Advanced Silicon Photonic Device Architectures for Optical Communications: Proposals and Demonstrations by Wesley David Sacher A

Advanced Silicon Photonic Device Architectures for Optical Communications: Proposals and Demonstrations

Wesley David Sacher

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto

Advanced Silicon Photonic Device Architectures for Optical Communications: Proposals and Demonstrations

Wesley David Sacher Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2015

Photonic integrated circuits implemented on silicon (Si) hold the potential for densely integrated electro-optic and passive devices manufactured by the high-volume fabrication and sophisticated assembly processes used for complementary metal-oxide-semiconductor (CMOS) electronics. However, high index contrast Si photonics has a number of func-

tional limitations. In this thesis, several devices are proposed, designed, and experimentally demonstrated to overcome challenges in the areas of resonant modulation, waveguide loss, ﬁber-to-chip coupling, and polarization control. The devices were fabricated using foundry services at IBM and A*STAR Institute of Microelectronics (IME). First, we describe coupling modulated microrings, in which the coupler between a

microring and the bus waveguide is modulated. The device circumvents the modulation bandwidth vs. resonator linewidth trade-oﬀ of conventional intracavity modulated microrings. We demonstrate a Si coupling-modulated microring with a small-signal modulation response free of the parasitic resonator linewidth limitations at frequencies up to

about 6× the linewidth. Comparisons of eye diagrams show that coupling modulation achieved data rates > 2× the rate attainable with intracavity modulation.

Second, we demonstrate a silicon nitride (Si3N4)-on-Si photonic platform with independent Si3N4 and Si waveguides and taper transitions to couple light between the layers. The platform combines the excellent passive waveguide properties of Si3N4 and the compatibility of Si waveguides with electro-optic devices. Within the platform, we propose and demonstrate dual-level, Si3N4-on-Si, ﬁber-to-chip grating couplers that si-

ii multaneously have wide bandwidths and high coupling eﬃciencies. Conventional Si and

Si3N4 grating couplers suffer from a trade-off between bandwidth and coupling efficiency. The dual-level grating coupler achieved a peak coupling efficiency of -1.3 dB and a 1-dB bandwidth of 80 nm, a record for the coupling efficiency-bandwidth product.

Finally, we describe polarization rotator-splitters and controllers based on mode conversion between the fundamental transverse magnetic polarized mode and a high order transverse electric polarized mode in vertically asymmetric waveguides. We demonstrate the ﬁrst polarization rotator-splitters and controllers that are fully compatible with standard active Si photonic platforms and extend the concept to our Si3N4-on-Si photonic platform.

iii Acknowledgements

I thank my supervisor, Prof. Joyce Poon, for her ongoing support and mentorship over the past six years, and for making my studies at the University of Toronto possible. The technical advice and training she provided have formed the basis of my graduate research and knowledge of integrated optics. Also, none of the experiments in this thesis would have been possible without her hard work and dedication to arranging collaborations and tapeouts and gathering the support and equipment necessary for our measurements. I also thank my mentors at IBM, Dr. William Green, Dr. Tymon Barwicz, and Dr. Yurii Vlasov for guiding me through my ﬁrst tapeouts and helping me develop photonic design and measurement skills. Our microring modulator demonstration was only possible because of Dr. William Green’s support and technical expertise. I credit our work on polarization management devices to many hours of training and technical advice from Dr. Tymon Barwicz. I thank Dr. Ying Huang and Dr. Patrick Guo-Qiang

Lo at IME A*STAR for their academic contributions, technical expertise, and patience throughout our tapeouts at IME. I thank Prof. Ted Sargent and Prof. J. Stewart Aitchison for being part of my thesis and candidacy committees. I thank Prof. Bruce Francis for being part of my thesis committee, discussions about block diagrams, and a great course on signals and systems. I thank Prof. Rajeev Ram and Prof. Sean Hum for being part of my thesis committee. I’m thankful for over ten years of friendship and technical discussions with Pete Scourboutakos. Also, I’m grateful for design and layout help from Jared Mikkelsen, Hasitha Jayatilleka, Alex Mackay, Jason Mak, and Zheng Yong, and measurement and design help from Benjamin Taylor, Junho Jeong, Torrey Thiessen, and Chaoxuan Ma. I’d also like to thank the Natural Sciences and Engineering Research Council (NSERC) for ﬁnancial support during my graduate studies. Above all, I thank my parents and brother for their constant encouragement and support.

iv Contents

Abstract ii

Acknowledgements iv

List of Figures viii

List of Symbols and Abbreviations xviii

1 Introduction 1 1.1 Silicon passive waveguide characteristics ...... 3 1.2Fiber-to-chipcoupling...... 7 1.3Microringmodulators...... 10 1.4Thesiscontributionsandorganization...... 12

2 Coupling modulated microrings 14 2.1Fabricateddevices...... 16 2.2Small-signalmodulationmeasurements...... 18 2.3PRBSmodulationandeyediagrammeasurements...... 21 2.4Overcominglowfrequencydistortionsincouplingmodulation...... 25 2.5Analysisofthemodulationeﬃciency...... 27 2.6Summary...... 31

3 Silicon polarization rotator-splitters 32 3.1Bi-leveltaperpolarizationrotator-splitter...... 33 3.1.1 Detailedpolarizationrotator-splitterdesignandoperation.... 35 3.1.2 Polarizationrotator-splittermeasurements...... 36 3.2Polarizationsplitter-rotatorwithimprovedcrosstalk...... 40 3.3Polarizationcontroller...... 42 3.4Summary...... 46

v 4 Silicon nitride on silicon photonic platform 47

4.1 Si3N4-on-SifabricationatIME...... 49 4.2Waveguideandtransitioncharacteristics...... 52 4.2.1 Propagation losses ...... 52 4.2.2 Interlayertransitions...... 53 4.2.3 Waveguidecrossings...... 57 4.3Summary...... 59

5 Silicon nitride on silicon grating coupler 60 5.1Devicedesign...... 62 5.2Experimentalresults...... 67 5.3 Integration example: 1 × 4tunablemultiplexer/demultiplexer...... 70 5.4Summary...... 74

6 Silicon nitride on silicon polarization rotator-splitters 75 6.1Polarizationrotator-splitterdesign...... 76 6.2Experimentalresults...... 78 6.3Polarizationcontroller...... 80 6.4Summary...... 84

7Conclusion 85 7.1Futurework:microringmodulators...... 86 7.2Futurework:polarizationrotator-splitters...... 88 7.3 Future work: silicon nitride on silicon photonic platform ...... 89

A Analysis of microring resonator modulators 91 A.1Time-dependentmicroringtransmission...... 92 A.2Intracavitylossmodulation...... 95 A.2.1Small-signalapproximation...... 96 A.2.2Numericalresults...... 98 A.3Intracavityindexmodulation...... 100 A.3.1Small-signalapproximation...... 100 A.3.2Numericalresults...... 102 A.4Couplingmodulation...... 103 A.4.1Small-signalapproximation...... 103 A.4.2Numericalresults...... 105 A.5Discussion...... 107

vi A.6Summary...... 110

B Coupling modulation for binary phase-shift keying 111 B.1Principleofoperation...... 114 B.2Experimentaldemonstration...... 117 B.3Summary...... 121

Bibliography 123

vii List of Figures

1.1 Cross-section schematic of a typical Si photonic platform consisting of three Si etch depths, metallization, Si doping, Ge deposition, and Ge doping. Typical thicknesses and cross-sections of the passive Si waveguide, grating coupler, electro-optic modulator, and photodiode are shown. The waveguide layer thicknesses are labeled in green, the Si modulator doped regions are labeled in red, and the Ge photodiode doping is omitted for simplicity.Nottoscale...... 2

1.2 Characteristics of Si waveguides with SiO2 cladding. (a), (b) Computed major electric ﬁeld components of (a) the TE0 mode and (b) the TM0 mode for a 220 nm × 500 nm waveguide at a wavelength of 1550 nm. (c)

Computed neff of 220 nm thick waveguides versus waveguide width at a wavelength of 1550 nm; the waveguide is single-mode for widths less than about450nm...... 4 1.3 Our measurement of the waveguide loss of the TE0 mode in a 150 nm × 500nmwaveguidefabricatedatA*STARIME...... 5 1.4 (a) Computed birefringence of 220 nm and 150 nm thick waveguides versus waveguide width at a wavelength of 1550 nm. (b) Schematic of a polarization diversity scheme for coupling single-mode optical ﬁber (SMF) to a Si PIC. On-chip polarization splitters/combiners and rotators are used at the input and output and the separated polarization components are sent throughnominallyidenticalphotoniccircuits...... 6

viii 1.5 (a) Cross-section schematic of a typical Si grating coupler and a tilted and polished single-mode fiber. (b) Optical micrograph of Si grating couplers connected by a Si waveguide fabricated at A*STAR IME. (c) Our measurement of the coupling efficiency versus wavelength for a single grating coupler in the test structure in (b); the grating used the thicknesses in Fig. 1.1, the grating period was 630 nm with a 50% duty cycle, and the measurements were performed with a fiber array polished and tilted at ◦ 8 . (d) Previously published Si and Si3N4 grating coupler demonstrations (coupling efficiencies and 1-dB bandwidths) in the C-band. The numbers nexttothemarkersindicatethereferences...... 9 1.6 (a) Schematic of a typical microring modulator. (b) Optical micrograph of a microring modulator with a PN diode fabricated at A*STAR IME. (c) Our measurement of the transmission spectrum of the microring in (b) showing multiple resonances with no voltage applied to the PN diode. (d) Our measurement of the transmission spectrum of the microring showing the resonance wavelength shift with increasing reverse bias (negative) voltagesappliedtothePNdiode...... 11 2.1 Schematics of (a) an intracavity modulated microring and (b) a coupling modulated microring that uses a 2 × 2 MZI-coupler as marked by the box. Optical microscope images of the fabricated SOI (c) microring with the 2 × 2 MZI-coupler marked by the box and (d) the reference MZI. The reference MZI was nominally identical to the MZI-coupler in the microring. The microring and MZI were separated by 620 μmonthedie...... 15 2.2 Measured transmission spectra for (a) tuning the coupling coefficient at a fixed resonance and (b) tuning the resonance wavelength with a fixed coupling coefficient. Independent tuning of the coupling and resonance wavelengthusingthethermaltunerswasachieved...... 18

ix 2.3 (a) Electro-optic S21 measurements of the reference MZI, coupling modulation, and intracavity modulation. The RF cables, RF adapters, and bias tees have been de-embedded. (b) Optical small-signal modulation responses of coupling and intracavity modulation. Each curve is obtained

by normalizing the electro-optic S21 of the microring to the S21 of the reference MZI and referencing to the value at 100 MHz. The microring was biased near critical coupling, with a cavity linewidth Δν ≈ 6GHz.The intracavity modulation response for a ∼ 1.3 GHz detuning from resonance (blue) has a 3 dB bandwidth of 4.4 GHz, similar to the linewidth. A ∼ 5 GHz detuning produces a resonant sideband peak near the value of the detuning (red), and the 3 dB bandwidth is extended to ∼ 13 GHz. The coupling modulation response (black) does not roll-oﬀ to 40 GHz (more than 6× thelinewidth)...... 19 2.4 Eye diagrams of coupling (top) and intracavity (bottom) modulation at 6-28 Gb/s for bias points near critical coupling (Δν ≈ 6 − 7GHz).The coupling modulation eye is open at 28 Gb/s, but the intracavity modulation eye closes at bit rates greater than roughly 2× thelinewidth..... 22 2.5 (a) Intracavity modulation eye diagrams of an over-coupled microring (Δν ≈ 9 GHz). The eye opening is larger than in Fig. 2.4, conﬁrming that the intracavity modulation bandwidth depends on the cavity linewidth. (b) Eye diagrams of the pre-emphasized electrical drive signals at 28 Gb/s (left) and the resultant optical output of the reference MZI (right). No remnantsofthepre-emphasisarepresentintheopticaloutput...... 24 2.6 Computed eye diagrams at several bit rates for (top) intracavity modulation and (center) coupling modulation driven by an uncoded NRZ signal, and (bottom) coupling modulation driven by a NRZ 8b/10b encoded signal. The calculations assume a group index of 4.3, a NRZ PRBS 217 − 1 data signal, Δν = 5 GHz, a round-trip length of 250 μm, a resonant input for coupling modulation, and critical coupling for intracavity modulation. With DC-balanced encoding, coupling modulation can achieve a 0-90% swing at 100 Gb/s. In contrast to intracavity modulation, the DC- balanced encoded coupling modulation eye diagram becomes more open athighbitrates...... 26

x 2.7 The coupling modulation eﬃciency, ηc, versus microring waveguide loss and cavity linewidth computed for several round-trip lengths, L.The calculations assume a 8b/10b encoded drive signal, a 0-90% output swing, a group index of 4.3, a NRZ PRBS 217−1 data signal, a resonant input, and

critical coupling. The intracavity efficiency, ηi,ofa5μm radius microring with the same output swing at 40 Gb/s and 100 Gb/s, using linewidths of 20 GHz and 50 GHz respectively, are marked for comparison. Critical coupling is assumed. Coupling modulation becomes increasingly efficient over intracavity modulation as the Q factorandbitrateincrease..... 29 3.1 (a) Schematic of the polarization rotator-splitter (PRS). Widths are labeled in red and purple; lengths use green labels. (b) Schematic showing the profiles of the modes with the first and second highest effective indices (i.e., “mode 1” and “mode 2”) at different points along the PRS. In the adiabatic coupler, “mode 1” and “mode 2” refer to supermodes

of the composite waveguide. (c) Eﬀective indices (neff ) along the ﬁrst half of the bi-level taper for modes 1 to 3 at a wavelength of 1550 nm.

(d) Electric field components (Ex and Ey) of modes 2 and 3 at 1550 nm in the hybridized region of (c) when the Si rib width is 486 nm and the partially-etchedSifinwidthis180nm...... 34 3.2 (a) An optical micrograph of the polarization rotator-splitter fabricated in the IME baseline process. Magnified optical micrographs are shown for (b),thebi-leveltaper,and(c),theendoftheadiabaticcoupler...... 36 3.3 Schematic of the experimental apparatus used for measurements of the polarizationrotator-splitter...... 37 3.4 Measurement data for the PRS in Fig. 3.2. (a) Transmission spectra of the PRS TE branch (top) output. (b) Transmission spectra of the PRS TM branch (bottom) output. (c) Magnified TE component of the TE branch transmission for a TE input. (d) Magnified TE component of the TM branch transmission for a TM input. The legends in (a) and (b) indicate the settings of the input and output polarizers (i.e., TE→TM means we had a TE input and measured the TM component of the output). (c) and (d) represent the PRS insertion loss, and the red curves have been post-processed to remove Fabry-Perot oscillations from the edge coupler facetsandthemeasurementapparatus...... 38 3.5 Annotated optical micrograph of the polarization splitter-rotator (PSR) withimprovedcrosstalk...... 40

xi 3.6 Measurement data for the PSR in Fig. 3.5. (a) Transmission spectra of the PSR TE branch (top) output. (b) Transmission spectra of the PSR TM branch (bottom) output. (c) Magniﬁed TE component of the TE branch transmission for a TE input. (d) Magniﬁed TE component of the TM branch transmission for a TM input. The legends in (a) and (b) indicate the settings of the input and output polarizers (i.e., TE→TM means we had a TE input and measured the TM component of the output). The red curves in (c) and (d) have been post-processed to remove Fabry-Perot oscillations from the chip facets and the measurement setup...... 41 3.7 (a) Schematic of the polarization controller. “3-dB DC” is a 3 dB directional coupler. (b) Optical micrograph of the polarizaton controller fabricatedintheIME-OpSISprocess...... 43 3.8 Polarization controller measurement data. (a) Current-voltage characteristics of the top-left thermal tuner and PIN diode. (b) Normalized output power as the output polarizer was rotated. With a TE-polarized input, bias conditions were chosen to obtain a TM-polarized output (black curve), a-45◦ linearly-polarized output (blue curve), and a circularly-polarized output (red curve). (c) Normalized output power as the top-left thermal tuner power was swept. (d) Normalized output power as the top-left PIN diode current was swept. In (c) and (d), the output polarizer was set to pass either TE or TM or removed from the optical path (“Total out”). The optical output power curves were normalized to the maximum value in each plot. The magenta labels and dashed lines indicate points where a TM or TE output was generated from the TE input (marked “TE→TM” and “TE→TE”,respectively)...... 45

4.1 Schematic of the fabrication ﬂow for the Si3N4-on-Si photonic platform showing the integration of thermal heaters. The process consists of a series of deposition, planarizing, and patterning steps. Ge epitaxial growth and ion implantation steps can be incorporated for the formation of pho- todiodesandPNjunctions...... 50 4.2 Cross-section schematic showing the layer thicknesses and waveguide ge-

ometries in the Si3N4-on-Si photonic platform. The heaters and contact metalsareomittedinthisschematic...... 51

xii 4.3 Measurements of the propagation losses of the Si3N4 and Si strip waveguides over (a) the SCL-bands (near λ = 1550 nm) and (b) the O-band

(near λ = 1310 nm). The Si3N4 waveguides had a height of 400 nm and a width of 900 nm, and the Si waveguides had a height of 150 nm and a widthof500nm...... 53 4.4 Schematic of the interlayer transition. The computed TE0 mode at various waveguide cross-sections along the transition are shown to illustrate the mode evolution. Scanning electron micrographs (SEMs) of the waveguide

tips in the Si3N4 and Si layers during fabrication are shown, and the nom-

inal widths of these tips were 200 nm and 180 nm, respectively. Lc is the

length of the interlayer transition; wSi,tip and wSi3N4,tip are the widths of

the Si and Si3N4 waveguide tips, respectively. wSi,wg and wSi3N4,wg are the

standard routing waveguide widths (wSi,wg = 500 nm and wSi3N4,wg = 900 nm)...... 54 4.5 (a) The computed transmission of the interlayer transition as a function

of Lc for λ = 1550 nm. (b) Examples of the measured raw transmission data of cutback structures as a function of the number of interlayer transitions at wavelengths of 1550 nm and 1310 nm. Linear ﬁtting yields the transmission per transition. (c), (d) Spectra of the loss per transition in (c) the SCL-bands and (d) the O-band extracted from linear ﬁts of the transmissionspectravs.numberoftransitions...... 56

4.6 (a) Top-down view schematic of the Si3N4 waveguide crossing. The crossing is designed for TE-polarized light in the C-band. (b) 3D-FDTD simulated profile of the optical power at λ = 1550 nm passing through the crossing. The TE0 input is injected at y =0μm. (c) Optical micrograph of the waveguide crossing. (d) Measured raw fiber-to-fiber transmission of the crossing cutback structures at λ = 1550 nm. (e) Transmission spectrum of a single crossing extracted from the cutback structures. (f) Measured raw through (thru) and crosstalk transmission spectra showing < -48dBofcrosstalkovera120nmbandwidth...... 58

5.1 Comparison of our Si3N4-on-Si dual-level grating coupler experimental re-

sult with previously published Si and Si3N4 grating coupler demonstrations in the C-band (coupling eﬃciencies and 1-dB bandwidths). The numbers nexttothemarkersarethereferences...... 61

xiii 5.2 (a) Perspective schematic of the Si3N4-on-Si dual-level grating coupler.

(b) Schematic of the waveguide cross-sections in the Si3N4-on-Si integrated photonics platform. (c) Cross-section schematic of the grating coupler and an input/output optical ﬁber. The following parameters of each grating

period are listed: Si3N4 grating tooth width (wSi3N4), Si grating tooth

width (wSi), gap between Si3N4 teeth (g), and the oﬀset between Si3N4 and Si teeth (L)...... 63 5.3 (a) Simulated coupling eﬃciency versus wavelength for the apodized and uniform grating couplers. (b) Simulated directionality (D) versus varia-

tions in the oﬀsets between the Si3N4 and Si teeth from their apodized values (ΔL). ΔL = 0 nm corresponds to the optimized grating in Fig. 5.2(c)...... 64 5.4 Simulated coupling eﬃciency versus wavelength with ±50 nm variations

in the oﬀsets between the Si3N4 and Si grating teeth from their apodized values (ΔL)...... 66

5.5 (a) Optical micrograph of the fabricated Si3N4-on-Si dual-level grating coupler. (b) Scanning electron microscope (SEM) image of the Si grating teeth during fabrication (i.e., after Si etching but before deposition of the

SiO2 spacer layer between the Si and Si3N4). (c) SEM image of the Si3N4

grating teeth during fabrication (i.e., after Si3N4 etching but before the

SiO2 topcladdingdeposition)...... 68

5.6 Annotated optical micrograph of the Si3N4-on-Si grating coupler test structure. Two nominally identical grating couplers are connected by a single-

mode Si3N4 waveguide...... 68 5.7 Measured and simulated coupling eﬃciency versus wavelength for the

Si3N4-on-Sidual-levelgratingcouplerinFig.5.5...... 69 5.8 (a) Optical micrograph of the 1 × 4 tunable multiplexer/demultiplexer.

