp. 325–327 (2005). [4] L. Zhou and A. W. Poon, "Silicon electro-optic modulators using pin diodes embedded 10-micron-diameter microdisk resonators," Opt. Express, 14, pp. 6851–6857 (2006). [5] A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, "High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express, 15, pp. 660–668 (2007). [6] C. A. Barrios, “Electrooptic modulation of multisilicon-on-insulator photonic wires,” J. Lightwave Technol., 24, pp. 2146–2155 (2006). [7] V.M.N. Passaro, F. Dell'Olio, "Scaling and Optimization of MOS Optical Modulators in Nanometer SOI Waveguides," IEEE Transactions on Nanotechnology 7 401 - 408 (2008). [8] D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE, 55, 2192–2193(1967). [9] R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron., QE-23, 123–129 (1987). [10] R. D. Kekatpure and M. L. Brongersma, “CMOS compatible high-speed electro-optical modulator,” Proc. SPIE 5926, paper G1 (2005). [11] R. D. Kekatpure, M. L. Brongersma, and R. S. Shenoy, "Design of a silicon-based field-effect electro-optic modulator with enhanced light-charge interaction," Opt. Lett. 30, pp. 2149–2151 (2006). [12] A. Liu, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the Modulation Bandwidth and Phase Efficiency of a Silicon Optical Modulator,” IEEE J. Sel. Topics Quantum Electron., 11, pp. 367–372 (2005). [13] L. Liao, D. Samara-Rubio, M. Morse, A. Liu, and D. Hodge, “High speed silicon Mach- Zehnder modulator,” Opt. Express, 13, pp. 3129–3135(2005). [14] F. Gan and F. X. Kartner, "High-speed silicon electrooptic modulator design," IEEE Photon. Technol. Lett., 17, pp. 1007–1009 (2005). [15] R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron., 23, pp. 123–129 (1987). [16] T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, "Fabrication of add-drop filter based on frequency-matched microring resonators," J. Lightwave Technol. 24, pp.2207-2218 (2006). 13 [17] P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, "Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator," Opt. Express 17, 22484-22490 (2009). [18] R. F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996), Chap. 7. 14 Chapter 3 Resonance-Switch Modulators 3.1 Introduction As described in our paper [1], microring and microdisk resonators have attracted a great deal of interest in the integrated photonics community in recent years. Various types of micro-resonator devices have been proposed for communication and signal processing applications. When designed and fabricated using silicon-on-insulator (SOI) platforms [1]– [3], the micro-resonators exhibit a great potential to build space-, power-, and spectrally efficient on-chip photonic networks that could be seamlessly integrated with CMOS electronics. This compatibility is becoming increasingly important, creating the emerging possibility of replacing electronic data buses with nanophotonic signaling links for global interconnects in high-performance computing systems [4]–[8]. Electrooptic modulation has been viewed as a fundamental function in on-chip communications. As compared to their peers built in lithium niobate [9], [10], polymer [11], [12], and compound semiconductors [13], [14], silicon modulators [15]–[18] exhibit better CMOS compatibility, but may require relatively high drive voltage and more power consumption. In addition, though microring modulators exhibit small chip size and capacitance, resonance-enhanced efficiency, and high wavelength selectivity in comparison to Mach–Zehnder modulators (MZMs) in silicon [19]–[22], cavity photon lifetime imposes a limitation on the ring modulators’ speed [23]. Much research has been done to design electrodes [24], [25], driving schemes [26], and ring structures [27], [28]. Design optimization of the microring modulators rely on joint consideration of both resonance shift and dynamic loss [27], [28] and a good understanding of the cavity dynamics [27]–[29]. Micro-resonators feature a sharp phase transition near each resonance wavelength. Although this can be used for phase modulation [30], [31], continuous-wave (CW) input 15 fields experience a phase variation in intensity modulation as the resonance wavelength shifts, which adds a frequency chirp to generated signals [27], [32], [33]. In chip-scale communications [34], one may not see a significant effect of the chirp on signal quality, with chromatic dispersion limited over short propagation distances, but it plays a critical role in determining the signal quality in fiber transmission [27], [32]. The single-ring modulator’s performance in fiber telecom systems has not been discussed in detail in previous work. 3.2 Dynamic model of single microring modulators: speed- linewidth trade-off Cooperating with Lin Zhang in Dr. Willner’s group [1], we numerically analyze both single-ring and coupled silicon modulators, in terms of extinction ratio, chirp, signal spectrum, pulsewidth, and signal Q-factor, focusing on a bit rate beyond 10 Gb/s. Three types of single-ring modulators are considered, based on their configurations in the optical domain. The dynamic responses of these modulators greatly affect their performance when used for intensity modulation, particularly in characteristics, such as modulation speed, power consumption, and signal quality. Resonance-induced negative chirp assists signal transmission over single-mode fibers. This section is mostly from our published paper in [1]. Electro-optic modulation using silicon microrings can be achieved by applying a drive voltage to change the refractive index inside the cavity, and thus, the resonance wavelength. In our model, a square-wave voltage signal providing a non-return-to- zero (NRZ) pseudo- random-bit-sequence (PRBS) at 10 Gb/s is sent through a five-pole Bessel filter with a bandwidth of 30 GHz. The positive output voltage with a 10-ps transition time [35] is obtained as a driving signal. In this way, the driving circuit’s bandwidth limitation [20] becomes negligible so that the microring modulator itself can be examined more closely. MOS capacitor electrodes operated at hole accumulation regime have been proposed for 16 high-speed silicon modulators [15], [19], [20], [35]–[37], which require low dc power consumption and no carrier confinement. Simulation shows good agreement with experimental results [37]. In the time domain, time-varying capacitances of the accumulation layer in the MOS capacitor are negligible [37], with only the fixed oxide capacitance left. The carrier density in the electrode then follows an exponential transition over time during the charging process [37].The carrier transit time, from 10% to 90% of the maximum carrier density, is set to be 23 ps, which is achievable in practice [15], [35], [37]. Note that the dependence of the transit time on drive voltage is ignored. We also assume that the transit time at the rising and falling edges is the same [15], [35]. Spatially, the carrier density is a 2- D distribution over the cross section of the electrode, and it can be simulated based on specific MOS structures and used to obtain the effective index change of an optical guided mode [15], [17], [35]–[37] due to the free carrier dispersion effect [38]. In our simplified model, a spatially averaged carrier density with its steady-state value linearly proportional to the peak-to-peak value of drive voltage is used so that the effective index change is calibrated to be 2.4 × 10 −4 at 5 V, which can be obtained using several proposed electrode designs [35]–[37]. Dynamic loss due to the varied carrier density is calculated [38], which results in a reshaped resonance profile when it is shifted [16], [17], [25]. A ring resonator typically has a Lorentzian spectral response when coupled to one or two waveguides. As shown in Fig. 3-1, in the single-waveguide case, the ring can be under- coupled (type I) or over-coupled (type II) [39], [40], depending on whether the coupling between the ring and the waveguide is weaker or stronger than the ring’s round-trip loss. In these cases, a notch resonance profile is seen at the output port. In the dual waveguide case (named type III) [15], the output port has a band-pass profile. Each of the operating regimes 17 of the ring modulators features a unique phase transition over frequency, accompanying the sharp amplitude response, as shown in Fig. 3-1. Fig.3-1. Single-ring modulators are divided into three types according to their operation regimes in optical domain: type I (single waveguide under-coupled), type II (single waveguide overcoupled), and type III (dual waveguide). A MOS electrode is integrated onto the ring resonator. Phase transition across resonance is plotted as a function of frequency for all the three types. To account for the effect of the cavity photon lifetime on generated waveform and chirp, a transient evolution of the optical field in the cavity has to be simulated using dynamic coupled mode theory, as described in either [29] or [41] and [42]. In some cases, where one has no need to examine the walk-off of optical waves traveling from different paths in ring resonators [15]–[17], [27], [43], the two models generate very similar results [44]. One may solve the dynamic equations for the “energy amplitude” that represents the total energy stored in the ring [41], [42], with a time step not limited by cavity round-trip time. This requires less memory and computation time than the method in [29]. However, in some other cases [18], [28], [45], the optical fields at different parts of the rings have to be solved to examine the optical waves’ interference and evolution. One need to use either the model in [29] or a modified version of the model in [42] by combining it with the steady-state coupled mode theory in [46], both of which require a time step less than one cavity round-trip time. 18 We use the model given in [42] here. The types I and II modulators are simulated using (3-1), and type III is simulated using (3-2). (3-1-a) (3-1-b) (3-2-a) (3-2-b) The energy amplitude is defined as a(t) = A(t)e −jωt , and and are the carrier and resonance angular frequencies, respectively. and represent the input CW and modulated signal. is the amplitude decay rate due to cavity loss, and , and are the amplitude decay rates due to ring waveguide coupling [42]. In the symmetric configuration of type III, , which means that it is also an under-coupled ring since the output waveguide equivalently adds loss to the cavity. Coupling factor μ satisfies , where is the power coupling coefficient, and is the group velocity in a ring with a radius of [42]. The differential equations are solved using the implicit Euler method with a time step of 0.8 ps. In our analysis, the ring has a diameter of 5.4 μm, with a mode number m = 28 at f = 193 THz. The cavity Q-factor is 19 000, corresponding to a resonance linewidth of 10 GHz and a photon lifetime τ = Q/2πf = 15.7 ps. This requires that types I, II, and III have an intrinsic loss of 13.9, 9.3, and 1 dB/cm, respectively. In reality, a type III modulator cannot have a loss as low as 1 dB/cm. However, for purpose of comparison, we set the same Q-factor for all three types. In Fig. 3-1, when the voltage is logic zero, types I and II are on resonance, 19 but type III is off resonance. In this way, the generated optical signals have a non-inverted logic pattern as compared to the driving signal. Modulation parameters such as transit time, modulation efficiency, and loss, which we use here, would be achievable by properly designing the waveguide/electrode cross section (e.g., as in [37]) and the spacing between the waveguide and ring, using device simulation packages, finite-difference time domain (FDTD) or finite-element algorithms [15], [35]–[37]. We note that different electrode and waveguide designs may cause similar modulation parameters [35], and one of our goals is to build a model applicable to various structural modifications of the MOS electrodes so that subsequent system performance characterization is more general. The signal waveform is examined with a CW laser power of 1 mW for convenience of normalization; two-photon absorption at this power in silicon is negligible. System performance of the microring modulators is evaluated using a signal Q-factor and power penalty [47].When calculating the signal Q’s in the back-to-back case in Section III, we set the laser output power to be −18 dBm for all three types, and receiver sensitivity is −25 dBm for a bit error rate at 10 −9 . Since the modulators have different intrinsic and dynamic losses for optical signals, and no optical amplifier (and thus no optical filter) is used, the received power at the photodiodes is not held fixed, which is typical for on-chip communications. In the power penalty calculation for fiber transmission in Section IV, we set the laser power to be −10 dBm, and receiver sensitivity is −20 dBm, with a fiber loss of 0.2 dB/km. Pre- amplification is used to compensate for the fiber loss and to keep the same received power, and an optical filter with 4× bit-rate bandwidth is built into the receivers to remove optical noise. In all the stimulations, an electrical filter with a bandwidth of 0.7× the bit rate is used 20 in the receivers. The PRBS length is 2 13 − 1 = 8191, which is long enough to examine data pattern dependencies induced by the modulators. A 10-Gb/s NRZ ON–OFF keying signal is generated by each type of modulator. Fig. 3- 2(a) shows output pulse trains, while Fig. 3-2(b)–(d) shows an optical pulse’s instantaneous amplitude for logic data “00111000” generated from types I, II, and III configurations, with a drive voltage of 5 V. The time window is 800 ps, and the vertical axis is 0 − 1.4(mW) 1/2 . There is an overshoot at rising edges of the pulses for types I and II, which results from interference between the CW input field and the optical wave coupled out of the ring. The voltage-induced index change in the cavity adds an instantaneous phase shift to the optical wave traveling around, which is an equivalent frequency change to the carrier [48]– [50].When coupled out of the ring, the optical wave interferes with the CW, resulting in the overshoot (similarly, an undershoot at falling edge in type III). The interference also induces phase oscillation, reflected as a strong frequency chirp in Fig. 3-2. This is why a static model would not correctly predict signal chirp [32]. All the chirps are plotted in the vertical axis from −120 to 80 GHz. Note that peak value of the chirp may occur at low instantaneous optical power, making it less effective. In contrast, the chirp accompanied by the overshoots causes an asymmetric spectral shape of the signals. Therefore, types I and II have the opposite chirp peak values, but both of them have spectral red-shift broadening, as shown in Fig. 3-2, while type III has a spectrum with strong blue- shifted components. In Fig. 3-2(e)–(g), vertical and horizontal axes are 10 dB/division and 20 GHz/division. We plot the generated 10 Gb/s NRZ spectra at drive voltage of 2, 4, and 6 V, which become more asymmetric as the voltage increases. It is important to mention that the overshoot can be seen experimentally from an electrical oscilloscope only when a 21 wideband photo-detector is used, otherwise the shifted frequency components and associated overshoot are removed by filtering effect in photo-detectors. Note that in Fig. 3-2 (b) and (c), the pulse from type II has a stronger overshoot and an intensity dip that follows the falling edge. This is because an over-coupled ring cavity stores more energy than an under-coupled one when they are on resonance, although they have the same steady-state transfer function. At the falling time, photons are accumulated in the cavity, and some of them are coupled out and destructively interfere with the CW field. The type II cavity has an energy that increases to a high enough value to deplete the CW and then produces output light after the intensity dip. In contrast, type I never has enough cavity energy to deplete the CW. The difference between the types I and II dynamic waveforms becomes more significant when the resonators are operated further away from critical coupling [39], [40]. 