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Ring resonator based silicon photonic transmitter and receiver Park, Anthony Hyunkyoo 2019

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Ring Resonator Based Silicon Photonic Transmitter andReceiverbyAnthony Hyunkyoo ParkB.A.Sc., The University of British Columbia, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electrical and Computer Engineering)The University of British Columbia(Vancouver)January 2019c© Anthony Hyunkyoo Park, 2019The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Ring Resonator Based Silicon Photonic Transmitter and Receiversubmitted by Anthony Hyunkyoo Park in partial fulfillment of the requirementsfor the degree of Master of Applied Science in Electrical and Computer Engi-neering.Examining Committee:Lukas Chrostowski, Electrical and Computer EngineeringCo-SupervisorSudip Shekhar, Electrical and Computer EngineeringCo-SupervisorShahriar Mirabbasi, Electrical and Computer EngineeringAdditional ExamineriiAbstractRing resonators in silicon photonics platform hold great potential in various ap-plications due to their compact size and wavelength selectivity, enabling denselyintegrated optical systems. This thesis focuses particularly on the application ofring resonators in silicon photonic transmitters and receivers.In transmitters, all-pass ring resonators with PN junctions can be driven indepletion mode to provide high-speed binary modulated signals. Pulse-amplitude-modulation-4 (PAM4) schemes can be adopted to achieve higher bit rates by provid-ing four levels of amplitude instead of two. Instead of relying on a power-hungrydigital-to-analog converter (DAC) in the driver, the four optical levels can be real-ized by using two separate non-return-to-zero (NRZ) drivers on either a single ringresonator with segmented PN junctions or a dual cascaded ring resonator. In thisthesis, the two DAC-less PAM4 modulation methods in ring resonators are com-pared using frequency and time domain analytic equations, with a target bit rateof 25Gb/s. Under the same constraints in terms of ring resonator dimensions andelectrical signal voltages, the single ring resonator with segmented PN junctionsis found to be the superior candidate, due to the smaller number of stabilizationcircuits required while achieving a larger modulation amplitude.In receivers, add-drop ring resonators can be used as wavelength division mul-tiplexing (WDM) channel filters, but they suffer from high polarization dependence,which motivates the need for a polarization management solution on chip. In thisthesis, a 4-channel polarization-insensitive WDM receiver is designed by forminga waveguide loop between the two output ports of a polarization-splitter-rotator.The input signals in the quasi-transverse-electric and the quasi-transverse-magneticpolarization states can be demultiplexed without active polarization tuning or in-iiidependent processing of the two polarization states. Large signal measurements at10 Gb/s indicate that the design can tolerate a signal delay of up to 30% of the unitinterval (UI) between the two polarization states, which implies that compensatingfor manufacturing variability with optical delay lines on chip is not necessary for arobust operation. The inter-channel crosstalk is found negligible down to 50 GHzspacing, proving its compatibility with dense WDM systems.ivLay SummaryRing resonators are small waveguide loops capable of generating optical signalsand filtering different wavelengths of light on a chip. Their compactness and ver-satility make them key building blocks on silicon photonic chips for data commu-nication. Challenges still remain, as it is difficult to choose the best design foroptical signal generation among the options presented in various publications, andthe ring resonators’ filtering performance is highly sensitive to the polarization ofthe input beam.This thesis focuses on the application of ring resonators in transmitters andreceivers on silicon photonic chips. On the transmitter side, two types of ring res-onators which are capable of generating optical signals with 4 levels of amplitudeare compared using analytic equations and time-domain simulations. On the re-ceiver side, a multi-channel optical receiver which can process input signals of dif-ferent polarizations is demonstrated using ring resonators and passive polarizationmanaging components.vPrefaceThe contents of this thesis are based on two publications for which I am the primaryauthor.1. A. H.K. Park, A S. Ramani, L. Chrostowski, and S. Shekhar, ”Comparison ofDAC-less PAM4 modulation in segmented ring resonator and dual cascadedring resonator,” in IEEE Optical Interconnects Conference (OI), 2017.S. Shekhar conceived the idea for this topic, as part of the EECE 571ZCMOS for Photonics course offered in UBC, 2017. I performed the opti-cal simulations and the comparison analysis of the modulators, and wrotethe first draft of the manuscript. A. S. Ramani designed the electrical driverfor the project, and edited the manuscript. S. Shekhar and L. Chrostowskisupervised the project and edited the manuscript.2. A. H.K. Park, H. Shoman, M. Ma, S. Shekhar, and L. Chrostowski, ”RingResonator Based Polarization Diversity WDM Receiver,” (in preparation).L. Chrostowski conceived the initial idea. I designed the device, conductedthe measurements, analyzed the data, and wrote the manuscript. H. Shomanand M. Ma assisted during the measurements. L. Chrostowski obtained thegrant and access to the fabrication technology for this device. L. Chros-towski and S. Shekhar supervised the project. All authors helped edit themanuscript.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Ring Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 52 Comparison of DAC-less PAM4Modulation in Segmented Ring Res-onator and Dual Cascaded Ring Resonator . . . . . . . . . . . . . . 72.1 Optical Single Ring Model . . . . . . . . . . . . . . . . . . . . . 82.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Electrical Driver . . . . . . . . . . . . . . . . . . . . . . . . . . . 15vii2.4 Modulator Performance Comparison . . . . . . . . . . . . . . . . 182.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Ring Resonator Based Polarization Diversity WDM Receiver . . . . 263.1 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Device Measurement . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . 414.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 414.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43viiiList of TablesTable 2.1 Physical parameters of the ring resonator used to match pub-lished results in [1] . . . . . . . . . . . . . . . . . . . . . . . . 12Table 2.2 Specifications for the 1 Vp-p Driver . . . . . . . . . . . . . . . 18Table 2.3 Figures of Merit for the PAM4 ring modulators . . . . . . . . . 25Table 3.1 4 Channel microring filter parameters . . . . . . . . . . . . . . 29ixList of FiguresFigure 1.1 Layer stack of a SOI wafer. n refers to the refractive index ofthe material at 1550 nm. . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 (a) Diagram of an all-pass ring resonator. (b) Diagram of anadd-drop ring resonator. (c) Sample transmission spectra of anadd-drop ring resonator. . . . . . . . . . . . . . . . . . . . . 3Figure 1.3 (a) Diagram of an all-pass ring resonator with PN junction. (b)Cross-sectional profile A–A’ of the waveguide with PN junc-tion in (a). (c) Sample transmission spectra of the ring modu-lator at two different bias voltages. . . . . . . . . . . . . . . 4Figure 1.4 Schematic of a 4 channel WDM demultiplexer based on add-drop ring resonator filters . . . . . . . . . . . . . . . . . . . . 5Figure 2.1 Schematic view of the segmented single ring and the dual cas-caded ring driven by NRZ signals. The most significant bitdriver outputs approximately twice the voltage of the least sig-nificant bit driver to generate a 2-bit overall output. . . . . . . 8Figure 2.2 All-pass ring resonator diagram. . . . . . . . . . . . . . . . . 9Figure 2.3 Transmission spectra of a ring resonator with R = 10um and Q= 5200, calculated from Eq. (2.1) and Eq. (2.10), plotted nearresonance in (a) 2.5nm bandwidth and (b) 20nm bandwidth. . 11xFigure 2.4 (a) Waveguide and dopant profile used in Lumerical Devicesimulation. The core waveguide has 500nm×220nm dimen-sions and the slab has 90nm thickness. The concentration ofeach dopant is as follows: p = 5e17 cm−3, p+ = 2e18 cm−3,p++ = 4.4e20 cm−3, n = 3e17 cm−3, n+ = 2e18 cm−3, and n++= 4.4e20 cm−3. (b) Lumerical Mode simulation of the waveg-uide cross-section with the embedded charge profile. Colorscale indicates normalized light intensity in linear scale. . . . 12Figure 2.5 (a) Transmission spectra at four input levels presented in [1],reprinted with permission from c©2016 Optical Society of Amer-ica. (b) The simulated spectra using parameters in Table 1 inMatlab. (c) The simulated spectra using parameters in Table 1in Lumerical Interconnect. . . . . . . . . . . . . . . . . . . . 13Figure 2.6 Eye diagrams generated from (a) TCMT equations in Matlaband (b) time domain simulation in Lumerical Interconnect. . . 13Figure 2.7 (a) Eye diagram generated from Lumerical Interconnect and(b) eye diagram published in [1], reprinted with permissionfrom c©2016 Optical Society of America. (c) The simulationschematic from which the eye diagram in (a) is generated. . . 14Figure 2.8 Eye diagram with operating wavelength and input voltages mod-ified from Fig. 2.6 (a). . . . . . . . . . . . . . . . . . . . . . 15Figure 2.9 Circuit equivalent model of the ring modulator PN junctionused in cadence simulation. . . . . . . . . . . . . . . . . . . 15Figure 2.10 Schematic of (a) the inverter-based driver cell and (b) the dif-ferential driver . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.11 The schematic of (a)the NAND gate and (b) the NOR gate usedin the design. The gates are sized to have the same resistanceas the inverter. . . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 2.12 Integration of the driver with the ring modulator along with thesupply/GND bondwire model [2] . . . . . . . . . . . . . . . 