“GC” refers to a Si3N4-on-Si dual-level grating coupler, and “Ring” refers to a Si add-drop microring with thermal tuning via a TiN heater. (b) Schematic of a Si microring resonator in the multiplexer/demultiplexer without the TiN and contact metals. The microring is connected to Si bus waveguidesandthedropportisconnectedtoagratingcoupler...... 71

xiv 5.9 Fiber-to-ﬁber transmission measurements for the 1 × 4 tunable multiplexer/demultiplexer in Fig. 5.8. (a) Thru port spectra before and after

thermal tuning (i.e., transmission from GCin to GCthru). (b) Drop port

spectra of Rings 1 to 4 after thermal tuning (i.e., transmission from GCin

to GC1 -GC4). “GC” refers to a grating coupler and “Ring” refers to a Simicroring;thenomenclatureisdeﬁnedinFig.5.8(a)...... 73

6.1 (a) Schematic of the Si3N4-on-Si PRS. Lengths are labeled in green; widths

are labeled in red for the Si layer and in purple for the Si3N4 layer. (b) Mode profiles of the modes with the first and second highest effective indices (i.e., “mode 1” and “mode 2”) along the PRS. (c) Modal effective

indices (neff ) in the TM0-TE1 mode converter showing hybridization of the TM0 and TE1 modes; the Si3N4 width is ﬁxed at 1.4 μmandtheSi width is increased. The calculations in (b) and (c) were performed at a wavelength of 1550 nm...... 77

6.2 Optical micrographs of the Si3N4-on-Si PRS. (a) The whole PRS. (b) The

point where the Si3N4 terminates before the adiabatic coupler; a Si3N4-Si composite waveguide is on the left of the termination and a Si waveguide isontheright...... 78 6.3 PRS transmission spectra measurements at (a) the TE branch output (i.e., the top output in Fig. 6.1(a)) and (b) the TM branch output (i.e., the bottom output in Fig. 6.1(a)). The legends in (a) and (b) indicate the input and output polarizer settings (e.g., TE→TM refers to a TE-polarized input and a measurement of the TM-component of the output)...... 79 6.4 (a) Schematic of the polarization controller. “Δφ” refers to a thermal phase-shifter (i.e., heater) and “3-dB MMI” is a 3-dB multimode interference coupler. (b) Optical micrograph of the polarization controller. . . . 81 6.5 Polarization controller output polarization state measurements on the Poincaré sphere for (a) a TE-polarized input and (b) a 45◦ linearly polarized input. In (a), different electrical powers were dissipated in Heater 2, and for each Heater 2 power, a sweep of the Heater 3 power was performed. Similarly, in (b), the Heater 2 power was swept at different Heater 1 power settings.

The heater numbering is deﬁned in Fig. 6.4(b), and Px refers to the power dissipated in Heater x...... 82 A.1Schematicofaringresonatormodulator...... 92

xv A.2 Modulation depths of a microring resonator with sinusoidal loss modulation between 2 dB/cm and 5 dB/cm. a0 =0.9975, a =0.0011, and σ =0.9928. (a): The input is on resonance. (b): Detuned input, with the

modulation resonance frequency at fm...... 99 A.3 Modulation depths of a microring resonator with a sinusoidal index modulation. φ0 =0.039477 and φ =0.005. The input is detuned from resonance,withthemodulationresonancefrequencyat10GHz...... 102 A.4 Modulation depths of a microring resonator with a sinusoidal modulation of the coupling strength. Over-coupled: σ =0.0013 and σ0 =0.9902. −4 Under-coupled: σ =3.5 × 10 and σ0 =0.999. The loss of the ring is 4dB/cm,a =0.9971. (a): The input is on resonance. (b): The input is detuned from resonance, with the modulation resonance frequency at 5 GHz...... 106 A.5 Device parameters (top) and the corresponding output intensities (bottom) versus time for single-pulse modulated microring resonators. (a), (d): Loss modulation, σ =0.9928, and the input is resonant. (b), (e):

Index modulation, φ0 =0.039477, σ =0.9928, and a loss of 4 dB/cm. (c), (f): Coupling modulation, the loss is 4 dB/cm, and the input is resonant. 109 B.1 Illustrations of BPSK modulation using (a) a phase modulator, (b) a MZI modulator, (c) an intracavity-modulated microring, and (d) a coupling- modulated microring. The illustrations show the similarities between MZI modulators and coupling-modulated microrings, as well as the similarities between phase modulators and intracavity-modulated microrings. Con- stellation diagrams and output intensity (|T |2) and phase (∠T )versus applied phase-shift (Δθ) are shown. For the intracavity-modulated microring, the input wavelength is on resonance for Δθ = 0; modulating Δθ shifts the resonance wavelength. For the coupling-modulated microring, the input wavelength is on resonance, and the drop port coupler is modulated; the ‘1’ and ‘0’ symbols correspond to the two critical coupling conditions...... 113

xvi B.2 Schematic of a coupling-modulated microring for BPSK. The microring is in an add-drop configuration with MZI-couplers at the through and drop sides. Either MZI-coupler can be modulated through its zero transmission point to achieve BPSK. Here, only the MZI-coupler at the drop side is modulated, and the MZI-coupler on the through side acts as a tunable coupler. This configuration matches the experimentally demonstrated device...... 114 B.3 (a) Optical micrograph of the fabricated device. The thermal tuners are 50 μm long, and the PN diode phase-shifters are 200 μm long. PN diode phase-shifters are only present in the MZI-coupler at the drop side. (b) Measured transmission spectra at the through (thru) and drop ports. The thermal tuners were set for critical coupling with a drop port transmission of 30% on-resonance relative to the off-resonance through port transmission.118 B.4 Measured eye diagrams of the DPSK microring modulator at 5 and 10 Gb/s before and after the fiber delay line interferometer demodulator. The open eye diagrams with large extinction ratios confirm DPSK operation. The drive signals were NRZ PRBS 231 − 1. The vertical scales differ between the 5 and 10 Gb/s eye diagrams and between the DPSK modulated and demodulated eye diagrams; accurate amplitude comparisons between the eye diagrams are difficult due to the different fiber paths and lossesforeachsetofmeasurements...... 119

xvii List of Symbols and Abbreviations

SOI Silicon-on-insulator

TE Transverse-electric

TM Transverse-magnetic

TE0 Fundamental transverse-electric mode

TM0 Fundamental transverse-magnetic mode

TE1 First-order transverse-electric mode

PRS Polarization rotator-splitter

PIC Photonic integrated circuit

neff Modal eﬀective index D Directionality

L Oﬀset between Si and Si3N4 grating teeth

FSR Free spectral range

FWHM Full-width half-maximum

Δν Resonator full-width half-maximum linewidth

Q Resonator quality factor

F Resonator ﬁnesse

DCA Digital communications analyzer

VNA Vector network analyzer

PRBS Pseudo-random bit sequence

NRZ Non-return-to-zero

xviii Chapter 1

Introduction

Photonic integrated circuits (PICs) fabricated on silicon (Si) substrates for data transmission have been the focus of extensive research over the past decade. The transparency of Si at the optical communication wavelength bands near 1310 nm (O-band) and 1550 nm (C-band) has led to potential applications in long-haul telecommunications [1,2], short- reach data communications [3,4], and inter/intra-chip optical interconnects [5,6]. One of the distinct advantages of Si PICs over other material systems (e.g., III-V semiconductor

PICs and silica planar lightwave circuits) is the compatibility with mature complemetary metal-oxide-semiconductor (CMOS) fabrication processes and sophisticated packaging processes typically used for electronic integrated circuits, which enables high-volume and high-yield manufacturing.

Similar to integrated circuit foundries in the electronics industry, Si photonic foundries have emerged for wafer-scale prototyping and manufacturing of Si PICs [7–9]. Generally, these Si photonic foundries use cross-sections similar to that in Fig. 1.1. Optical devices are fabricated on a 8 or 12 diameter silicon-on-insulator (SOI) wafer with a typically

150-500 nm thick monocrystalline Si layer atop a typically 1-3 μm thick buried oxide (BOX) layer on a Si substrate. Multiple Si etch steps, Si doping, metallization, germanium (Ge) deposition, and Ge doping steps enable the integration of passive devices, Si electro-optic modulators, and Ge photodiodes. Though this approach does not directly

1 Chapter 1. Introduction 2

SiO2

Metal layer 2

Via

Waveguide Metal layer 1 150nm Via P N 90nm Ge Si P++ N++ 500nm 220nm Grating coupler Si modulator 2μm BOX Ge photodetector Si substrate

Figure 1.1: Cross-section schematic of a typical Si photonic platform consisting of three Si etch depths, metallization, Si doping, Ge deposition, and Ge doping. Typical thicknesses and cross-sections of the passive Si waveguide, grating coupler, electro-optic modulator, and photodiode are shown. The waveguide layer thicknesses are labeled in green, the Si modulator doped regions are labeled in red, and the Ge photodiode doping is omitted for simplicity. Not to scale.

enable integration with lasers, packaging with laser dies [10, 11] and bonding of III-V semiconductor dies onto the Si wafers [12,13] have been used for laser integration. Thus, together with laser packaging or bonding techniques, Si PICs fabricated by foundries, in

principle, integrate all the functionalities required for optical communications. In addition to CMOS compatibility, Si PICs support ultra-compact and densely-

integrated optical devices. The high refractive index contrast of Si waveguides (nSi ≈

3.48) with SiO2 cladding (nSiO2 ≈ 1.45) allows high optical conﬁnement in sub-micron waveguides as shown in Figs. 1.2(a) and 1.2(b), which enables compact optical devices with waveguide bend radii less than 5 μm [14]. In contrast, typical III-V semiconductor PICs and silica planar lightwave circuits require radii greater than 200 μm for low-loss waveguide bends [15,16].

With the availability of mature fabrication processes and the capability for densely- packed devices, large-scale, complex PICs, such as optical interconnect networks, multi- wavelength transceivers, and optical switching networks should be ideal for foundry- Chapter 1. Introduction 3 fabricated Si photonic platforms. However, the high refractive index contrast leads to unique challenges that can limit the implementations of complex PICs. Some of these problems include waveguide losses, dimensional sensitivity, coupling to standard single mode fiber, birefringence, polarization crosstalk, power handling, low-loss and low crosstalk crossings, and electrical power consumption [17–26]. In this thesis, we propose and demonstrate several foundry-fabricated photonic devices and PICs in Si photonic platforms that offer solutions to the challenges of: 1. Improved waveguide losses and polarization dependence in Si PICs. 2. Broadband and efficient out-of-plane fiber-to-chip coupling.

3. High-speed modulation of resonators scalable to ultra-high-Q devices. In the following sections, we brieﬂy describe these above issues and the state-of-the-art approaches in overcoming the challenges prior to the contributions of this thesis.

1.1 Silicon passive waveguide characteristics

The high refractive index contrast of Si waveguides comes with the disadvantages of sig- niﬁcant waveguide loss and sensitivity of the modal eﬀective indices (neff ) to nanometer variations in waveguide dimensions. First, the high index contrast causes large overlaps of the waveguide modes with the roughness on the etched sidewalls and the top polished surface as shown in Figs. 1.2(a) - 1.2(b), which leads to high scattering losses [27]. Typ- ical waveguide losses in the C and O-bands for 150-220 nm thick, single-mode, Si strip waveguides produced by foundries are between 2 - 4 dB/cm [8,18,28], and in Fig. 1.3, we measured waveguide losses of about 3 dB/cm in the C-band for the TE0 mode of a 150 nm thick, single-mode, Si strip waveguide fabricated at the Institute of Microelectronics

(A*STAR IME) Si photonics foundry in Singapore. In comparison, silica planar lightwave circuits can have waveguide losses as low as 0.3 dB/m [15]. In addition, as shown in Fig.

1.2(c), the high index contrast causes sensitivity of neff of the fundamental transverse Chapter 1. Introduction 4

(a) (b)

3 TE0 )

eff Single−mode TM0 2.5

Multi−mode 2 Effective index (n

1.5 300 400 500 600 Waveguide width (nm) (c)

Figure 1.2: Characteristics of Si waveguides with SiO2 cladding. (a), (b) Computed major electric ﬁeld components of (a) the TE0 mode and (b) the TM0 mode for a 220 nm × 500 nm waveguide at a wavelength of 1550 nm. (c) Computed neff of 220 nm thick waveguides versus waveguide width at a wavelength of 1550 nm; the waveguide is single-mode for widths less than about 450 nm.

electric (TE0) waveguide mode and the fundamental transverse magnetic (TM0) mode to nanometer variations in the waveguide dimensions. This leads to large wafer-scale and wafer-to-wafer variation of Si passive device performance such as the center wavelengths of ﬁlters. One approach to reducing the waveguide losses and the sensitivity to waveguide dimension variations is the integration of waveguides with lower refractive index contrasts.

Silicon nitride (Si3N4) is a CMOS compatible dielectric with a signiﬁcantly lower refractive index than Si (nSi3N4 ≈ 2.0 in the C and O-bands), and waveguide losses as low as

0.1 dB/m have been demonstrated in the C-band [29]. Also, Si3N4 arrayed waveguide Chapter 1. Introduction 5

−1

−2

−3

Waveguide loss (dB/cm) −4

1480 1510 1540 1570 1600 Wavelength (nm)

Figure 1.3: Our measurement of the waveguide loss of the TE0 mode in a 150 nm × 500 nm waveguide fabricated at A*STAR IME.

grating (AWG) ﬁlters with reduced sensitivity to dimensional variations compared to

Si have been demonstrated [30, 31]. Integrating Si3N4 into Si photonic platforms is an active area of research, and this is discussed further in Chapter 4 where we describe our demonstration of a Si3N4-on-Si photonic platform. The high refractive index contrast of Si waveguides also comes with the disadvantage of polarization sensitivity. This is evident from the birefringence calculation in

Fig. 1.4(a), which is the effective index difference between the TE0 and TM0 modes, as a function of waveguide width for 220 nm and 150 nm tall strip waveguides. For single-mode waveguides (i.e., supporting only the TE0 and TM0 modes), the birefringence is large and sensitive to small fluctuations in the waveguide width, which makes

the design and fabrication of polarization-independent optical devices diﬃcult. Though square waveguides have zero birefringence, the polarization sensitivity is not alleviated since the birefringence changes signiﬁcantly with nanometer variations in the waveguide dimensions [20], which is already beyond the precision of current waveguide fabrication

processes. Achieving polarization independence in PICs is important since the input polarization to the PIC from standard single-mode optical ﬁber ﬂuctuates in time. Polarization Chapter 1. Introduction 6 ) 0 0.8 eff,TM

−n 0.6

eff,TE0 0.4

220nm thick Si 0.2 150nm thick Si

300 400 500 600

Birefringence (n Waveguide width (nm) (a)

Chip Polarization TE0 Photonic TE0 rotator circuit Opticalinput TM0 Opticaloutput fromSMF Polarization Polarization toSMF TE+TM splitter combiner TE+TM TE0 Photonic Polarization TM0 circuit rotator

(b)

Figure 1.4: (a) Computed birefringence of 220 nm and 150 nm thick waveguides versus waveguide width at a wavelength of 1550 nm. (b) Schematic of a polarization diversity scheme for coupling single-mode optical fiber (SMF) to a Si PIC. On-chip polarization splitters/combiners and rotators are used at the input and output and the separated polarization components are sent through nominally identical photonic circuits. Chapter 1. Introduction 7 maintaining fiber could be used to control the input polarization, but this is not cost- effective in many applications. To overcome the polarization dependence of Si PICs, polarization diversity is typically employed as shown in Fig. 1.4(b) [20]. Polarization splitters/combiners and rotators are used to separate the TE0 and TM0 component of the optical input, the TM0 component is rotated into the TE0 mode, the two TE0 signals are passed through nominally identical photonic circuits, one of the TE0 signals is rotated into the TM0 mode, and finally, the polarization components are combined and output off the chip. The TE0 mode is preferred for Si PICs since it is more confined than the TM0 mode, and this is the reason for rotating the input TM0 light into the TE0 mode

and not vice-versa. The success of polarization diversity relies on the performance of the polarization splitters and rotators. Prior to the work in this thesis, polarization rotator-splitters had required extra fabrication steps [32–36] and were not compatible with standard Si photonic foundry platforms as shown in Fig. 1.1. Chapter 3 describes

our demonstration of the ﬁrst polarization-rotator splitter compatible with a standard Si photonic platform.

1.2 Fiber-to-chip coupling

Eﬃcient optical coupling between standard single-mode optical ﬁbers and sub-micrometer optical waveguides is critical for the operation of Si PICs, and the two most common

approaches are edge coupling and grating coupling. Edge couplers typically use spot-size converters [37] or cantilever coupler [38] at the edge of the die to couple light between Si waveguides and cleaved or lensed single-mode ﬁber. Grating couplers, as shown in Fig. 1.5(a), couple light between angle-polished single-mode ﬁber and Si waveguides through

the top of the die using a grating etched into the waveguide [17, 23, 39–41]. Compared to edge couplers, grating couplers can be deﬁned anywhere on the photonic die and do not require dicing and polishing steps prior to optical measurements, which enables Chapter 1. Introduction 8 wafer-scale testing [23]. Though grating couplers simplify measurements, circuit design, and facet preparation, edge couplers outperform grating couplers with state-of-the-art peak coupling eﬃciencies better than -1 dB and 1-dB bandwidths > 100 nm [38]. For comparison, as shown in

Figs. 1.5(b) and 1.5(c), our measurement of a Si grating coupler fabricated at A*STAR IME showed a peak coupling efficiency of -3.7 dB and a 1-dB bandwidth of 33 nm. Figure 1.5(d) shows a summary of published grating coupler results for Si PICs, and overall, the coupling efficiency and/or bandwidth are significantly lower than those of edge couplers. The highest coupling efficiencies in Fig. 1.5(d) are Si grating couplers with efficiencies

from -0.64 to -1.6 dB [42–51], which were achieved by apodizing the gratings to improve mode-matching to single-mode ﬁber and reducing the amount of light lost into the sub-

strate through optimizing the directionality, D (i.e., D = Pup/Pdown in Fig. 1.5(a)) and/or integrating back-reflectors. However, the 1-dB bandwidths of these Si grating couplers have been limited to about 24-48 nm. Reducing the refractive index contrast between the grating and its cladding can increase the bandwidth [52], but for published demonstrations, reduced index contrasts have resulted in a low directionalities and coupling efficiencies [40,53,54]. This is evident in Fig. 1.5(d) where, in [40], a Si3N4 grating coupler exhibited a wide 67 nm 1-dB bandwidth but a low -4.2 dB peak coupling efficiency, and in [54], a grating coupler with a low refractive index effective medium formed from ≈ 50 nm Si features exhibited a very wide 122 nm 1-dB bandwidth but only a -4.7 dB peak coupling efficiency. Overall, designing grating couplers with both high coupling efficiencies and wide band-

widths is a standing problem in Si photonics and is necessary for using grating-coupled Si PICs for wavelength-division multiplexed systems. This is discussed further in Chapter

5 with our proposal and demonstration of a dual-level Si3N4-on-Si grating coupler, which had a wide 80 nm 1-dB bandwidth and a high -1.3 dB peak coupling eﬃciency. Chapter 1. Introduction 9

ɽ Fibercore

TopSiO2 cladding P up Pin … Si BOX ToPIC

Sisubstrate Pdown

(a)

−3.7 dB −5 Δλ = 33 nm 1dB Grating 50μm couplers −10 Coupling efficiency (dB) 1500 1525 1550 1575 1600 Wavelength (nm) (b) (c)

) 0 Si N − only 47 51 3 4 49 −1 44 Si N + back reflector 42 43 3 4 50 48 Si − only 46 −2 45 Si + back reflector 53 41 Si − ≈ 50nm features −3

−4 40 54

−5

Peak coupling efficiency (dB 0 20 40 60 80 100 120 1−dB bandwidth (nm) (d)