22 Fig. 3-2. Pulse waveforms and signal spectra generated by the three types of the microring modulators. (a) Generated pulse trains from type I, II, and III (top to bottom). (b)–(d) Amplitude (solid line) and frequency chirp (dotted line) of a pulse for types I, II, and III. (e)–(g) Signal spectra for type I, II, and III, with drive voltage of 2, 4, and 6 V (bottom to top), respectively. All the plots are in the same scale. Fig. 3-3 shows the extinction ratio of the modulated signals as the peak-to-peak drive voltage increases from 1.2 to 8 V. A 2.2-V drive voltage blue shifts the resonance peak by 10 GHz. The carrier-induced dynamic loss depends on doping density and is 2.5, 5, and 7.5 dB/cm for a drive voltage of 2, 4, and 6 V, respectively. Modulator types I and II have the same extinction ratio since they share a common steady-state output. The extinction ratio saturates quickly, and the 4-V drive voltage produces an extinction ratio of 13.8 dB. When the ring resonator is operated near critical coupling, the saturated extinction ratio can be higher. In contrast, for type III, the high voltage, and thus, dynamic loss apply to “1” bits, producing relatively low signal peak power and small extinction ratio under the optical bias condition. However, an increased voltage reduces “0” level in the signal and improves the extinction ratio, as shown in Fig. 3-3. Fig. 3-3. Extinction ratio is increased by applying a large drive voltage, which is saturated for types I and II, and is improved greatly for type III. 23 Fig. 3-4. Pulse width is examined as a function of drive voltage. Due to the nonlinearity of the microring-based modulation, types I and II have a broader pulse as the voltage increases, while the pulse width from type III decreases. Pulse-width at full width at half maximum (FWHM) of a single ‘1’ pulse is plotted in Fig. 3-4, with the same parameters as in Fig. 3-3. The pulses become broader for types I & II and narrower for type III as the voltage increases, because of the modulation nonlinearity caused by the Lorentzian resonance profile and cavity dynamics [44]. The pulsewidth, together with the frequency chirp, affects the signal spectra. Unlike the extinction ratio that is mostly related to the steady states of the modulators, the pulsewidth reflects cavity dynamics. The type II modulator produces a narrower pulsewidth than type I, since an over=coupled ring modulator is faster than an under-coupled one with the same Q-factor [27]–[29]. At the rising time of the generated pulses from types I and II, the resonance shifts away from the CW, and the photons stored in the ring escape outwards by both loss and coupling. With the same Q-factor and the slightly different photon storage mentioned above, types I and II have a similar rising edge in Fig. 3-2, associated with photon lifetime. However, at the falling time when the ring becomes on-resonance again, the loss discounts the efforts of incoming photons to re-build the optical field in the cavity. The falling time thus must be longer than the photon lifetime, which is why both types I and II have a falling time longer than the rising time. Also, a stronger coupling in type II allows for a faster build- 24 up of optical field, and the falling edge for type II is steeper. Type II thus has narrower pulses than type I as shown in Fig. 3-4. Fig. 3-5(a) shows 3-dB modulation bandwidth for the three types of modulators with drive voltage at 3 V. Types I, II and III have a bandwidth of 15.5, 19.5 and 9.6 GHz. There is a peaking effect for type II, which is associated with overcoupling (small damping). The overshoot and intensity dip cause steep pulse edges and a fast response of the modulator. The peaking effect in type II decreases with drive voltage from 3 to 1 V, as shown in Fig. 3- 5 (b). Accordingly, 3-dB bandwidth is reduced from 19.5 to 10.5 GHz. This is because, with a small voltage, the photons in the cavity are not fully removed at logic ‘1’, producing a small overshoot. With driving circuit’s effect on modulation speed ignored here, the bandwidth is limited by carrier transit time and photon lifetime. A fast optical response in type II makes it more tolerant to a long transit time. 25 Fig. 3-5. 3-dB modulation bandwidth of the microring modulators. (a) For all the three types at drive voltage of 3 V. (b) For type II with a decreased voltage. We examine how the drive voltage affects signal quality, keeping other modulator parameters the same. As shown in Fig. 3-6, signal Q-factor is improved by increasing the voltage, which is mainly due to a better extinction ratio. When voltage is larger, type III becomes worse with reduced pulse peak power and a small eye-opening, due to the dynamic loss, although a high voltage produces a low “0” level and a good extinction ratio, as shown in Fig. 3-3. Types I and II have much better signal quality but it saturates at a high voltage. Type II keeps improving, with steep pulse edges. In contrast, type I suffers from a long pulse tail at the falling time (see Fig. 3-2) and an ever-increasing pulsewidth, which causes the signal Q to slightly drop at a high voltage. We believe that, when many data channels are 26 densely multiplexed and a relatively narrow filter is added to each channel, the signal quality would decrease with the drive voltage after an optimal value. Signal quality also strongly depends on laser phase noise and linewidth. Fig. 3-7 shows that signal Q decreases quickly with the laser linewidth more than 100 MHz, at drive voltage of 3 V. All the three types perform quite similar at a large linewidth. Signals degrade because the laser phase noise is converted to amplitude noise by the resonator-based active devices [51], [52], which may become a critical issue when an on-chip laser with a large linewidth [53] is integrated together with the modulators. Based on the simulation results given above, we note that the type III modulator requires low cavity loss to obtain the same cavity Q as types I and II, and that it does not perform well due to a small extinction ratio at low drive voltage. For a feasible cavity loss, type III has a lower cavity Q, and drive voltage has to be much higher to produce an acceptable extinction ratio, which is power consuming. Hence, in the following section, we limit our discussion only to types I and II modulators. To now, frequency chirp in the modulated signals has not been fully discussed. It is negligible for 10 Gb/s signals in short-reach optical communications where signals travel over a few meters at most, even if the waveguide dispersion can be as high as several thousand picoseconds per nanometer per kilometer [54], [55]. However, the frequency chirp has a significant effect on data transmission over optical fibers. Besides the steady-state phase properties shown in Fig. 3-1, cavity dynamics also strongly affects the signal chirp [33]. As a result, the three types of modulators have a quite different chirp waveform in Fig. 3-2. It is important to mention that the chirp is difficult to be evaluated using conventional α- parameter [56], because, based on its definition , where E and φ are the amplitude and phase of an optical field, the calculated α-parameter becomes a temporal function oscillating quickly from negative to positive 27 Fig. 3-6. Signal quality is examined as the drive voltage increases. Type II modulators exhibit a better performance at a high drive voltage than the others. Fig. 3-7. Signal quality is examined as laser linewidth increases at drive voltage of 3 V. All the modulator types have similar signal quality at a large linewidth. at bit transitions. This is partially originated from the interference effect explained earlier. Instead, we define “effective chirp” as (t) to evaluate chirp effect, where is the instantaneous carrier frequency variation in gigahertzs, and is the instantaneous optical power in milliwatts [27]. This generates a chirp waveform weighted by power so that the absolute chirp peak occurring at low power duration would not be concerned much. In Fig. 3-8, we plot the amplitude and effective chirp for the pulse “00111000” generated from the types I and II modulators. Since a high drive voltage produces a very 28 asymmetric signal spectrum, we consider a voltage <3 V for data transmission over fibers. Fig. 3-8 (a) and (b) compares types I and II with a drive voltage at 1.25 V, and Fig. 3-8 (c) and (d) shows type II with a voltage reduced to 1 and 0.75 V. In the same scale, horizontal axis shows an 800-ps time window, and vertical axes are 0.1 to 0.9 (mW) 1/2 for the amplitude and −1 to 0.4 GHz∙mW for the effective chirp. We note that type I essentially has red-shifted frequency components at rising time when the chirp is weighted by optical power, which is different from the absolute chirp shown in Fig. 3-2. Importantly, the frequency components at falling time are also red-shifted, which means that the high frequency components at both pulse edges will walk off with carrier frequency due to chromatic dispersion in fibers, producing data distortion. In contrast, type II has red shift at rising time and blue shift at falling time, so-called negative chirp [56], which is useful to compensate for the positive dispersion in standard single-mode fibers. As voltage increases from 0.75 to 1.25 V for type II, the effective chirps at the pulse edges become more unbalanced, with the red shift enhanced partially by the increased overshoot and the blue shift remaining almost the same. We simulate signal transmission in a single-channel fiber link, in which chromatic dispersion is 16.3 ps/nm/km at 193 THz. Fiber nonlinearity is negligible since launched signal power of −10 dBm is relatively low. Polarization-mode dispersion in the fibers is ignored. Types I and II modulators with 1-V drive voltage 29 Fig. 3-8. Pulse waveforms (dotted line) and effective chirps (solid line) generated by the types I and II modulators, with different drive voltages. All the plots are in the same scale. (a) Type I at 1.25 V. (b) Type II at 1.25 V. (c) Type II at 1.00 V. (d) Type II at 0.75 V. are compared to a 10-GHz MZM that has V π = 4V, 30-dB extinction ratio, and no chirp. Power penalty is measured as the difference of required received power for signal detection at bit error rate of 10 −9 with and without fibers. Fig. 3-9 shows power penalty over fiber length for the types I and II modulators and the MZM, without dispersion compensation. One can see a great reach extension for type II due to its negative effective chirp. In contrast, type I suffers from the chirp-induced data distortion and performs worse than the MZM. At 1-dB power penalty, fiber transmission distance is 16, 83, and 30 km for types I and II, and MZM, respectively. Drive voltage greatly changes extinction ratio, pulse-width, chirp and spectrum shape, and all these affect data transmission over fibers. In Fig. 3-10, power penalty is plotted as a function of drive voltage for types I and II, at a fiber length of 80 km. We note that type II has a range of the voltage from 0.75 to 1.75 V where power penalty as low as 1 dB is achieved. This can be explained as follows. With a small drive voltage, the effective chirp at pulse edges in Fig. 3-8 is more balanced, partially due to a reduced overshoot, and the red- 30 shift frequencies less weighted in the effective chirp. However, the extinction ratio is also smaller. On the other hand, a high drive voltage increases the extinction ratio but produces a strong chirp only at the rising edge, which results in a significant walk-off between different frequency components in fiber transmission. Below 0.75 V, the penalty is dominated by low extinction ratio, while the chirp becomes a major degrading effect above 1.75 V. Fig. 3-9. Power penalty as a function of fiber transmission distance for types I and II modulators and a MZM. Type II exhibits negative chirp, and thus, greatly extended fiber distance at power penalty of 1 dB. The microring modulator could be operated in a detuning situation, and for type I or II, this means that CW is not exactly aligned to resonance frequency when drive voltage is logic “0”. We call it positive detuning when CW is originally on the left side of resonance in frequency domain. Fig. 3-11 shows the detuning-induced power penalty for type II, which is now the difference of the received power required for signal detection at bit error rate of 10 −9 with and without detuning. Transmission distance is fixed at 80 km, and drive voltage is 1.25 V, near the middle of the voltage range for low penalty in Fig. 3-10. We note that the signal transmission performance is sensitive to positive detuning, which can be attributed to two reasons. First, the detuning causes an increased “0” level in the generated signals, and thus, reduces extinction ratio. Second, detuning the CW with the same drive voltage increases 31 steady-state output optical power, which means that more photons are coupled out of the cavity at rising time, resulting in a stronger overshoot and unbalanced chirp. On the other hand, a negative detuning produces subpulses at “0” level in output and significantly degrades signals. From Fig. 3-11, >5 dB power penalty is seen for a detuning of 0.01 nm. Fig. 3-10. Power penalty in signal transmission over 80-km fibers is examined as a function of drive voltage for types I and II modulators. With a voltage ranging from 0.75 to 1.75 V, around 1 dB power penalty can be achieved using type II. Fig. 3-11. Power penalty caused by detuning the type II modulator. Signal performance is sensitive to detuning. 