17Figure 2.13 The output eye diagrams of (a) the single-ended 1Vp-p driverand (b) the differential 2.2Vp-p driver. . . . . . . . . . . . . . 18xiFigure 2.14 Transmission spectra of (a) the single segmented ring and (b)the dual cascaded ring. . . . . . . . . . . . . . . . . . . . . . 20Figure 2.15 Eye diagrams of (a) the segmented ring at 1558.032 nm and(b) the dual cascaded ring at 1557.953 nm, modulated at 12.5Gbaud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.16 The electro-optic output transmission with respect to the sinu-soidal input voltage perturbation for a single ring modulatorand dual cascaded ring modulators. . . . . . . . . . . . . . . 23Figure 2.17 Eye diagrams of (a) the segmented ring at 1558.032 nm and(b) the dual cascaded ring at 1557.953 nm, driven by the 12.5Gbaud NRZ drivers designed in Cadence . . . . . . . . . . . 23Figure 2.18 Gaussian signal distribution at the 102 level of the PAM4 eyediagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 3.1 Schematic of the 4-channel polarization diversity receiver im-plemented in this study. . . . . . . . . . . . . . . . . . . . . . 28Figure 3.2 Adjusted schematic of the 4-channel polarization diversity re-ceiver where the TE path and the TM path leading to each PDhas equal length. . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 3.3 (a) Cross-sectional schematic of the floating Ge photodetector[3]. (b) Top view schematic of the photodetector. . . . . . . . 29Figure 3.4 (a) Layout of the receiver. (b) Micrograph of the receiver,showing the PDs and ring filters for channels 1 and 2, and thePSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.5 (a) Through-port spectrum of the receiver, (b) Output currentspectrum at each PD, normalized to the input power at the PSR. 30Figure 3.6 Measurement setup for the through-port transmission spectrumof the receiver chip and the output current spectrum at each PD. 31Figure 3.7 (a) S11 Measurement setup. The dotted line represents the cal-ibration link. (b)The equivalent circuit model for the PD. Thefitted results are: Cp = 15.2 fF, Cox = 8.8 fF, Rsi = 12.7 kΩ,Cj = 12.6 fF, and Rs = 715Ω. (c) Measured and fitted S11magnitude and phase at 0V bias. . . . . . . . . . . . . . . . . 32xiiFigure 3.8 (a) S21 Measurement setup. The dotted lines represent the cal-ibration link. (b) Measured S21 data -6V bias. . . . . . . . . . 32Figure 3.9 Measured eye diagrams for the four channels at different inputpolarization states. . . . . . . . . . . . . . . . . . . . . . . . 33Figure 3.10 Measurement setup for the eye diagram and bit error rate. . . . 34Figure 3.11 Alignment setup for each polarization input. By maximizingthe h polarization output after the SA polarizer, the output ofthe polarization controller is aligned to (a) h, (b) v, and (c) 45◦polarizations. . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.12 Normalized sum of the TE and the TM signals with a delaybetween them, corresponding to (a) channel 1 and (b) channel 4. 35Figure 3.13 Simulated eye diagrams for the four channels at different inputpolarization states. . . . . . . . . . . . . . . . . . . . . . . . 36Figure 3.14 Schematic of the 4 channel receiver for time-domain simula-tion in Lumerical Interconnect. Only the PD for a single chan-nel is shown in the schematic for clear illustration. . . . . . . 36Figure 3.15 BER measurements with TE, TM, and 45◦ polarization input,for channel (a) 1, (b) 2, (c) 3, and (d) 4. . . . . . . . . . . . . 37Figure 3.16 (a) Transmission spectrum of the receiver where channel 3’sresonance is tuned to be 0.4nm away from channel 4’s reso-nance. (b) BER measurement results at channel 4 PD, wherethe adjacent channel is tuned to be 0.4nm, 0.3nm or 0.2nm away. 37Figure 3.17 Measured eye diagrams for channel 4, with channel spacing of(a) 0.4nm, (b) 0.3nm, and (c) 0.2nm. . . . . . . . . . . . . . . 38Figure 3.18 Through-port group delay vs. wavelength for a single ring filter. 39xiiiList of AbbreviationsBER Bit Error RateBW BandwidthCMOS Complementary Metal Oxide SemiconductorDAC Digital-to-Analog ConverterDUT Device Under TestDWDM Dense Wavelength Division MultiplexingFSR Free Spectral RangeGSG Ground-Signal-GroundLSB Least Significant BitMSB Most Significant BitMUX MultiplexerMZM Mach Zehnder ModulatorNMOS N-type Metal Oxide SemiconductorNRZ Non-Return-to-ZeroOMA Optical Modulation AmplitudePAM4 Pulse-Amplitude-Modulation 4xivPD PhotodetectorPDL Polarization Dependent LossPMOS P-type Metal Oxide SemiconductorPPG Pulse Pattern GeneratorPRBS Pseudo-random Binary SequencePSR Polarization Splitter-RotatorSER Symbol Error RateSNR Signal-to-Noise RatioSOI Silicon-on-InsulatorTCMT Temporal Coupled Mode TheoryTE Transverse-electricTIA Trans-impedance AmplifierTM Transverse-magneticUI Unit IntervalVNA Vector Network AnalyzerWDM Wavelength Division MultiplexingxvAcknowledgmentsI would first like to thank my supervisors Dr. Lukas Chrostowski and Dr. SudipShekhar for their guidance throughout my Master’s program. They have taughtme all the basics of silicon photonics and CMOS designs, and I was able to gain amuch better understanding of photonic systems as a result. I also greatly appreciateall the advice they have given me regarding my soft skill development and careerguidance. I would like to thank Dr. Nicolas Jaeger for the support he has givenme with the laboratory equipment. Without his help, I would not have been ableto properly conduct the necessary measurements for my research. I would like tothank Dr. Roberto Rosales for the advice he has given me with RF measurementsand PCB designs.I would like to also thank all of my colleagues in the silicon photonics groupand the System-on-a-Chip group, including Hasitha Jayatilleka, Minglei Ma, HanYun, Hossam Shoman, Enxiao Luan, Zeqin Lu, Yun Wang, Loic Laplatine, JaspreetJhoja, Stephen Lin, Mustafa Hammood, Ajith S. R., Mohammad AlTaha, ChenYuan, Abdelrahman Ahmed, and Mengye Cai, for the valuable discussions, assis-tance, and friendship. I am grateful for the Refined Manufacturing AccelerationProcess (ReMAP) network, part of Canada’s Business-led Networks of Centres ofExcellence, and Natural Sciences and Engineering Research Council of Canadafor the funding of my research. I would also like to thank CMC Microsystems andLumerical Solutions, Inc., for their assistance in device design and simulations.Finally, I would like to thank my family - my father, my mother, and my sister- for all the support they have given me.xviChapter 1Introduction1.1 Silicon PhotonicsIn recent years, there has been a tremendous growth of industrial interest and com-ponent library development in the field of silicon photonics. The ability to fabri-cate photonic chips on a silicon-on-insulator (SOI) wafer by leveraging the maturemanufacturing processes in Complementary Metal Oxide Semiconductor (CMOS)foundries has allowed various research groups around the world to partake in lowcost development of photonic devices [4]. Although significant constraints arepresent due to the limitations of available materials and processes, the low barrierof entry has enabled rapid development of silicon photonic components which arenow mature enough to be considered for commercialization.One of the key benefits of silicon photonics is the ability to integrate multiplecomponents into a small area. Due to the high refractive index contrast betweenthe active silicon layer and the silicon dioxide cladding on the SOI wafer, as shownin Fig. 1.1, the optical mode can be tightly confined within a small cross-sectionalarea of the silicon layer. A typical silicon waveguide for a single mode opera-tion has 500nm width and 220nm thickness. This allows for compact and denselyrouted photonic devices on a single chip. This presents a clear advantage overlegacy optics, which require significant effort in packaging different componentstogether, each of which is developed in its own specialized process.This benefit has attracted the attention of several large companies around the1Silicon SubstrateSiO2 Buried Oxide (n = 1.44)SiO2 Cladding (n = 1.44)Silicon layer (n = 3.47)Figure 1.1: Layer stack of a SOI wafer. n refers to the refractive index of thematerial at 1550, such as Intel and Luxtera which currently sell 100G silicon photonic transceivermodules. Other companies like Inphi, Finisar, Acacia, Kaiam, and Oclaro havepublicly announced invested interest in silicon photonics and have demonstratedprogress in their transceiver module development as well. Silicon photonics is nolonger just a potential technology for the future - it is an economic, competitivetechnology in today’s photonics industry.1.2 Ring ResonatorsRing resonators are waveguide loops which can selectively filter different wave-lengths of light on chip. By leveraging the high confinement factor in the SOIplatform, a ring resonator can be made very small, with a radius on the order ofmicrometers.An all-pass ring resonator, which is the most basic form of a ring resonator,consists of a waveguide loop placed next to a straight waveguide, also known asa bus waveguide [Fig. 1.2(a)]. After light from the bus waveguide couples tothe ring, it starts circulating within the loop. When light constructively interfereswithin the ring by meeting the resonance condition, energy builds up inside. Theresonance condition is written in Eq. (1.1).mλresne f f= L (1.1)Here, m is a positive integer, λres is the resonant wavelength, ne f f is the effec-2tive index of the light within the waveguide, and L is the circumference of the ring.For a given waveguide cross-sectional profile, a commercial eigenmode solver,such as Lumerical Mode, can be used to determine the effective index at a partic-ular wavelength. When the resonance condition is met, the light that couples outof the ring destructively interferes with the light in the bus waveguide. Therefore,the through port transmission of the light drops near resonance, as the light insteadaccumulates and eventually dissipates within the ring. To detect the light accumu-lating inside the ring, another waveguide can be placed on the other side of thering resonator, creating an add-drop ring resonator configuration [Fig. 1.2(b)]. Thetransmission spectra from the input port to the through