Figure 1.5: (a) Cross-section schematic of a typical Si grating coupler and a tilted and polished single-mode fiber. (b) Optical micrograph of Si grating couplers connected by a Si waveguide fabricated at A*STAR IME. (c) Our measurement of the coupling efficiency versus wavelength for a single grating coupler in the test structure in (b); the grating used the thicknesses in Fig. 1.1, the grating period was 630 nm with a 50% duty cycle, and the measurements were performed with a fiber array polished and tilted at 8◦.(d) Previously published Si and Si3N4 grating coupler demonstrations (coupling efficiencies and 1-dB bandwidths) in the C-band. The numbers next to the markers indicate the references. Chapter 1. Introduction 10

1.3 Microring modulators

The high refractive index contrast makes possible microcavity devices such as microrings in Si photonic platforms. Microrings have emerged as a popular choice for modulators

and filters because the minimum feature sizes required for microrings are compatible with the resolution of many of today’s photonic foundry processes. Microring modulators have the potential to greatly reduce the power consumption and footprint of Si modulators compared to single-pass devices such as MZI modulators [55–61]. Si microring modulators with compact footprints < 500 μm2 and low electrical power consumption < 10 fJ/bit have been demonstrated [58]. A schematic of a typical Si microring modulator is shown in Fig. 1.6(a). A closed waveguide loop is coupled to a bus waveguide and a modulation section is integrated into the waveguide loop. A continuous-wave (CW) optical signal is the input, and the applied voltage to the modulation section modulates the optical output. The modulation section is often a PN diode defined near the center of the waveguide as shown in Fig. 1.1, and carrier injection or depletion modulates the refractive index and loss of the waveguide via the plasma dispersion effect [62]. The operation of a typical microring modulator can be understood from our measurements of a microring modulator fabricated at A*STAR IME shown in Figs. 1.6(b) - 1.6(d). The transmission spectrum of the microring contains many notches due to optical resonances (Fig. 1.6(c)), the input wavelength is aligned near one of the resonance wavelengths, and varying the applied voltage to the PN diode shifts the resonance back and forth across the input wavelength (Fig. 1.6(d)), which modulates the transmission of the microring. Generally, the modulation efficiency of microrings scale with the finesse, F , and therefore, low-loss and high quality factor, Q, microrings will have high modulation efficiencies. For the type of microring modulation in Fig. 1.6, which we refer to as intracavity modulation, the modulation bandwidth is limited by the resonator linewidth, i.e., the full-width at half-maximum (FWHM) width of the notches in Fig. 1.6(d) [63,64]. Since Chapter 1. Introduction 11

Optical Modulated input output

Coupling region

Modulation section 50μm (e.g., PN diode) (a) (b)

0 0

−5 −5

−10 −10

0 V −15 −15 −2 V

Normalized transmission (dB) −4 V Normalized transmission (dB)

1500 1520 1540 1560 1580 1556.6 1556.7 1556.8 1556.9 Wavelength (nm) Wavelength (nm) (c) (d)

Figure 1.6: (a) Schematic of a typical microring modulator. (b) Optical micrograph of a microring modulator with a PN diode fabricated at A*STAR IME. (c) Our measurement of the transmission spectrum of the microring in (b) showing multiple resonances with no voltage applied to the PN diode. (d) Our measurement of the transmission spectrum of the microring showing the resonance wavelength shift with increasing reverse bias (negative) voltages applied to the PN diode. Chapter 1. Introduction 12 the linewidth is inversely proportional to Q, intracavity modulation suffers from a tradeoff between the modulation efficiency and the modulation bandwidth. Resonator linewidths of Si microrings can be lower than 15 GHz [57,58], and the linewidth of the microring in Fig. 1.6(d) is about 5 GHz. The dynamics of microring resonators are discussed further in Chapter 2 with our proposal and demonstration of modulating the input/output coupler of the microring (i.e., coupling modulation) to circumvent the linewidth limit to the modulation bandwidth.

1.4 Thesis contributions and organization

In this thesis, devices and strategies are proposed and demonstrated to overcome the

limitations of Si photonics discussed above. Chapter 2 contains our proposal and demonstration of modulating the input/output coupler of a microring to circumvent the linewidth limitation to the modulation bandwidth of microrings. This work is the ﬁrst to identify and experimentally demonstrate this property of microring modulators [64–68]. Chapter 2 is supported by supplemen-

tary material in the appendices. Appendix A contains our mathematical analysis of microring modulators and clariﬁes the modulation bandwidth limitations of microrings. Appendix B contains our proposal and demonstration of binary phase-shift keying using coupling modulated microrings, which is the ﬁrst to show that coupling modulation can

be extended to advanced modulation formats. In Chapter 3, Si polarization rotator-splitters that rely on TM0-TE1 mode conversion in a bi-level taper are demonstrated for the ﬁrst time. This device eliminates the extra processing steps and high aspect ratio features required by previous Si polarization

splitting and rotating devices, and this work is the ﬁrst experimental demonstration of a polarization rotator-splitter compatible with standard active silicon photonic platforms as in Fig. 1.1 [69,70]. Chapter 1. Introduction 13

To overcome Si waveguide losses and waveguide dimension variation sensitivity, in

Chapter 4, a Si3N4-on-Si platform is demonstrated, which integrates independent Si3N4 and Si waveguides as well as taper transitions to couple light between the two types of

waveguides [71]. Chapters 5 and 6 describe novel devices that use both the Si3N4 and Si layers in our Si3N4-on-Si platform to achieve advanced functionality. Speciﬁcally, Chapter

5 contains our proposal and demonstration of a dual-level Si3N4-on-Si grating coupler that has a record coupling eﬃciency-bandwidth product [72], and Chapter 6 discusses our demonstration of a polarization rotator-splitter and a polarization controller that use

Si3N4-on-Si waveguides for TM0-TE1 mode conversion [73].

Taken together, this thesis shows that device and integration innovations remain necessary for the realization of complex, large-scale high index contrast photonic integrated circuits in Si. The device designs and Si3N4 integration strategy in this thesis mitigate some of the limitations of Si photonics, but achieving consistent and reliable performance of > 1000’s of devices in Si PICs across wafers with low power consumption will require new device designs to extend performance (e.g., reduce losses, increase modulation eﬃ- ciency) as well as solutions to the fabrication variation and thermal sensitivity problems of Si devices. Chapter 2

Coupling modulated microrings

In this chapter1, we experimentally demonstrate that modulating the input/output coupler of a microring (“coupling modulation”) can circumvent the linewidth limitation to the modulation bandwidth of microrings, which was introduced in Section 1.3. Also, we present an analysis of the eﬃciency of coupling modulation compared to conventional approaches of microring modulation.

Two distinct operation modes of microring modulators are intracavity and coupling modulation. The vast majority of microring modulators to date use intracavity modulation (Fig. 2.1a), where the circulating optical field is modulated by the intracavity round-trip phase, φ(t), and/or loss, a(t), while the coupler is fixed [55–61, 74]. Because the intracavity optical field amplitude rises and falls at a time-scale set by the photon cavity lifetime, the maximum intracavity modulation bandwidth diminishes with increasing Q [64]. Additionally, complete on/off modulation (0-100% transmission) requires the stored intracavity optical energy be completely charged and depleted in each switching cycle. Thus, whether in the small- or large- output signal regime, the intracavity modulation bandwidth is inherently limited by the cavity linewidth. Coupling modulation circumvents this linewidth limitation. We first identified this modulation property in [64, 65], and a mathematical analysis of the modulation band- 1c OSA. Reprinted, with permission, from [68]

14 Chapter 2. Coupling modulated microrings 15

a Optical input Optical output b Optical input Optical output (t) σ κ (t)

a(t) e–iφ (t)

c d

Figure 2.1: Schematics of (a) an intracavity modulated microring and (b) a coupling modulated microring that uses a 2 × 2 MZI-coupler as marked by the box. Optical microscope images of the fabricated SOI (c) microring with the 2×2 MZI-coupler marked by the box and (d) the reference MZI. The reference MZI was nominally identical to the MZI-coupler in the microring. The microring and MZI were separated by 620 μmonthe die.

width of coupling and intracavity modulation is presented in Appendix A. In coupling modulation, the intracavity parameters, φ and a, remain constant, while the through- and cross-coupling coeﬃcients, σ(t)andκ(t) respectively, are modulated (Fig. 2.1b) [64,65]. We term the regime where the modulation rate is greater than the cavity linewidth “non- quasi-static (NQS) coupling modulation” [65]. “Quasi-static (QS) coupling modulation” refers to modulation rates less than the linewidth, when the output can be described by simply changing the expression for the static transmission to be time-dependent [75–78]. Distinct from the QS regime, intracavity modulation, and Q-switching (cavity dump-

ing) [79], NQS coupling modulation does not completely deplete the intracavity optical energy to generate near 0-100% transmission swings. Instead, it extracts, in the tran- sient, minor fractions of the intracavity optical ﬁeld in a high ﬁnesse cavity to produce output optical pulses with peak powers that can equal the input optical power. The cou-

pler gates the intracavity optical field as it exits the microring to enable NQS coupling modulation bandwidth to exceed the cavity linewidth [65]. The effect is akin to “homo- dyne modulation,” where the circulating resonant light is the “local oscillator.” NQS Chapter 2. Coupling modulated microrings 16 coupling modulation is resonantly enhanced, since the required changes to the coupling coefficients, and hence the device power consumption, reduce as the stored intracavity optical energy increases [65]. In this chapter, we demonstrate NQS coupling modulation using a Si microring incor- porating a 2 × 2 Mach-Zehnder interferometer (MZI) as a coupler, as illustrated in Fig. 2.1(b) [75–78, 80]. The MZI-coupler provides independent control of the coupling coefficient and resonance wavelength. The differential phase-shift between the MZI-coupler arms changes κ(t)andσ(t) [75, 76], while the common-mode phase-shift changes the round-trip optical path length. When the MZI is driven in push-pull mode, the microring

has no chirp beyond that of the material (i.e., free carrier dispersion in silicon) [62,65,66]. Although periodic modulation at rates greater than linewdith due to a slight variation of the coupling coeﬃcient has been recently observed [81], data modulation has not been studied.

This chapter is organized as follows. In Section 2.1, we describe the fabricated devices. In Sections 2.2 and 2.3, we present small-signal and eye diagram measurements comparing intracavity and coupling modulation to clearly show that coupling modulation enables modulation rates exceeding the cavity linewidth limit, while intracavity modu-

lation does not. In Section 2.4, we discuss how inter-symbol interference in coupling modulation due to the low frequency content in the modulation signal can be overcome with coding. Finally, in Section 2.5, we compare the theoretical eﬃciency of coupling and intracavity modulation to show the regimes where coupling modulation has a lower energy consumption.

2.1 Fabricated devices

Microring and reference MZI modulators were fabricated using the IBM Silicon CMOS Integrated Nanophotonics process on a 200 mm-diameter silicon-on-insulator (SOI) wafer Chapter 2. Coupling modulated microrings 17 with a 2 μm-thick buried-oxide layer and a 220 nm-thick top silicon layer [82,83] . Fully- etched silicon access waveguides and partially-etched PN diode waveguides were deﬁned and planarized with silicon dioxide through a shallow trench isolation module. Typical CMOS ion implantation conditions formed a lateral PN diode junction at the center of

each phase-shifter. The junction was designed with a nominal carrier concentration of 5 × 1017 cm−3 in the P- and N-type regions. After a rapid thermal activation anneal, silicide ohmic contacts to the phase-shifters and silicide resistive thermal tuners were formed. Finally, tungsten vias and copper metal interconnects electrically contacted the phase-shifters and thermal tuners. Dies were prepared with cleaved facets for on/off-chip optical coupling using tapered optical fibers. Figure 2.1(c) shows the specific microring investigated. The microring was designed for exploring the optical dynamics and was not optimized for power consumption. The 2×2 MZI-coupler had 3 dB directional couplers, 50 μm long thermal tuners, and matched

200 μm long PN diode phase-shifters for push-pull modulation. An identical PN diode phase-shifter was included inside the microring to facilitate direct comparisons between intracavity and coupling modulation with the same device. The PN diode phase-shifter length was chosen such that a reference MZI, which is

nominally identical to the output coupler of the microring (i.e., designed to have identical waveguides, PN diode phase-shifters, thermal tuners, and wiring), could be measured (see Sections 2.2 and 2.3). Figure 2.1(d) shows the reference MZI for the microring in Fig. 2.1(c). The reference MZI and microring modulator were on the same die and separated by about 620 μm.

Figure 2.2(a)-(b) shows the static transmission spectra of the microring. The results demonstrate the precise and independent tuning of the coupling coeﬃcient and resonance wavelength, achieved by adjusting the thermal tuners to create a common or diﬀerential phase-shift in the MZI-coupler arms. An extinction ratio near 30 dB was reached at

critical coupling. With no voltage applied to the PN diode phase-shifters, the cavity Chapter 2. Coupling modulated microrings 18

a 0 b 0

-10 -10

-20 -20 critically-coupled -30 Transmission (dB) Transmission Transmission (dB) -30 over-coupled under-coupled -40 1549.8 1549.9 1550 1550.1 1550.2 1549.8 1550 1550.2 1550.4 1550.6 Wavelength (nm) Wavelength (nm)

Figure 2.2: Measured transmission spectra for (a) tuning the coupling coefficient at a fixed resonance and (b) tuning the resonance wavelength with a fixed coupling coefficient. Independent tuning of the coupling and resonance wavelength using the thermal tuners was achieved.

linewidth at critical coupling was Δν ≈ 7 GHz, corresponding to a loaded Q of about 28000 and a ﬁnesse of 14. The free spectral range (FSR) was about 99 GHz near a wavelength of 1550 nm.

2.2 Small-signal modulation measurements

To extract the small-signal optical modulation characteristics of coupling and intracavity

modulation, we measured electro-optic S21 parameters by collecting the voltage of a 40 GHz InGaAs photoreceiver referenced to a vector network analyzer (VNA) output.

Specifically, the electro-optic S21 parameter refers to the response of the modulator’s optical output to RF drive signals from the VNA via the plasma dispersion effect in the PN diode phase-shifters. For coupling modulation, the MZI phase-shifters in the microring were driven in push-pull. To generate a differential drive signal, the VNA output was fed into a fanout circuit (Hittite HMC842LC4B), which had a bandwidth of about 32 GHz. For intracavity modulation, a single-ended signal generated from the

VNA was applied to the intracavity phase-shifter without the fanout. Custom 40 GHz RF probes contacted the devices.

Figure 2.3(a) shows the measured S21 of the reference MZI as well as the microring Chapter 2. Coupling modulated microrings 19

Figure 2.3: (a) Electro-optic S21 measurements of the reference MZI, coupling modulation, and intracavity modulation. The RF cables, RF adapters, and bias tees have been de-embedded. (b) Optical small-signal modulation responses of coupling and intracavity modulation. Each curve is obtained by normalizing the electro-optic S21 of the microring to the S21 of the reference MZI and referencing to the value at 100 MHz. The microring was biased near critical coupling, with a cavity linewidth Δν ≈ 6 GHz. The intracavity modulation response for a ∼ 1.3 GHz detuning from resonance (blue) has a 3 dB bandwidth of 4.4 GHz, similar to the linewidth. A ∼ 5 GHz detuning produces a resonant sideband peak near the value of the detuning (red), and the 3 dB bandwidth is extended to ∼ 13 GHz. The coupling modulation response (black) does not roll-off to 40 GHz (more than 6× the linewidth). Chapter 2. Coupling modulated microrings 20 operated under coupling and intracavity modulation modes. Each curve is referenced to its value at 100 MHz. The responses of the RF cables, RF adapters, and bias tees were de-embedded from the S21 data; however, the responses of the fanout, RF probes, and on-chip wiring remained embedded. The S21 of the reference MZI when driven in push-pull used the fanout, while the fanout was not used for for the single-arm drive measurement. This led to slight differences in the S21 between the two cases. The reference MZI was baised at quadrature using the thermal tuners to maximize the modulation efficiency of the MZI and reduce the relative noise in the measurements. Experimentally, we found that the shape of the reference MZI S21 curves was insensitive to changes in the MZI bias. The coupling modulation S21 measurements were taken with the input wavelength on resonance and a slightly under-coupled bias. The intracavity modulation

S21 measurements were taken at critical coupling with the input wavelength roughly 1.3 GHz and 5 GHz detuned from resonance to obtain an appreciable modulation depth. In all cases, the PN diode phase-shifters were biased at −1 V (i.e., reverse-biased). To extract the small-signal modulation response due to the optical cavity dynamics,

we normalize the electro-optic S21 parameter of the microring modulator to the electro- optic S21 of the reference MZI to remove the electrical characteristics of the measurement setup, on-chip wiring, and PN diode phase-shifters. The normalized coupling modulation response, Scm, and normalized intracavity modulation response, Sim,aregivenby

S21,cm Scm = , (2.1a) S21,MZI,push−pull

S21,im Sim = , (2.1b) S21,MZI,single where S21,MZI,push−pull and S21,MZI,single are the electro-optic S21 of the reference MZI under push-pull and single-arm drive, respectively; and S21,cm and S21,im are the electro- optic S21 of the coupling and intracavity modulation, respectively. S21,MZI,push−pull,

S21,MZI,single, S21,cm,andS21,im are as shown in Fig. 2.3(a). Chapter 2. Coupling modulated microrings 21

Figure 2.3(b) shows the small-signal optical modulation characteristics, Scm and Sim. The coupling modulation bandwidth significantly exceeds the traditional cavity linewidth limit, while intracavity modulation does not. Under bias, the microring had a cavity linewidth of Δν ≈ 6 GHz. The black curve in Fig. 2.3 shows the coupling modulation response did not roll off to 40 GHz, more than 6× the cavity linewidth. The maximum frequency measured was limited by the instrumentation. The flat response indicates that the frequency characteristics of the NQS coupling modulation resembled those of the non-resonant reference MZI. The slight decrease in the modulation depth near the frequency corresponding to the cavity linewidth was due to a slight under-coupling of the

microring [64]. In contrast, the intracavity modulation response with input light that was 1.3 GHz detuned from resonance (blue curve) had a 3 dB bandwidth of about 4.4 GHz, conﬁrming that the intrinsic modulation bandwidth was limited by the cavity linewidth. For larger

detunings, a peak occurs when a modulation sideband is on resonance and becomes comparable to or greater than the carrier in amplitude within the microring [64,78,80]; this eﬀect is predicted by the mathematical models in Sections A.2 and A.3 of Appendix A. The peak is exaggerated for large detunings, because the circulating amplitude of an

oﬀ-resonant carrier is small. This eﬀect is shown by the ∼ 5 GHz detuning measurement (red curve). Although the modulation sideband peak extended the 3 dB bandwidth to about 13 GHz, intracavity modulation of a highly detuned carrier is not practical, because the absolute modulation depth and the linearity of the modulator are compromised.

2.3 PRBS modulation and eye diagram measure-

ments

Large-signal data modulation and optical eye diagram measurements provide further ev- idence that the coupling modulation bandwidth is not similarly limited by the cavity Chapter 2. Coupling modulated microrings 22

Figure 2.4: Eye diagrams of coupling (top) and intracavity (bottom) modulation at 6-28 Gb/s for bias points near critical coupling (Δν ≈ 6 − 7 GHz). The coupling modulation eye is open at 28 Gb/s, but the intracavity modulation eye closes at bit rates greater than roughly 2× the linewidth.

linewidth as intracavity modulation. Since the PN diode phase-shifters were not optimized and the modulation efficiency in reverse bias was relatively low, the PN diodes were driven in forward bias to reduce the required drive voltage for data modulation. The PN diodes were driven with single-tap pre-emphasized non-return-to-zero (NRZ) 231 − 1 pseudo-random bit sequence (PRBS) signals with a DC offset of 0.28 V. The electrical pre-emphasis extended the modulation bandwidth of the PN diode phase-shifters beyond their minority carrier lifetime limit of ∼ 1 GHz [84–86]. The drive signals were generated by feeding the output of a PRBS generator to a pre-emphasis converter which operated up to 28 Gb/s (Anritsu MP1825B-002), and then to the RF probes. The applied single- ended voltage swing of the pre-emphasized bits was 1.5 Vpp, and the non-emphasized bits were between 0.24-0.3 Vpp. To measure the eye diagrams, the optical output of the modulator was amplified using an erbium doped fiber amplifier, bandpass filtered (full-width at half-maximum bandwidth of 0.8 nm), and captured on a digital communications analyzer with a 28 Gb/s optical module. All eye diagrams were obtained using 231 − 1PRBS.