32 3.3 Coupled-ring modulator: over-coupling and transient effect Typically, as shown in Fig. 3-12(a), in a single ring modulator, a continuous wave (CW) laser source is fixed at the ring resonance wavelength. When the drive voltage is turned on/off, the resonance is shifted back and forth due to the carrier density change in the ring waveguide, and thus the CW laser light is modulated [67,68]. In the optical domain, the modulation speed depends on how fast the light can be coupled in and out of the cavity, which is related to the photon lifetime and the resonance linewidth of the cavity [69-75]. Hence increasing the coupling helps achieve a shorter photon lifetime and larger bandwidth. However, simply increasing the coupling will decrease the cavity Q and enlarge the resonator linewidth, which may either cause a lower extinction ratio in the modulated signals or require a larger resonance shift [67]. Inevitably, there is a tradeoff between the bandwidth and resonance shift for single ring modulator when keeping a certain extinction ratio. Instead, as illustrated in Fig. 3-12(b), we describe a coupled-ring-based modulator, which utilizes two coupled rings. We designate the ring immediately adjacent to the waveguide as the “inner” ring and the other one as the “outer” ring. The inner ring is heavily over-coupled (i.e., coupling » loss) to the bus waveguide, and only this ring is actively driven to produce data modulation. Given a fixed cavity Q, and considering that the loss is less than the coupling, the light energy in the inner ring can be accumulated much faster compared to the critical coupling case (coupling = loss) that is desired in the single-ring modulator. Since the output signal in the waveguide is determined by the interference of the input CW light with the light coupled from only the inner ring, the over-coupled ring can potentially respond to a higher-speed electrical signal due to the faster energy accumulation speed. Moreover, compared to the single-ring modulator, the proposed coupled-ring modulator features several potential advantages: (1) as shown in Fig. 3-1(b), the coupled- 33 ring structure has a deeper notch profile, and thus enables relatively high extinction ratio, (2) the transmission profile of the coupled-ring structure becomes steeper, which may allow a smaller resonance shift and lower driving electrical power, and (3) increased design degrees- of-freedom provide us with better design flexibility to optimize the performance of the modulated signals in different communication scenarios, such as when chirp adjustment is desired. (a) (b) Fig. 3-12 (a) Single ring modulator scheme. (b) The proposed coupled-ring modulator scheme: only the ring adjacent to waveguide is driven, which requires smaller resonance shift and enables higher modulation speed and higher extinction ratio. Referring to [76], to model the coupled-ring modulator, we utilized an ideal 60 Gb/s NRZ drive voltage sent through a five-pole Bessel electrical filter as the electrical input signal. The variation in carrier density is simulated as a charging process following the applied voltage. According to [77], this is believed to be a good fit to real behavior in MOS capacitors. The carrier transit time, defined as the duration for carrier density to increase from 10% to 90% of its peak value when a voltage step is applied, is considered to be 10 ps [76, 78]. The continuous wave from laser source is then modulated. The relationship between the resonance frequency and the index is given by the resonance condition = mc/n eff R, where is the resonance frequency, m an integar, c the light speeding vacuum, n eff the effective index and R the ring radius. Change in voltage from 0 to 5 V causes a resonance peak shift of 0.16 nm towards shorter wavelength. To obtain the modulated 34 optical signals, a set of differential equations are solved. The following derivations are essentially based on Refs. [69, 79]. The time rate equations of the energy amplitude change in the coupled-ring resonator with the inner ring coupled to a single waveguide are: 1 1 1 2 2 1 1 1 1 ( ) in o e d a j a j a j E dt (3-2-a) 2 2 2 2 1 2 1 ( ) o d a j a j a dt (3-2-b) 1 1 out in E E j a (3-2-c) where and are the energy amplitudes and and are the resonance angular frequencies in the inner ring and outer ring, respectively; E in and E out are the incident wave field and transmitted wave field; 1/ e is the amplitude decay rate due to the power coupling into the waveguide; 1/ o1 and 1/ o2 are amplitude decay rates due to the intrinsic loss in the inner ring and outer ring; and ; is the power coupling between the ring and the bus waveguide; is the mutual power coupling between the rings; and are the inner ring radius and outer ring radius respectively. and are the group velocities in the inner ring and outer ring; and is the carrier wave frequency. Since the inner ring is active while the outer ring is passive, is modulated around the carrier frequency , whereas is actually fixed at . The operation principle of the coupled-ring modulator is as follows. First we focus on the inner ring, which is over-coupled to the waveguide. Assuming 2 = 0 in equations (1-a, b, c) and ref, the energy in the inner ring resonator evolves as: 2 2 2 * 1 1 1 1 1 1 2 2 2 Im( ) in e o d a a a j E a dt (3-2-2) Since the cavity Q is fixed, the sum of 1/ e and 1/ 01 is also fixed. As shown in Eq. (2) for an over-coupled ring resonator, the ring energy |a 1 | 2 can increase faster compared to the critically coupled scenario with same cavity Q, due to a higher 1 , thereby resulting in a 35 potentially higher response speed. Over-coupling, however, will result in the energy amplitude inside the ring being stronger than that in the critical-coupling condition, which produces a high signal ‘0’ level and a low extinction ratio. In order to remove extra energy in the inner ring, the outer ring is needed. Given 2 0 and using equations (1-a) and (1-b), the time rate change of the energy in the rings evolves as: 2 2 2 * * 1 1 1 2 1 2 1 1 1 2 2 2 Im( ) 2 Im( ) in e o d a a a j aa j E a dt (3-2-3a) 2 2 * 2 2 2 1 2 2 2 2 Im( ) o d a a j aa dt (3-2-3b) As compared to equation (2), the mutual energy coupling (2j 2 Im(a 1 a 2 *)) from the inner ring to the outer ring in Eq.(3-a) can decrease the inner-ring energy |a 1 | 2 , resulting in a low signal ‘0’ level and a high extinction ratio. Adding an outer ring produces mutual coupling loss in the inner ring while it won’t decrease the modulation bandwidth significantly: the mutual coupling loss (2j 2 Im(a 1 a 2 *)) in inner ring is proportional to the energy amplitudes in both inner and outer ring (a 1 and a 2 ); according to Eq. (3-b), the accumulation rate of a 2 is proportional to a 1 , so the substantial growth of a 2 , as well as the mutual coupling loss, only happens as a 1 accumulates, at which time the signal ‘0’ level is already generated by interference of the input CW light with the light coupled from the inner ring. As shown in Fig. 3-13, the proposed modulator achieves both high response speed and high extinction ratio, exhibiting the same modulation performance with only 1/3 resonance shift, while the over-coupled single ring modulator produces heavily distorted signals. 36 Fig. 3-13 Comparison among the three examples of the modulation of a 60-Gb/s NRZ signal shows that the proposed modulator requires 1/3 resonance shift (R.S.) to achieve the modulation with negligible distortion compared to the critically coupled sing ring modulator. All figures are plotted in the same scale with the same output power. In Fig. 3-14, the 3-dB bandwidth and extinction ratio of the modulated signals are examined. The single ring modulator is compared to the coupled-ring modulator, where the power coupling coefficient 1 between the ring and waveguide (WG) is varied. For the single ring modulator, the cavity Q of the ring cavity is maintained at 9500, corresponding to a 20-GHz resonance linewidth, and the ring radius is 2.7 m. These parameters can be feasible according to the state-of-the-art fabrication [80]. As shown in Fig. 3-14 (a) and with a 20 GHz resonance shift, the 3-dB bandwidth of the single ring resonator modulator increases with the coupling coefficient . Critical coupling occurs around = 0.095. As > 0.1, the modulation bandwidth has a trade-off with the extinction ratio and is limited to 30 GHz with extinction ratio >10 dB. For the proposed structure, we would like to utilize an over-coupled inner ring with which the energy can be accumulated very fast at the resonance. Hence the probe wavelength is set equal to the inner ring resonance and the ring-ring coupling is set small enough to make the profile as a deep notch profile. The inner ring has a cavity Q-factor of 9500 for a fair comparison and its round-trip loss coefficient is 0.9991. The coupling coefficient is set to be 0.0094, and the round-trip loss coefficient of the outer ring is 0.9787. The two rings have the same radii of 2.7 m. In Fig. 3-14 (b), the critical coupling 37 occurs at = 0.012. Given a resonance shift of 20 GHz, the simulated modulation bandwidth up to 50 GHz is observed with 12-dB extinction ratio. (a) (b) Fig.3-14 Modulation bandwidth and extinction ratio versus the ring-to-waveguide coupling coefficient 1 for the (a) single ring and (b) coupled ring modulators The coupling coefficient between the two rings plays a critical role in optimizing the performance of the coupled-ring modulator. One can consider the coupled-ring structure as a single compound resonator and can be varied to adjust the energy distribution between the inner and outer rings. Noticing the loss in outer ring is larger than that in inner ring, people can modify overall loss coefficient of the compound resonator by changing , which is different from a single ring resonator in which the loss is determined by the fabrication technique [69]. As increases, the compound resonator becomes lossier and is switched from the over-coupled condition to the under-coupled one. Critical coupling is observed near = 0.013, in which the extinction ratio of the modulated signal is more than 20 dB (Fig. 3- 15(a)). As a result, the frequency chirp is switched across the critical point (Fig. 3-15(b)). However, we note that large instantaneous frequency chirp occurs at the low-power region of pulse waveforms. Thus it is important to consider the chirp together with the instantaneous power. We define “effective chirp” as f(t)p(t), where f(t) and p(t) represent the instantaneous frequency and power of the modulated pulses, respectively. With the input 38 power of 0 dBm, we choose the peak value of the calculated effective chirp to evaluate the chirp effect of the modulated signals, as plotted in Fig. 3-15(b). As increases from 0.009 to 0.016, the peak value of effective chirp changes from -4.45 to -1.0 mWGHz. The system performance of the coupled-ring modulator is simulated and compared to a single ring modulator. In the back-to-back case, a 60-Gb/s NRZ signal is modulated with a single ring modulator (both linewidth and resonance shift = 60 GHz) and a coupled-ring modulator (both inner ring linewidth and resonance shift = 20 GHz), respectively. As shown in Fig. 3-16(a), two bit-error-rate (BER) curves are quite close to each other, indicating that the coupled ring modulator can modulate 60 Gb/s NRZ signal by only 20 GHz resonance shift of the inner ring under negligible degradation. In contrast, a critical-coupled single ring modulator operated with both the linewidth and resonance shift = 20 GHz will result in a low extinction ratio and cannot achieve a low BER<10 -9 . Fig. 3-15 (a) Extinction ratio versus the coupling coefficient between the inner and outer rings. Critical coupling occurs around = 0.013 and the extinction ratio tends to be infinite. (b) Frequency chirp is switched from negative to positive as increases. As stated above, the modulated signal exhibits the negative effective chirp, which can be controlled by . As an example, a 40-Gb/s NRZ is modulated by the coupled-ring modulators with different , compared to a single ring modulator. Fig. 3-16(b) shows the simulated power penalty of the 40-Gb/s signal in the SMF transmision without dispersion 39 compensation. We note that less than 0.5 dB power penalty due to 85 ps /nm chromatic dispersion is achieved for the 40-Gb/s NRZ signal with the coupled ring modulator. This is consistent with the trend shown in Fig. 3-15(b). In contrast, a single-ring modulator shows power penalty as high as 3.5 dB under 35 ps/nm chromatic dispersion and exhibits less flexibility to modify the properties of the modulated signal due to the request to keep critically coupling. Dispersion tolerance at 0.5-dB power penalty is extended from 18 to 85 ps/nm, as shown in Fig. 3-16(b). (a) (b) Fig. 3-16 (a) Back-to-back BER curves of the 60-Gb/s NRZ signals modulated with the single ring (linewidth = 60 GHz, resonance shift = 60 GHz and 20 GHz) and coupled-ring modulators (linewidth = 20 GHz, resonance = 20 GHz). (b) A 40-Gb/s NRZ signal under different chromatic dispersion values, where the coupled-ring modulators with different effective chirps are achieved by varying the ring–to- ring coupling coefficient 2 . 40 3.4 Summary A silicon microring modulator with coupled-ring-resonator structure is proposed. A 60-Gb/s NRZ signal has been obtained from a 20 GHz resonance shift of the inner ring. This design is particular meaningful for the high speed signal modulation based on microring resonators. Through the above discussions, we notice that the resonance-switching-based silicon modulator can achieve compact size, moderate drive voltage and good extinction ratio. By this mean, although we can enhance the modulation speed to be around 3 times above the resonance’s linewidth, we can never separate the modulation speed from the optical linewidth. 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Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96, 6008-6015, (2004). 79. H. A. Haus, Waves and fields in optoelectronics (Prentic-Hall, Inc. Englewood Cliffs New Jersey 07632, 1984) chap. 7. 80. Q. Xu, D. Fattal, and R. G. Beausoleil, “1.5-μm-radius high-Q silicon microring resonators,” Opt. Express 16, 4309-4315, (2008). 