port and the drop port areshown in Fig. 1.2(c) as an example.Input Through Input ThroughDrop 1551.2 1551.4 1551.6 1551.8 1552Wavelength (nm)-25-20-15-10-50Transmission (dB)Through PortDrop Port(a) (b) (c)Figure 1.2: (a) Diagram of an all-pass ring resonator. (b) Diagram of an add-drop ring resonator. (c) Sample transmission spectra of an add-drop ringresonator.All-pass ring resonators can be used as high speed modulators by doping thering waveguide with PN junctions [Fig. 1.3(a)]. By keeping the PN junction re-verse biased and driving it in carrier depletion mode, modulation frequency in therange of 10s of GHz can be achieved. An example of through port transmissionof the ring resonator at different bias voltages are shown in Fig. 1.3(c). Chang-ing the bias voltage on the PN junction modifies the carrier distribution within thedoped waveguide, which in turn changes the ne f f off the waveguide. This causes ashift in the resonant wavelength of the ring resonator. At a given laser wavelength,represented as the grey dotted line in Fig. 1.3(c), the shift in the resonant wave-length corresponds to a change in the transmission amplitude. Therefore, drivingthe PN junction results in a binary amplitude-modulated optical signal from thering resonator.3By modifying the ring modulator design, either by dividing the PN junctioninto two segments within the ring or by adding another PN-doped ring resonatorin series, 4-levels of amplitude can be generated to create a Pulse-Amplitude-Modulation-4 (PAM4) signal. For a given modulation bandwidth, PAM4 signalscan be used to double the transmitted bit rate compared to binary signals. Thistype of multi-level modulation format has become a necessity to meet the ever-increasing data traffic of the modern world, while working within the bandwidthlimit of the optical devices. Therefore, developing and analyzing PAM4 opticalmodulators is important, especially since PAM4 signal has been designated as therecommended signal format for data center applications by the IEEE P802.3bs200Gb/s and 400Gb/s ethernet task force [5].(a) (b) (c)AA'p n1551.5 1551.55 1551.6 1551.65 1551.7Wavelength (nm)-25-20-15-10-50Transmission (dB)V1V2Figure 1.3: (a) Diagram of an all-pass ring resonator with PN junction. (b)Cross-sectional profile A–A’ of the waveguide with PN junction in (a).(c) Sample transmission spectra of the ring modulator at two differentbias voltages.Add-drop ring resonators can be used as channel filters for wavelength divisionmultiplexing (WDM) applications. Optical signals of different wavelengths prop-agate independently of each other, which make them perfectly suitable for WDMsignal transmission. The schematic for a ring resonator based WDM demultiplexeris shown in Fig. 1.4 where four add-drop ring resonators of different diametersare cascaded in series, each of which filters out one of the four wavelengths inthe multiplexed input signal. This type of design can be implemented as a com-pact demultiplexer in a silicon photonic receiver chip supporting multiple wave-lengths. This demultiplexer works well in a single polarization input state. How-ever, when the polarization of the input signal changes after traveling through asingle mode fiber, the demultiplexers can no longer work at the same wavelengths.4This is because SOI waveguides suffer from high birefringence due to their rectan-gular cross-section and high confinement factor. Both a “quasi-transverse-electric(quasi-TE)” mode, where the electrical field of the mode is polarized horizontally,and a “quasi-transverse-magnetic (quasi-TM)” mode, where the electrical field ofthe mode is polarized vertically, can be supported in an SOI waveguide as eigen-modes, but the two modes have very different ne f f values. Because the resonantcondition of a ring resonator is dependent on the ne f f of the mode in the waveg-uide, the resonant wavelength changes along with the polarization of the input sig-nal. Therefore, a polarization management structure is desired on-chip to mitigatethis issue in the silicon photonic receiver.Figure 1.4: Schematic of a 4 channel WDM demultiplexer based on add-dropring resonator filters1.3 Thesis OrganizationThis thesis focuses on the challenges associated with ring resonators in the trans-mitter side and the receiver side of a silicon photonic link.In Chapter 2, PAM4 modulation performance is compared between a singlesegmented ring resonator and a dual cascaded ring resonator at 25 Gb/s, using ana-lytic equations and time-domain simulations. The optical PAM4 signal modulationis emulated by modulating the two ring modulators with CMOS drivers designedin a 65nm process, and the resulting eye diagrams for the two modulators are com-pared in terms of optical modulation amplitude and bit error rate.In Chapter 3, a ring resonator based 4 channel WDM receiver with polariza-tion diversity is experimentally demonstrated at 10 Gb/s per channel. By forminga waveguide loop between the two output ports of a polarization splitter-rotator(PSR), the input signals in the quasi-TE and quasi-TM polarizations can be de-5multiplexed by the same set of ring resonator filters. The receiver’s tolerance tothe relative delay between the quasi-TE and the quasi-TM signals on chip and thereceiver’s compatibility for dense WDM application are addressed in the analysis.In Chapter 4, the summary and suggestions for future work are provided.6Chapter 2Comparison of DAC-less PAM4Modulation in Segmented RingResonator and Dual CascadedRing ResonatorTo meet the demand for energy-efficient high speed data transmission, multi-levelpulse amplitude modulation (PAM) schemes, such as PAM4, are being pursued torealize performance superior to conventional non-return-to-zero (NRZ) modulatedsilicon microring resonators. While an electrical 2-bit DAC driver can be used togenerate the multiple amplitude levels [6], a “DAC-less” implementation is prefer-able to reduce the overall power consumption [1, 7]. Multiple optical levels forPAM4 can be realized using two separate NRZ drivers driving either a single ringresonator with segmented PN junctions [7], or a dual cascaded ring resonator [1],as shown in Fig. 2.1. This work presents a comparison of the two PAM4 ring mod-ulators’ performance at 25Gb/s using Matlab, Lumerical softwares, and Cadence,and shows that the segmented ring modulator attains larger eye opening with lowerpower consumption under identical design constraints.The document is organized as follows. In Section 2.1, the frequency and timedomain models for a single ring resonator is described. In Section 2.2, the model7Eo EoLSB MSBEi τc Eiarτc τcar arx1 x2MSBx2LSBx1 0 1 0 1 1 0Ei = input fieldEo = output fieldar = field amplitude within ringτc = coupling photon lifetimeNRZ signalFigure 2.1: Schematic view of the segmented single ring and the dual cas-caded ring driven by NRZ signals. The most significant bit driver out-puts approximately twice the voltage of the least significant bit driver togenerate a 2-bit overall compared with the results from Lumerical Interconnect simulation, where thephysical parameters required for the model are derived from Lumerical Device,Mode, and FDTD. To further confirm the validity of the model, the results arecompared with the data in [1]. In Section 2.3, the electrical CMOS drivers for thering modulators are described and developed in Cadence. Finally, in Section 2.4,the two PAM4 ring modulators are simulated and compared.2.1 Optical Single Ring ModelThe basic set of equations for the frequency domain description of a ring resonatorcan be found in [8]. The field transmission of an all-pass ring resonator, as visual-ized in Fig. 2.2, can be described by Eq. (2.1).EoEi= ei(pi+φ)a− re−iφ1− raeiφ . (2.1)Here, a = e−αL2 is the round-trip field transmission amplitude for a ring ofradius R, with L = 2piR and propagation loss α . φ = 2pine f fλ L is the round-tripphase change in a waveguide with a mode effective index of ne f f . The equationassumes that the coupler is lossless (κ2 + r2 = 1). The power transmission througha ring resonator can be obtained by taking a conjugate square of Eq. (2.1). Thecritical coupling condition, where the transmission becomes 0 on resonance, isachieved when a = |r|. When a > |r|, more light is coupled to the ring than whatis lost during propagation, and thus the ring is “over-coupled”. When a < |r|, the8opposite is true and thus the ring is “under-coupled”.rκ Ei EoaFigure 2.2: All-pass ring resonator diagram.A ring resonator is often characterized by its total quality factor, defined byQT = λresFWHM = ωrτ where λres is the resonant wavelength, ωr is the resonant an-gular frequency, and FWHM is the full width at half maximum of resonance. HighQT corresponds to a narrow resonance, which also indicates high photon lifetime(τ) on resonance. QT consists of intrinsic quality factor(Qi) and coupling qualityfactor (Qc), described by the equations below [4]:1QT=1Qi+1Qc(2.2)Qi =2pingλα(2.3)Qc =− piLngλ loge|r| . (2.4)ng refers to the group index, which is related to the wavelength dependence ofthe effective index, and is inversely proportional to the group velocity of the mode.The frequency domain equation can be used to describe a static ring. However,for a dynamic ring modulator, a time-domain description is required. One way ofmodeling the transient behaviour of a ring is through the Temporal Coupled ModeTheory (TCMT) for ring resonators [9, 10]:δArδ t=(− iωr− 12τ)Ar + i1τ(1/2)cEieiωt (2.5)9Eoeiωt = Eieiωt + i1τ(1/2)cAr(t) (2.6)τc is the coupling photon lifetime in each ring defined by Qc = ωrτc, ω is thelaser’s angular frequency, and other parameters are defined in Fig. 2.1. The firstterm inside the bracket on right hand side of Eq. (2.5) represents light circulatingwith the ring’s resonant frequency. The second term inside the same bracket rep-resents the field loss in the ring due to intrinsic loss and coupling loss. Finally thelast term represents the light coupled from the input waveguide. The derivation forthe coefficients can be found in [11]. One can define the field inside the ring asAr = are(−iωt) and arrive at modified versions of Eq. (2.5) and (2.6):δarδ t=(− i(ωr−ω)− 12τ)ar + i1τ(1/2)cEi (2.7)Eo = Ei + i1τ(1/2)car(t) (2.8)To check the validity of the TCMT equations, we can find the steady statesolution to Eq. (2.5) and derive new equations for the field transmission of a ringresonator:Ar =i 1τ(1/2)ci(ωr−ω)+ 12τEi (2.9)EoEi=i(ωr−ω)+ 12τ − 1τci(ωr−ω)+ 12τ(2.10)For a given ring, the transmission spectra from Eq. (2.1) and Eq. (2.10) canbe compared as shown in Figure 2.3. A 10 µm-radius ring with a quality factor of5200 is used for this and it shows a strong agreement between the two equationsnear resonance in 2.3(a). It is worth noting that Eq. (2.10) only holds true for asingle resonant wavelength, and thus cannot account for multiple resonant wave-lengths as Eq. (2.1) does, as shown in 2.3(b). Nevertheless, since the accuracy ofthe TCMT equations are verified near the resonant wavelength of interest, it can beused to calculate the transient response of a modulated ring resonator and generate10an eye diagram.1557 1557.5 1558 1558.5 1559 1559.5Wavelength (nm)-15-10-50Transmission (dB)Eq. (2.1)Eq. (2.10)1548 1552 1556 1560 1564 1568Wavelength (nm)-15-10-50Transmission (dB)Eq. (2.1)Eq. (2.10)(a) (b)Figure 2.3: Transmission spectra of a ring resonator with R = 10um and Q =5200, calculated from Eq. (2.1) and Eq. (2.10), plotted near resonancein (a) 2.5nm bandwidth and (b) 20nm bandwidth.Readers may find that the TCMT equations for a ring resonator differ betweenvarious sources. Mainly, there is a discrepancy by a factor of 2 on the time con-stants τ and τc. This arises due to the discrepancy in the definition of the qualityfactor of a ring. For example, in [4], quality factor is defined as Q = ωrτ whereasin [11], it is defined as Q = ωrτ2 . For this report, we follow the definition set out in[4].2.2 Model ValidationTo further validate the accuracy of the TCMT model, the ring modulator in [1] isused as reference for comparison. To obtain the parameters in the model, Lumericalsoftwares are used.First, the cross-section of a doped waveguide is modeled using Lumerical De-vice. Based on the dopant profile shown in Fig 2.4(a), charge profile at differentbias voltages can be generated. The charge profiles are then imported to LumericalMode Solutions to overlap with the waveguide mode as shown in Fig 2.4(b). Thisprovides the effective index and the propagation loss of the ring resonator. Thecoupling coefficient can be determined using Lumerical FDTD Solutions to modelthe bus-to-ring directional coupler.Although the initial simulations were modeled after the nominal design listedin [1], namely a 10 µm radius ring resonator with a 300nm coupling gap and ionimplanted according to process specifications at IME A*STAR, the resulting ring11(a) (b)pn p+ p++n++ n+0 0.5 1-0.5-1 3-3 [µm]Figure 2.4: (a) Waveguide and dopant profile used in Lumerical Device simu-lation. The core waveguide has 500nm×220nm dimensions and the slabhas 90nm thickness. The concentration of each dopant is as follows: p= 5e17 cm−3, p+ = 2e18 cm−3, p++ = 4.4e20 cm−3, n = 3e17 cm−3, n+= 2e18 cm−3, and n++ = 4.4e20 cm−3. (b) Lumerical Mode simulationof the waveguide cross-section with the embedded charge profile. Colorscale indicates normalized light intensity in linear scale.had a much higher quality factor than what is published. This is very likely due tothe process variation during fabrication, resulting in a ring which deviated heavilyfrom the nominal design. Taking this possibility into account, the dopant pro-file, the waveguide propagation loss, and the coupling gap of the ring resonatorare modified to match the published results. The physical parameters, under theassumption that the directional coupler is lossless, are listed in Table 2.1. Thepropagation loss of 78 dB/cm for a doped waveguide is severely high, which couldbe a sign of errors during fabrication.Table 2.1: Physical parameters of the ring resonator used to match publishedresults in [1]Parameters ValuesRadius 10 µmne f f (undoped WG) 2.56166ne f f (doped WG @ 0V) 2.56105ng (undoped & doped WG @ 0V) 3.9097Propagation Loss (undoped WG) 3 dB/cmPropagation loss (doped WG) @ 0V 78 dB/cmPN junction span in the ring 0.70Coupling Coefficient κ 0.329Based on these parameters, the transmission spectra at different voltages areplotted and compared with [1] in Fig. 2.5, showing strong agreement.121557.8 1558 1558.2Wavelength (nm)-30-25-20-15-10-50Transmission (dB)0V, 0V0V, -5V-2V, 0V-2V, -5V(a) (b) (c)Figure 2.5: (a) Transmission spectra at four input levels presented in [1],reprinted with permission from c©2016 Optical Society of America. (b)The simulated spectra using parameters in Table 1 in Matlab. (c) Thesimulated spectra using parameters in Table 1 in Lumerical Intercon-nect.Based on these parameters, the TCMT equations are used to simulate the idealtransient response in Matlab, and the resulting eye diagram is compared to thetime domain simulation result from Lumerical Interconnect in Fig. 2.6, once againshowing strong agreement between the plots. The rise and fall times of the inputsignals are assumed to be 30% of the unit interval (UI).(a) (b)Figure 2.6: Eye diagrams generated from (a) TCMT equations in Matlab and(b) time domain simulation in Lumerical Interconnect.However, these eye diagrams do not resemble the reported eye diagrams from[1]. A number of extra components are added to the original schematic in Lumer-ical Interconnect to produce an eye diagram resembling the result in [1], as shownin Figure 2.7. These extra components include: a jitter element with a random13jitter of 6% of the UI at the output of each NRZ signal generator, a noise sourcewith a power spectral density (PSD) of 6e-16 W/Hz added to each jitter element, atime delay element with a 15 ps delay at the output of the second ring driver, andanother noise source with a PSD of 8e-20 W/Hz added to the PIN photodetectoroutput. The time delay element is the most crucial differentiating factor betweenthe eye diagrams in Fig. 2.6 and Fig. 2.7. For DAC-less PAM4 systems, the delaybetween the two NRZ driver signals must be tuned precisely during operation, asit makes a large difference in the resulting PAM4 signal.(a) (b)(c)Figure 2.7: (a) Eye diagram generated from Lumerical Interconnect and (b)eye diagram published in [1], reprinted with permission from c©2016Optical Society of America. (c) The simulation schematic from whichthe eye diagram in (a) is generated.In both Fig. 2.6 and Fig. 2.7, the eye diagrams exhibit unequal eye amplitudebetween the 4 signal levels, which is an undesirable effect. Fortunately this canbe fixed by simply adjusting the input voltages and the laser wavelength. For ex-ample, by changing the input voltages to -1.5V and -5V, and by changing the laserwavelength from 1558.03nm to 1557.96nm, a modified eye diagram with equal eyeheight between the 4 signal levels can be achieved, as shown in Fig. 2.8.14Figure 2.8: Eye diagram with operating wavelength and input voltages mod-ified from Fig. 2.6 (a).2.3 Electrical DriverPrior to designing the electrical driver, the ring resonator’s reverse-biased PN junc-tion is modeled as a simplified RC load in Cadence as shown in Figure 2.9. Theseries resistance Rs comes from the doped silicon slab between the cathode/an-ode contacts to the PN junction, and the junction capacitance C j comes from thePN junction itself, along with other sources of capacitance present on an silicon-on-insulator chip. Rs of 25Ω is assumed based on IME A*STAR foundry’s sheetresistance data and C j of 100 fF is estimated from the ring resonator size.CjRsRsFigure 2.9: Circuit equivalent model of the ring modulator PN junction usedin cadence simulation.Unlike the example used for model validation, a 5Vp-p signal is difficult toproduce in a CMOS circuit due to the limit in the supply voltage. Therefore, forcomparing the segmented and the cascaded ring modulators, a 2.2Vp-p and a 1Vp-p data signal swing are provided as the input at 12.5Gb/s each for optimal 25Gb/sPAM4 modulation. The two voltages are different by a factor slightly larger than 2to account for the nonlinearity in the PN junction response with respect to voltage.15A single ended driver is used for the 1Vp-p data and a differential driver is used forthe 2.2Vp-p data. Thus, both drivers can share the same supply voltage of 1.1V.However, for the purposes of output waveform generation in the context of thiswork, 1V supply voltage is used for the 1Vp-p driver and 1.1V supply voltage isused for 2.2Vp-p data. The drivers are designed in a 65nm node.(a) (b)Figure 2.10: Schematic of (a) the inverter-based driver cell and (b) the differ-ential driverThe driver cell schematic is shown in Fig. 2.10. An inverter based driver is usedbecause the PN junction load can be treated as a compact lumped element. WhenEN=1, the driver cell is enabled. The output of the driver is the non-inverting datainput. However, when EN=0, the output driver cell is in “High Z” state. Scan bitscan be used to select the slices of the driver cell and 15 thermometric cells are usedin this design as the load capacitance of the ring modulator is about 100fF. In Fig.2.10, the width of the NMOS is 200nm and the width of the PMOS is 400nm. Thechannel length for both the PMOS and the NMOS is 60nm.Since all the signals are of CMOS levels, the pre-driver used in the design is asimple CMOS buffer. To save power, the pre-driver is implemented as slices. Fourslices (Fo4 when all of the driver slices are selected) are used in this design.The differential output of the ring modulator is AC coupled and biased with aresistor before feeding it to the ring modulator load to ensure proper reverse biasof operation during modulation. The damping resistor (Rdamp = 30Ω) is added toreduce ringing at the output caused by the output bondwire, as shown in Fig. 2.12.The AC coupling capacitance is chosen to be 3pF and the bias resistor is 40kΩ sothat the lower cut off is below 1MHz.16(a) (b)Figure 2.11: The schematic of (a)the NAND gate and (b) the NOR gate usedin the design. The gates are sized to have the same resistance as theinverter.Figure 2.12: Integration of the driver with the ring modulator along with thesupply/GND bondwire model [2]A PRBS-32 pattern is applied at 12.5Gb/s using