Figure 2.4 summarizes the coupling and intracavity modulation eye diagrams at bit rates between 6 and 28 Gb/s. The cavity linewidths at the operating biases were Δν ≈ 6 − 7 GHz. At each bit rate, identical drive signals were applied to the coupler or Chapter 2. Coupling modulated microrings 23 intracavity phase-shifters, except the MZI-coupler was driven in push-pull while the intracavity phase-shifter was driven single-ended. For coupling modulation, the microring was modulated between critical and under- coupling with the input light on resonance. For intracavity modulation, the microring was biased at critical coupling and the input wavelength was slightly detuned from resonance. Thus, the quasi-static cavity linewidth for coupling modulation was less than or equal to that for the corresponding intracavity modulation case. The pre-emphasis ratio and detuning were optimized to maximize the eye opening for each case. At 6 Gb/s and 12.5 Gb/s, both the coupling and intracavity modulation eye diagrams had extinction ratios of 10-13 dB and a maximum optical transmission > 40%. As the bit rate increased, the coupling modulation eye remained wide open up to 28 Gb/s, whereas the intracavity modulation eye was closed at 22 Gb/s. However, because of the modest finesse and the roll-off of the PN diode phase-shifter efficiency at high modulation

frequencies, the extinction ratio of coupling modulation at 22 Gb/s and 28 Gb/s decreased to 10 dB, and the maximum optical transmission was only about 10 to 20% of the oﬀ- resonance transmission. At 28 Gb/s, the peak-to-peak phase-shift in each PN diode phase-shifter was about 0.18 rad., and the coupler swung between |κ|2 ≈ 0.2and|κ|2 ≈

0.08. The reduction in maximum optical transmission at high data rates is not necessar- ily a characteristic of coupling modulation.AsdiscussedinSection2.4and[65],near unity transmission is achievable, particularly when the bit rate is much higher than the linewidth and when the stored optical energy in the cavity is not signiﬁcantly depleted during modulation. The Q factor of the modulator here was compromised by the intracavity PN diode phase-shifter, which was necessary to compare the dynamics of intracavity and coupling modulation. Nonetheless, coupling modulation of the demonstrated microring should function beyond 28 Gb/s. The measurements were limited by the instrumentation. Chapter 2. Coupling modulated microrings 24

a b

"" ""

"# "#

Figure 2.5: (a) Intracavity modulation eye diagrams of an over-coupled microring (Δν ≈ 9 GHz). The eye opening is larger than in Fig. 2.4, conﬁrming that the intracavity modulation bandwidth depends on the cavity linewidth. (b) Eye diagrams of the pre- emphasized electrical drive signals at 28 Gb/s (left) and the resultant optical output of the reference MZI (right). No remnants of the pre-emphasis are present in the optical output.

To check that the intracavity modulation eye closure was due to the cavity linewidth and not to an electrical artifact, we over-coupled the microring by adjusting the thermal tuners to increase the linewidth to 9 GHz at the expense of modulator efficiency and extinction ratio. Figure 2.5(a) shows that the eye opening increased at 22 Gb/s, but remained closed at 28 Gb/s. The eye diagrams show that intracavity modulation suffered from severe inter-symbol interference at bit rates greater than roughly 2× the cavity linewidth (i.e. > 12.5 Gb/s), while coupling modulation at up to 4× the linewidth was not similarly affected. To determine that the pre-emphasized drive signals only compensated for the modulation bandwidth of the PN diodes, we measured the optical output of the reference MZI. Figure 2.5(b) (left) shows the eye diagram of the pre-emphasized 28 Gb/s drive signal. The optical output of the reference MZI driven with this signal in push-pull mode (Fig. 2.5(b), right) shows that the MZI-coupler optical output did not contain any remnants of the pre-emphasis in the drive signal which could potentially extend the microring modulation bandwidth beyond the limits of the resonant optical dynamics. Because the PN diodes were swinging between forward and reverse biased states, Chapter 2. Coupling modulated microrings 25 the dynamic power consumption of the device was difficult to estimate. To obtain an upper-bound to the power consumption, we directly measured the average dynamic power incident on the probes using a RF power detector. For the measurements at 28 Gb/s (Fig. 2.4), this power was about 750 fJ/bit. The device dynamic power consumption was likely less due to the impedance mismatch and RF reflection between the modulator and the test equipment. The die lacked the necessary electrical calibration structures to measure the impedance and RF reflection of the PN diode phase-shifters. This measured power consumption is not a fundamental limitation of the MZI-microring geometry. The power consumption can be reduced by replacing the thermal tuners with a length mismatch in the MZI as in [77], shortening the MZI PN diode phase-shifters to reduce the diode capacitance, removing the intracavity PN diode, increasing the Q factor and improving the diode efficiency. At the PN diode lengths in this work and the shorter lengths necessary for an optimal device, traveling wave electrodes are unnecessary and the diodes can be treated as lumped elements.

2.4 Overcoming low frequency distortions in cou-

pling modulation

The results in Sections 2.2 and 2.3 clearly demonstrate that the long-held cavity linewidth limit to the intracavity modulation bandwidth can be broken with coupling modulation.

However, a potential drawback to coupling modulation is the inter-symbol interference (ISI) from the low frequency content of the drive signal, which depletes the stored optical energy in the cavity. More specifically, NQS coupling modulation at rates beyond the linewidth requires the intracavity field in the cavity to remain nearly constant, and low frequency content in the drive signal (e.g., long runs of 1’s or 0’s in on-off keyed data modulation) tend to cause large changes in the intracavity field, which distorts the optical output leading to ISI. To mitigate the ISI, one suggestion is to modulate two couplers to Chapter 2. Coupling modulated microrings 26

2 Gb/s 10 Gb/s 40 Gb/s 100 Gb/s

Uncoded 1 Intracavity Modulation 0 1 Uncoded Coupling Modulation 0 1 8b/10b Coupling Modulation 0

Figure 2.6: Computed eye diagrams at several bit rates for (top) intracavity modulation and (center) coupling modulation driven by an uncoded NRZ signal, and (bottom) coupling modulation driven by a NRZ 8b/10b encoded signal. The calculations assume a group index of 4.3, a NRZ PRBS 217 − 1 data signal, Δν = 5 GHz, a round-trip length of 250 μm, a resonant input for coupling modulation, and critical coupling for intracavity modulation. With DC-balanced encoding, coupling modulation can achieve a 0-90% swing at 100 Gb/s. In contrast to intracavity modulation, the DC-balanced encoded coupling modulation eye diagram becomes more open at high bit rates.

maintain a constant intracavity optical power at the expense of device complexity, cavity

finesse, and power efficiency for large-signal modulation [87]. As a more straight-forward alternative, we propose to encode the electrical data to produce a DC-balanced drive signal. An example is the 8b/10b code, a typical line code for Ethernet and InfiniBand standards. The computed eye diagrams in Fig. 2.6 illustrate the effect of the encoding at bit rates from 2 Gb/s to 100 Gb/s. The calculations use the time-dependent transmission equations for microrings developed in Appendix A. Also, the calculations use a NRZ PRBS 217 − 1 pattern, a 5 GHz cavity linewidth, and a 250 μm round-trip length.

The top row shows that uncoded intracavity modulation requires a linewidth that is at least half the bit rate, in agreement with our measurements. The middle row shows that for uncoded non-quasi-static (NQS) coupling modulation at 40 Gb/s and 100 Gb/s, Chapter 2. Coupling modulated microrings 27 the transmission swing in the eye opening is about 25%, and increasing the amplitude of the drive signals would increase the ISI since more energy would be discharged from the cavity. As in our experiment, the resonator in the calculation is driven between under- and critical coupling. NQS coupling modulation in the over-coupled regime incurs more

ISI due to the increased discharge of the stored optical energy [64,65], but it can generate pulses with peak powers greater than the input power [79] similar to intracavity modulation in the top row. At a ﬁxed modulation rate, microrings with narrower linewidths would improve the eye opening for uncoded NQS coupling modulation, since the circulating energy would be higher, and a smaller fraction of the circulating energy would be discharged to form the output. The bottom row shows that an 8b/10b encoded drive signal enables NQS coupling modulation at 40 Gb/s and 100 Gb/s to have an eye opening of about 90% and low ISI at 100 Gb/s, characteristics not possible with intracavity modulation. Importantly, the coupling modulation ISI diminishes as the bit rate increases, since the low frequency content of the modulation signal is reduced.

2.5 Analysis of the modulation eﬃciency

Although our results show that the coupling modulation bandwidth can be substantially larger than the intracavity modulation bandwidth, an essential question is whether

coupling modulation of a narrow linewidth resonator can be more power efficient than intracavity modulation of a small resonator with a broad linewidth. In practice, both types of modulation may require some encoding, pre-distortion, or equalization energy overhead; therefore, here, we seek to determine and compare the fundamental, optical efficiency scaling of coupling and intracavity modulation. The analysis shows that coupling modulation can indeed be more efficient for high bit rate and large-signal modulation using high-Q resonators. Chapter 2. Coupling modulated microrings 28

We deﬁne an eﬃciency metric,

Δφ η = MZI , (2.2) Δφring

where Δφring and ΔφMZI are respectively the phase-shifts of a microring and a MZI biased at quadrature required to produce the same output transmission swing, assuming identical phase-shifters. Δφ is single-ended for intracavity modulation and is applied push-pull as ±Δφ/2 for coupling modulation. Referencing to ΔφMZI allows for a comparison between coupling and intracavity modulation independent of material platforms. The phase-shifts are related to the power consumption by the electro-optic mechanism and associated drive circuitry. For intracavity modulation, from the microring transmission function [75], the eﬃ- ciency, ηi, is roughly proportional to the intracavity power or ﬁnesse, F :

ηi ≈ kiF, (2.3)

where ki 0.42 depends on the high and low transmission levels, and the ratio of the

round-trip loss to the coupling. ki can be computed from the static transmission of a microring [75]. For example, at critical coupling and F 5, ki =0.24 for a 0-90% output swing and ki =0.41 for a 20-30% swing. ki is lower for in the large-signal modulation regime because the microring transmission spectrum ﬂattens at wavelengths detuned from the resonance.

In contrast, the eﬃciency of coupling modulation, ηc, scales with the intracavity ﬁeld. For a MZI-coupler and a resonant input,

√ ηc ≈ kc F, (2.4)

where kc 1 depends on the transmission levels and F is the ﬁnesse at critical coupling. Chapter 2. Coupling modulated microrings 29

Figure 2.7: The coupling modulation efficiency, ηc, versus microring waveguide loss and cavity linewidth computed for several round-trip lengths, L. The calculations assume a 8b/10b encoded drive signal, a 0-90% output swing, a group index of 4.3, a NRZ PRBS 217 − 1 data signal, a resonant input, and critical coupling. The intracavity efficiency, ηi,ofa5μm radius microring with the same output swing at 40 Gb/s and 100 Gb/s, using linewidths of 20 GHz and 50 GHz respectively, are marked for comparison. Critical coupling is assumed. Coupling modulation becomes increasingly efficient over intracavity modulation as the Q factor and bit rate increase.

For the same transmission levels, kc is smaller in the NQS than quasi-static (QS) regime due to a lower intracavity field. In the QS case, kc can again be computed from the static microring transmission. For example, for F 5, kc =0.85 for a 0-90% output swing and kc =0.73 for a 20-30% swing. In the NQS regime, we derived an analytic form for kc by assuming a periodic square-wave drive signal and solved for the average intracavity field with a rate equation. The approximation neglects the shape and low-frequency content of the drive signal. We found that in the NQS regime, F 20, kc =0.41 for a 0-90% output swing. From Eq. 2.3 and 2.4, QS coupling modulation is more efficient than intracavity

2 modulation in cavities with the same F and phase-shifters when F (kc/ki) . Intracavity modulation is more efficient in the small-signal regime if the resonator has a moderate finesse (e.g. 20-30% swing, F 5), but QS coupling modulation is more efficient for

large-signal modulation; e.g. ηc >ηi for a 0-90% output swing when F 10 and for a Chapter 2. Coupling modulated microrings 30

0-99% swing when F 87. The eﬃciency scaling becomes especially favourable to NQS coupling modulation over intracavity modulation at high Q factors and high bit rates. Because the minimum

cavity linewidth is set by the desired modulation rate, improvements in ηi of intracavity modulation via F must come from the cavity size reduction. However, tuning structures needed for large extinction ratios and large-signal swings are diﬃcult to incorporate into ultra-small cavities. Thus, the advantage of coupling modulated microrings is that they can be kept larger (to accommodate tunable couplers), while ηc can, in principle, be arbitrarily boosted by increasing Q to raise the ﬁnesse.

Figure 2.7 shows the scaling of ηc for several round-trip lengths assuming a 0-90% output swing calculated using the microring modulator model in [64, 65]. The values of

ηi for SOI microrings with a 5 μm radius and the same output swings at 40 Gb/s and 100 Gb/s are marked. As the round-trip length of a coupling-modulated microring increases, a narrower linewidth is required for ηc >ηi. In principle, both the modulation quality (e.g., eye opening) and energy eﬃciency of coupling modulation improve as the resonator linewidth decreases relative to the modulation rate if the modulation is DC balanced. However, modulation rates approaching the

FSR can cause distortion in the output optical signal, since the modulation time-scale would be similar to or shorter than the resonator round-trip time. In microrings, the FSRs are usually 100 GHz, so typical modulation rates are much lower than the FSR. A second limitation is the onset of optical nonlinearities, e.g., frequency generation or absorption, in the resonator, which may occur at sub-mW input powers if the ﬁnesse is high. The input laser power should be kept to less than the nonlinearity threshold, which reduces the maximum output power. Chapter 2. Coupling modulated microrings 31

2.6 Summary

We have demonstrated experimentally that coupling modulation circumvents the conventional limit on the maximum modulation rate of microcavities due to the photon cavity lifetime. The result is substantiated by small-signal sinusoidal and large-signal bit stream modulation measurements. We have proposed DC-balanced coding as a way to mitigate low frequency inter-symbol interference in coupling modulation. In the quasi- static regime, coupling modulation is more energy eﬃcient than intracavity modulation when large output swings are required. In the non-quasi-static regime, coupling modulation has higher energy eﬃciencies compared to intracavity modulation when the cavity Q factor is high.

By combining the benefits of resonant enhancement with the large bandwidths of non- resonant modulators, coupling modulation, for the first time, opens the avenue toward ultra-low power yet high-speed modulation of ultra-high-Q resonators. Such resonators on silicon chips can possess finesse values exceeding 10000 [88]. Although a silicon microring was used in this demonstration, we emphasize that the results presented here apply generally to other types of monolithically or hybrid integrated photonic platforms. Coupling modulation of resonators can also be used to generate modulation formats be- sides NRZ/RZ on-off keying, such as binary phase-shift keying, which is demonstrated in Appendix B, and quadrature amplitude modulation [89], as well as to achieve high-speed modulation of lasers [90]. Chapter 3

Silicon polarization rotator-splitters

As discussed in Section 1.1, since the input polarization to Si PICs from standard single- mode optical ﬁber is not ﬁxed and Si waveguides typically have a large birefringence, polarization transparent devices and circuits are necessary for the implementation of Si PICs in optical communication links. Polarization diversity can overcome these challenges, and essential to this scheme are polarization splitters and polarization rota-

tors [20, 91, 92]. Prior to this work [69, 70], polarization splitters and rotators demonstrated in Si photonic platforms required high aspect ratio features, extra layers, or an air cladding [20,21,32–36,91,92], and were not compatible with typical foundry processes. In this chapter1, we combine the splitter and rotator functionalities into a polarization rotator-splitter (PRS) that is fully compatible with standard foundry processes. The

PRS requires only a single Si material layer with top and bottom SiO2 cladding. This Si layer must be patterned with both a full and partially-etched level; no high aspect ratio features are required. The compatibility with standard foundry processes enables us to demonstrate the PRS and an active polarization controller using the IME baseline and IME-OpSIS silicon photonics processes [9, 93, 94]. The PRS uses a bi-level taper that converts a fundamental TM mode (TM0) input into a ﬁrst-order TE mode (TE1) output, as proposed in [95, 96]. Although TM0-TE1 mode conversion in bi-level tapers 1c OSA. Reprinted, with permission, from [70]

32 Chapter 3. Silicon polarization rotator-splitters 33 was demonstrated in [96], a full PRS was not demonstrated. Overall, our work paves the way for polarization diversity, polarization controllers, and polarization-multiplexed transmitters and receivers in standard active Si photonic platforms. The chapter is organized as follows: we describe our adiabatic bi-level taper PRS de-

sign and demonstration in Section 3.1; then, we show the PRS integrated with directional coupler polarization ﬁlters for improved polarization crosstalk in Section 3.2; ﬁnally, we apply the PRS to an active polarization controller in Section 3.3.

3.1 Bi-level taper polarization rotator-splitter

Our PRS design is shown in Fig. 3.1(a), where the red regions represent the full height of the Si and the purple regions represent the partially-etched level of Si. We designed the PRS for the IME baseline and OpSIS silicon photonics processes, which have a top silicon thickness of 220 nm and a partially-etched thickness of 90 nm. Our PRS uses a bi-level taper for TM0-TE1 mode conversion and symmetric SiO2 cladding. After the bi-level taper, the TE0 and TE1 modes are separated into two waveguides using an adiabatic coupler instead of the directional coupler proposed in [34], the Y-branch proposed in [95], or the Y-branch and multi-mode interferometer in [36]. Overall, our

PRS design is entirely adiabatic. This is a key distinction from the earlier PRS designs in [34,36,95], which have non-adiabatic elements that limit the bandwidth, increase the senstivity to variations in waveguide dimensions, and increase the insertion loss. The total length of the PRS design is about 475 μm.

The remainder of this section is organized as follows: in Section 3.1.1, we provide a detailed description of the PRS design and operating principles, and in Section 3.1.2, we describe our experimental demonstration of a bi-level taper PRS. Chapter 3. Silicon polarization rotator-splitters 34

50μm 50μm 300μm TE0 TE0 Optical 850nm 650nm 500nm input Optical TE0, 550nm TE0, 200nm 450nm 200nm outputs TM0 1.55μm TE1 500nm

TM0 TE1 TE0 Bi level taper Adiabatic coupler

220nm Si 90nm Partially etched slab (a)

Mode1 Mode1 Mode1 Mode1 2.6 TE0 TE0 TE0 TE0 TE0 Mode 2 Mode 3 2.2 TE1

eff Hybridized n TM0 1.8 TM0

TE1 Hybridized

1.4 Mode2 Mode2 Mode2 Mode2 0(450) 125(475) 250(500) 375(525) 500(550) TM0 TE1 TE1 TE1 Partially−etched Si fin width (Si rib width) (nm) (b) (c) Mode2 Mode3

Ex (V/m) Ey (V/m) Ex (V/m) Ey (V/m)

(d)

Figure 3.1: (a) Schematic of the polarization rotator-splitter (PRS). Widths are labeled in red and purple; lengths use green labels. (b) Schematic showing the profiles of the modes with the first and second highest effective indices (i.e., “mode 1” and “mode 2”) at different points along the PRS. In the adiabatic coupler, “mode 1” and “mode 2” refer to supermodes of the composite waveguide. (c) Effective indices (neff ) along the first half of the bi-level taper for modes 1 to 3 at a wavelength of 1550 nm. (d) Electric field components (Ex and Ey) of modes 2 and 3 at 1550 nm in the hybridized region of (c) when the Si rib width is 486 nm and the partially-etched Si fin width is 180 nm. Chapter 3. Silicon polarization rotator-splitters 35

3.1.1 Detailed polarization rotator-splitter design and opera-

tion

The PRS operation relies on the principle of mode evolution [91, 92]. The evolution of

the modes with the first and second highest effective indices (i.e., “mode 1” and “mode 2”) in the PRS is illustrated in Fig. 3.1(b). In the first half of the bi-level taper, the Si ridge and partially-etched slab continuously widen, and this is where the TM0-TE1 mode conversion occurs. The partially-etched slab breaks the vertical symmetry of the

waveguide [34, 96], which produces a large difference in the effective indices of modes 2 and 3 throughout the structure, as shown in Fig. 3.1(c). This allows a TM0 input to remain in mode 2 all along the bi-level taper and evolve into, first, a “hybridized” mode with TM0 and TE1 features as shown in Fig. 3.1(d), and finally, the TE1 mode. A

TE0 input simply remains in mode 1 and exits the bi-level taper in the TE0 mode. The second half of the bi-level taper, where the Si ridge continues to widen and the partially- etched slab narrows, is used to provide a fully-etched, wide waveguide as the input to the adiabatic coupler. The adiabatic coupler follows the bi-level taper and consists entirely of fully-etched Si

waveguides with symmetric SiO2 cladding, which prevents crosstalk between the TE1 and TM0 modes. The mode evolution in the adiabatic coupler can be understood from the mode profiles in Fig. 3.1(b). Here, TE0 and TE1 refer to supermodes of the composite two-waveguide structure. At the start of the coupler, a “narrow” 200 nm wide waveguide begins with a blunt tip next to a “broad” 850 nm wide waveguide; the gap between the waveguides is 200 nm. The TE0 and TE1 modes are well confined in the broad waveguide and have little overlap with the narrow waveguide. Then, the broad waveguide is narrowed to a 650 nm width and the narrow waveguide is widened to a 500 nm width; the gap is held constant at 200 nm. At this point, the TE0 mode is well confined in the broad waveguide while the TE1 mode is well confined in the narrow waveguide. Finally, the narrow waveguide is bent away from the broad waveguide using an arc with Chapter 3. Silicon polarization rotator-splitters 36

100ʅm

BiͲleveltaper Adiabaticcoupler

(a)

50ʅm 50ʅm

(b) (c)

Figure 3.2: (a) An optical micrograph of the polarization rotator-splitter fabricated in the IME baseline process. Magniﬁed optical micrographs are shown for (b), the bi-level taper, and (c), the end of the adiabatic coupler. a radius of 450 μm. As the waveguides separate, the TE0 and TE1 supermodes of the adiabatic coupler evolve into the TE0 modes of the isolated top and bottom waveguides, respectively.