47 Chapter 4 Coupling-switching modulators 4.1. Introduction Last chapter, we mentioned that the resonance switch modulator can’t completely break the linewidth limitation although it can achieve speed 3 times higher than the optical linewidth. Very recent progress has shown that RC constant as short as 1 ps can be achieved by using compact silicon-micro-resonator-based active elements [1-9]. Currently the fundamental limitation to the silicon modulator's speed comes mainly from the optical domain. The speed of most recent silicon micro-resonators-based modulators is limited within tens of GHz [6-11] due to the strict requirement on power consumption [10]. Recently, a theory of coupling modulation [12-15] was proposed for achieving very high bandwidth that is not constrained by photon lifetime, in which the waveguide-ring coupling in a single ring notch filter is modulated (defined here as a ‘notch design’, shown in Fig.4- 1(a)). However, a few critical drawbacks exist in this design: (1) a long ‘1’ pattern leads to intra-cavity energy depletion, which removes the stable energy amplitude and induces severe pattern dependence; (2) relatively long arms of several hundred micrometers are needed to implement the coupling structure, which leads to a considerable capacitive loading [1]. Although the design proposed in [16] can help relieve the intra-cavity energy fluctuation problem in [14], it generates another two new problems: (1) compared to the notch design, it asks for two (instead of one) composite interferometers with the exactly the same structure to each other, which greatly increases the structure complexity; (2) since the design counts on extremely high cavity energy density to allow for small coupling modulation and short phase shifters, nearly lossless 3 dB couplers and phase shifters are needed to implement the design, which is extremely challenging. A novel and practical modulation scheme is required 48 to separate the bandwidth from the photon lifetime restriction, remove pattern dependence, reduce the RC time constant and ease the requirement on active element intrinsic loss. In this chapter, a light drop structure (Fig.4-1(b)) is proposed in which one waveguide couples CW light into the large ring resonator and the coupling between the large ring and another waveguide is modulated with a small amplitude by using one composite interferometer. Compared to the notch design (Fig. 4-1a), CW light coupling into the large ring is not interrupted by the signal modulation. As a result, the light dissipation in the large ring is compensated by continuous input of CW light and the intracavity energy remains relatively stable instead of depleting. The severe intracavity energy fluctuation inherent to the notch design is removed by the proposed design, and the extinction ratio is improved from <1 dB to >20 dB with a factor of 25 smaller drive voltage. Two low Q ring phase shifters are used in the push-pull configuration to allow for both very small capacitance and high response speed in optical domain. Non-return-to-zero (NRZ) signals with performance comparable to that of MZMs at 40 Gb/s is obtained with 0.4 V drive voltage. As the RC constant scales down to 1 ps, it is shown that up to 160 Gb/s NRZ signal can be achieved with no more than 4 V drive voltage and < 5 dB insertion loss. Compared to [11], the tolerance to active ring propagation loss is increased from 5 dB/cm to over 25 dB/cm with less than 5% modulation bandwidth change. As shown in Fig. 4-1(a), in the notch design, the energy amplitude inside the resonator is assumed to be constant due to the long photon lifetime enabled by the extremely high cavity Q. The ring-waveguide coupling is modulated to control the destructive interference between the CW light in waveguide and the light coupled out of the cavity, thus the modulation speed depends only on the bandwidth of the composite coupler (inside dashed line region) which is presented in [14]. The modulation of the coupling coefficient is achieved by a push-pull 49 (a) (b) Fig.4-1 (a) notch design relies on ultra long photon lifetime to maintain constant energy amplitude while the intracavity energy may deplete as the coupling is zero during a long ‘1’ signal pattern; (b) the light drop design maintains the energy amplitude in the large ring resonator in a very small range by coupling light continuously from the lower waveguide into the large ring and modulating the upper waveguide to large ring coupling in a small range. configuration with equal but reverse phase shifts on the upper and lower arms. However, for long NRZ ‘1’ pattern, the signal pulse width is comparable to the photon lifetime. Since the coupling is 0 during this time, the intra-cavity energy may deplete, which contradicts the constant energy amplitude assumption [14] and leads to severe pattern dependence. As shown in Fig. 4-1(b), a light drop structure is proposed in which one waveguide couples CW light into the large ring resonator and the coupling between the large ring and another waveguide is switched via the composite coupler inside the dash line region. Both the large ring and the waveguides are passive components. The signal is generated by modulating the upper waveguide-to-large ring coupling using the ‘composite interferometer’ in the dashed line region in Fig.4-1(b), in which two very low cavity Q ring phase shifters are used. The proposed modulator features the following important advantages: (1) since CW light is coupled continuously from the lower waveguide to the large ring resonator, the CW light coupling is not disturbed by the coupling modulation and the intra-cavity energy depletion is avoided; (2) since compact ring phase shifters are used, very short RC constant 50 can be obtained; (3) the ring phase shifters linewidth is around 160 GHz and photon lifetime is only 1 ps, which allows for high coupler response speed; (3) due to ring enhancement of the ring phase shifter and relatively high cavity Q of the large ring, small coupling modulation is needed to obtain signals with low insertion loss, enabling small drive power; (4) because signals are generated by light drop instead of destructive interference, the signal is purely 0 when the upper waveguide-ring coupling is 0, which enables a high extinction ratio. 4.2. Principle of Compound Coupler To describe the operating principles of the proposed design, it is necessary to introduce the “notch” design of Fig, 4-1(a) for first. As shown in Fig.4-2, the coupling region in Fig.4- 1(a), can be seen as a ‘composite interferometer’. The transfer function between a 4 , b 4 and a 1 , b 1 are derived as [3,12] Fig.4-2 schematic diagram of the composite interferometer (4-1) , (4-2) in which t 1 , 1 , t 2 , and 2 refers to the reflectivity coefficient, amplitude coupling coefficient of the left 3 dB coupler, the reflectivity coefficient, amplitude coupling coefficient of the 51 right 3 dB coupler; is the amplitude transmission of the phase shifter; the phase shift in upper and lower arms are /2; t and are the reflectivity coefficient and amplitude coupling coefficient of the whole composite interferometer. There is a π phase difference between the upper arm and the lower arm. As shown in Eq. (2), the coupling can be controlled by the equal but reverse phase shift /2 in the upper and lower arms, i.e. push- pull operation. According to [11,17-18], the dynamic equations for notch design in Fig.4-1(a) are (4-3a) (4-3b) (4-3c) in which, |a(t)| 2 is the intracavity energy of the ring resonator and A(t) is the time-varying amplitude of a(t), ω and ω r are the carrier wave angular frequency and the resonance angular frequency of the ring; 1 2 = k 1 2 V g1 /2πR 1 = 2/ e1 ; k 1 is the large ring and the waveguide amplitude coupling coefficient and V g1 is the group velocity inside the large ring; 1/ e1 and 1/ p are the amplitude decay rate due to the phase shifter, including power coupling from the large ring into the waveguide (1/ e1 ) and the power loss induced by the phase shifter (1/ p ). 1/ l is the amplitude decaying rate due to the loss in the passive part of the large ring. k 1 is modulated to generate signals. R 1 is the radius of the large ring. E in =E in0 e −jωt and E out =E out0 e −jωt represent the input CW and modulated signal respectively. Substitute (3-c) into (3-a) and let r = , (4-4a) (4-4b) 52 Signals are obtained by the cancellation between the light coupled-out of the cavity and CW light in the waveguide. As 1 =0, no light is coupled into the waveguide to cancel the CW light and signal ‘1’ is generated. However, in this time period, no CW light is coupled into the cavity either. The equation (4-a) changes into (4-5) In which indicates the energy amplitude is depleting with a time constant of (1/ p +1/ l ) -1 . For NRZ signals at a bit rate beyond the resonator linewidth and for a continuous ‘1’ pattern with a length comparable to (1/ p +1/ l ) -1 , the intra-cavity energy amplitude will be depleted and severe signal pattern dependence will occur. These conditions will result in unacceptably low signal quality. For the design in (Fig.4-1(b)), after cancelling e −jωt and making the CW light frequency equal to the large ring resonance frequency, the dynamic equations are (4-6a) (4-6b) in which (< 1) refers to the energy amplitude transmission of the ring phase shifter, A(t) is the intra-cavity energy amplitude inside the large ring, k 1 and k 2 are the amplitude coupling coefficient between the large ring and the upper waveguide and that between large ring and the lower waveguide, respectively. 1 2 = k 1 2 V g1 /2πR 1 = 2/ e1 . 2 2 = k 2 2 V g1 /2πR 1 = 2/ e2 . V g1 is the group velocity in the large ring. R 1 is the large ring’s radius. 1 is switched between zero and non-zero to generate signals. 1/ e1 , 1/ p are the amplitude decaying rate due to the phase shifter, including power coupling from the large ring into the waveguide (1/ e1 ) and the power loss due to the phase shifter (1/ p ). 1/ l and 1/ e2 are the amplitude 53 decay rates due to the intrinsic loss in the passive large ring waveguide and the power coupling from the large ring into the lower waveguide, respectively. Two ring phase shifters are simulated with push-pull operation to generate phase change /2. Both of the two ring phase shifters are designed to have cavity Q of 1200 with photon lifetime around 1 ps. They are heavily over-coupled to the arms. Their modeling essentially follows our previous work in [17]. The CW light coupling ( 2 ) into the large ring cavity is time-independent since the coupling from lower waveguide to large ring is passive. This is different from notch design. 1 is modulated to generate signals. As 1 0, (4-7) Let , (4-8) As 1 = 0, (4-9) Let , (4-10) A(t) is fixed at a non-zero value, because light is coupled into the large ring cavity via 2 continuously and compensates the dissipated intracavity energy. This is entirely different 54 from the notch design. The intracavity energy reaches a dynamic balance state. Hence, as 1 is modulated, the energy amplitude switches between two non-zero values, and . The energy amplitude fluctuation ratio is (4-11) According to (6-b), |E out | 2 is purely zero as 1 is 0. Therefore, high extinction ratio signals can be obtained even when 1 2 switches between 0 and a value that is small compared to (1/ p +1/ l +1/ e2 ). Notice that 1 2 = 2/ e1 , small 1 2 amplitude makes the energy amplitude fluctuation ratio in Eq.(11) tend to 1, indicating relatively stable intra- cavity energy amplitude. 4.3. Breaking the Trade-Off of Speed-Linewidth In our simulations, the large ring radius in Fig.4-1(b) is set equal to the ring radius in Fig. 4-1 (a) and a large radius of 64.8 m is used to achieve large cavity Q and narrow linewidth, corresponding to a FSR of 287 GHz. In Fig. 4-1(b), the power coupling coefficient between the lower waveguide and the large ring is 0.1089. The cavity Q of Fig. 4-1(a) is calculated to be around 68,000 and linewidth is 3 GHz. For Fig. 4-2(b), they are 19,000 and 10 GHz respectively. The cavity Q of the large ring in Fig. 4-1(b) is lower because the ring phase shifters introduce higher loss than the active arms in Fig. 4-1(a). The propagation loss is set as 1 dB/cm [19] in passive rings/waveguides in Fig. 4-1(a) & (b) (not in phase shifters). The arm length in Fig. 4-1(a) is chosen to be 100 m for the notch design, based on [3, 14-15]. The ring phase shifters radii in Fig. 4-1(b) are both 5.4 m. The ring resonator phase shifters are heavily over-coupled to the short waveguides. Their cavity Q is 1200 (linewidth = 160 55 GHz) and roundtrip loss coefficient is 0.9961. The low quality factor of coupling is shown to be realizable in [20-21]. Among forward biased p-i-n junctions, reverse biased p-n junctions, and sub-micrometer MOS structures, sub-micrometer MOS structure enables modulator designs with both high modulation efficiency and high speed [9, 22-23]. Here an MOS structure is simulated to realize electro-optic modulation. A time constant of 5.68 ps is chosen for the carrier density to fall to 1/e of its peak and a V π ∙L of 1.6 V∙cm is assumed, which follows reported structures [1,22]. Since our ring phase-shifter’s perimeter is tens of times shorter than the phase shifter length in [22], significantly smaller RC constant could be obtained. For straight-waveguide-based phase-shifters in the notch design and the ring phase shifters in our design, a propagation loss of 10 dB/cm is assumed [1, 22]. 