Cadence Analog Lib sourceto generate the waveforms for 1Vp-p and 2.2 Vp-p signals, which will later beimported to Lumerical Interconnect for optical simulation. The driver signals’ eyediagrams are plotted in Fig. 2.13. The specifications for the 1Vp-p driver aresummarized in Table 2.2.17(a) (b)Figure 2.13: The output eye diagrams of (a) the single-ended 1Vp-p driverand (b) the differential 2.2Vp-p driver.Table 2.2: Specifications for the 1 Vp-p DriverParameters ValuesSupply Voltage [V] 1.0UI [ps] 80Supply Current [mA] 2.52.4 Modulator Performance ComparisonFor the comparison of the two types of PAM4 modulators at 25 Gb/s, identicalring resonators with the parameters listed in Table 2.1 are used, with the excep-tion of the PN junction span. The PN junction is assumed to span 75% of eachring in the dual cascaded ring modulator, whereas it is assumed to span only 70%of the segmented single ring due to the gap required between the segmented PNjunctions. Therefore identical design constraints are enforced for both modulatorswhile keeping their free spectral range constant. Both ring modulators have qual-ity factors of approximately 5200, but the cascaded dual ring has a slightly lowerquality factor due to the larger PN junction span. It is assumed that the two ringsin the cascaded ring modulator are aligned to the same resonant wavelength. It isalso assumed that the noise crosstalk between two adjacent pn junction segmentsis negligible.Ring modulators have a trade-off relation between their optical modulation am-plitude (OMA) and their bandwidth (BW), dictated by their quality factor. For ex-ample, large quality factor leads to large OMA but low BW. In a dual cascaded ring18modulator, if the two cascaded ring resonators are modulated together with identi-cal signals, the OMA-BW trade-off relation may be different from that of a singlering modulator because the effective photon lifetime is reduced from the presenceof a second ring. However, for PAM4 application, the two cascaded ring resonatorsare modulated independently of each other. In this case, each ring is bound to thesame OMA-BW trade-off relation as that of a single ring modulator. Therefore,identical ring resonators are used for a fair PAM4 modulator comparison under thesame design constraints.The rings are designed to be undercoupled for this comparison, which is againstthe norm for high speed ring modulators. Normally, overcoupled rings are used dueto fast transition speed between the ’0’ state and the ’1’ state for NRZ modulation.This fast transition can result in an overshoot, much like an underdamped oscil-lator, which can even be leveraged to increase the modulation amplitude at highfrequencies [12] . However, for a PAM4 system, the overshoot directly affects thesignal levels above or below the target level. To some degree, this effect can bemitigated by using an overdamped driving signal. However, to counter this effectwithin the optical domain, undercoupled rings can be used, which behave like anoverdamped oscillator.The transmission spectra of the two modulators are plotted in Fig. 2.14. As-suming that the laser is biased to the lower wavelength side of the ring resonance,the largest normalized OMA in the segmented ring is 0.091, whereas the largestnormalized OMA in the cascaded ring is 0.076, at 1558.032nm and 1557.953nm,respectively. The OMA values are calculated as the difference between the highestlevel and the lowest level of the modulated signal.Despite having less overlap with the PN junction, the segmented ring achieveshigher OMA with the same input voltages. This is primarily because the cas-caded ring suffers from higher insertion loss, which reduces the OMA at all wave-lengths. The other reason for this is because the least-significant-bit (LSB) ring inthe dual cascaded ring modulator experiences less change in the effective indexduring PAM4 modulation compared to the single segmented ring. At (0V, 0V) in-put, the resonant wavelengths of the most-significant-bit (MSB) ring and the LSBring are aligned. However, at (-1V, -2.2V) input, the LSB ring experiences lessshift in the resonant wavelength compared to the MSB ring, which also affects191557.9 1558 1558.1 1558.2Wavelength (nm) (dB)0V, 0V0V, -2.2V-1V, 0V-1V, -2.2V1557.9 1558 1558.1 1558.2Wavelength (nm) (dB)0V, 0V0V, -2.2V-1V, 0V-1V, -2.2V(a) (b)Figure 2.14: Transmission spectra of (a) the single segmented ring and (b)the dual cascaded ring.the total shift of the spectrum at the left side (the lower wavelength side) of thering resonance. Therefore, despite applying the same set of voltages to more thantwice the length of the PN junction in the single segmented ring, the spectrum shiftobserved in the cascaded ring is comparable to that in the single segmented ring.The OMA difference can also be seen in the ideal 12.5 Gbaud eye diagrams inFig. 2.15, which are obtained at the optimal wavelengths for maximized OMA andeye opening. Signal rise time and fall time are assumed to be 30% of the UI. Thesegmented ring displays a wide eye opening, whereas the cascaded ring suffersfrom overshoot dynamics, resulting in reduced eye opening. The overshoot in asingle ring modulator arises due to the interference effect between the input beamand the light inside the ring during modulation, generating a beat frequency closeto the detuning of the laser (ωr−ω) [12]. When cascaded with another ring formodulation, this interference becomes stronger as there is laser-to-ring detuningand inter-ring detuning affecting the transmitted beam.The overshoot dynamics of the two modulators can be analyzed in more de-tail using the perturbation model introduced in the supplementary informationof [12]. Starting from the single ring TCMT equations (Eqs. (2.5) - (2.8)), asmall perturbation in the input voltage is represented as a change in the resonantwavelength ωr→ ωr +δωr, resulting in the field amplitude change within ring asar → ar + δar. The resonant wavelength perturbation is modeled as a sinusoidalsignal with a single modulation frequency, represented as δωr → δωrcos(ωmt),where ωm represents the angular modulation frequency. Then, the field amplitudechange within the ring can be expressed as Eq. (2.11) where a¯r represents the20(a) (b)Figure 2.15: Eye diagrams of (a) the segmented ring at 1558.032 nm and (b)the dual cascaded ring at 1557.953 nm, modulated at 12.5 Gbaud.average field amplitude within ring. The corresponding output power change isexpressed as Eq. (2.12), where µ represents the coupling strength equivalent to1τ(1/2)c.δar =−i(ωr2)a¯r(eiωmtiωr− iω+ iωm + 1τ+e−iωmtiωr− iω− iωm + 1τ)(2.11)|E¯o|2−< |E¯o|>2= |iµδar|2 +(1+ iµ a¯r)∗(iµδar)+(1+ iµ a¯r)(iµδar)∗ (2.12)By adding another ring at the output, which may be modulated with the samesignal but in or out of phase with the first ring, the expression can be further ex-panded for the cascaded ring model. Equation (2.13) shows the expression for thefield amplitude within the second ring. Here, the subscripts 1 and 2 represent theparameters associated with ring 1 and ring 2, respectively. The field amplitude val-ues ar and a¯r are simplified by replacing the subscript r with the ring number. Aminus sign in front of the first term represents ring 2 and ring 1 being modulated inphase, whereas a plus sign represents the two rings being modulated out of phase.Finally, Eq. (2.14) shows the expression for the output power change of a dualcascaded ring.21δa2 =∓i(ωr22)a¯2(eiωmtiωr2− iω+ iωm + 1τ2+e−iωmtiωr2− iω− iωm + 1τ2)+iµ2(ωr12)a¯1(eiωmt(iωr1− iω+ iωm + 1τ1 )(iωr2− iω+ iωm + 1τ2 )+e−iωmt(iωr1− iω− iωm + 1τ1 )(iωr2− iω− iωm + 1τ2 )) (2.13)|E¯o|2−< |E¯o|>2= |iµ(δa1 +δa1)|2 +(1+ iµ(a¯1 + a¯2))∗(iµ(δa1 +δa2))+(1+ iµ(a¯1 + a¯2))(iµ(δa1 +δa2))∗(2.14)Based on Eqs. (2.12) and (2.14), the output powers with respect to the per-turbation in the input signal at different modulation frequencies are plotted in Fig.2.16, for a single ring modulator and a dual cascaded ring modulator where thetwo rings are modulated in phase and out of phase. The same ring resonators andoperating wavelength from Fig. 2.15(b) are used, and the input signal is modeled at-1V bias for all rings with a 0.1V perturbation at different modulation frequencies.The output responses are normalized to the DC E/O transmission of the single ringmodulator. The peaking behaviour is not visible for the single ring and the dualring modulated in phase, as the perturbation voltage is very small. However, aclear peaking effect is visible in the dual ring modulated out of phase. This effectcan also be observed in Fig. 2.15(b) where the signal peaking is most pronouncedduring transitions between the two middle levels of the PAM4 signal. These transi-tions require the two cascaded rings to be modulated out of phase with each other- when one voltage increases, the other decreases.Unlike the single segmented ring modulator where the peaking behaviour isrelatively similar across all transitions, the varying levels of peaking effect in thedual cascaded ring modulator can become problematic for commercial applica-tions, where pre-emphasis techniques may be necessary to make the optical sig-nal clean at high data rates. The transition-dependent peaking effect requirespre-emphasis customized for each transition, which may be difficult and power-22consuming. Therefore, using a single segmented ring modulator is preferable inthis regard.0 10 20 30 40 50 60Modulation Frequency (GHz)-10-8-6-4-20E/O Transmission (dB)Single RingDual Ring - in phaseDual Ring - out of phaseFigure 2.16: The electro-optic output transmission with respect to the sinu-soidal input voltage perturbation for a single ring modulator and dualcascaded ring modulators.For a more realistic simulation of the modulators, the NRZ PRBS32 electricaldriver signals from Cadence are applied. This ensures that jitter and noise are takeninto account for the performance assessment. The final eye diagrams are generatedthrough Lumerical Interconnect, as shown in Fig. 2.17.