The PRS was designed using a two-dimensional finite element method (2D-FEM) mode solver (COMSOL) and a three-dimensional finite-difference time-domain (3D-FDTD) solver (Lumerical). The mode calculations were used to choose the cross-section dimensions in Fig. 3.1(a). For example, the waveguide widths in the bi-level taper were chosen to achieve a large effective index difference between modes 2 and 3 in the hybridized anti- crossing region in Fig. 3.1(c). With the cross-sections fixed, the lengths of the transitions were chosen using 3D-FDTD simulations to achieve low crosstalk.

3.1.2 Polarization rotator-splitter measurements

PRSs were fabricated in the IME baseline process, and optical micrographs of the PRS are shown in Fig. 3.2. The PRS inputs and outputs lead to edge couplers with 220 nm wide square tips. The PRS was measured using the experimental apparatus shown in Chapter 3. Silicon polarization rotator-splitters 37

SweptͲwavelength Detector tunablelaser

TEorTM SingleͲmode Broadbandfiber componentof opticalfiber polarization Adjustable output controller linear polarizer Chip

Coupling FiberͲtoͲ CircularlyͲ lens freeͲspace polarizedlight collimator LinearlyͲ Chipoutput polarizedlight (TE+TM) (TEorTM)

Figure 3.3: Schematic of the experimental apparatus used for measurements of the polarization rotator-splitter.

Fig. 3.3. Light from a swept-wavelength tunable laser was coupled onto and off the chip using aspherical lenses. Manually-adjustable, free-space, linear polarizers were placed at the input and output of the chip to control the input polarization and analyze the output polarization. To prevent input power differences between the TE and TM polarizations, a fiber-based, broadband, Babinet-Soleil polarization controller was used to circularly- polarize the light prior to transmission through the linear polarizer on the input side of the chip. Figure 3.4 shows the measured transmission spectra of the two PRS outputs for TE and TM inputs. The transmission spectra have been normalized to the transmission spectra of the edge couplers to extract the spectral characteristics of the PRS only. From Figs. 3.4(a) and 3.4(b), the polarization crosstalk at both output ports was less than -13 dB over a wavelength range between 1530 nm and 1580 nm; the crosstalk increased to about -10 dB for wavelengths between 1500 nm and 1530 nm. Due to inaccuracies in aligning the coupling lenses between measurements, the error in the transmission values was about ± 0.5 dB. Other than normalizing out the edge coupler transmission, no Chapter 3. Silicon polarization rotator-splitters 38

TE branch output TM branch output

0 TE−>TE 0 TE−>TE TE−>TM TE−>TM TM−>TE TM−>TE −20 TM−>TM −20 TM−>TM

−40 −40 Transmission (dB) Transmission (dB)

−60 −60 1500 1520 1540 1560 1580 1500 1520 1540 1560 1580 Wavelength (nm) Wavelength (nm) (a) (b) TE branch output (TE −> TE) TM branch output (TM −> TE) 1 1

0 0

−1 −1

−2 −2

Transmission (dB) Raw data Raw data Transmission (dB) Fabry−Perot removed Fabry−Perot removed −3 −3 1530 1540 1550 1560 1570 1580 1530 1540 1550 1560 1570 1580 Wavelength (nm) Wavelength (nm) (c) (d)

Figure 3.4: Measurement data for the PRS in Fig. 3.2. (a) Transmission spectra of the PRS TE branch (top) output. (b) Transmission spectra of the PRS TM branch (bottom) output. (c) Magniﬁed TE component of the TE branch transmission for a TE input. (d) Magniﬁed TE component of the TM branch transmission for a TM input. The legends in (a) and (b) indicate the settings of the input and output polarizers (i.e., TE→TM means we had a TE input and measured the TM component of the output). (c) and (d) represent the PRS insertion loss, and the red curves have been post-processed to remove Fabry-Perot oscillations from the edge coupler facets and the measurement apparatus. post-processing was applied to the data in Figs. 3.4(a) and 3.4(b).

The extracted insertion loss of the PRS is shown in Figs. 3.4(c) and 3.4(d). The raw transmission spectra in the black curves overestimate the PRS insertion loss since Fabry-Perot oscillations from the chip facets and measurement apparatus were not fully removed by normalizing the data to the transmission of the edge couplers. The edge coupler loss calibration structures and PRS had different Fabry-Perot oscillations, and the Fabry-Perot oscillations of the measurement setup changed between measurements due to realignments. We post-processed the raw transmission spectra of the PRS and edge Chapter 3. Silicon polarization rotator-splitters 39 couplers to reduce the contribution of the Fabry-Perot oscillations and obtained the more accurate insertion loss data in the red curves. Chip facet Fabry-Perot oscillations were easily identified from the waveguide lengths and group indices, and oscillations that dif- fered little between devices and polarization settings were attributed to the measurement apparatus. From the post-processed data, the insertion loss and polarization-dependent loss (PDL) were less than 1.5 dB and 1.6 dB, respectively, over a wavelength range from 1530 nm to 1580 nm. Our ± 0.5 dB realignment error estimate is evident from the red curves, which have some points with transmission > 0 dB. The large-period oscillations in Fig. 3.4(d) may be Fabry-Perot oscillations from reflections at the chip facets and the waveguide discontinuity at the beginning of the adiabatic coupler or within the bi-level taper. Through this first demonstration of a bi-level taper PRS, we can identify four simple design improvements to reduce the crosstalk and increase the bandwidth. First, the blunt-tip at the start of the adiabatic coupler in Fig. 3.1(a) could be replaced by an arc with a large radius to eliminate any mode coupling caused by the waveguide discontinuity. Second, reducing the waveguide gap in the adiabatic coupler will reduce the crosstalk or the coupler length required to achieve the crosstalk we demonstrated; this is due to an increase in the effective index difference between the TE0 and TE1 modes [91, 92]. Third, the widths and length of the bi-level taper can be optimized; from Fig. 3.4(a), the incomplete TM0-TE1 mode conversion in the bi-level taper is a large component of the crosstalk. Finally, the PRS can be cascaded with additional PRSs or other types of polarization clean-up filters [32]. This latter approach is demonstrated in Section 3.2 where the PRS is integrated with directional coupler clean-up filters for reduced crosstalk. Chapter 3. Silicon polarization rotator-splitters 40

Directionalcoupler Directionalcoupler polarizationsplitter TEͲpassfilters 100ʅm

TE0+ TE0 TM0 TE0 TE0 TM0 TM0 TE1 TE0

Directionalcoupler PRSusedasapolarizationrotator Directionalcoupler TMͲpassfilters TEͲpassfilters

Figure 3.5: Annotated optical micrograph of the polarization splitter-rotator (PSR) with improved crosstalk.

3.2 Polarization splitter-rotator with improved

crosstalk

One approach to improving the performance of the PRS is to cascade it with polarization clean-up filters. This is demonstrated here using directional coupler clean-up filters [21, 32] placed in front of the PRS as shown in Fig. 3.5. In this configuration, it is more appropriate to refer to this structure as a polarization splitter-rotator (PSR) than a polarization rotator-splitter (PRS). In contrast to the PRS by itself, which converts the

TM polarization to the TE1 mode before splitting, here, the polarizations are ﬁrst split with a directional coupler before TM is rotated into TE. This device was fabricated with the IME baseline process as well. The detailed operation of the PSR can be understood from the annotated micrograph

in Fig. 3.5. The input is ﬁrst separated into TE (top branch) and TM (bottom branch) polarizations using a directional coupler. Directional coupler clean-up ﬁlters are integrated into both branches to reduce the polarization crosstalk. All directional couplers in the PSR are nominally identical and use 440 nm wide strip waveguides, 10 μmlong

coupling regions, 400 nm wide coupling gaps, and 10 μm radius bends leading to and from the coupling region. The TE (top) branch uses four clean-up ﬁlters. The TM (bottom) branch uses two clean-up ﬁlters followed by a PRS for polarization rotation and then Chapter 3. Silicon polarization rotator-splitters 41

TE branch output TM branch output 0 0 TE−>TE TE−>TE TE−>TM TE−>TM −20 TM−>TE −20 TM−>TE TM−>TM TM−>TM −40 −40

−60 −60 Transmission (dB) Transmission (dB)

−80 −80 1500 1520 1540 1560 1580 1500 1520 1540 1560 1580 Wavelength (nm) Wavelength (nm) (a) (b)

TE branch output (TE −> TE) TM branch output (TM −> TE) 1 1 Raw data Raw data Fabry−Perot removed Fabry−Perot removed 0 0

−1 −1

−2 −2 Transmission (dB) Transmission (dB)

−3 −3 1530 1540 1550 1560 1570 1580 1530 1540 1550 1560 1570 1580 Wavelength (nm) Wavelength (nm) (c) (d)

Figure 3.6: Measurement data for the PSR in Fig. 3.5. (a) Transmission spectra of the PSR TE branch (top) output. (b) Transmission spectra of the PSR TM branch (bottom) output. (c) Magnified TE component of the TE branch transmission for a TE input. (d) Magnified TE component of the TM branch transmission for a TM input. The legends in (a) and (b) indicate the settings of the input and output polarizers (i.e., TE→TM means we had a TE input and measured the TM component of the output). The red curves in (c) and (d) have been post-processed to remove Fabry-Perot oscillations from the chip facets and the measurement setup. two additional clean-up filters. The unused ports of the PRS and directional couplers are terminated with waveguide tapers leading to 200 nm wide blunt tips. The PRS is nominally identical to the PRS demonstrated in Section 3.1. The inputs and outputs of the whole PSR lead to edge couplers with 220 nm wide tips. The PSR was measured using the same method as Section 3.1.2 (i.e., free-space cou-

pling with linear polarizers at the input and output of the chip). Figures 3.6(a) and 3.6(b) show the measured transmission spectra of the two PSR outputs normalized to the transmission spectra of the edge couplers for TE and TM inputs. The polariza- Chapter 3. Silicon polarization rotator-splitters 42 tion crosstalk at both outputs was less than -22 dB over a wavelength range from 1500 nm to 1580 nm, which was an improvement of 9 dB over the PRS in Section 3.1.2. In principle, the clean-up ﬁlters should have provided a signiﬁcantly lower crosstalk, but the measurements may have been limited by the accuracy of the input and output polarizers.

The insertion loss of the PSR is shown in Figs. 3.6(c) and 3.6(d). The black curves are raw data and the red curves have been post-processed to remove Fabry-Perot oscillations from the chip facets and the measurement apparatus, as explained in Section 3.1.2. From the post-processed data, the insertion loss and PDL of the PSR were less than 2.3 dB and 1.9 dB over a wavelength range from 1530 nm to 1580 nm; the error in the insertion loss was roughly ± 0.5 dB due to realignment error of the coupling lenses. Compared to the PRS in Section 3.1.2, the insertion loss of the PSR in this section was larger and varied more with wavelength due to the loss and limited bandwidth of the directional coupler polarization splitter and clean-up ﬁlters.

A more optimal design that has low polarization crosstalk, low insertion loss, and a broad bandwidth will likely involve optimizing our PRS design using the methods we described at the end of Section 3.1.2 and then cascading the PRSs (i.e., the two outputs of a PRS are routed to additional PRSs, which act as polarization clean-up ﬁlters). This will result in an entirely adiabatic design that is not subject to the bandwidth and insertion loss limitations of directional couplers.

3.3 Polarization controller

Finally, as an example of integration of the PRS with tuning and modulation elements, we demonstrate the simple polarization controller shown in Fig. 3.7. The polarization

controller consists of a PRS followed by a variable 2 × 2 Mach-Zehnder interferometer (MZI), phase-shifters, and a second PRS to combine the two branches. The MZI and phase-shifters modify the relative amplitudes and phases of the output TE and TM- Chapter 3. Silicon polarization rotator-splitters 43

PIN diode Thermal tuner PIN diode Thermal tuner 3-dB (500 ȝm) (500 ȝm) (500 ȝm) (500 ȝm) PRS 3-dB PRS DC Input PIN diode Thermal tuner DC PIN diode Thermal tuner Output (500 ȝm) (500 ȝm) (500 ȝm) (500 ȝm)

2x2MZIcontrolsamplituderatioofTEandTM ControlsphasebetweenTEandTM (a) Thermal Thermal PINdiode tuner PINdiode tuner 500ʅm

PRS 3ͲdBDC 3ͲdBDC PRS (b)

Figure 3.7: (a) Schematic of the polarization controller. “3-dB DC” is a 3 dB directional coupler. (b) Optical micrograph of the polarizaton controller fabricated in the IME- OpSIS process. components to control the output polarization. Although this design uses both PIN diode and thermal phase-shifters to demonstrate the compatibility of the PRS with a standard active Si photonic platform, in practice, only one type of phase-shifter (thermal tuner or PIN diode) would be needed depending on the desired tuning speed.

The polarization controllers were fabricated at IME using the OpSIS service [9]. The thermal tuners and PIN diodes are each 500 μm long and use the same etch depths as the PRS. The 3-dB directional couplers use 500 nm wide fully-etched waveguides, a 13.5 μm long coupling region with a 200 nm gap, and 20 μm radius S-bends leading to and from the coupling region. Tuning voltages were only applied to the top thermal tuners and PIN diodes in Fig. 3.7(a), while the bottom PIN diodes and thermal tuners balanced the loss in the two arms of the polarization controller. Figure 3.8(a) shows the measured current-voltage characteristics of the top-left PIN diode and thermal tuner in the polarization controller. We measured the polarization controllers using the method in Section 3.1.2 (i.e., free- space coupling with linear polarizers at the input and output of the chip); the input Chapter 3. Silicon polarization rotator-splitters 44 wavelength was ﬁxed at 1570 nm and the input was chosen to be TE-polarized for simplicity. This simple measurement setup did not allow for the extraction of the phase between the output TE and TM polarization components. The polarization controller insertion loss was < 2.5 dB. By driving the top-left and top-right thermal tuners, we

generated TM-polarized, -45◦ linearly-polarized, and circularly-polarized outputs, which is evident from the output power as a function of the output polarizer angle in Fig. 3.8(b). 0◦ corresponds to a horizontal (TE) polarization axis; the uncertainty in the angle was about ±2◦. Crosstalk in the PRSs and non-ideal 3-dB directional couplers limited the extinction for the TM and -45◦ measurements. The red curve corresponds to a circularly-polarized output since the power only ﬂuctuates by about 0.2 dB over all output polarizer angles. It was achieved with powers of 15 mW and 12 mW dissipated in the top-left and top-right thermal tuners, respectively. Next, as a simple demonstration of switching between TM and TE-polarized outputs, we input TE light into the polarization controller and applied voltages only to the top- left thermal tuner [Fig. 3.8(c)] or the top-left PIN diode [Fig. 3.8(d)]; the other tuning elements were not driven. The applied voltage was swept with the output polarizer ﬁxed to pass either TE or TM (marked “TE out” and “TM out” in the plots) or with the output polarizer removed from the optical path (marked “Total out” in the plots). Increasing the voltage on the thermal tuner or the PIN diode shifted the output polarization between TM and TE. At PIN diode currents beyond 10 mA, the optical loss increased substantially, which imbalanced the MZI and increased the total insertion loss of the polarization controller.

The polarization controller presented here is intended to show the full compatability of the PRS with a standard Si photonics platform. Its simple design limits its optical bandwidth and the polarization states that it can create. A complete polarization controller can be achieved with two simple design modiﬁcations. First, the optical bandwidth can be extended by compensating for the group delay diﬀerences between the TE0 and Chapter 3. Silicon polarization rotator-splitters 45

100 0 Thermal tuner 75 PIN diode −10

50 −20 TM −30 Normalized Current (mA) 25 −45 deg. output power (dB) Circular 0 −40 0 0.5 1 1.5 2 0 90 180 270 360 Voltage (V) Output polarizer angle (degrees) (a) (b) TE −> TM TE −> TE TE −> TM TE −> TE 0 0

−5 −5

−10 −10 Normalized −15 Total out Normalized −15 Total out output power (dB) output power (dB) TE out TE out TM out TM out −20 −20 0 20 40 60 0 10 20 30 40 Thermal tuner power (mW) Diode current (mA) (c) (d)

Figure 3.8: Polarization controller measurement data. (a) Current-voltage characteristics of the top-left thermal tuner and PIN diode. (b) Normalized output power as the output polarizer was rotated. With a TE-polarized input, bias conditions were chosen to obtain a TM-polarized output (black curve), a -45◦ linearly-polarized output (blue curve), and a circularly-polarized output (red curve). (c) Normalized output power as the top-left thermal tuner power was swept. (d) Normalized output power as the top-left PIN diode current was swept. In (c) and (d), the output polarizer was set to pass either TE or TM or removed from the optical path (“Total out”). The optical output power curves were normalized to the maximum value in each plot. The magenta labels and dashed lines indicate points where a TM or TE output was generated from the TE input (marked “TE→TM” and “TE→TE”, respectively). Chapter 3. Silicon polarization rotator-splitters 46

TM0/TE1 modes in the PRS. This compensation should be applied to both PRSs and can be implemented as an extra length of straight waveguide at one of the PRS outputs. Second, an additional set of phase-shifters should be included before the 2 × 2MZIto create the full range of relative weights between the TE and TM components required to

convert any arbitrary input polarization to an arbitrary output polarization. An endless polarization controller, which can be used in polarization-division multiplexed receivers for polarization-tracking, would further require two extra sets of phase-shifters and two extra directional couplers [97–100].