10 V drive voltage is needed to achieve critical coupling in the notch design. In our model, a laser with a linewidth of 100 KHz is used, with output power of 1 mW. A square-wave voltage signal providing a non-return-to-zero (NRZ) pseudo-random-bit- sequence (PRBS) is used as the drive signal. The receiver sensitivity is −17.9 dBm for a bit error rate at 10 −9 at 40 Gb/s. To observe the pattern dependence induced signal degradation, erbum doped fiber amplifier simulation models are used to maintain the same received power. An optical filter with 4× bit-rate bandwidth is used before the receivers to remove optical noise. Fig. 4-3(a) and (b) show the simulated coupling, intra cavity energy amplitude and the signal power over time of both designs at the bit-rate of 40 Gb/s in NRZ format. The insertion loss of the notch design is less than 1 dB. The insertion loss of the proposed design depends on the drive voltage. When drive voltage is 2.6 V, the insertion loss (signal peak power over laser power) is less than 5 dB. Here, to avoid strong signal overshoots, a drive voltage of 1V is used. Fig. 4-3(a) and (b) are drawn with the same time scale at the same received power, by assuming that the propagation loss of the large ring passive waveguide is 1dB/cm. In Fig. 4-3(a), the energy amplitude in the notch design is almost depleted during a 56 continuous long '1' signal pattern in which the coupling is zero, and consequently the signal suffers from non-uniform ‘0’ patterns. Contrary to the notch design, as shown in Fig. 4-3(b), the energy amplitude in the large ring in Fig. 4-1(b) fluctuates in a very small range and nearly uniform ‘0’ /’1’ signal patterns are generated. Fig.4-3(c) and (d) show the energy amplitude fluctuation and the extinction ratio of both designs over the propagation loss of the passive waveguide in the large ring. In Fig. 4-3(c), the intracavity energy amplitude is shown to change greatly, with energy amplitude ratio of 9 to 12 dB. And this intense change is independent of the passive ring waveguide loss because the active arm loss dominates the roundtrip loss and the photon lifetime of the ring resonator is limited. In Fig. 4-3(d), the energy amplitude fluctuates by less than 1 dB and the exctination ratio is improved by 20 dB, compared to the notch design. (a) (b) (c) 57 (d) Fig.4-3 (a) and (b) show the absolute coupling coefficient, intra-cavity energy amplitude and output signal power of the notch design and the proposed design respectively, which are obtained under the same time scale and the same received power; (c) and (d) show the ratio of max/min intracavity energy amplitude and the extinction ratio over the passive large ring propagation loss of notch design and the proprosed design. Since our research focuses on enhancing the modulation speed in optical domain, we scan the RC constant from 6 ps to 1 ps and examine the modulator’s 3 dB bandwidth. Here we examined two cases: (1) the ring phase shifter’s resonance is exactly the same with the laser frequency and the main cavity resonance, i.e. 0 offset; (2) the upper and lower ring phase shifter’s resonance is 80 GHz off from the laser frequency and the main cavity resonance, i.e. half linewidth offset. For both cases, the phase difference between the upper and the lower phase shifters is assumed to be biased at (2m+1)π. The drive voltage is 2.5 V. As shown in Fig. 4-4(a), as the RC constant is larger than 2 ps, the modulator’s 3 dB bandwidth is essentially proportional to the RC cutoff frequency (dotted line). As the RC constant decreases to 1 ps, a 3dB modulation bandwidth as 98 GHz can be obtained for the 0 offset case and 122 GHz for the half linewidth offset case. In both cases, the modulation speed is independent of the main cavity’s linewidth (around 10 GHz). It is found that the 3 dB bandwidth is higher for the half linewidth offset case because the ring phase shifter receives less influence from cavity dynamics, as discussed in [24]. In contrast, the coupled 58 ring design in [11] can only achieve a bandwidth as 47 GHz even the RC constant is 1 ps, because its speed is limited by its linewidth (20 GHz). The influence of the propagation loss inside the ring resonator on 3 dB bandwidth is compared between this design and our previous design in [11] in Fig. 4-4(b). A RC constant of 1 ps is assumed for the active rings in two cases. The 3 dB bandwidth decreases from 72 GHz to 54 GHz as the loss increases from 5 dB/cm to 30 dB/cm with our previous design in [11] when a drive voltage of 5 V is used. On the contrary, the 3dB bandwidth of the proposed modulator changes from 124 GHz to 118 GHz for the half linewidth offset case and from 98 GHz to 94 GHz for the 0 offset case. The modulation bandwidth of the proposed modulator changes no more than 5 %. This high tolerance to the intrinsic loss allows for higher doping concentration, which implies short RC constant and higher electro-optic modulation efficiency [25]. For instance, the intrinsic loss in [9] is around 20 dB/cm, in which a RC constant of 1 ps is presented. (a) 59 (b) Fig.4-4. (a) the proposed modulator’s bandwidth and the bandwidth of the modulator in [11] over the RC cutoff frequency; (b) the 3dB bandwidths over ring instrinsic loss of this design and [11], which shows that the tolearance to intrinsic loss is improved by the proposed design. The system performance of the proposed modulator is examined. 40 Gb/s NRZ signal BER curves are presented in Fig. 4-5(a). A traditional Mach-Zehnder Modulator (MZM) with V π voltage of 5 V is used as the benchmark. A single ring modulator with 40 GHz linewidth (nearly critical coupling with roundtrip loss of 0.9781 and reflection reflectivity coefficient of 0.9819, same radius, RC constant of 5.68 ps and same V π ∙L with the active rings in Fig. 4-1(b)) driven by 0.4 V is compared to the proposed modulator as well. As shown in Fig. 4-5(a), the proposed modulator shows performance comparable to the MZM, though nearly 2 dB power penalty is observed. On the contrary, neither the notch design driven by 10 V nor the SRM driven by 0.4 V is capable of 40 Gb/s NRZ signals with acceptable quality, due to the poor extinction ratio. Compared to a SRM design that requires a resonance shift comparable to the bit rate (40 GHz), this design needs a resonance shift as small as 1/20 of 40 GHz to achieve good signal quality. In Fig. 4-5(b), with a RC constant of 5.68 ps, the power penalty of the notch design modulator and the proposed modulator (0 offset) are compared over different bit-rates for NRZ signal format referenced to a MZM. Within a power penalty of 2 dB, the proposed modulator can achieve NRZ modulation up to 60 4 times the linewidth (‘B’ point in Fig. 4-5(b)). For comparison, the notch design shows power penalty no more than 2dB only when the bit rate is lower than the linewidth (‘A’ point) [26]. In Fig. 4-5(c), with a RC constant of 1 ps, the power penalty of the notch design modulator and the proposed modulator are compared over different bit-rates for NRZ signal format referenced to a MZM. Within a power penalty of 4 dB, the proposed modulator can achieve NRZ modulation up to 12 times of the linewidth (‘B’ point in Fig. 4-5(c)) for the 0 offset case and 16 times of the linewidth for the half linewidth offset case. The response speed is independent on the main cavity linewidth but mainly determined by the RC constant. Nevertheless, for the half linewidth offset case, a drive voltage of 4 V will be needed to obtain insertion loss no more than 5 dB, because smaller phase change is obtained compared to the 0 offset case. The notch design can achieve bit rate only 1.6 times of its linewidth (‘A’ point) even 1 ps RC constant is given and 4 dB power penalty is allowed. It is shown that, the proposed design performs a little bit worse with 2.5 V drive voltage at low speed than it does with 0.4 V drive voltage. It is mainly due to the signal overshoots. (a) (b) 61 (c) Fig.4-5 (a) BER curve of 40 Gb/s NRZ signals: the proposed modulator’s performance is comparable to the MZM, with a 2 dB power penalty. Its drive voltage is only 1/25 of the notch design. (b) The power penalty of the notch design and the modulator proposed by this paper over bit rate with RC constant equal to 5.68 ps. Modulation speed as 4 times as the main cavity linewidth can be achieved by the proposed modulator with power penalty no more than 2 dB. (c) The power penalty of the notch design and the modulator proposed by this paper over bit rate as the RC = 1 ps. Modulation speed more than 16 times as the main cavity linewidth can be achieved by the proposed modulator with power penalty less than 3 dB when the low Q ring phase shifter is biased 80 GHz off the laser frequency . 4.4 Model accuracy In addition to the dynamic equation model utilized here, another dynamic modulation model, known as the time dependent model [12] can be used to study the performance of the notch design and the proposed modulator. To check the accuracy of our model, the notch design modulator was simulated using both modeling methods. Fig. 4-6 shows 40 Gb/s RZ signals obtained with the notch design modulator using the time dependent model and our dynamic equations model. The data are simulated with the same simulation parameters and structure parameters. The signal pulses obtained with the two 62 models agree with each other according to Fig. 4-6. The difference is less than 1%, nearly negligible. Time dependent model Dynamic equations model Fig.4-6 Signal pulses of 40 Gb/s RZ signals obtained using the time dependent model and the dynamic equations model agree with each other very well. 4.5 Summary According to [22], we estimated the capacitance of our ring phase shifter to be around 60 fF. The power consumption is estimated to be 45 fJ/bit for 1 V drive voltage, according to the Eq. (12) given by [22]. (4-12) If an insertion loss less than 5 dB is required, a drive voltage of 2.6 V will be needed for the 0 offset case and the power consumption will go up to 304.2 fJ/bit. It can be greatly reduced by tens of times if a MOS depletion structure is used, as proved in [9]. Resonance alignment of multiple rings by thermal tuning has been demonstrated in our recent paper [27] and the thermal tuning to the upper and lower arms of the composite interferometer has also been demonstrated in [6]. These progresses have shown that 63 alignment of the resonances between the ring phase shifters and the large ring is doable by employing current technology. In conclusion, a silicon microring-based coupling modulator with light drop structure is proposed. The critical problem of severe pattern dependence with the notch-design-based coupling modulator is solved. A 40-Gb/s NRZ signal has been obtained with extinction ratio improvement from less than 1 dB to 20 dB by only 0.4 V drive voltage. 4.6 References 1. L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, "High speed silicon Mach-Zehnder modulator," Opt. Express 13, 3129-3135 (2005). 2. T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Tech. Lett. 17, 414-416, (2005). 3. A. 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Dapkus, "In-plane thermally tuned silicon-on-insulator wavelength selective reflector," in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper IME2. 70 Chapter 5 Design of high speed DPSK modulator 5.1. Introduction Differential-phase-shift-keying (DPSK), which carries data by phase difference of adjacent symbols, is one of the most popular advanced data modulation formats in optical communication system, owing to a 3 dB increase in receiver sensitivity and high tolerance to fiber nonlinearity[1-2]. Traditionally, the DPSK signal is generated using a Mach Zehnder modulator(MZM) [2] which has the dimension on the order of centimeter and may request high power consumption. Compared to MZMs, microring-based DPSK modulators and demodulators enable less chip area, smaller capacitance and lower power consumption [3-5]. To date, the modulation bandwidth of a resonance-shifting-based microring DPSK modulator [3] (Fig. 5-1(a)) is limited by its photon lifetime and the resonance shift is typically comparable to the resonance linewidth. Owing to the requirement on power consumption [6], the 3 dB bandwidth of the resonance-shifting-based DPSK micoring modulator is within 10 GHz [3-4]. In the past several years, coupling-modulation-based microring modulators have been [7-13] proposed and demonstrated for On-Off- Keying(OOK) and DPSK modulation to achieve high modulation speed independent on photon lifetime, which is recognized as a ‘notch design’[14]. However, as pointed out in our previous work [14], the intracavity energy in notch design tends to deplete as a long ‘1’ logic pattern arrives, which leads to very limited modulation speed and severe signal distortion. Although biasing the coupling coefficient at the critical coupling condition helps relieve problem [10,15], it leads to very high insertion loss and requires complicated pre-amplified circuits [15] or large drive voltage [10]. Furthermore, the long straight waveguide phase shifters in these designs also tend to induce large RC constant. 71 In this chapter, we propose a DPSK modulator based on a microring drop filter (Fig. 5- 1(b)) in which the coupling coefficient between the drop waveguide and the ring is switched between two opposite sign but equal magnitude values. Compared to the resonance-shifting- based DPSK modulator (Fig. 5-1(a)), the modulation bandwidth is independent on the ring resonator’s linewidth and 3 dB bandwidth as high as 100 GHz is obtained in simulations. NRZ-DPSK signals are modulated and demodulated successfully at 120 Gb/s with 4 V voltage. When demodulated with a Mach Zehnder delay line interferometer, the signals show nearly the same good quality with those NRZ-DPSK signals generated by an ideal MZM. When using a microring filter as demodulator, there is an extra power penalty of 0.8 dB. The tolerance to the active ring intrinsic loss has been significantly increased from 9 dB/cm to 30 dB/cm with the proposed design. We also compared this coupling modulator’s performance with those of other coupling modulators that claim high speed modulation. It is shown that 7.33 dB eye opening penalty existing in the DPSK signals at 120 Gb/s with the notch design is removed by the proposed design. The insertion loss of the proposed modulator can also be 5 dB lower than that of the notch design. And the signal overshoots problem in our previous design [14] is solved and up to 9 dB eye opening power penalty is removed with the new design. 5.2. Principle of DPSK modulator 1, Basic principle As shown in Fig. 5-1(a), in the resonance-shifting-based DPSK design, the ring is over- coupled to the waveguide and there is a 2π phase shift across the resonance. As the resonance is switched forth and back, the CW light experiences a π phase shift. However, its speed is limited by the ring resonator’s photon lifetime and the necessary condition of over coupling demands pretty low propagation loss. Although this low loss requirement can be 72 released by utilizing a smaller cavity Q microring, larger voltage and higher power consumption will be needed to achieve the π phase shift. (a) (b) (c) Fig.5-1 (a) In traditional resonance-shifting-based DPSK microring modulator, an over coupled ring that has 2 π phase change across its resonance is utilized to generate π phase change, whose performance is limited by the photon lifetime and the propagation loss in the ring resonator; (b) In the proposed design, the coupling coefficient at the drop port of a microring drop filter is switched between two opposite sign and equal magnitude values to generate exact π phase change, whose speed is not limited by the photon life time as the intra-cavity energy is always stable; (c)a composite interferometer is used to realize the coupling modulation. 