(a) (b)Figure 2.17: Eye diagrams of (a) the segmented ring at 1558.032 nm and (b)the dual cascaded ring at 1557.953 nm, driven by the 12.5 Gbaud NRZdrivers designed in CadenceThe quality of the eye diagrams can be quantified into the Bit Error Rate (BER)metric. However, the BER calculation method which compares the input bits to theoutput eye diagram cannot apply here, as the simulation gives clear eye opening be-tween all four levels for both ring modulators, leading to zero error bits. Instead, a23signal-to-noise ratio (SNR) based BER estimate method can be applied. Assumingeach of the four levels has a Gaussian noise distribution, the Symbol Error Rate(SER) can be first quantified by taking an averaged sum of error probabilities ateach level, just as it is done in a PAM2 system [13], which can then be convertedto BER using the method cited in [14].Figure 2.18 illustrates an ideal PAM4 signal. When a Gaussian noise distribu-tion is assumed at the 102 level, the tail ends of the distribution which lie outsidethe decision thresholds marked by the grey dotted lines count as errors. Therefore,the areas shaded in pink represent the error rate at the 102 level. The error fromeach tail end can be calculated using Eq. (2.15) [13].ErrorRate =∫ ∞QGauss(x)dx≈ 12piexp(−Q2/2)Q(2.15)Here, the Q represents Personick’s Q-factor, which is equivalent to the SNRof the eye diagram between 102 level and 112 level, or between 102 level and 012level, depending on which tail is being calculated. Only a single tail needs to beconsidered for error calculation at the 002 level and the 112 level. Once the errorrate at each level is calculated, the SER of the PAM4 eye diagram is calculated asthe weighted sum of the error rate at each level. Then, SER is converted into BERusing the approximate definition shown in Eq. (2.16) [14].BERapprox ≈ 23SER (2.16)002012102112Figure 2.18: Gaussian signal distribution at the 102 level of the PAM4 eyediagramFor BER calculation, the optimal decision thresholds are defined for each eyediagram in Fig. 2.17, and the decision time window is set to be 10% of the UI near24the optimal decision point. Using Eqs. (2.15) and (2.16), the figures of merit foreach modulator design are calculated and listed in Table 4. The normalized Peak-to-Peak OMA in the table is calculated based on the average value at each level,and therefore is not exactly the same as the estimated value from the transmissionspectra in Fig. 2.14.Across all figures of metric, the segmented ring proves superior to the cascadedring. With identical number of CMOS drivers, the driver power consumption forthe cascaded ring modulator is larger than the single segmented ring modulator,due to the larger PN junction capacitance. Furthermore, due to fabrication andtemperature variations, each ring requires additional tuning and stabilization circuitin practice. Compared to the single segmented ring modulator, the dual cascadedring modulator therefore requires more circuitry and power consumption.Table 2.3: Figures of Merit for the PAM4 ring modulatorsSegmented Ring Cascaded RingNormalized Peak-to-Peak OMA 0.0844 0.0702Insertion Loss [dB] 4.85 5.18Symbol Error Rate 1.34e-5 3.57e-5Bit Error Rate 8.93e-6 2.38e-52.5 SummaryThe PAM4 modulation of the segmented single ring resonator and the dual cas-caded ring resonator is modeled and co-simulated with CMOS drivers at 25Gb/s.The segmented ring is shown to yield superior signal quality, with the benefit ofreduced power consumption, owing to higher index shift per voltage change, fewersources of frequency detuning, and smaller number of circuits required.25Chapter 3Ring Resonator BasedPolarization Diversity WDMReceiverSilicon photonics has emerged as a promising candidate for low cost, high speed in-terconnects in data centers, due to its CMOS compatibility, low cost of production,and large-scale integration capability [15]. However, silicon-on-insulator (SOI)waveguides can suffer from strong polarization dependence due to their high modeconfinement factor and rectangular cross-sections.This is particularly troublesome for silicon photonic wavelength division mul-tiplexing (WDM) receivers, where the performance of the channel filters changeswith respect to the polarization of the optical input from a single mode fiber.Polarization-maintaining fibers can be used to keep the input in a single polar-ization state, but they are expensive to deploy in commercial applications [16].Instead, polarization can be managed on the receiver chip by using polarizationsplitters and rotators available in the silicon photonics platform [17–20].One can use a polarization splitter to separate the input beam into two paths,and place channel filters on each path, to later combine the signals at the pho-todetector (PD) [16]. Alternatively, one can reduce the number of channel filters bysimply placing a polarization rotator in one of the paths, and then connecting it backto the other path to form a loop, such that the two signals can counter-propagate26along the same waveguide in the same polarization [21, 22]. This method is furtherexpanded as a polarization and wavelength division demultiplexer in [23] usingmicroring resonator filters. However, to the best of our knowledge, the operationof a multi-channel WDM receiver with integrated PDs based on the loop methodhas not been demonstrated yet.In this paper, for the first time, we experimentally demonstrate the operationof a 4 channel WDM polarization insensitive receiver based on the loop designwith ring resonator filters. Large signal measurements are made at 10 Gb/s perchannel to evaluate the performance at different input polarizations. For practi-cality assessment, the impact of interchannel crosstalk at DWDM grid spacing andits operational tolerance against mismatches in the length of the signal path areevaluated.3.1 Device DesignThe schematic of the receiver is shown in Fig. 3.1. An edge coupler is used tocouple the horizontally (h) and vertically (v) polarized components of a light sourcefrom an optical fiber into the quasi-transverse-electric (quasi-TE) and the quasi-transverse-magnetic (quasi-TM) modes in the waveguide, respectively. We willrefer to these two modes simply as the ”TE” mode and the ”TM” mode for the restof this paper. The two orthogonal modes in the waveguide are then separated intotwo paths by a PSR. The TE mode input passes through the first path (herein calledthe ‘TE path’) as a TE mode, and the TM mode input rotates and passes throughthe second path (herein called the ‘TM path’) as a TE mode. The two paths areconnected into a loop, along which four add-drop ring resonator filters are placed.In this work, the mode evolution based PSR as described in [24] is used. The dropports of the rings are connected to on-chip PDs.Compared to polarization diversity circuits presented in [16, 25], this designrequires half as many control circuits corresponding to the halved number of mi-croring resonator filters. As the outputs of the PSR are counter-propagating withrespect to each other, they do not cause interference unless there is a backscatteringelement which couples the two paths.One potential performance concern in this design relates to the length differ-27ence between the TE path and the TM path leading to each PD. For example, inFig. 3.1, because the signal in TM path arrives at the channel 1 PD earlier thanthe TE path signal, the overall output of the PD could be distorted if the inputsignal is at an arbitrary polarization state. This can be easily solved by adjustingthe waveguide path between the ring resonator filter and the PD for each channel,as shown in the adjusted schematic in Fig. 3.2. However, to assess the impact ofthe delay between the TE path signal and the TM path signal on the receiver, theoriginal schematic in Fig. 3.1 is adopted for this study. In fact, as described in thenext section, the receiver can tolerate a significant amount of delay between thetwo signals, before the bit error rate (BER) starts to deteriorate.PSR→→PD→→PD→→PD→→PDCh. 1 Ch. 2 Ch. 3 Ch. 4nano-taperedge coupler"TE path""TM path"TE TETMTEhvFigure 3.1: Schematic of the 4-channel polarization diversity receiver imple-mented in this study.PSRPDCh. 1 Ch. 2 Ch. 3 Ch. 4nano-taperedge coupler"TE path""TM path"TE TETMTEhv→→PD→→PD→→PD→→Figure 3.2: Adjusted schematic of the 4-channel polarization diversity re-ceiver where the TE path and the TM path leading to each PD has equallength.A floating germanium PD [3] design is used due to its low dark current, high28P++ N++P+ N+GeBoxSi SubstrateSiO2 claddingMetal Metal(a) (b)Figure 3.3: (a) Cross-sectional schematic of the floating Ge photodetector[3]. (b) Top view schematic of the photodetector.responsivity, and large bandwidth. It consists of a 1.25 µm wide Ge deposition ontop of a p-i-n doped rib waveguide, as shown in Fig. 3.3. The PD is sufficientlylong (21µm) to absorb all of the incident light without letting any residual lightpass through.The microring filter parameters are listed in Table 3.1. Rib waveguides withcore dimensions of 500nm width and 220nm thickness, and a slab thickness of90nm, are used for the filters. Although the nominal channel spacing is set to2.5nm, the ring filters can be tuned with metal heaters to accommodate a tighterchannel spacing.Table 3.1: 4 Channel microring filter parametersParameters ValuesDiameter [µm] 20.00, 20.05, 20.10, 20.15Through port gap [nm] 300Drop port gap [nm] 320Free Spectral Range [nm] 10Channel Spacing [nm] 2.5Quality Factor 150003.2 Device MeasurementA test structure layout and an optical micrograph of the fabricated device are shownin Fig. 3.4. A coplanar Ground-Signal-Ground (GSG) probe is used to measure the29output of the PDs. The device is fabricated at the A*STAR Institute of Microelec-tronics (IME) foundry.InCh. 1Ch. 2Ch. 3Ch. 4filtersPDsPSR(a) (b)InFigure 3.4: (a) Layout of the receiver. (b) Micrograph of the receiver, show-ing the PDs and ring filters for channels 1 and 2, and the PSR.The through-port spectrum of the 4-channel WDM receiver is shown in Fig.3.5(a). The spectrum is obtained by using an external PSR to separate the input andthe output path, as shown in Fig. 3.6. Due to multiple sources of reflections alongthe beam path, the spectrum contains multiple fringes. A duplicate measurement isalso made by swapping the ports for the laser and the detector, resulting in a similarspectrum