3.4 Summary

In summary, we have demonstrated the ﬁrst polarization rotator-splitter using a TM0- TE1 mode converter based on an adiabatic bi-level taper and extended the concept to a polarization controller and a polarization splitter-rotator with improved crosstalk using directional coupler clean-up ﬁlters. The main advantage of the designs in this work is that they are fully compatible with standard silicon photonic foundry processes and do not

require specialty high aspect ratio features, extra layers, or an air cladding. Although the adiabatic transitions make the polarization rotator-splitter long, the design is inherently broadband and tolerant to dimensional variations. Chapter 4

Silicon nitride on silicon photonic platform

1 In this chapter , we discuss the design and characteristics of a multilayer Si3N4-on-Si photonic platform. The primary motivation for a Si3N4-on-Si photonic platform is to combine the excellent passive waveguide properties of Si3N4 with the compatibility of Si waveguides with electro-optic modulators and Ge photodiodes. As discussed in Section

1.1, the lower refractive index contrast of Si3N4 waveguides with SiO2 cladding compared to Si waveguides reduces the waveguide losses due to sidewall roughness scattering, dispersion, and sensitivity to variations in waveguide dimensions. In addition, Si3N4 does not suﬀer from two photon and free carrier absorption over the telecommunication wavelength ranges; and its lowest order nonlinear susceptibility, χ(3), is about 20 times smaller than that of Si [101,102], which means Si3N4 waveguides can handle higher optical powers than Si waveguides. Si3N4 photonic components are also less temperature sensitive owing to a thermo-optic coeﬃcient that is about 5 times smaller than that of Si [103,104]. Building on the brief discussion of silicon nitride waveguides in Section 1.1, CMOS electronic fabrication processes use silicon nitride for masking, passivation, and strain en-

1c IEEE. Reprinted, with permission, from [71]

47 Chapter 4. Silicon nitride on silicon photonic platform 48

gineering; it is deposited either using low-pressure chemical vapor deposition (LPCVD) or plasma-enhanced chemical vapor deposition (PECVD). LPCVD requires high tem-

o peratures around 800 C and typically results in stoichiometric silicon nitride (Si3N4), while PECVD can be carried out at temperatures less than 400oC and can result in non-stoichiometric silicon nitride (SixNy). The high temperatures in LPCVD drive out N-H and O-H bonds that absorb light in the infrared wavelength range, but cause stress and cracks in the ﬁlm which can be mitigated by wafer patterning [105]. Film stress is reduced with PECVD, which allows thicker and more uniform ﬁlms at the expense of increased infrared absorption compared to LPCVD Si3N4. For the remainder of this thesis, we use Si3N4 to refer to stoichiometric silicon nitride and the abbreviation, SiN, to refer generally to both stoichiometric and non-stoichiometric silicon nitride.

Several geometries of SiN optical waveguides with SiO2 cladding are commonly used today: a high confinement type (with effective mode areas < 1 μm2 in the O and C bands) that requires SiN with thickness in the range of 400 nm to 800 nm; a moderate confinement type (with effective mode areas ∼ 1 μm2 in the O and C bands) that confines light using two strips of SiN that are about 170 nm thick separated by 500 nm [106]; and a low confinement type (with effective mode areas about 5 μm2 in the O and C bands) which uses a single strip of SiN that is about 80 nm to 100 nm thick [107]. The moderate and low confinement types of waveguides use LPCVD Si3N4, while the high confinement type of waveguides can be formed from either LPCVD or PECVD. Today, the lowest loss SiN waveguides use the low optical confinement geometry to limit sidewall roughness scattering losses, and an ultra-low propagation loss of 0.1 dB/m has been reported [29].

This reported loss is competitive even when compared to waveguides in silica planar lightwave circuits, which have losses as low as about 0.3 dB/m in the C band [15]. For high conﬁnement waveguides, the lowest reported loss is 4.2 dB/m [105], and the sidewall roughness scattering losses are reduced by increasing the thickness of the SiN layer. In contrast, a typical standard Si channel waveguide that is 500 nm wide and 220 nm tall Chapter 4. Silicon nitride on silicon photonic platform 49

has a propagation loss of about 2 to 3 dB/cm in the C-band [8]. To integrate SiN with Si for photonic circuits, oxide-assisted wafer bonding and the

direct deposition of SiN on SiO2 on SOI have been demonstrated [30,31,72,73,108–112]. In the wafer bonding approach [31,108], the active optical functionality is not provided in the Si but rather by III-V semiconductor devices that are bonded onto the Si. Because of the low conﬁnement waveguides, a large separation of 15 μm is needed between the SiN waveguide core and the Si substrate. The mode mismatch between the SiN waveguides and Si waveguides causes about 1 dB of loss per interlayer transition. In the direct deposition approach, which is used in this chapter and was also demonstrated in [30,109], high conﬁnement SiN waveguides are integrated in close proximity (within a vertical separation in the range of 50 to 200 nm) to Si waveguides. PN modulation diodes and germanium (Ge) photodiodes are sometimes formed in the Si. This method of integration results in photonic devices and circuits that are compact (micro-scale) in size. The top

Si layer is separated from the Si substrate by a 2 to 3 μm thick buried oxide layer. This chapter is organized as follows: in Section 4.1, we describe the fabrication processes for our Si3N4-on-Si photonic platform, and in Section 4.2, we characterize waveg-

uide losses, interlayer transitions (i.e., couplers between Si3N4 and Si waveguides), and waveguide crossings.

4.1 Si3N4-on-Si fabrication at IME

Figure 4.1 illustrates the process ﬂow for the Si3N4-on-Si photonic platform, which was performed at A*STAR IME, and Fig. 4.2 shows the waveguide layer thicknesses. The fabrication started with an 8” diameter SOI wafer with a 220 nm-thick, single crystal, top Si layer and a 2 μm thick buried oxide (BOX) layer. The top Si layer was thinned to

150 nm by thermal oxidation and SiO2 etching. The relatively thin top Si layer improves the losses of the interlayer transitions as discussed in Section 4.2.2. Next, Si rib and Chapter 4. Silicon nitride on silicon photonic platform 50

(1) Si layer patterning (2) SiO2 deposition + (3) Si3N4 deposition + Planarization Patterning

Si3N4

Si SiO2 Si SiO2 Si

BOX BOX BOX

Si substrate Si substrate Si substrate

(4) SiO2 deposition (5) SiO2 deposition + (6) Contact metal patterning + Planarization Via formation + Deep trench formation + Heater patterning TaN + Al

TiN TiN TiN

SiO2 Si3N4 SiO2 Si3N4 SiO2 Si3N4 Si Si Si

BOX BOX BOX

Si substrate Si substrate Si substrate

Figure 4.1: Schematic of the fabrication ﬂow for the Si3N4-on-Si photonic platform showing the integration of thermal heaters. The process consists of a series of deposition, planarizing, and patterning steps. Ge epitaxial growth and ion implantation steps can be incorporated for the formation of photodiodes and PN junctions. Chapter 4. Silicon nitride on silicon photonic platform 51

SiO2

400nm Si3N4 150nm 65nm Si 50nm

2ʅm BOX

Si substrate

Figure 4.2: Cross-section schematic showing the layer thicknesses and waveguide geometries in the Si3N4-on-Si photonic platform. The heaters and contact metals are omitted in this schematic.

channel waveguides were formed using deep ultraviolet (DUV) photolithography (248 nm exposure) and reactive ion etching (RIE); the partially-etched Si slab thickness for the rib waveguides was 65 nm. Then, the ﬁrst SiO2 layer was deposited, followed by chemical-mechanical polishing to obtain a 50 nm thick SiO2 layer between the Si3N4

and Si levels. Using two LPCVD steps, a 400 nm thick Si3N4 layer was deposited, and waveguides were formed by DUV photolithography and a one-step RIE full etch. A second

SiO2 layer was then deposited and planarized, followed by titanium nitride (TiN) heater

formation. Next, a third SiO2 layer was deposited for via formation and aluminum (Al) contact metal and bond pads were formed. Finally, deep trench etching was carried out to separate the dies. This deposition-based integration ﬂow enables scaling to incorporate more optical layers. Though not demonstrated in this ﬁrst fabrication run, ion implantation and germanium (Ge) epitaxial growth steps for the formation of active devices can be included after Si3N4 deposition. In addition, lateral under-cut trenches for thermal isolation [113] and suspended spot size converters [114] can be incorporated before the deep trench Chapter 4. Silicon nitride on silicon photonic platform 52

fabrication.

4.2 Waveguide and transition characteristics

The main advantage of Si3N4 waveguides over Si waveguides is their improved passive optical properties. In this section, we describe the waveguide characteristics in the Si3N4- on-Si platform fabricated using the processes described above. Measurements of the waveguide losses, the transition losses between the Si3N4 and Si layers, and the losses and crosstalk of Si3N4 waveguide crossings are presented. All devices discussed in this section were connected to inverse-taper edge couplers in either the Si3N4 or Si layers; lensed ﬁbers were used for on/oﬀ chip optical coupling.

4.2.1 Propagation losses

We measured the propagation loss of TE-polarized light in waveguides realized in the platform in Fig. 4.2 using the cut-back method as reported in [112], and the results are

summarized in Fig. 4.3. The Si3N4 waveguides had a height of 400 nm and a width of

900 nm, and the Si waveguides had a height of 150 nm and a width of 500 nm. These waveguides are single-mode in the C-band and slightly multi-mode in the O-band. For clarity, Fabry-Perot resonances, which were most prominent over the O-band, have been ﬁltered from the O-band data of the 150 nm thick Si waveguides.

Figure 4.3(a) shows the waveguide losses over the wavelength range of 1480 nm -

1600 nm, which covers the S, C, and L bands. The Si3N4 waveguides exhibited a peak in waveguide loss of about 2.9 dB/cm at a wavelength of 1520 nm due to absorption from vibrational modes of N-H bonds in the Si3N4 ﬁlm. The Si3N4 waveguide losses were considerably lower away from the absorption peak. At a wavelength of 1550 nm, the propagation loss was 1.3 dB/cm, and at a wavelength of 1580 nm, the loss decreased to 0.4 dB/cm. The Si3N4 waveguide loss was generally lower than that of the Si strip Chapter 4. Silicon nitride on silicon photonic platform 53

0 0

−1 −2

−2 −4

−3 −6 Si N Si N 3 4 3 4 Si Si

−4 −8 Waveguide transmission (dB/cm) Waveguide transmission (dB/cm) 1480 1510 1540 1570 1600 1260 1280 1300 1320 1340 1360 Wavelength (nm) Wavelength (nm) (a) (b)

Figure 4.3: Measurements of the propagation losses of the Si3N4 and Si strip waveguides over (a) the SCL-bands (near λ = 1550 nm) and (b) the O-band (near λ = 1310 nm). The Si3N4 waveguides had a height of 400 nm and a width of 900 nm, and the Si waveguides had a height of 150 nm and a width of 500 nm.

waveguides, which was about 2.9 dB/cm.

Figure 4.3(b) contains the waveguide losses over the O-band (near a wavelength of

1310 nm), which is far from the N-H bond absorption peak in the Si3N4. The propagation loss of the Si3N4 waveguides exhibited no large peaks and was signiﬁcantly lower than the 4-6 dB/cm loss of the Si waveguides. At a wavelength of 1270 nm, the Si3N4

waveguide loss was 0.34 dB/cm. The low waveguide losses in the O-band imply that the multilayer platform can be useful for Ethernet and data center interconnects. Further loss reduction can be achieved by process optimization that reduces the hydrogen content during deposition [115].

4.2.2 Interlayer transitions

To transfer light between the levels, we used adiabatic linear tapers in the Si and Si3N4

levels as illustrated in Fig. 4.4, which also shows the evolution of the TE0 mode along the transition. Most of the loss in the adiabatic transition is incurred by the blunt tips at the ends of the waveguide tapers. Scanning electron micrographs of the taper tips Chapter 4. Silicon nitride on silicon photonic platform 54

Si Si3N4 w w wSi,wg Si3N4,tip Si,tip wSi3N4,wg

800nm Lc

Si3N4 tip Si tip

Figure 4.4: Schematic of the interlayer transition. The computed TE0 mode at various waveguide cross-sections along the transition are shown to illustrate the mode evolution. Scanning electron micrographs (SEMs) of the waveguide tips in the Si3N4 and Si layers during fabrication are shown, and the nominal widths of these tips were 200 nm and 180 nm, respectively. Lc is the length of the interlayer transition; wSi,tip and wSi3N4,tip are the widths of the Si and Si3N4 waveguide tips, respectively. wSi,wg and wSi3N4,wg are the standard routing waveguide widths (wSi,wg = 500 nm and wSi3N4,wg = 900 nm). Chapter 4. Silicon nitride on silicon photonic platform 55

are included as insets in Fig. 4.4. Figure 4.5(a) shows the transmission for the TE0

mode at a wavelength of 1550 nm as a function of the interlayer transition length, Lc, computed using three-dimensional ﬁnite-diﬀerence time-domain (3D-FDTD) simulations.

The waveguide tip widths are 180 nm and 200 nm for the Si and Si3N4 levels, respectively.

Taper lengths > 10 μm are suﬃcient for an interlayer transition loss of < 0.09 dB over the SCL bands. As Lc increases, the transmission approaches an upper-bound set by the scattering loss of the blunt tips, and this loss can be reduced by decreasing the tip widths and the Si layer thickness. Additional 3D-FDTD simulations showed that the transitions were robust against interlayer misalignment, which could be as high as ±50 nm. The simulated excess loss in the SCL-bands was < 0.03 dB and < 0.001 dB for ±50 nm alignment oﬀsets in the directions perpendicular to and along the optical propagation axis, respectively. The measurements of the interlayer transitions for TE-polarized light are summarized

in Figs. 4.5(b)-(d). Two transition geometries have been considered: 1) a 180 nm wide

Si tip, a 200 nm wide Si3N4 tip, and Lc =15μm for the SCL-bands, and 2) a 140 nm wide Si tip, a 200 nm wide Si3N4 tip, and Lc =15μmfortheO-band.Thetwotypes of transitions had similar optical losses in the SCL-bands, but the transition with the smaller (140 nm wide) Si tip was superior in the O-band. The transition loss was < 0.07 dB over the SCL-bands and < 0.09 dB over the O-band. These numbers represent the upper-bounds on the loss including the experimental uncertainty from alignment errors and Fabry-Perot oscillations in the transmission spectrum of each cutback structure, which introduce errors in the linear ﬁts and loss per transition. More speciﬁcally, the raw loss per transition extracted from the cutback measurements was < 0.06 dB over the SCL-bands and < 0.07 dB over the O-band; the experimental uncertainty in these values was < 0.01 dB for the SCL-bands measurement and < 0.02 dB for the O-band measurement. The measured transition losses were slightly lower than the simulated values likely due to the rounding of the Si tip during fabrication, which reduced the Chapter 4. Silicon nitride on silicon photonic platform 56

0 −5

−0.5 −10

−1 −15 −1.5 −20 1550nm, L =15μm, w =180nm −2 c Si,tip −25 1310nm, L =15μm, w =140nm −2.5 Raw transmission (dB) c Si,tip Fits

Transmission (dB/transition) −30 0 10 20 30 40 50 0 100 200 300 L (μm) Number of transitions c (a) (b)

0 0

−0.05 −0.05

−0.1 −0.1

−0.15 −0.15 Transmission (dB/transition) Transmission (dB/transition)

1480 1510 1540 1570 1600 1260 1280 1300 1320 1340 1360 Wavelength (nm) Wavelength (nm) (c) (d)

Figure 4.5: (a) The computed transmission of the interlayer transition as a function of Lc for λ = 1550 nm. (b) Examples of the measured raw transmission data of cutback structures as a function of the number of interlayer transitions at wavelengths of 1550 nm and 1310 nm. Linear ﬁtting yields the transmission per transition. (c), (d) Spectra of the loss per transition in (c) the SCL-bands and (d) the O-band extracted from linear ﬁts of the transmission spectra vs. number of transitions. Chapter 4. Silicon nitride on silicon photonic platform 57

eﬀective width of the Si tip. The simulation assumed a rectangular blunt Si tip, not a rounded tip.

4.2.3 Waveguide crossings

The reduced index contrast of the Si3N4 waveguide makes the realization of low-loss and low-crosstalk waveguide crossings more straightforward. In Si, compact, fully-etched waveguide crossings fabricated using photolithography (i.e., without sub-wavelength features) at best have an insertion loss in the range of 0.04 dB to 0.1 dB and a crosstalk of -35 dB in the C-band [116], and using genetic algorithms, an insertion loss better than 0.04 dB can be achieved over a bandwidth of about 45 nm and crosstalk can be improved to −40 dB [117]. To reduce the insertion loss, the index contrast of the Si waveguides is lowered at the crossing by using the partially-etched level at the expense of a larger crossing size [19,24]; losses as low as 0.015 dB per crossing have been predicted [24]. Here, we use the multimode interference concept in [118, 119] to realize compact crossings using the fully-etched Si3N4 waveguides in the FEOL platform. The crossings were implemented for the TE-polarization in the SCL-bands. Figure 4.6(a) illustrates the design and dimensions, and Fig. 4.6(b) shows the optical power proﬁle from a 3D- FDTD simulation. The input was the TE0 mode, and the incoming light entered a taper transition which excited the TE0 and TE2 modes of the multimode waveguide section. Due to the interference of these two modes, the beam narrowed at the crossing to reduce the insertion loss [119]. Figure 4.6(c) shows an optical micrograph of a fabricated waveguide crossing. The measurement results of the crossings are summarized in Figs. 4.6(d)-(f). The loss measurements were carried out using the cutback method and a sample set of raw data with a linear ﬁt is shown in Fig. 4.6(d). By measuring the transmission spectra from the cutback structures, the transition loss spectrum in Fig. 4.6(e) was extracted. The insertion loss was found to be < 0.07 ± 0.01 dB per crossing over a broad bandwidth Chapter 4. Silicon nitride on silicon photonic platform 58

SingleͲmode SingleͲmode 1.0 40 waveguide waveguide Multimode Linear interference Linear taper region taper m)

ʅ 0.5 20 Y(

6 ʅm 23ʅm 6 ʅm 3.5ʅm 0 0.0 Ͳ200 20 0.9ʅm X(ʅm) (a) (b)

−5 Data Fit −6

−7

−8 Raw transmission (dB) −9 0 20 40 60 80 Number of crossings (c) (d)

0 0

−0.02 −20 Thru Crosstalk −0.04 −40 −0.06

−0.08 −60 Raw transmission (dB)

−0.1

Transmission (dB/crossing) −80 1480 1510 1540 1570 1600 1480 1510 1540 1570 1600 Wavelength (nm) Wavelength (nm) (e) (f)

Figure 4.6: (a) Top-down view schematic of the Si3N4 waveguide crossing. The crossing is designed for TE-polarized light in the C-band. (b) 3D-FDTD simulated profile of the optical power at λ = 1550 nm passing through the crossing. The TE0 input is injected at y =0μm. (c) Optical micrograph of the waveguide crossing. (d) Measured raw fiber-to- fiber transmission of the crossing cutback structures at λ = 1550 nm. (e) Transmission spectrum of a single crossing extracted from the cutback structures. (f) Measured raw through (thru) and crosstalk transmission spectra showing < -48 dB of crosstalk over a 120 nm bandwidth. Chapter 4. Silicon nitride on silicon photonic platform 59

of 120 nm across the SCL-bands. The uncertainty is due to alignment errors and Fabry- Perot oscillations in the transmission spectra of the diﬀerent cutback structures. From Fig. 4.6(f), the measured crosstalk was < −48 dB over a wavelength range from 1480 nm to 1600 nm. The measured crosstalk was larger than the simulated crosstalk of < −70

dB, and the measurement was likely limited by the collection of light scattered from the lensed ﬁber input coupling.

4.3 Summary

In summary, we have demonstrated a multilayer Si3N4-on-Si integrated photonic platform with independent and aligned Si3N4 and Si waveguides. The Si3N4 waveguides generally exhibited signiﬁcantly lower waveguide losses than the Si waveguides, especially in the

O-band where the Si3N4 waveguide loss was < 0.5 dB/cm. Using adiabatic tapers,

light was eﬃciently transferred between the Si3N4 and Si layers with < 0.07 dB and < 0.09 dB of insertion loss per transition in the C- and O- bands, respectively. The reduced index contrast of the Si3N4 layer enabled the simple implementation of multimode waveguide crossings with low losses and crosstalk. In addition to the capability of separately implementing devices in each level, optical devices can be designed that take advantage of the composite optical modes or ﬁelds that arise from the strong interactions between the two levels, and in Chapters 5 and 6, we apply this principle to grating coupler and polarization rotator-splitter designs. Chapter 5

Silicon nitride on silicon grating coupler

As discussed in Section 1.2, designing fiber-to-chip grating couplers with high coupling efficiencies and large bandwidths is a standing problem in Si photonics, and prior to this work, high efficiency grating couplers (> −2 dB peak coupling efficiency) had 1-dB bandwidths < 50 nm, and wide bandwidth grating couplers (1-dB bandwidth > 65 nm) had

1 coupling eﬃciencies < −4 dB. In this chapter , we propose and demonstrate Si3N4-on- Si dual-level grating couplers that have high coupling eﬃciencies and large bandwidths.