73 As shown in Fig. 5-1(b), a coupling-switching-based microring modulator is proposed. The resonance is placed at the CW laser frequency and the coupling at the drop port of a drop filter is switched between two inverted-sign but same magnitude values. The coupling modulation is achieved by using a composite interferometer [11] as shown in Fig. 5-1(c). Two small ring phase shifters with small RC constant are operated in push-pull scheme to achieve the coupling modulation. It is shown in our previous work [14] that the coupling modulation based on a drop structure can remove the linewidth limitation to the modulation bandwidth. To describe the operating principles of the proposed design, it is necessary to introduce the “compound coupler” design. As shown in Fig. 5-2, the coupling region in Fig. 5-1(c), can be seen as a ‘composite interferometer’. The transfer function between A, B, C and D ports are derived as [7,11] Fig.5-2 schematic diagram of the composite interferometer (5-1) , (5-2) in which r (0<r< 1) is the amplitude transmissivity of the phase shifter; t and are the reflectivity coefficient and amplitude coupling coefficient of the whole composite interferometer. There is a π phase difference between the upper arm and the lower arm. As shown in Eq. (2), the coupling can be controlled by the equal but reverse phase shift in the upper and lower arms, i.e. push-pull operation. One critical difference between this design 74 and the previous design[14] is: is modulated between ± 0 ( 0 > 0), instead of 0 and 0. According to [16], the transmissivity of the drop filter is (5-3) where 1 and t 1 are the coupling coefficient and reflection efficient between the large ring and the upper waveguide in Fig. 5-1(b), 2 and t 2 are the coupling and reflection coefficient between the large ring and the lower waveguide, a is the roundtrip loss in the large ring, and is the roundtrip phase shift in the large ring. Considering that the upper waveguide to ring coupling is realized by a compound interferometer as shown in Fig. 5-2, we combine Eqs. (1), (2)and (3) and obtain (5-4) Since 2 , t 2 , a and are constant, r is essentially a positive constant (fluctuates slightly in modulation) and cos(/2) is an even function over , the output optical field will change its phase by exactly π as the is switched from a negative constant - 0 to a positive constant 0 ( 0 < π) . According to (2), is then modulated between i 0 and -i 0 while t remains the same since t is even function and is odd function over . According to [17-18], the dynamic equations for notch design in Fig. 5-1(b) are (5-4a) (5-4b) (5-5c) 75 in which, |a(t)| 2 is the intra-cavity energy of the ring resonator and A(t) is the time- varying amplitude of a(t), ω and ω r are the carrier wave angular frequency and the resonance angular frequency of the ring; 1 2 = (k 1 ) 2 V g1 /2πR 1 =|| 2 V g1 /2πR 1 = 2/ e1 ; 2 2 = (k 2 ) 2 V g1 /2πR 1 = | 2 | 2 V g1 /2πR 1 =2/ e2 ; k 1 is the magnitude of the large ring to the upper waveguide amplitude coupling coefficient and k 2 is magnitude of the large ring to the lower waveguide amplitude coupling coefficient; V g1 is the group velocity inside the large ring; 1/ e1 and 1/ p are the amplitude decay rate due to the phase shifter, including power coupling from the large ring into the upper waveguide (1/ e1 ) and the power loss induced by the phase shifter (1/ p ); 1/ e2 is the amplitude decay rate due to the power coupling from the large ring into the lower waveguide;1/ l is the amplitude decaying rate due to the loss in the passive part of the large ring; (0< <1) stands for the coupling loss of compound coupler and =r 1/2 . The k 1 is modulated to generate signals. R 1 is the radius of the large ring. E in =E in0 e −jωt and E out =E out0 e −jωt represent the input CW and modulated signal respectively. After cancelling e −jωt and making the CW light frequency equal to the large ring resonance frequency, the dynamic equations are (5-6a) (5-6b) Two ring phase shifters are simulated with push-pull operation. Both of the two ring phase shifters are designed to have cavity Q of 1100 with photon lifetime of no more than the RC constant, i.e. 1 ps. They are heavily over-coupled to the arms. Their modeling essentially follows our previous work in [3]. Let , as =-i 0 we have 76 (5-7) As =i 0 , we have (5-8) A(t) is fixed at a non-zero value, because || 2 V g1 /2πR 1 = 2/ e1 and || 2 is very the same for ± i 0 . Hence, as 1 is modulated, the energy amplitude is fixed. The energy amplitude fluctuation ratio is (5-9) Eq.(9) indicates extremely stable intra-cavity energy amplitude which is independent on the modulate signals. It implies that the influence of the large ring’s photon lifetime is removed from the signal modulation, compared to the resonance-switching-based microring modulators and the notch design. 2, Influence of nonlinear effective index change of pn junction Among the silicon electro-optic modulation structures, forward biased p-i-n junctions, reverse biased p-n junctions, and sub-micrometer MOS structures designs are those who have been mostly utilized and demonstrated [15, 19-22]. There has been much interest in reversely biased pn junction since the device speed for a reverse biased pn junction is only limited by the RC constant[22]. Recently, it is demonstrated that the electro-optic modulation efficiency V π L of reversely biased pn junction can significantly improved to 1.5 cm∙V[23]. Here a reversely biased pn step junction is considered and the modeling follows the modeling method in [24] and [25]. The specific waveguide scheme follows [23] and ring 77 phase shifter radius is assumed to be 5 m. The optical mode distribution was simulated and obtained by Olympios software. The calculated effective index change and the fitted curve (n(v)) is shown in Fig. 5-3. Here the positive voltages are the voltages applied in the reverse-bias direction. When phase shifter is reversely biased at 1V, the V π L is calculated to be 1.5 cm∙V, which agrees exactly with the experimental results in [23]. The loss change is also calculated and fitted in the same way. The frequency of the light is assumed to be fixed at 193.5 THz. Fig.5-3 The calculated effective index change over voltage and the fitted curve of the simulated reverse biased pn junction Considering the nonlinear effective index and absorption change over voltage, the Eq.(1) becomes (5-10) In which r u and r l stand for the amplitude transmissivity of the upper and lower phase shifters, u and l are the phase change of the upper and lower phase shifters. Due to the large linewidth (160 GHz) and symmetric transmissivity profile(around the resonance) of the ring phase shifters, the difference between r u and r l is very small ((r u - r l )/( r u + r l ) < 0.1%), essentially negligible. We assume r u = r l = r and get 78 (5-11) When both the upper and lower phase shifters are biased at 2V, u = l = 0 and =0. To make =i 0 , the upper phase shifter is applied with a voltage of 4 V and lower 0V. Since the effective index change from 0~2 V is larger than that from 2 V to 4V, we define the phase shift induced by former is b and the phase shift induced by the latter is s . At this time, u = s and l = b . We have = i∙sin(( b + s )/4) and u - l = s - b <0. To make =-i 0 , the upper phase shifter is switched to voltage of 0 V and lower 4V. At this time, u = - b and l = - s . We have = -i∙sin(( b + s )/4) and u - l = - b + s = s - b <0. We can notice that no matter is equal to i 0 or -i 0 , the exp(i( u - l )/4) in Eq.(11) is the same, which implies that the signal modulation hardly influences the resonance of the large ring due to the DPSK modulation scheme. Eq.6(a) will be revised to Δ (5-12) where =c( u - l )/8πR 1 n eff , c is the light speed in vacuum, and n eff is the effective index in the large ring. The large ring’s resonance fluctuates slightly (< 0.5 GHz) as drive signal sequence is applied, compared to large ring’s 10 GHz linewidth. The intracavity energy is still stable. 5.3. Advantages to Notch Design In our simulations, the ring radius of both the microring modulator in Fig. 5-1(a) and the ring phase shifters in Fig. 5-1(b) is 5 m. Since the radius is 1/3 of that in [23], we assume the RC constant to vary from 3 ps down to 1 ps. The large ring radius in Fig. 5-1(b) is 60 m and it is simply passive. In Fig. 5-1(b), the power coupling coefficient between the lower 79 waveguide and the large ring is 0.1089. The cavity Q of Fig. 5-1(a) is set to be around 19000 and linewidth is 10 GHz. For the large ring in Fig. 5-1(b), they are 19,000 and 10 GHz as well for a fair comparison. The propagation loss is set as 1 dB/cm [26] in passive rings/waveguides in Fig. 5-1(a) & (b) (not in phase shifters). The ring resonator phase shifters are heavily over-coupled to the short waveguides. Their cavity Q is about 1100 (linewidth = 170 GHz) such that the photon lifetime (~1 ps) is no more than the RC constant. The low quality factor of coupling is shown to be realizable in [27-28]. For the active ring in Fig. 5-1(a) and the phase-shifters in the Fig. 5-1(b) the propagation loss is assumed to be the same. In our model, a laser with a linewidth of 100 kHz is used, with output power of 1 mW. A square-wave voltage signal providing a non-return-to-zero (NRZ) pseudo-random-bit- sequence (PRBS) is used as the drive signal. For the modulator in Fig. 5-1(b), the original signal pattern is pre-coded to generate the correct phase pattern before being applied on the ring phase shifters . The receiver sensitivity is −17.9 dBm for a bit error rate at 10 −9 at 40 Gb/s. To observe the pattern dependence induced signal degradation, erbum doped fiber amplifier simulation models are used to maintain the same received power. An optical filter with 5× bit-rate bandwidth is used before the receivers to remove optical noise. Fig. 5-4 shows the orginal logic sequence and the received intensity signals after balanced detection (there is one bit delay between the orginal logic sequence and the demodulated signals due to the demodulation scheme). Here the DPSK signals are demodulated with a Mach Zehnder delayline interferometer. We can see that the demodulated signals carry the correct data pattern. 80 Fig.5-4 The original logic (a) and the received signals after balanced detection (b), which shows that the demodulated signals carry the correct data pattern Fig. 5-5(a) compares the 3dB bandwidth of the single ring resonance-shifting DPSK modulator [3] with the proposed design. As the RC constant is decreasing from 6 ps to 2ps, the 3dB bandwidth of the proposed modulator increases essentially linearly along with the RC cutoff frequency (2πRC) -1 . A 3dB modulation bandwidth as 100 GHz can be obtained as the RC constant is 1 ps. If the RC constant can be decreased to be less than 1 ps, ring phase shifters with smaller cavity Q can be employed and higher modulation bandwidth could be obtained. Hence, it is clearly shown that the modulation speed is limited only by the RC constant and independent of the main cavity’s linewidth (10 GHz). In contrast, the resonance-switching-based microring DPSK design in [3] can only achieve a bandwidth about 11 GHz even the RC constant is 1 ps, because its speed is limited by its linewidth (10 GHz). It is even lower (9~10 GHz) for larger RC constant. The influence of the propagation loss coefficient inside the ring resonator on phase shift is compared between this design and resonance-shift-based DPSK modulator in [3] in Fig. 5-5(b). The phase shift of the resonance-shift-based DPSK modulator drops from 1.1 π to nearly 0 π as the propagation loss increases from 6 dB/cm to 24 dB/cm. The reason is: as the propagation loss coefficient exceeds 9 dB/cm, the ring resonator switches from over-coupling condition to under- coupling condition. Consequently, the phase change across the resonance is no more than 81 π[16]. As the propagation loss continues increasing, the cavity Q drops and the phase shift for a certain drive voltage decreases as well. On the contrary, the phase change of the proposed design keeps as π despite of a loss coefficient of 30 dB/cm, because its π phase shift is induced by the sign-inverting of the coupling. This high tolerance to the intrinsic loss allows for higher doping concentration, thus higher electro-optic modulation efficiency. (a) (b) Fig.5-5. (a) the proposed modulator’s bandwidth increases almost linearly as the RC constant drops shile the bandwidth of the resonance-shift-based DPSK modulator in [3] is limited by its optical linewidth, i.e.10 GHz; (b) the phase change over ring instrinsic loss of this design and [3], which shows that the tolearance to intrinsic loss is improved from 9 dB/cm to 30 dB/cm by the proposed design. Fig. 5-6 compares the total transmission loss and eye opening penalty of a DPSK MZM, notch-design-based DPSK modulator [10] and the proposed modulator. In Fig. 5-6 and for the rest the work, the MZM modulator is assumed to be ideal, i.e. infinite bandwidth and zero insertion loss (at maximum transmissivity). The MZM’s V π is assumed to be 5 V. To generate DPSK signals, the MZM is biased at zero transmissivity point. The perimeter of the large ring of the notch design is same as that of the proposed modulator, i.e. 2 π 60 m. The phase shifters in notch design are also assumed to be based on reversely biased pn junction and driven with 4 V. The upper and lower active waveguide phase shifters are 82 assumed to be 150 m long. The loss coefficient is assumed to 12 dB/cm for both designs. According to [10,15], to avoid the intracavity depletion, the notch design is biased at the critical coupling condition and switched between critical coupling and under coupling. The cavity Q is around 46,500 and linewidth is 4 GHz. The ideal MZM’s transmission loss is about 3 dB as bit rate increases from 10 Gb/s to 120 Gb/s, which is due to its biasing point. The proposed modulator’s transmission loss is 8.5 dB at 10 Gb/s and increases slightly to 9.5 dB. It corresponds to a 5.5~6.5 dB insertion loss when compared with OOK MZMs. In comparison, the notch design’s total transmission loss is 10.3 dB and increases to over 14.1 dB, corresponding to 11.1 dB insertion loss for an OOK MZM. Such high insertion loss of notch design has been verified in experiments [15]. To check the signal degradation, Fig. 5- 6(b) shows eye opening penalty of the notch design and the proposed design. The output optical power is amplified to be the same power for each modulators. The penalty is calculated by comparing the eye opening to the MZM. It shows that the eye opening penalty of the proposed design is around 0 dB as the bit-rate increases from 10 Gb/s to 120 Gb/s. The notch design’s eye opening penalty is 3.04 dB at 10 Gb/s and increases to 7.33 dB at 120 Gb/s. The reason is the optical transmissivity at under-coupling and over-coupling point is not the same. Hence, the optical output power for the ‘0’ and ‘π’ symbol is not equal. In demodulation, neither the construction nor the destruction is complete, which leads to very low optical signal noise ratio (a) (b) 83 Fig.5-6 (a) total transmission loss comparison between an ideal MZM, the proposed modulator and the notch design over bit-rate, which shows that the proposed modulator’s insertion loss is much lower than the notch design and about 6 dB higher than the 0 dB insertion loss MZM; (b) the eye opening penalty comparison between the notch design and the proposed modulator: the notch design suffers from its large RC constant due to the straight waveguide phase shifters. Although our previous design [14] utilizes the small ring phase shifters (to reach small RC constant), it has a drawback: since it modulates the upper-waveguide-to-large-ring coupling between zero and non-zero value, signal overshoots are induced as the intracavity energy fluctuates. The higher the coupling modulation amplitude, the more severe the overshoots will be. However, if the coupling coefficient modulation amplitude is too small, the insertion loss of the modulator will go up. Consequently, there is a tradeoff between high signal quality and lower insertion loss with the previous design. This problem is solved with the proposed design: since the coupling coefficient is switching between two opposite sign and equal magnitude value, the intracavity energy hardly fluctuates (Eq.