with minor differences in the fringe patterns.1546 1548 1550 1552 1554Wavelength (nm)-25-20-15-10-50Transmission (dB)Q = 15000TE inTM inFitted data1546 1548 1550 1552 1554Wavelength (nm) PD / Pin-PSR (A/W)Ch.1Ch.2Ch.3Ch.4(a) (b)Figure 3.5: (a) Through-port spectrum of the receiver, (b) Output currentspectrum at each PD, normalized to the input power at the PSR.The wavelength dependent responsivity of the WDM channel filters is derivedfrom measurement of the photocurrent in the PDs as a function of the on-chipoptical power before the PSR (Fig. 3.5(b)). Normalization to the input power at theon-chip PSR (the input port of Fig. 3.1) is done in order to exclude the couplinglosses from the edge couplers and the alignment errors. The PSR has a 0.4 dB30LaserDetectorexternal PSRhhhvTETMSOI WDM receiver chipSourcemeterPD outputsFigure 3.6: Measurement setup for the through-port transmission spectrumof the receiver chip and the output current spectrum at each PD.insertion loss with negligible polarization dependent loss (PDL). At a reverse biasvoltage of 6 V, the average responsivity of the PDs is 1.05 A/W, with an averagedark current of 1.2 µA.The -3 dB bandwidth of the PD is characterized from S11 and S21 measure-ments. The S11 measurement at 0V bias is made using a 67GHz Agilent VectorNetwork Analyzer (VNA) and a coplanar GSG probe, as shown in Fig. 3.7. Themeasurement link is first calibrated using a GGB CS-5 calibration substrate for theprobe. Afterwards the calibration substrate is replaced by the on-chip PD, also re-ferred as the Device-Under-Test (DUT). The magnitude and phase response of theS11 measurement in Fig, 3.7(c) is fitted to the equivalent circuit model shown inFig. 3.7(b) using Keysight Advanced Design Systems (ADS) [26]. In the circuitmodel, Cp represents pad capacitance, Cox represents the capacitance between thesubstrate and the silicon layer or the metal layers, Rsi represents substrate resis-tance, C j represents junction capacitance of the PD, and Rs represents the seriesresistance of the PD including the electrode path. The electrical -3dB bandwidthof the PD connected to a transmission line with 50 Ω characteristic impedance canbe calculated using Eq. (3.1).BW3dB =12pi(Rs +Zo)C j= 16.5GHz (3.1)The calculated -3dB bandwidth of 16.5 GHz is much lower than the valuesreported in [3], mainly due to the large Rs value. Assuming the equivalent circuitmodel to be correct, the unexpectedly large series resistance may be a result of amanufacturing error, possibly in the dopant alignment or weak connections in themetal layer and the vias connecting the PD to the pads.The S21 measurement is made at -6V bias using the VNA and a 10GHz LiNbO3Mach Zehnder Modulator (MZM), as shown in Fig. 3.8. The calibration link is first31VNAPort 1DUT CS-5GSGProbeGSGProbe0 10 20 30 40Frequency (GHz)-1-0.8-0.6-0.4-0.20Magnitude (dB)-30-25-20-15-10-50Phase (deg)Measured MagnitudeFitted MagnitudeMeasured PhaseFitted PhaseCpCox CjRsi Rs(a) (b) (c)Figure 3.7: (a) S11 Measurement setup. The dotted line represents the cal-ibration link. (b)The equivalent circuit model for the PD. The fittedresults are: Cp = 15.2 fF, Cox = 8.8 fF, Rsi = 12.7 kΩ, Cj = 12.6 fF,and Rs = 715Ω. (c) Measured and fitted S11 magnitude and phase at 0Vbias.formed by connecting the output of the LiNbO3 modulator to DSC-R411 externalPD+Transimpedance Amplifier (TIA) unit with 30 GHz bandwidth. By normaliz-ing the S21 response in this configuration, the low bandwidth of the modulator canbe compensated in the DUT measurement. After the normalization, the externalPD+TIA unit is replaced by the DUT. Unlike the external PD+TIA unit, the DUThas high impedance and needs to be measured with a coplanar GSG probe. Asthese factors could not be taken into account in the calibration link, the DUT S21measurement shows high frequency noise and large oscillations as a result of re-flections in the link. The S21 data is median-averaged to remove high frequencynoise, and plotted in Fig. 3.8(b). Although a lot of oscillations are present, the-3dB Optical-to-Electrical (OE) bandwidth can be visually estimated as 20 GHz. Itis worth noting that the S21 calibration link hits the noise limit of the VNA near 18GHz, which means the DUT S21 response above 18 GHz may not be trustworthy.VNAMZMLaserVBias Bias TeeDCGSG ProbePort 1DUTexternalPD+TIABias Tee VBiasDCPort 21 3 5 7 9 11 13 15 17 19 21Frequency (GHz)-4-3-2-10S21 (dB)-6V Bias(a) (b)Figure 3.8: (a) S21 Measurement setup. The dotted lines represent the cali-bration link. (b) Measured S21 data -6V bias.32A discrepancy arises, as the electrical bandwidth predicted from the S11 re-sponse is lower than the OE bandwidth predicted from the S21 response. Onereason for this is due to the difference in the bias voltage, since larger reverse biasvoltage leads to reduced junction capacitance and thus a larger bandwidth. How-ever, the uncertainty in the OE bandwidth estimate from the S21 response may alsobe a reason. Nevertheless, the bandwidth of the PD at -6V bias is at least 16 GHz,which is sufficiently large for measuring 10 Gb/s data.TE45ºTMCh. 1 Ch. 2 Ch. 3 Ch. 420 ps/divFigure 3.9: Measured eye diagrams for the four channels at different inputpolarization states.The 10 Gb/s eye diagram for each channel is presented in Fig. 3.9, obtainedfrom the setup in Fig. 3.10. Pulse Pattern Generators (PPGs) provide non-return-to-zero (NRZ) 231 - 1 pseudo random binary sequence (PRBS) signals to the 10GHz LiNbO3 MZMs to generate 10 Gb/s modulated optical signals. The outputof each MZM passes through a polarization controller and an off-chip multiplexer(MUX), which consists of two cascaded 3dB couplers, before entering the chip.The resonant wavelength of each channel is tuned by applying current to the metalheater on top of each ring filter. The response from the PD passes through a biastee, and the RF output goes to either the oscilloscope for eye diagram measure-ment, or the error detector (ED) for BER measurement. A 15 GHz RF amplifier isplaced before the ED due to the minimum peak-to-peak voltage requirement of theinstrument. Due to limitations of our instrumentation, only up to three channels33are simultaneously tested.PPG 1MZM 1PPG 2PPG 3Laser 1Laser 2Laser 3RF AmpVBiasBias TeeOscilloscopeDUTMuxMZM 2MZM 3EDVTuningDCRFPol. ControllersPD OutputFigure 3.10: Measurement setup for the eye diagram and bit error rate.Pol. ControllerSA Pol.h ↑ h ↑Pol. ControllerSA Pol.FA-SAv ↑ h ↑h ↑Pol. Controller45o-SA SA Pol.h ↑h ↑45o ↑(a) (b) (c)Figure 3.11: Alignment setup for each polarization input. By maximizing theh polarization output after the SA polarizer, the output of the polariza-tion controller is aligned to (a) h, (b) v, and (c) 45◦ polarizations.The eye diagrams for the three different input polarization states of TE, TM,and 45◦ on chip are obtained by using a polarization controller, an axis rotatingfiber, and a slow-axis (SA) polarizer to maximize the response for the h, v, and45◦ polarizations in the fiber respectively. For example, to align the output to h,a slow-axis polarizer is placed in the beam path, and the polarization controller istuned until the output is maximized (Fig. 3.11(a)). For v alignment, a fast-axisto slow-axis (FA-to-SA) fiber is placed at the output of the polarizer, and onceagain the polarization controller is tuned to maximize the output (Fig. 3.11(b)).For 45◦ alignment, the FA-to-SA fiber is replaced with a 45◦-to-SA fiber (Fig.3.11(c)). After each alignment step, the slow-axis polarizer and the polarizationrotating fiber (if used) are carefully removed from the link, which ensures that thepropagation delay through those components are not added to the link. This isimportant for eye diagram assessment of this receiver.The eye diagrams in Fig. 3.9 reveal a clear time delay between TE and TMinput signals, as predicted in Section 3.1. The delay between TE and TM signalsare 44ps, 32ps, 20ps, and 8ps (± 2ps) for channels 1, 2, 3, and 4, respectively.The amplitude difference between the TE and TM eyes primarily comes from the34edge coupler, which exhibits PDL of approximately 1 dB. It should be noted thatthe reduced eye amplitude in channel 4 TM polarization is due to an alignment er-ror during the measurement. Nevertheless, clear eye diagrams are obtained for allstates, including the mixed polarization states labeled as ”45◦”. Although only the45◦ data is shown, open eye diagrams at other polarization angles are also experi-mentally verified. All eye diagrams are round, except for the 45◦ eye for channel 1which has sharper corners at the top and bottom. Eye diagrams at 45◦ polarizationrepresent an equal weight sum of the TE and TM signals, and the sharp corners inthe eye diagram arise as a result of a large delay between the two signals. This isclearly visible in Fig. 3.12, which shows the summation and relative time delay ofthe simulated TE and TM pulses in channels 1 and 4. Fig. 3.12(a) shows a sharperpeak at the top of the summed signal, with a slightly reduced pulse amplitude com-pared to Fig. 3.12(b). This leads to reduced height and width in the eye diagram ofthe summed signal.0 50 100 150 200 250 300time [ps]- pathTM pathSum0 50 100 150 200 250 300time [ps]- pathTM pathSum(a) (b)Figure 3.12: Normalized sum of the TE and the TM signals with a delay be-tween them, corresponding to (a) channel 1 and (b) channel 4.As shown in Fig. 3.13, similar eye diagrams are obtained through simulationusing Lumerical Interconnect. The schematic of the 4 channel receiver for time-domain simulation is shown in Fig. 3.14. The PSR is modeled as a combination ofan ideal polarization splitter and an ideal polarization rotator. The PDL of the edgecoupler is included in this schematic by adding an extra attenuator in the beginningof the TM path. The input signal is modeled as an amplitude modulated signalwith 40 ps rise time and fall time. The PD for each channel is represented as twoseparate PDs - one for each direction of the input beam, with their outputs added inthe electrical domain. A random jitter corresponding to 2% of the unit interval (UI)35is added to the electrical input of the modulator, and a noise source with a powerspectral density of 5e-20 W/Hz is added to the output sum of the PDs, to matchthe noise level in the measured eye diagrams. The TE-TM delay shifts by 12.5 psbetween adjacent channels, which agrees with the measured data.TE45ºTMCh. 