The grating couplers use aligned Si3N4 and Si grating teeth, a moderate 400 nm Si3N4 thickness, and no bottom reﬂectors. Our demonstrated coupling eﬃciency to standard

single-mode ﬁber is -1.3 dB (74%), and our demonstrated 1-dB bandwidth is 80 nm. In

Fig. 5.1, our experimental result is plotted next to a summary of the best SOI and Si3N4 grating coupler demonstrations in the C-band; the numbers next to the markers indicate the references [40, 42–51, 53, 54]. Relative to past demonstrations, our grating coupler exhibits the highest eﬃciency-bandwidth product. Concurrent to the publication of this work in 2014 [72, 120], a dual-level grating coupler using two Si layers for the O-band

1c OSA. Reprinted, with permission, from [72]

60 Chapter 5. Silicon nitride on silicon grating coupler 61

0 This work (Si N −on−Si) 3 4 47 51 Si N − only 3 4 −1 49 44 Si N + back reflector 50 43 3 4 48 Si − only 46 42 45 −2 Si + back reflector Si − ≈ 50nm features 41 53 −3

−4 40

Peak coupling efficiency (dB) 54

−5 0 20 40 60 80 100 120 1−dB bandwidth (nm)

Figure 5.1: Comparison of our Si3N4-on-Si dual-level grating coupler experimental result with previously published Si and Si3N4 grating coupler demonstrations in the C-band (coupling eﬃciencies and 1-dB bandwidths). The numbers next to the markers are the references.

was published [121] with a measured peak coupling eﬃcency of -3.8 dB and a measured

1-dB bandwidth less than 50 nm. In 2015, the device was improved in [122] and a peak coupling eﬃciency of -1.2 dB and a 1-dB bandwith of 78 nm were measured, which is nearly identical to our grating coupler performance.

The Si3N4 and Si layer thicknesses of our grating coupler are compatible with Si3N4- on-Si photonic platforms, and the devices demonstrated in this chapter were fabricated using our Si3N4-on-Si platform demonstrated in Chapter 4. As an example of this platform compatibility, we demonstrate a 1 × 4 tunable multiplexer/demultiplexer using the

Si3N4-on-Si dual-level grating couplers and thermally-tuned Si microring resonators.

This chapter is organized as follows: Section 5.1 describes our Si3N4-on-Si grating coupler design, Section 5.2 describes our experimental demonstration of the grating coupler, and Section 5.3 describes our 1 × 4 tunable multiplexer/demultiplexer demonstration. Chapter 5. Silicon nitride on silicon grating coupler 62

5.1 Device design

The Si3N4-on-Si dual-level grating coupler is shown in Fig. 5.2(a) and consists of moderately-

thick Si3N4 grating teeth above a set of thin, aligned, Si grating teeth. Owing to the prox-

imity of the Si3N4 and Si teeth ( 200 nm), the grating behaves as a collection of composite Si3N4-Si grating teeth and not as a Si3N4 grating coupler with a Si back reflector. The combination of Si3N4 and Si breaks the vertical symmetry of the grating, and with proper design, we achieve constructively (destructively) interfering upwards (downwards) radiation from the different scattering interfaces (i.e., high directionality). Si grating couplers typically achieve this vertical asymmetry and high directionality through design of the Si thickness and partial-etch depth, but for Si3N4 grating couplers, the moderate refractive index contrast necessitates large thicknesses to simultaneously achieve high directionalities and appropriate grating strengths. Through optical simulations, we have found that partially-etched Si3N4 grating couplers require the Si3N4 thickness to be > 800 nm to ra- diate > 80% of the input optical power upwards over twice the fiber mode-field-diameter.

Our composite Si3N4-Si grating tooth design circumvents this coupling eﬃciency limitation of Si3N4 grating couplers. In addition, since the Si3N4 is moderately-thick and the

Si is relatively thin, the dual-level grating coupler’s period remains comparable to those of purely Si3N4 grating couplers, which allows large bandwidths due to fewer grating periods over the ﬁber mode diameter compared to Si grating couplers [40].

The grating coupler’s Si3N4 and Si thicknesses were chosen to be compatible with

the Si3N4-on-Si photonic platform in Fig. 5.2(b) and demonstrated in Chapter 4. The

grating coupler uses the fully-etched, 400 nm thick Si3N4 level and the partially-etched,

65 nm thick Si level. A planar, 135 nm thick layer of SiO2 exists between the Si3N4 and Si grating teeth.

The dimensions of our apodized dual-level grating coupler design are shown in Fig. 5.2(c); the design is targeted at the TE-polarization and coupling to standard single-mode ﬁber. The parameters of the ﬁrst 11 grating periods are listed in the schematic; the last Chapter 5. Silicon nitride on silicon grating coupler 63

TiN heater

1.5ʅm TopSiO2 cladding

150nm 400nm Si3N4 65nm Si 50nm

Si3N4 Si strip Si rib Si3N4ͲonͲSOI waveguide waveguide waveguide grating coupler BOX 2ʅm

Sisubstrate

(a) (b)

21o Fibercore

Si3N4 TopSiO2 cladding& PartiallyͲ indexmatchingfluid w g etchedSi Si3N4 ToPIC … L BOX wSi 425nm 200nm 675nm 700nm 700nm 700nm 725nm 700nm 700nm 825nm 950nm wSi3N4= 775nm 875nm wSi= 400nm 400nm 400nm 400nm 400nm 400nm 400nm 400nm 400nm g = 725nm 700nm 700nm 700nm 700nm 725nm 725nm 550nm 275nm y L= 350nm 325nm 350nm 350nm 325nm 275nm 225nm 125nm 50nm Sisubstrate x z

(c)

Figure 5.2: (a) Perspective schematic of the Si3N4-on-Si dual-level grating coupler. (b) Schematic of the waveguide cross-sections in the Si3N4-on-Si integrated photonics platform. (c) Cross-section schematic of the grating coupler and an input/output optical ﬁber. The following parameters of each grating period are listed: Si3N4 grating tooth width (wSi3N4), Si grating tooth width (wSi), gap between Si3N4 teeth (g), and the oﬀset between Si3N4 andSiteeth(L). Chapter 5. Silicon nitride on silicon grating coupler 64

−1 0.9

0.8 −2 0.7 −3 0.6 Apodized Directionality, D Uniform Coupling efficiency (dB) −4 0.5 1460 1480 1500 1520 1540 1560 1580 −300 −200 −100 0 100 200 300 Wavelength (nm) ΔL (nm) (a) (b)

Figure 5.3: (a) Simulated coupling eﬃciency versus wavelength for the apodized and uniform grating couplers. (b) Simulated directionality (D) versus variations in the oﬀsets between the Si3N4 and Si teeth from their apodized values (ΔL). ΔL = 0 nm corresponds to the optimized grating in Fig. 5.2(c).

5 periods are identical to the period on the far left. We chose a relatively large coupling angle of 21◦ to slightly enhance the bandwidth and coupling efficiency. In general, the bandwidth of a grating coupler increases weakly with the coupling angle [40]. Also, for the 2 μm buried-oxide (BOX) thickness in the Si3N4-on-SOI platform, reflections from the substrate are in phase with the grating coupler’s upward radiation at a coupling angle of 21◦. The efficiency of the grating coupler is optimized by: 1) improving the mode-matching to fiber via apodization, 2) choosing the offsets between the Si3N4 and Si teeth (L) to achieve a high directionality. To obtain the apodized grating coupler parameters, we started with a uniform grating coupler with a period of 1.4 μm, wSi3N4 = 750 nm, wSi = 400 nm, and L = 250 nm, which we found to have a high directionality of 80%. Two extra Si teeth were included before the first Si3N4 tooth to provide a weak coupling strength at the beginning of the grating; the number of extra Si teeth was chosen to optimize the peak coupling efficiency of the uniform grating. The uniform grating coupler was apodized using two- dimensional finite-difference time-domain (2D-FDTD) simulations with the Si substrate included; fiber modes were launched toward the grating coupler and overlap integrals were calculated at the Si3N4 waveguide output. We performed exhaustive parameter sweeps Chapter 5. Silicon nitride on silicon grating coupler 65

on sets of two adjacent grating periods. Specifically, the period, wSi3N4, wSi,andL values were exhaustively swept for periods 1 and 2 and the parameters that maximized the peak coupling efficiency were applied to the grating; the process was repeated for periods 2 and 3, 3 and 4, etc. Figure 5.3(a) shows simulations of the coupling efficiency versus wavelength for the uniform and apodized grating couplers. The uniform design has a peak coupling efficiency of -1.8 dB and a 1-dB bandwidth of 114 nm, and the apodized design has a peak coupling efficiency of -1.0 dB and a 1-dB bandwidth of 82 nm. The 0.8 dB improvement in peak coupling efficiency via apodization is similar to Si grating coupler apodization results, however, a more complex apodization procedure using a genetic algorithm may yield improved performance [43]. Also, the uniform design’s larger 1-dB bandwidth is due to the longer optical path lengths of the periods with the two extra Si teeth compared to the remaining periods; this difference in optical path lengths is removed in the apodized design.

The importance of L to the directionality, D, is evident from Fig. 5.3(b). From Section 1.2, D is defined as the fraction of radiated power from the grating directed toward the superstrate. In the figure, D is plotted against ΔL, the deviation in L from the apodized values, i.e., all the Si grating teeth are shifted by the same distance, ΔL,onthe z-axis in Fig. 5.2(c). These simulation results were obtained using the 2D-FDTD method without the Si substrate; light was launched into the Si3N4 waveguide and scattered by the grating coupler. High directionalities (> 80%) are achieved when the Si teeth are pushed ahead of the Si3N4 teeth on the z-axis (ΔL ≈ 0). The directionality remains high for ΔL ≈±50 nm. For |ΔL| > 150 nm, the directionality degrades significantly, and this degradation is larger when ΔL<0. ΔL = −50 nm is a more optimal point in terms of directionality, but ΔL = 0 nm was used for the final design because it provided a slightly higher peak coupling efficiency due to the substrate reflections and the mode-matching to fiber.

Alignment error between the Si3N4 and Si grating teeth will deteriorate the grating Chapter 5. Silicon nitride on silicon grating coupler 66

−1

0.2 dB −2

−3

Δ −4 L = 0 nm ΔL = +50 nm

Coupling efficiency (dB) ΔL = −50 nm −5 1460 1480 1500 1520 1540 1560 1580 Wavelength (nm)

Figure 5.4: Simulated coupling eﬃciency versus wavelength with ±50 nm variations in the oﬀsets between the Si3N4 and Si grating teeth from their apodized values (ΔL). coupler performance. Alignment along the propagation axis (z-axis) of the grating (i.e.,

ΔL) is the most critical. CMOS fabrication processes allow alignment accuracy better than ±50 nm, and Fig. 5.4 shows the simulated spectra of the apodized grating coupler efficiency for ΔL = ±50 nm. The reduction in peak coupling efficiency is only 0.2 dB, and the 1-dB bandwidth grows to 94 nm for a +50 nm error and shrinks to 72 nm for a -50 nm error; the center wavelength is not significantly altered. Overall, the

Si3N4-on-Si grating coupler design can withstand ±50 nm of alignment error with only marginal performance degradations. Alignment errors perpendicular to the propagation axis (x-axis) of the grating are only relevant for focusing grating coupler designs, and for the focusing design in this work, misalignment on the x-axis has little eﬀect on the

performance. From 3D-FDTD simulations, alignment errors of ±100 nm on the x-axis reduce the peak coupling eﬃciency and 1-dB bandwidth by < 0.1dBand< 1nm, respectively. The ﬁnal step in the grating coupler design was curving the grating teeth to obtain

a focusing grating coupler with a compact footprint. Following the design procedure in [39], we curved the grating teeth into confocal ellipses with a minimum grating order

of 20. Si3N4 and Si grating teeth from the same period followed the same elliptical shape Chapter 5. Silicon nitride on silicon grating coupler 67

along their center-lines but had diﬀerent tooth widths and the oﬀset, L, applied to the Si tooth. The overall design is shown in the optical microscope image of the fabricated grating coupler [Fig. 5.5(a)] in the next subsection. From 3D-FDTD simulations, we found that this grating coupler design focused incident light into a spot size larger than

the 900 nm single-mode Si3N4 waveguides, and to eliminate loss from this effect, we included a two-stage taper after the elliptical grating teeth. The Si3N4 is rapidly tapered down from the fiber mode width to a width of 4.3 μm over a length of 21.5 μm, and then, the Si3N4 istapereddowntoawidthof900nmusinga40μm long taper. Lastly, the fiber alignment sensitivity of our grating coupler is similar to that of Si grating couplers. This is expected since the grating’s radiation is well mode-matched to standard single-mode fiber and the alignment sensitivity is set by the profiles of the fiber mode and the grating’s radiation. We used FDTD simulations to verify that the 1-dB alignment sensitivity is ≈ 2 μm.

5.2 Experimental results

Grating couplers were fabricated in the Si3N4-on-Si photonic platform in Fig. 5.2(b) at IME, A*STAR. The fabrication process is described in Chapter 4. An optical microscope image of a fabricated, apodized, focusing, Si3N4-on-Si grating coupler is shown in Fig. 5.5(a). The grating coupler footprint is 27 μm × 87 μm, and the grating coupler connects to a 900 nm wide, single-mode, Si3N4 routing waveguide. Scanning electron microscope

(SEM) images of the Si and Si3N4 grating teeth during fabrication are shown in Figs. 5.5(b) and 5.5(c). The grating coupler measurements were performed on the test structure shown in

Fig. 5.6, which consists of two nominally identical grating couplers connected by a U- shaped, single-mode, 900 nm wide, 351 μm long, Si3N4 waveguide. The grating couplers are on a 250 μm pitch, and the short length of routing waveguide connecting the grating Chapter 5. Silicon nitride on silicon grating coupler 68

20ʅm

(a)

8 ʅm 6ʅm

(b) (c)

Figure 5.5: (a) Optical micrograph of the fabricated Si3N4-on-Si dual-level grating coupler. (b) Scanning electron microscope (SEM) image of the Si grating teeth during fabrication (i.e., after Si etching but before deposition of the SiO2 spacer layer between the Si and Si3N4). (c) SEM image of the Si3N4 grating teeth during fabrication (i.e., after Si3N4 etching but before the SiO2 top cladding deposition).

Si3N4 waveguide

Gratingcouplers

100μm

Figure 5.6: Annotated optical micrograph of the Si3N4-on-Si grating coupler test structure. Two nominally identical grating couplers are connected by a single-mode Si3N4 waveguide. Chapter 5. Silicon nitride on silicon grating coupler 69

−1 −1.29 dB

−2 Δλ = 80 nm 1dB −3

−4

Coupling efficiency (dB) Simulation Measurement −5 1460 1480 1500 1520 1540 1560 1580 Wavelength (nm)

Figure 5.7: Measured and simulated coupling eﬃciency versus wavelength for the Si3N4- on-Si dual-level grating coupler in Fig. 5.5.

couplers was not normalized out of the measurement data. Light from a tunable laser was TE-polarized and coupled on/off the chip using a standard single-mode fiber array that was polished and tilted at 21◦. Index matching fluid was applied to the chip to reduce reflections at the fiber-to-chip interface. The coupling efficiency versus wavelength of a single grating coupler was obtained by taking the square root of the raw transmission spectrum data of the two-grating-coupler structure on a linear-scale.

Figure 5.7 shows the measured coupling eﬃciency versus wavelength for the Si3N4- on-Si grating coupler. The peak coupling eﬃciency was -1.3 dB (74%) at a wavelength of

1536 nm, and the 1-dB bandwidth was 80 nm. A 2D-FDTD simulation of the coupling efficiency versus wavelength is also shown in Fig. 5.7, and it closely agrees with the measurement data; the simulated peak coupling efficiency and 1-dB bandwidth are - 1.0 dB and 82 nm, respectively. The ripples in the measured coupling efficiency versus wavelength plot were Fabry-Perot oscillations due to reflections from the grating couplers and the end of the fiber array. By assuming all the reflections were due to on-chip back- reflections from the grating couplers, we calculate the worst-case, on-chip reflectivity of Chapter 5. Silicon nitride on silicon grating coupler 70

a single grating coupler to be -16 dB over the 1-dB bandwidth [41]. The reflectivity could be improved significantly by applying the design strategy in [123, 124], where the elliptical grating teeth are modified so that the on-chip reflections are directed away from the aperture of the focusing grating coupler.

Following the publication of our work, the analysis and simulations in [125] predicted that coupling eﬃciencies of -0.2 dB are possible with dual-level grating couplers. Opti- mizing the thickness and refractive index of the silicon nitride in our photonic platform may improve the coupling eﬃciency of our grating coupler design towards the -0.2 dB prediction, however, this may come at the expense of reduced performance of the other

components in the platform.

5.3 Integration example: 1 × 4 tunable multi-

plexer/demultiplexer

To demonstrate integration of the Si3N4-on-Si grating couplers on an integrated optics platform, we fabricated and measured the 1 × 4 tunable multiplexer/demultiplexer shown in Fig. 5.8(a) on the platform described in Fig. 5.2(b). The PIC consists of four add- drop Si microrings coupled to a Si bus waveguide, which is connected to grating couplers at the input and output (“GCin”and“GCthru,” respectively). Each microring has an independent TiN thin ﬁlm heater, and the drop port of each microring is connected to a grating coupler. The microrings are labeled as “Ring 1” to “Ring 4,” and the drop port grating couplers are labeled as “GC1”to“GC4.” The PIC uses the microring ﬁlters to demultiplex a multi-wavelength input at GCin into single-wavelength outputs at GC1 to

GC4. The PIC is also capable of multiplexing inputs at GC1 to GC4 into an output at

GCthru. Overall, the PIC uses all the levels in the platform, i.e., the Si3N4 and partially- etched Si for the grating couplers, the fully-etched Si for microrings and bus waveguides, and the TiN and contact metals for thin ﬁlm heaters. Chapter 5. Silicon nitride on silicon grating coupler 71

Ring1 Ring2 Ring3 Ring4 200ʅm

GCin GC1 GC2 GC3 GC4 GCthru

(a) Thruportcoupler

Simicroring

Si3N4ͲSi waveguide Dropport transition coupler

Si3N4ͲonͲSOI dualͲlevel gratingcoupler 150nmthickSi 65nmthickSi

Si3N4

(b)

Figure 5.8: (a) Optical micrograph of the 1 × 4 tunable multiplexer/demultiplexer. “GC” refers to a Si3N4-on-Si dual-level grating coupler, and “Ring” refers to a Si add- drop microring with thermal tuning via a TiN heater. (b) Schematic of a Si microring resonator in the multiplexer/demultiplexer without the TiN and contact metals. The microring is connected to Si bus waveguides and the drop port is connected to a grating coupler. Chapter 5. Silicon nitride on silicon grating coupler 72

All the microrings in the PIC are nominally identical, and a schematic of the microring design is shown in Fig. 5.8(b). The Si waveguides are 500 nm wide and fully-etched. The microrings use 7.5 μm radius bends, and the through (“thru”) and drop port couplers are nominally identical and consist of 2.5 μm long straight coupling regions with 230 nm wide coupling gaps. The Si waveguides connect to grating couplers via adiabatic transitions from the Si to Si3N4 levels (i.e., the interlayer transitions discussed in Section 4.2.2). Over a length of 15 μm, the Si narrows down from a width of 500 nm to a 180

nm wide blunt tip while the Si3N4 begins with a blunt 200 nm tip and widens to a 900 nm width.