(9)) and thus the signal overshoots are removed. To quantify the intracavity energy fluctuation, we define energy amplitude variation depth as (5-13) As shown in Fig. 5-7, as the drive voltage goes up from 0.5 V to 4 V, the energy amplitude variation depth of the previous design increases to 30% while it remains under 3% for the proposed design. The system performance of the proposed modulator is examined in Fig. 5-8. BER curves of 120 Gb/s NRZ DPSK signals demodulated by a delay line interferometer and a microring drop filter (radius = 5 m) are presented. DPSK signals generated by an ideal Mach-Zehnder Modulator (MZM) with V π voltage of 5 V is used as the benchmark. The notch-design-based 84 DPSK signals are compared to the proposed modulator as well. As shown in Fig. 5-8, the proposed DPSK modulator shows nearly the same performance to the MZM, when the DPSK signals are demodulated by the delay line interferometer. When the DPSK signals are demodulated by a microring drop filter with cavity Q of 1200, 0.8 dB extra power penalty is observed. This implies that the proposed modulator along with the microring demodulator can be utilized in on-chip optical interconnects. On the other hand, the notch design is not capable of 120 Gb/s NRZ signals with acceptable quality. Fig.5-7. The energy amplitude variaton depth comparison between our previous design and the proposed design. It is shown that the intracavity energy amplitude fluctuation has been greatly reduced and the inracavity energy of the proposed design is extremely stable. The upper inset shows the intracavity energy amplitude of the previous design and the lower for the proposed design. Fig.5-8. When demodulated by a Mach Zehnder delay line interferometer (DLI), the signals generated by the proposed design show nearly the same quality as that of the DPSK signals generated by an 85 idealMZM (RC 0); when demodulated by a microring drop filter (MRD with cavity Q of 1,200), there is 0.8 dB extra power penalty; the DPSK signals generated by the notch design can never reach bit error free (10 -9 ). In Fig. 5-9(a), the system performance over bit-rate of the proposed design is studied and the power penalty is still calculated by comparing to the MZM-DPSK. Here the DPSK signals are demodulated by delay line interferometer. As the bit rate increases from 10 Gb/s to 120 Gb/s, the power penalty is always below 1.5 dB. In contrast, the notch design can’t reach bit-error-free operation and thus has infinite power penalty, which is due to its high insertion loss and large eye opening penalty as shown in Fig. 5-6(b). In Fig. 5- 9(b), the power penalty of the previous design(OOK) and the proposed design over drive voltage is compared. It is shown the power penalty of the previous design goes up steeply as the drive voltage increases while the proposed design remains below 3 dB. Compared to the previous design, up to 9 dB power penalty can be avoided by utilizing the proposed modulator. This trend agrees with what is shown in Fig. 5-7 (a) (b) Fig.5-9 (a) The power penalty of the DPSK signals generated by proposed modulator and the OOK signals generated by notch design over bit rate when compared to the DPSK signals generated by the ideal MZM ; (b) the power penalty of the previous design and the proposed design over drive voltage when compared to the DPSK signals generated by the ideal MZM, which shows that up to 9.1 dB power penalty can be avoided with the proposed modulator employed. 86 5.4. Summary According to [23], we estimated the capacitance of our ring phase shifter to be around 18 fF. The power consumption is estimated to be 216 fJ/bit for 4 V drive voltage[20]. Though this power consumption is not very small, it can be improved by utilizing a main ring with larger radius or utilizing novel eletro-optic modulation scheme[29]. The utilization of the microring demodulator adds more complexity into the system. However, it is demonstrated that accurate resonance alignment of multiple rings is completely achievable [30-31] with existing techniques. In conclusion, a silicon DPSK modulator based on coupling modulation of a microring drop filter is proposed. The respond speed is independent of the main ring’s linewidth and up to 120 Gb/s NRZ-DPSK signal is generated and demodulated with both MZM delay line interferometer and microring filter. The data shows the same good quality with an ideal OOK MZM. Compared to other coupling modulation scheme, this design shows much better signal quality and much lower insertion loss with relatively smaller footprint, which makes it a good choice for high speed optical interconnect application. 5.5. References 1. A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23, 115-130 (2005). 2. P. J. Winzer, "Advanced modulation formats for high-capacity optical transport networks," J. 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Krishnamoorthy, and M. Asghari, "Low V pp , ultralow-energy, compact, high-speed silicon electro-optic modulator," Opt. Express 17, 22484-22490 (2009). 24. G. Rasigade, D. Marris-Morini, M. Ziebell, E. Cassan, and L. Vivien, "Analytical model for depletion-based silicon modulator simulation," Opt. Express 19, 3919-3924 (2011). 25. R. F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996), Chap. 7. 26. R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, "Low-loss silicon-on- insulator shallow-ridge TE and TM waveguides formed using thermal oxidation," Appl. Opt. 48, 958- 963 (2009). 27. Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, "Design and demonstration of compact, wide bandwidth coupled-resonator filters on a silicon-on-insulator platform," Opt. Express 17, 2247- 2254 (2009). 28. M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide- resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46, 1158-1169 (2010). 29. R. Soref, J. Guo, and G. Sun, "Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides," Opt. Express 19, 18122-18134 (2011). 30. D. M. Gill, S. S. Patel, M. Rasras, K.-Y. Tu, A. E. White, Y.-K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach– Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Topics Quantum Electron. 16, 45–52 (2010). 31. L. S. Stewart and P. D. Dapkus, "In-plane thermally tuned silicon-on-insulator wavelength selective reflector," in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper IME2. 89 Chapter 6 Systematic Analysis of Microring Filter 6.1. Introduction Recently, WDM optical interconnect systems built on the micro-cavity-based devices have also been reported and analyzed [1-11]. However, as the bit rate in optical interconnects increases, the bit time shrinks, and the tolerance of data timing errors drops. Up to now, the data timing issue in intra-chip optical interconnects has not been systematically analyzed. A fundamental feature of micro-cavities is that they act as filters. The amplitude response provides the basic modulating, switching, and dropping functions; however, the phase response gives rise to a wavelength-dependent delay in the data stream [12]. The amount of delay depends on several factors, including the filter structure and the ratio of the passband linewidth to the bit rate from channel to channel, and the filter linewidth may vary as a result of fabrication errors. All these factors can lead to non-uniformity of data timing. Since efficient on-chip optical interconnects rely on accurate sampling of the data bits within their bit times, any drift in bit arrival time may lead to detection errors [13, 14]. This is a serious problem, given that clock-tracking phase-locked loops might be too complex and power-consuming to be implemented in on-chip WDM optical interconnects. To be specific, the gap width between the waveguide and the ring in micro-ring resonators is one of the factors that dominate the filter’s transmission profile and linewidth [15]. Although fabrication accuracy within 20 nm has been achieved [16], precise control of the lateral gap width is difficult [17], and non-uniformities in gap width may generate considerable non- uniformity in optical data timing. 90 In this chapter, we analyze the system penalties that are due to the optical data timing skews that arise from ring-resonator-based devices in WDM on-chip optical interconnects. Simulations show that timing skews as much as 28 ps can be induced by variations in the lateral gap width between the waveguide and the ring in ring-resonator-based devices. This leads to a 3.75 dB signal eye-opening penalty in a 10 Gb/s NRZ on-chip system. Our findings show that the coupled filter structure can reduce the timing skews, although it may be challenging for the fabrication process [18]. 6.2. Concept of optical data timing skew Fig. 6-1-(a) shows the structures of ring-resonator-based modulators, filters, and switches. Filters and switches based on a cascade of ring resonators are used for good channel isolation in WDM systems [19-20].They can be either “isolated” type or “coupled” type. The isolated type consists of 2 (or more) single ring resonators that are independent of each other, while the coupled type is comprised of cascades of 2 or more micro-rings coupled to each other and to the dual waveguides on either side. Compared to the isolated type, the coupled type requires a much more accurate control of the waveguide-ring coupling and ring-ring coupling to realize a maximally flat passband [21]. This requirement may be challenging for mass manufacturing in WDM optical interconnect systems to meet. For these devices, variations in structure parameters can alter the resonator’s transmission profile and linewidth, leading to variations in the optical group delay. If devices with non-uniform parameters are employed in on-chip WDM systems, the data delay may vary from channel to channel (Fig. 6-1-(b)), causing signals in different channels to reach receivers at different times. This difference is referred to as the optical data timing skew (Fig. 6-1-(c)). In clock- synchronized interconnects, the data is not sampled at the optimal sampling instant of each channel, as in telecommunication systems, but at the uniform clock-triggered sampling 91 instant [13]. Thus, signal detection suffers from the mismatch between the clock and the optimal sampling instants, which leads to degradation in the overall system performance. Fig.6-1. (a) Micro-ring modulator, isolated-type and coupled-type cascaded ring resonator filters. (b) Cavity Q and linewidth non-uniformities in the ring-resonator-based devices can lead to differences in the delays. (c) Timing skew between channels resulting from the delay difference The gap width between the waveguide and the ring is one of the factors that dominate [14]. the resonator transmission profile and linewidth. To study this factor, we model ring resonator-based devices with finite-difference-time-domain (FDTD) simulations and solve the dynamic equations in [21]. The devices modeled are for 10 Gb/s NRZ signal transmission. The micro-ring modulator has cavity Q of 19000 and linewidth of 10 GHz. A pseudorandom binary sequence (PRBS) with 2^13-1 = 8191-bit-length is input as the electrical signal. The 10 Gb/s NRZ signal modulated by the microring modulator has signal 92 bandwidth of 7~8 GHz [22], and the filter/switch linewidth chosen is twice this value, i.e., 15 GHz. The rings that make up the modulators, filters, and switches have a radius of 2.7 m, and the waveguide width is 400 nm. We focus on the timing skew induced by the variation in the lateral gap width, so the simulations are 2-dimensional. The material refractive index is set to be 3.4, just as silicon is. The designed gap width between the ring and the waveguide is 210 nm, and the gap width is assumed to drift in a range of 16 nm. The switching time is assumed to be much shorter than the packet duration, so it can be treated as a filter. We assume the switch has the same structure as the filter does. The gap spacing between the waveguide and the ring is assumed to vary simultaneously for modulators, filters and switches. 