1 Ch. 2 Ch. 3 Ch. 420 ps/divFigure 3.13: Simulated eye diagrams for the four channels at different inputpolarization states.Figure 3.14: Schematic of the 4 channel receiver for time-domain simulationin Lumerical Interconnect. Only the PD for a single channel is shownin the schematic for clear illustration.The BER measurement results are presented in Fig. 3.15. With the PDL fromthe edge couplers properly calibrated, the measured BERs are virtually indistin-36guishable for TE, TM, and 45◦ polarizations. The only case with a clear differenceacross all input powers is the 45◦ BER for channel 1, which has the largest delaybetween the signals in the TE path and the TM path.-8 -7 -6 -5 -4 -3 -2 -1 0Power at PSR input (dBm)-10-8-6-4-2log 10(BER)forCh.1TETM45°-8 -7 -6 -5 -4 -3 -2 -1 0Power at PSR input (dBm)-10-8-6-4-2log 10(BER)forCh.2TETM45°-8 -7 -6 -5 -4 -3 -2 -1 0Power at PSR input (dBm)-10-8-6-4-2log 10(BER)forCh.3TETM45°-8 -7 -6 -5 -4 -3 -2 -1 0Power at PSR input (dBm)-10-8-6-4-2log 10(BER)forCh.4TETM45°(a) (b)(c) (d)Figure 3.15: BER measurements with TE, TM, and 45◦ polarization input,for channel (a) 1, (b) 2, (c) 3, and (d) 4.1545 1546 1547 1548Wavelength (nm)-25-20-15-10-50Transmission (dB)ThroughCh.3 DropCh.4 Drop-8 -7 -6 -5 -4 -3 -2 -1 0Power at PSR input (dBm)-10-8-6-4-2log 10(BER)forCh.40.4nm spacing0.3nm spacing0.2nm spacing(a) (b)Figure 3.16: (a) Transmission spectrum of the receiver where channel 3’s res-onance is tuned to be 0.4nm away from channel 4’s resonance. (b)BER measurement results at channel 4 PD, where the adjacent chan-nel is tuned to be 0.4nm, 0.3nm or 0.2nm away.At the nominal channel spacing of 2.5 nm, due to the high Q-factor and large37channel spacing, the crosstalk between adjacent channels is negligible. To deter-mine the receiver’s applicability in a DWDM system, the spacing between channel3 and channel 4 is tuned from 2.5nm down to 0.4nm (50.0 GHz), 0.3nm (37.5GHz), and 0.2nm (25 GHz). The tuned spectra for 0.4 nm spacing and the BERdata at the different spacings are plotted in Fig. 3.16. The horizontal polarizationinput is used for testing. Because the signal for channel 4 gets dropped first alongthe TE path, channel 3 only experiences a small amount of crosstalk from channel4. Therefore, for the crosstalk assessment with the BER plot, only channel 4 ismeasured [27, 28]. Adjacent channel isolation between channel 3 and channel 4are 17 dB, 14 dB, and 11 dB, for channel spacings of 0.4nm, 0.3nm, and 0.2nm,respectively.The power penalty from the inter-channel crosstalk is quantified as the addi-tional input power required to achieve a BER of 1e-9, in comparison to the casewithout any crosstalk. The BER values at 2.5nm spacing remain the same downto 0.4nm spacing. At 0.3nm spacing, there is a small change, resulting in 0.2 dBpower penalty. At 0.2nm spacing, the crosstalk significantly increases, resulting in1.0 dB power penalty. The progressive degradation in the eye diagrams shown inFig. 3.17 is due to the effects of the crosstalk.(a) (b) (c)Figure 3.17: Measured eye diagrams for channel 4, with channel spacing of(a) 0.4nm, (b) 0.3nm, and (c) 0.2nm.3.3 DiscussionThe BER measurement at the 45◦ polarization state indicates that a 10Gb/s signal,which translates to a UI of 100ps, can withstand up to at least 32ps of delay be-tween the TE and TM signals without impairment. The 32ps delay corresponds38to about 2200µm difference in the strip waveguide path. This BER tolerance toTE-TM signal delay implies that optical delay lines, as suggested in [21], are infact not necessary to fine tune the optical path lengths, provided the TE-TM delayis less than 30% of the UI. For each receiver channel, the waveguide between thering filter and the PD can be adjusted such that the total TE signal path and the TMsignal path leading to the PD are nominally equal in length. Due to the large toler-ance for path length difference, the receiver performance should remain unaffectedagainst on-chip variation of waveguide dimensions.Because the BER measurement is performed at the optimal decision point ineach eye diagram, only the eye height, and not the eye width, is taken into con-sideration for this delay tolerance assessment, assuming reasonably open eyes (eyewidths). This is a valid assumption, as the clock and data recovery (CDR) circuitsimplemented in commercial receivers [29] can always tune themselves to the op-timal decision point, and thus compensate for any slow polarization change in thesingle mode fiber. The TE-TM delay tolerance will scale with the UI of the modu-lated signal. For example, a 50 Gb/s signal (UI = 20ps) will withstand up to 6.4psof TE-TM delay, corresponding to about 440µm strip waveguide path length dif-ference. This may be significantly smaller than the tolerable path length differencefor a 10 Gb/s signal, but it is still sufficiently large that on-chip tunable delay lineswill not be necessary.-0.8 -0.6 -0.4 -0.2 0 0.2 0.4Wavelength offset from resonance (nm)050100150200250300350400Group delay (ps)-0.8 -0.7 -0.6 -0.5 -0.4 -0.300. 3.18: Through-port group delay vs. wavelength for a single ring filter.39For DWDM application, each add-drop ring filter may add a group delay tothe propagating signal, which could potentially worsen the TE-TM delay for thereceiver. For example, the add-drop filters used in this work can theoretically addup to 390ps of group delay close to resonance, as shown in Fig. 3.18. However, thegroup delay is significantly reduced to only 0.4ps at 0.4nm offset from resonance,and it gets smaller with increasing offset from resonance. Assuming a total of25 DWDM channels with 0.4nm spacing, which can be accommodated for ringfilters with a free spectral range (FSR) of 10nm, a signal can accumulate up to1.4ps of additional group delay as it passes through the 24 other channel filters,before arriving at the target channel filter. This value is small in comparison tothe aforementioned 32ps tolerance for TE-TM delay. Therefore, the group delayfrom each ring filter will not pose a major problem to the receiver performance ina DWDM link.3.4 SummaryThe operation of a 4-channel WDM polarization insensitive receiver based on mi-croring resonator filters and a looped PSR is demonstrated at 10Gb/s per channel.Large signal measurements at TE, TM, and 45◦ polarization states show that eachchannel can tolerate up to 32ps delay between the TE and TM signals before theBER degrades at an arbitrary polarization. This indicates the receiver’s robustnessagainst on-chip variations. Furthermore, the large signal measurements at reducedchannel spacings indicate the inter-channel crosstalk is negligible down to 0.4nmspacing, thus demonstrating its compatibility for DWDM operation.40Chapter 4Conclusions and Future Work4.1 Summary and ConclusionsThis thesis presented the application of ring resonators for optical modulation anddetection.First, two types of DAC-less PAM4 ring modulators are compared: (1) a singlering resonator with segmented PN junctions, and (2) a dual cascaded ring resonator.Using a ring resonator with a quality factor of 5200 for both designs, the two mod-ulators are simulated in frequency domain and time domain. Due to the higherinsertion loss and erratic dynamic overshoots during bit transitions, the dual cas-caded ring modulator is shown to perform worse than the single segmented ringmodulator despite driving a twice as long PN junction load. Considering the factthat using two ring resonators instead of one requires more stabilization control inpractice, which adds to the overall power consumption and complexity of the de-vice, the single segmented ring resonator is determined to be the superior candidatefor DAC-less PAM4 modulation.Then, a ring resonator based polarization diversity receiver is designed byforming a waveguide loop between the two output ports of a polarization splitter-rotator. This 4 channel device is demonstrated at 10 Gb/s for each channel. Themeasured BER results are virtually indistinguishable between TE, TM, and 45◦input polarization states after calibrating for the polarization dependent power lossin the edge couplers. The BER results also imply that the receiver can tolerate a41delay of up to 32 ps between the TE portion and the TM portion of the modulatedsignal from a 10 GHz LiNbO3 modulator. This indicates the receiver’s robustnessagainst on-chip variations of the fabricated device, which also implies that on-chip delay lines are not required for practical deployment. Furthermore, negligibleinter-channel crosstalk at 50 GHz channel spacing is observed, demonstrating thereceiver’s compatibility for DWDM application.4.2 Future WorkThe current method of comparison between the DAC-less PAM4 ring modulatorsis limited in scope, as it assumes identical ring resonators to be used and assumeslaser to be biased to the lower wavelength side of ring resonances. For the dualcascaded ring modulator in particular, different methods of design and modula-tion may need to be explored, by cascading rings of different quality factors andcoupling regimes, for example. More importantly, the comparison study is onlyconducted theoretically. Therefore, it needs to be followed up with an experimen-tal demonstration to validate the results. Finally, it is currently assumed that the PNjunctions adjacent to each other in the single segmented ring resonator introducenegligible crosstalk to each other. However, this needs to be verified experimen-tally, and its impact on the integrity of the modulated signal needs to be assessedas well.The polarization diversity WDM receiver shows promise for practical appli-cations, but it is currently demonstrated only at 10 Gb/s, which is much slowerthan the current generation of transceivers in the industry. To prove the receiver’scompatibility for the current and next generation of optical transceiver products,the receiver needs to be demonstrated for up to 50 Gb/s data transmission. 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