6.3. Characterization and link performance Fig. 6-2(a) shows the linewidth of the modulators and filters versus the gap width variation. For both modulators and filters, the linewidth decreases as the gap width increases. The change in the isolated-type filter’s total linewidth is as much as 12 GHz, compared to the single ring modulator and the coupled type filter. For the coupled-type filter, a certain relationship between the waveguide-ring coupling and the ring-ring coupling is needed for a maximally flat passband. If the gap width between the waveguide and the ring deviates from the ideal value, the relationship will be broken and the filter’s passband will show peak splitting or transmission degradations (Fig.6-2(c) insets), while its linewidth changes slightly. Since optical delay is inversely proportional to linewidth [23], if the linewidth of modulators and filters drifts because of variations in gap width, their optical delay will also vary. Fig. 6-2(b) shows the timing skew of the modulators and filters versus linewidth, in which the timing skew is the difference in optical delay between the devices with and without linewidth drifts. The isolated-type filter’s group delay is the sum of the single ring 93 resonators’ delays. This type of filter can induce larger timing skews (from -8 to 12.5 ps) than a single ring modulator element or a coupled-type filter element does. In an optical link composed of a modulator, a filter and a switch, if both filter and switch are based on the isolated-type filter structure, as much as a 28 ps timing skews can be introduced. Fig. 6-2(c) shows the signal power loss from the two types of filters. The coupled filter suffers from about 1 dB power loss at +/- 16 nm gap width variation, and the isolated type suffers a 0.6 dB at + 16 nm loss that is due to over-filtering of the signal power. Besides timing skew and power loss, the variation in gap width can also induce pattern dependence. For common filters, e.g., Lorenztian or Gussian, the high-frequency components of the optical signal occur in regions of low transmission rate, as compared to carrier frequency. The pattern dependence is quantified by calculating the ‘1’-level ratio, i.e. the signal power of single ‘1’-bit over that of consecutive ‘1’-bits (B/A, Fig.6-3(a)) [23]. For an isolated filter, as shown in Fig. 6-3(a) and the black boxes in Fig. 6-3(b), the single ‘1’-bit (i.e., ‘010’) is filtered more than the consecutive ‘1’-bits (e.g., ‘01110’), which leads to a level ratio less than 1. As depicted by the white boxes in Fig. 6-3(b), for the coupled filter, the low-frequency components suffer greater loss as a result of the filter’s passband splitting, thus making the level ratio larger than 1. 94 Fig. 6-2. (a) Linewidth of the microring modulator and filter versus gap width variation. (b) timing skew of the modulator and filter versus linewidth (for single element). (c) signal power loss of the isolated and coupled type filters (for single element). We evaluate the effect of optical data timing skews on system performance by comparing the eye-opening penalty of our optical circuits (Fig. 6-1(c)) with that of a system that integrates a Mach-Zehnder Interferometer (MZI) modulator and 2 Gaussian filters. Besides timing skew, either power loss or pattern dependence can lead to signal eye-opening penalty. In order to deduce the influence of timing skew alone on system performance, we must separate the penalty induced by timing skew from that induced by power loss and pattern dependence. First, we examine the eye-opening penalty over the variation in gap width when the data in each channel is optimally sampled, in which case the penalty is simply induced by pattern dependence and power loss. Second, we examine the penalty 95 when the data is clock sampled, in which case the timing skew-induced penalty is also included. The difference between the two gives the penalty that is induced purely by the timing skews. Fig. 6-4(a) shows the penalty coming from power loss and pattern dependence, which penalty has a similar trend to that in Fig. 6-2(c). The isolated-type filter reflects a greater penalty caused by more significant pattern dependence as the gap width grows and the filter linewidth decreases. Fig. 6-4(b) is the net eye-opening penalty caused by timing skews. A 3.75 dB penalty is observed in the link utilizing an isolated-type filter and switch, while negligible penalty is found when the coupled-type filter and switch are utilized. Fig. 6-3 (a) pattern dependence induced by gap width variation; (b) the level ratio vs. variation in gap width of isolated and coupled ring resonators Enhancing the ratio of passband linewidth over the bit rate can decrease the optical delay as well as the timing skew. However, doing so will cost more bandwidth resources. It is desirable to establish the minimum ratio of filter passband linewidth to signal bit rate with which the effect of the timing skews can be eliminated. 96 Fig. 6-4. (a) Eye-opening penalty induced by power loss and signal distortion. (b) Eye-opening penalty induced by timing skew. In Fig. 6-5, the eye-opening penalty caused by a +16 nm variation in gap width is examined with different ratios of filter linewidth to signal bit-rate. In the link with the isolated filter, a 6 dB eye-opening penalty is observed when the filter bandwidth is less than 1.4 times the bit-rate; to keep the penalty below 1 dB, the filter linewidth has to be at least 2.2 times of the signal bit-rate. On the other hand, the link with the coupled-type filter shows a penalty less than 1 dB even for filters with linewidth as narrow as one time bit-rate. This occurs because coupled-type filters introduce a much smaller timing skew. Fig. 6-5 Maximum eye-opening penalty versus the ratio of the filter linewidth to the bitrate of the NRZ signal. 97 6.4. Summary The concept of optical data timing skew in clock-synchronized WDM on-chip optical interconnects is introduced and its effect on system performance is analyzed. It is found the non-uniformities in gap width between the waveguide and the ring in the micro-ring resonator can lead to significant optical data timing skews that may induce considerable eye- opening penalties in WDM optical interconnects. The coupled-type filterer and switches introduce much smaller timing skews, so they are more viable components for optical circuits, although using them may be challenging in fabrication processes. This work was supported in part by HP Labs, the DARPA University Photonics Research Program, the Optical Code Division Multiple Access (OCDMA) program of DARPA administered by SPAWAR, Contract no. N66001-02-1-8939, and the Chip Scale WDM (CSWDM) program of DARPA monitored by AFOSR, Contract no. F49620-02-1-0403. 6.5. References 1. M.W. Haney, M. Iqbal, M.J. McFadden, M. Iqbal, D. W. Prather, and T. Dillon, "Optical Interconnects: A Potential Solution to the Intrachip Interconnect Problem? "in: IEEE LEOS Annual Meeting, 2005, p.206. 2. M. Haurylau, G.Q. Chen, H. Chen, J.D. Zhang, N.A. Nelson, D.H. Albonesi, E.G. Friedman, P.M. Fauchet, "On-chip optical interconnect roadmap: Challenges and critical directions," IEEE J. Sel. Top. Quantum Electron. 12 1699 (2006). 3. D.A.B. Miller, "Rationale and Challenges for Optical Interconnects to Electronic Chips," Proc. IEEE 88 728 (2000). 4. J.D. O’Brien, P.T. Lee, J.R. Cao, W. Kuang, C. Kim, W.-J. Kim, T. Yang, S.-J. Choi, P.D. Dapkus, "Photonic Crystal Lasers," Proc. SPIE 4942 194 (2003). 5. Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, S. Noda, "-dimensional photonic-crystal-slab channel drop filter with flat-top response, " Opt. Express 13 2512 (2005). 98 6. S.F. Preble, Q.-F. Xu, B.S. Schmidt, M. Lipson, "Ultrafast all-optical modulation on a silicon chip," Opt. Lett. 30 2891 (2005). 7. P. Rabiei, W.H. Steier, "Tunable polymer double micro-ring filters," IEEE Photon. Tech. Lett. 15 1255 (2003). 8. A. Yariv, Y. Xu, R.K. Lee, A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24 711 (1999). 9. J.E. Heebner, R.W. Boyd, J. Mod. "'Slow and 'Fast Light in Resonator-Coupled. Waveguides," Opt. Lett. 49 2629 (2002). 10. Q. Xu, B. Schmidt, J. Shakya, M. Lipson, "Cascaded silicon micro-ring modulators for WDM optical interconnection," Opt. Express 14 9430 (2006). 11. B.A. Small, B.G. Lee, K. Bergman, "'On cascades of resonators for ... interconnection networks," Opt. Express 14 10811 (2006). 12. G. Lenz, B.J. Eggleton, C.K. Madsen, R.E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37 525 (2001). 13. H. Devos, J. Dambre, W. Meeus, D. Stroobandt, J.M. Van Campenhout, "An exploration of synchronization solutions for parallel short-range optical interconnect in mesochronous systems," Proc. SPIE 4942 258 (2002). 14. A. Shacham, K. Bergman, "Building Ultralow-Latency Interconnection Networks Using Photonic Integration," IEEE Micro 27 6 (2007). 15. M.K. Chin, S.T. Ho, "Design and modeling of waveguide-coupled-single-mode microring resonators," J. Lightwave Technol. 16 1433 (1998). 16. T. Barwicz, M.A. Popovic′ , M. Watts, P.T. Rakich, E.P. Ippen, H.I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," J.Lightwave Technol. 24 2207 (2006). 17. D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Gü nter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Tech. Lett. 18 865 (2006). 18. C. Li, L. Zhou, A.W. Poon, "Silicon microring carrier-injection-based modulators/switches with tunable extinction ratios and OR-logic switching by using waveguide cross-coupling," Opt. Express 15 5069 (2007). 19. C.K. Madsen, J.H. Zhao, Optical Filter Design and Analysis – A Signal Processing Approach, John Willey & Sons, Inc. US, New York, 1999. 20. D. Geuzebroek, E. Klein, H. Kelderman, N. Baker, A. Driessen, "Compact wavelength- selective switch for gigabit filtering in access networks," IEEE J. Photon.Tech. Lett. 17 336 (2005). 99 21. B.E. Little, S.T. Chu, H.A. Haus, J. Foresi, J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15 998 (1997). 22. L. Zhang, Y. Li, J.-Y. Yang, B. Zhang, R.G. Beausoleil, A.E. Willner, "Performance and Design Guidelines for 10-Gbit/s Systems Using Silicon-Based Ring-Resonator Modulators," in: Optical Fiber Communication Conference, OFC, Academic, San Diego, California, 2007. JWA39. 23. L. Zhang, T. Luo, C. Yu, W. Zhang, A.E. Willner, "Pattern dependence of data distortion in slow-light elements," J. Lightwave Technol. 25 1754 (2007). 100 Chapter 7 Conclusion and future work Silicon ring resonator based devices such as OOK modulators, DPSK modulators and filters were designed and discussed. Free carrier plasma dispersion based modulation mechanisms were investigated for application to silicon-based devices, and characteristics of the both devices and systems were studied. Multiple OOK modulator designs were proposed to break the optical linewidth of the ring resonator. Unique coupling-switching-based modulators employing a drop structure was simulated and characterized in details, which is shown to be able to generate signals much beyond the optical linewidth with very good signal quality and moderate drive power. This device should be of great value in designing power efficient optical interconnects. A DPSK modulator was proposed and studied to reach ultrahigh DPSK signal bit rate and be free from the limitation of the propagation loss. Modeling of the reversely biased pn junction and simulation of this high speed DPSK modulator was performed. It shows that this modulator can achieve extremely stable intracavity energy which is able to completely remove the signal distortion which exist in the other coupling-switching-based modulators Two type of dual ring optical filters have been simulated by using FDTD and studied in the optical interconnect WDM system. The problem of optical data timing skew was pointed out. The results show that the timing skew problem will probably still exist in the future optical interconnects, rather than disappear. In the future, the optical interconnects will be integrated with the optical devices on one chip. Hence designing more ring resonator devices which are compatible with CMOS platform becomes more and more important. 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Willner, “Data quality dependencies in microring-based DPSK transmitter and receiver,” Optics Express 16, 5739-5745 (2008). Lin Zhang, Jeng-Yuan Yang, Muping Song, Yunchu Li, Bo Zhang, Ray G. Beausoleil, and Alan E. Willner, “Microring-based modulation and demodulation of DPSK signal,” Optics Express 15, 11564- 11569 (2007). Lin Zhang, Jeng-Yuan Yang, Muping Song, Yunchu Li, Ray G. Beausoleil, and Alan E. Willner, “Advanced data formats in chip-scale optical interconnects using microring resonators,” 19th Annual Workshop on Interconnections within High Speed Digital Systems, (LEOS ‘08), Santa Fe, New Mexico, selected poster with awarded travel grant, (2008). Lin Zhang, Yunchu Li, Muping Song, Ray G. Beausoleil, and Alan E. Willner, “DPSK data quality dependencies in microring-based transmitter and receiver,” Optical Fiber Communication Conference(OFC’08), San Diego, California, JThA19 (2008). Lin Zhang, Jeng-Yuan Yang, Yunchu Li, Ray G. Beausoleil, and Alan E. 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Abstract (if available)
Abstract
Optical interconnect systems is one of the most promising solutions to surpass the speed bottleneck of CPU from the electrical interconnects. To realize this idea, one of the key topics is to design compact photonic devices suitable for building the optical interconnects. ❧ The use of silicon microring resonators is an attractive technology for the integrated photonics pursuing optical interconnect applications, highly exciting due to the high integration density, low power consumption, and versatile functionalities. The platform technologies available for silicon microring resonators can be categorized by their structures, functions in optical interconnect systems, etc. Specific designs are in great needed to break off some critical tradeoffs in these silicon microring-based devices performances. ❧ In this dissertation, the design and simulations of silicon microring based photonic devices for optical interconnects are presented. Utilizing the proposed technologies, various types of optical elements such as resonance-switching/coupling-switching OOK modulators, DPSK modulators and filters are designed. The systematic performance is studied as well. The data have shown that, by employing our unique designs critical tradeoffs in the device performance can be successfully broken and great data quality at ultra-high data transmission speed can be obtained.
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Creator
Li, Yunchu
(author)
Core Title
Silicon micro-ring resonator device design for optical interconnect systems
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
04/08/2013
Defense Date
03/07/2013
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
advanced modulation formats,microring,modulator,OAI-PMH Harvest,optical communications,optical interconnects,ring resonator,silicon photonics
Language
English
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Electronically uploaded by the author
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Advisor
Dapkus, Paul Daniel (
committee chair
), Kalia, Rajiv (
committee member
), O'Brien, John (
committee member
), Povinelli, Michelle (
committee member
), Zhou, Chongwu (
committee member
)
Creator Email
wayofflying@gmail.com,yunchuli@usc.edu
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https://doi.org/10.25549/usctheses-c3-233594
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usctheses-c3-233594 (legacy record id)
Legacy Identifier
etd-LiYunchu-1524.pdf
Dmrecord
233594
Document Type
Dissertation
Rights
Li, Yunchu
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
advanced modulation formats
microring
modulator
optical communications
optical interconnects
ring resonator
silicon photonics