The PIC was measured in the demultiplexer mode of operation. Light from a tunable laser was input into GCin and the transmission spectra at GCthru and GC1 to GC4 were measured. The input laser light was TE-polarized and coupled on/off the chip via a fiber array. We electrically probed the thermal tuners using a multi-contact wedge, and this prevented us from applying index matching fluid to the chip. The fiber-to-fiber transmission measurement data is shown in Fig. 5.9. Figure 5.9(a) shows the thru port transmission spectra, over a wavelength range from 1510 to 1550 nm, before and after the microrings were thermally tuned, i.e., transmission from GCin

to GCthru. Three of the four microrings were tuned, and the tuning powers for each microring were < 35 mW. The free-spectral range of the microrings was about 11.4 nm. Before thermal tuning, the microring resonances were unevenly spread due to fabrication variations in the waveguide dimensions. After thermal tuning, the resonances were evenly distributed with a channel spacing of about 2.5 nm and extinction ratios > 15 dB. The thru port spectrum had a peak transmission of about -5 dB, and we estimate the insertion loss can be broken down into about 1.5 - 2 dB per grating coupler and about 1 - 2 dB due to the Si3N4 to Si adiabatic transitions, microring directional couplers, and waveguide losses. Our loss estimate of the grating couplers is larger than the measurements in

Section 5.1 for two reasons: 1) no index matching ﬂuid was used, 2) the alignment Chapter 5. Silicon nitride on silicon grating coupler 73

−5 Not tuned Tuned −15

−25

−35 Thru port transmission (dB) −45 1510 1520 1530 1540 1550 Wavelength (nm) (a)

−5 Ring 1 Ring 2 −15 Ring 3 Ring 4

−25

−35 Drop port transmission (dB) −45 1510 1520 1530 1540 1550 Wavelength (nm) (b)

Figure 5.9: Fiber-to-ﬁber transmission measurements for the 1 × 4 tunable multiplexer/demultiplexer in Fig. 5.8. (a) Thru port spectra before and after thermal tuning (i.e., transmission from GCin to GCthru). (b) Drop port spectra of Rings 1 to 4 after thermal tuning (i.e., transmission from GCin to GC1 -GC4). “GC” refers to a grating coupler and “Ring” refers to a Si microring; the nomenclature is deﬁned in Fig. 5.8(a). Chapter 5. Silicon nitride on silicon grating coupler 74

accuracy of our measurement apparatus was worse since the ﬁber array and electrical probes simultaneously contacted the chip. Figure 5.9(b) shows the drop port transmission spectra of the PIC with the micror-

ings thermally tuned, i.e., transmission from GCin to GC1 -GC4. Over a wavelength range between 1510 and 1550 nm, the maximum transmission values of the drop port resonances ranged from -5.3 to -6.8 dB, and the 3-dB bandwidths and loaded quality factors of the resonances were about 0.5 nm and 3100, respectively. The variation in the maximum transmission values was due to the wavelength variation of the microring couplers, the Fabry-Perot oscillations from the grating coupler reﬂections, and the 80 nm

1-dB bandwidth per grating coupler. From Fig. 5.1, if the Si3N4-on-Si grating couplers were replaced with Si-only grating couplers, the variation in the maximum transmission values of the drop port resonances would increase by about 1.5 dB or more over the 40 nm wavelength measurement range. The 40 nm wavelength range corresponds roughly to the 0.5-dB bandwidth for transmission through two Si3N4-on-Si grating couplers and to the 2-dB or 3-dB bandwidth for transmission through two Si grating couplers.

5.4 Summary

In summary, we have proposed and demonstrated a high-eﬃciency, wide bandwidth grat-

ing coupler using aligned Si3N4 and Si teeth. The grating coupler uses the Si3N4 to achieve a wide bandwidth and the Si for a high directionality. The grating coupler can be integrated in Si3N4-on-Si photonic platforms, and we demonstrated this by fabricating and measuring a thermally-tunable multiplexer/demultiplexer PIC that uses the grating couplers as well as independent waveguides in Si3N4 and Si. Our design approach of using moderate and high refractive index materials to produce high-performance grating couplers can be applied to other material systems such as Si3N4 on III-V semiconductors and aluminum nitride on SOI. Chapter 6

Silicon nitride on silicon polarization rotator-splitters

In this chapter1, we extend the polarization rotator-splitter (PRS) design presented in

Chapter 3 to the Si3N4-on-Si photonic platform demonstrated in Chapter 4. The PRS

design is based on TM0-TE1 mode conversion in a composite Si3N4-Si waveguide. The design is entirely adiabatic and is inherently more broadband and fabrication tolerant than the first demonstration of a polarization splitter-rotator in a Si3N4-on-Si platform in [32], which used a directional coupler for polarization splitting and a Si3N4-on-Si adiabatic polarization rotator. Compared to our PRS demonstration based on Si ridge waveguides in Chapter 3, our Si3N4-on-Si design has improved fabrication yield since it lacks the inherently difficult to control partial-etch depth of Si ridge waveguides. This chapter is organized as follows: we discuss the PRS design in Section 6.1; we present measurements of the PRS in Section 6.2; finally, we apply the PRS to an active polarization controller in Section 6.3.

1c OSA. Reprinted, with permission, from [73]

75 Chapter 6. Silicon nitride on silicon polarization rotator-splitters 76

6.1 Polarization rotator-splitter design

Our PRS design is shown in Fig. 6.1(a). The design uses the 150 nm thick Si layer and

the 400 nm thick Si3N4 layer in our Si3N4-on-Si platform from Chapter 4. The vertical asymmetry of a composite waveguide formed out of the Si3N4 andSilayersisusedto adiabatically transform the TM0 mode to the TE1 mode before separating the TE1 and TE0 modes into two output waveguides using an adiabatic coupler. Similar to the Si

PRS in Chapter 3, the Si3N4-on-Si PRS design implemented here is entirely adiabatic to improve the fabrication tolerance and operation bandwidth. Figure 6.1(b) illustrates the detailed PRS operation, which is based on mode evolution. The two modes with the highest eﬀective indices at various positions along the PRS are indicated (i.e., “mode 1” and “mode 2”). At the input, a single-mode 900 nm wide Si3N4 input waveguide is widened to 1.4 μm. Then, a Si waveguide begins with a

180 nm wide tip underneath the Si3N4. At this point, modes 1 and 2 are TE0 and TM0, respectively, and are mostly confined in the Si3N4. The Si waveguide is then widened while the Si3N4 width is unchanged, enabling the conversion from TM0 to TE1. In this section of the PRS, the composite Si3N4-Si waveguide is vertically asymmetric, leading to a large difference in the effective indices of modes 2 and 3 throughout the structure [Fig. 6.1(c)]. As a result, a TM0 input remains as mode 2 through the TM0-TE1 mode converter. It first evolves into a “hybridized” mode, which has TM0 and TE1 characteristics, and then the TE1 mode. A TE0 input remains in mode 1, the TE0 mode. After the TM0-TE1 mode converter, the Si3N4 is tapered down and terminated with a blunt 200 nm wide tip while the Si width is constant at 930 nm. Since the TE0 and TE1 modes are confined primarily in the Si, the Si3N4 termination is low-loss and has the benefit of restoring vertical symmetry, which prevents any further interaction between the TM0 and TE1 modes. An adiabatic coupler follows the TM0-TE1 mode converter. The design is similar to that in Chapter 3, and it uses only fully-etched Si waveguides. The TE0 and TE1 Chapter 6. Silicon nitride on silicon polarization rotator-splitters 77

(a)

Mode1 Mode1 Mode1 Mode1

TE0 TE0 TE0 TE0 2.5 TE0 Mode 2 2.25 Mode 3 TE1

eff 2 n Hybridized TM0 1.75 TM0 TE1 Hybridized 1.5 Mode2 Mode2 Mode2 Mode2 180 330 480 630 780 930 TM0 TE1 TE1 TE1 Si width (nm) (b) (c)

Figure 6.1: (a) Schematic of the Si3N4-on-Si PRS. Lengths are labeled in green; widths are labeled in red for the Si layer and in purple for the Si3N4 layer. (b) Mode profiles of the modes with the first and second highest effective indices (i.e., “mode 1” and “mode 2”) along the PRS. (c) Modal effective indices (neff ) in the TM0-TE1 mode converter showing hybridization of the TM0 and TE1 modes; the Si3N4 widthisfixedat1.4μmand the Si width is increased. The calculations in (b) and (c) were performed at a wavelength of 1550 nm. Chapter 6. Silicon nitride on silicon polarization rotator-splitters 78

(a)

(b)

Figure 6.2: Optical micrographs of the Si3N4-on-Si PRS. (a) The whole PRS. (b) The point where the Si3N4 terminates before the adiabatic coupler; a Si3N4-Si composite waveguide is on the left of the termination and a Si waveguide is on the right. modes are now the supermodes of the adiabatic coupler. A narrow waveguide starts with a 180 nm wide tip next to a broad 930 nm wide waveguide, in which both the TE0 and TE1 modes are almost entirely confined. Then, the narrow waveguide widens to a width of 500 nm and the broad waveguide width decreases to 630 nm, while the gap remains at 200 nm. This transition causes the TE1 mode to become mostly confined in the narrow waveguide while the TE0 mode is confined in the broad waveguide. The narrow waveguide is then bent away using an arc with a radius of 500 μm, and the TE0 and TE1 modes evolve into the TE0 modes of the isolated top and bottom waveguides, respectively. Finally, adiabatic transitions couple light from the Si waveguides to 900 nm wide Si3N4 output waveguides.

6.2 Experimental results

Figure 6.2 shows the microscope images of the fabricated PRS. The total device length

is 576 μm. The device is connected to Si3N4 inverse-taper edge couplers at both ends for efficient coupling to tapered fibers with spot sizes of about 2 μm in diameter. To eliminate the effects of fiber polarization rotation on the device measurements, we used Chapter 6. Silicon nitride on silicon polarization rotator-splitters 79

TE branch output

0 TE−>TE −10 TE−>TM TM−>TE −20 TM−>TM −30 −40

Transmission (dB) −50

−60 1500 1520 1540 1560 1580 Wavelength (nm) (a) TM branch output

0 TE−>TE −10 TE−>TM TM−>TE −20 TM−>TM −30 −40

Transmission (dB) −50

−60 1500 1520 1540 1560 1580 Wavelength (nm) (b)

Figure 6.3: PRS transmission spectra measurements at (a) the TE branch output (i.e., the top output in Fig. 6.1(a)) and (b) the TM branch output (i.e., the bottom output in Fig. 6.1(a)). The legends in (a) and (b) indicate the input and output polarizer settings (e.g., TE→TM refers to a TE-polarized input and a measurement of the TM-component of the output). Chapter 6. Silicon nitride on silicon polarization rotator-splitters 80 the measurement setup in Fig. 3.3 of Chapter 3, which relied on free-space coupling and free-space polarizers. Speciﬁcally, light from a tunable laser was coupled onto/oﬀ the chip using aspherical lenses, and manually-adjustable, free-space, linear polarizers were placed at the input and output of the chip to set the input polarization and analyze the output polarization. The measured transmission spectra of the PRS are shown in Fig. 6.3. The PRS transmission spectra have been normalized to the edge coupler transmission spectra to remove contributions from the measurement apparatus and edge couplers. The legend indicates the input polarization and the setting of the output polarizer, e.g., “TE →

TM” is the measurement of the TM component of the output with a TE-polarized input. The polarization crosstalk at both outputs was less than -19 dB, the insertion loss was less than 1.5 dB, and the polarization-dependent loss (PDL) was less than 1.0 dB over a wavelength range from 1500 nm to 1580 nm. These values have an error of about ±0.5dB

due to errors in aligning the coupling lenses to the chip. The oscillations in the spectra of the crosstalk components were due to small errors in the alignment of the input and output free-space polarizers. Compared to [32], our PRS has a similar insertion loss and a broader bandwidth. As discussed in Chapter 3, the polarization crosstalk of our PRS

can be further improved by using polarization clean-up ﬁlters at both outputs, such as directional couplers, waveguide bends, or additional PRSs.

6.3 Polarization controller

To extend the PRS concept and to demonstrate integration of the PRS into a Si3N4-on-Si PIC, we implemented the polarization controller shown in Fig. 6.4(a). The polarization controller consists of a PRS followed by a series of 3-dB multimode interference couplers (MMIs) and phase shifters, and ﬁnally, a second PRS to combine the two branches. The design is based on the proposal in [126], and allows any input polarization state to be Chapter 6. Silicon nitride on silicon polarization rotator-splitters 81

Input ¨ĭ ¨ĭ ¨ĭ ¨ĭ ¨ĭ Output 3-dB 3-dB 3-dB 3-dB PRS MMI MMI MMI PRS ¨ĭ MMI ¨ĭ ¨ĭ ¨ĭ ¨ĭ

(a)

300ʅm Heater1 Heater2 Heater3 Heater4 Heater5

PRS Si3N4 3ͲdB Si3N4 3ͲdB Si3N4 3ͲdB Si3N4 3ͲdB PRS MMI MMI MMI MMI (b)

Figure 6.4: (a) Schematic of the polarization controller. “Δφ” refers to a thermal phase- shifter (i.e., heater) and “3-dB MMI” is a 3-dB multimode interference coupler. (b) Optical micrograph of the polarization controller.

transformed into any output polarization state. The phase shifters were implemented using TiN thin ﬁlm heaters above Si waveguides, and adiabatic transitions were used to transfer light between the Si3N4 routing waveguides and the Si waveguides in the phase shifters. Figure 6.4(b) shows an optical microscope image of the fabricated polarization controller. We measured the polarization controller using free-space coupling with a free- space linear polarizer at the input of the chip to set the input polarization. The output polarization state was analyzed with a polarimeter (Agilent N7788B). The input wavelength was ﬁxed at 1550 nm. The polarization controller insertion loss was < 4.5dB.

Only the top heater of each pair was driven; the unused heaters balanced the loss of each pair of arms in the polarization controller. The heater numbering is indicated in Fig. 6.4(b). Figure 6.5 shows measurement data for the polarization controller using a TE-polarized input and a 45◦ linearly polarized input. The output polarization state was plotted on the Poincar´e sphere as two of the heaters were separately tuned. For a TE-polarized input [Fig. 6.5(a)], Heater 2 was powered at various steps corresponding to phase shifts Chapter 6. Silicon nitride on silicon polarization rotator-splitters 82

TEinput

(a) 45o input

(b)

Figure 6.5: Polarization controller output polarization state measurements on the Poincaré sphere for (a) a TE-polarized input and (b) a 45◦ linearly polarized input. In (a), different electrical powers were dissipated in Heater 2, and for each Heater 2 power, a sweep of the Heater 3 power was performed. Similarly, in (b), the Heater 2 power was swept at different Heater 1 power settings. The heater numbering is defined in Fig. 6.4(b), and Px refers to the power dissipated in Heater x. Chapter 6. Silicon nitride on silicon polarization rotator-splitters 83 between 0 and about π radians. For each Heater 2 power, the phase shift at Heater 3 was swept from 0 to 2π radians. The Heater 3 sweeps traced parallel circular orbits on the Poincaré sphere, and the spacing between the orbits was set by the Heater 2 power step size. When the Heater 2 power was 0 mW, the Heater 3 sweep should have ideally pro-

duced no change in the output polarization, but the crosstalk of the PRSs and non-ideal 3-dB MMIs led to a small distorted path traced on the Poincaré sphere [126]. Similar parallel circular orbits were seen for a 45◦ linearly polarized input when Heater 1 was stepped and Heater 2 was swept [Fig. 6.5(b)]. Overall, controlling two heaters allows us to reach any point on the Poincaré sphere for any input polarization, and the choice of these two heaters depends on the input and desired output polarization. In practice, where the polarization controller is used to stabilize a fluctuating input polarization (e.g., in a coherent receiver or polarization-division multiplexed link), applying a control algorithm for the five heaters eliminates the impact of non-ideal PRSs and 3-dB MMIs. Only one or two thermal tuners will cause distorted paths to be traced on the Poincaré sphere at a given bias and input polarization, and these heaters can be avoided. In addition, the heaters can be “reset” when they reach their maximum power dissipation, i.e., we can gradually reduce the power to a heater while modifying the remaining heater powers to maintain the output polarization state [97,126]. In [99], a similar polarization controller geometry was used in a silicon-photonic polarization- division multiplexed receiver, and the simultaneous control of all heaters enabled stabilization (with resets) of a fluctuating input polarization from a standard single-mode fiber despite imperfect 3-dB MMIs, separation of polarization, and polarization rotation.

In our polarization controller, Heaters 4 and 5 were functional, but a demonstration of polarization stabilization and reset procedures using Heaters 4 and 5 is beyond the scope of this work. Chapter 6. Silicon nitride on silicon polarization rotator-splitters 84

6.4 Summary

In summary, we have demonstrated a polarization rotator-splitter and a polarization controller in a Si3N4-on-Si integrated optics platform. The polarization rotator-splitter

is based on TM0-TE1 mode conversion in a composite Si3N4-on-Si waveguide, and is entirely adiabatic for improved tolerance to fabrication error and large operating bandwidths. This device design can be applied to fully active Si3N4-on-Si platforms and other

SOI photonic platforms where Si3N4 can be deposited near the Si waveguides. This demonstration shows that not only can a mulitlayer Si3N4-on-Si platform support optical functionalities in the constituent layers separately, it can also enable new device designs that rely on composite waveguides formed from the layers and the close interaction of light between the layers. Chapter 7

Conclusion

Despite signiﬁcant advances in Si photonic platforms, which now integrate passive devices, modulators, detectors, and bonded or packaged lasers, many challenges remain that prevent the realization of complex, large-scale, high index contrast Si PICs with high-yield and uniformity across wafers. The objective of this thesis has been to present device design and integration approaches to overcome some of these challenges.

Coupling modulation of microrings was proposed and demonstrated as a method to overcome the modulation bandwidth limitations of microrings, which provides an avenue toward ultra-high modulation eﬃciencies and large modulation bandwidths. A Si PRS was demonstrated based on TM0-TE1 mode conversion in a bi-level taper, which enables polarization diversity and control in typical foundry-based Si photonic platforms by eliminating the high aspect ratio features and additional layers required by previous po-

larization splitter and rotator designs. A Si3N4-on-Si photonic platform was designed and demonstrated, which combines the excellent passive waveguide properties of Si3N4 and the compatibility of Si waveguides with modulators and detectors. Implementing passive devices in Si3N4 instead of Si provides a path toward reducing thermal and dimensional variation sensitivites, improving power handling, and reducing optical losses. In addition, the close proximity of the Si3N4 and Si layers in the platform enables devices with

85 Chapter 7. Conclusion 86

composite, multilayer waveguides, and a Si3N4-on-Si grating coupler was demonstrated, which overcomes the bandwidth limitations of high-eﬃciency, ﬁber-to-chip grating couplers. Also, Si3N4-Si waveguides were shown to be capable of TM0-TE1 mode conversion and PRSs were demonstrated within the Si3N4-on-Si platform.

The remainder of this chapter describes future research directions for microring modulators (Section 7.1), PRS designs (Section 7.2), and Si3N4-on-Si photonic platforms (Section 7.3) that may extend the contributions of this thesis towards overcoming some of the remaining challenges in Si photonics.

7.1 Future work: microring modulators

Moving beyond our proof-of-concept demonstrations in Chapter 2 and Appendix B, sig- niﬁcant research will be required to demonstrate coupling modulated microrings that surpass the performance of conventional intracavity modulated microrings and satisfy the performance speciﬁcations required for optical communication links. This section outlines three avenues for advancing the state of the art in coupling modulated micror-

ings: improving the cavity losses and modulation efficiency, reducing the low frequency distortion, and extending coupling modulation beyond intensity modulation and binary phase-shift keying to more complex advanced modulation formats. The true potential of coupling modulation can only be met with high Q microcavities. From Section 2.5, coupling modulation can provide an efficiency advantage over intracavity modulation for narrow linewidths 100 MHz, and this will also reduce the low frequency distortion discussed in Section 2.4. Achieving such narrow linewidths will require device and integration innovations to significantly reduce the cavity losses far below those of our demonstrated microring in Chapter 2. A potential path forward is the integration of low-loss Si3N4 waveguides for the passive portion of the microring and Si waveguides for the modulation sections. This would eliminate much of the waveguide Chapter 7. Conclusion 87

loss in the microring and could be accomplished using a more advanced version of our

Si3N4-on-Si photonic platform in Chapter 4, which would require integrated PN diode

phase-shifters and optimized Si3N4 waveguide losses and interlayer transition losses. Another aspect of coupling modulation that requires further research is the low frequency distortion discussed in Section 2.4. In Chapter 2, we proposed to use coding of the drive signal to circumvent this limitation, but the additional bandwidth and complexity required for coding may the limit the practicality of this solution. An alternative approach to eliminating the low frequency distortion, which was proposed in [87, 127] following our initial high speed coupling modulation work in [64, 65], involves simultaneously modulating two independent couplers in a microring to balance the intracavity energy. When one coupler outputs more light from the ring, the other coupler outputs less, and a modulated output is achieved while the intracavity energy remains constant. Presently, this approach has not been experimentally demonstrated, and such work would be a valuable contribution to microring modulator research. Owing to the increased device complexity, achieving a narrow linewidth and high modulation eﬃciency will be even more diﬃcult than for our design in Chapter 2, and again, a Si3N4-on-Si photonic platform may provide a path towards reduced cavity losses.

If the cavity loss and low frequency distortion problems can be solved, the performance of the BPSK, coupling modulated microring modulator in Appendix B would be drastically improved, and the demonstration of more complex advanced modulation formats would be straightforward. As explained in Appendix B, integrating a microring into each arm of a MZI with a π/2 phase shift between the paths would enable diﬀerential quaternary phase-shift keying (DQPSK) and quadrature amplitude modulation (QAM) and lead to potential applications in long-haul telecommunications. Chapter 7. Conclusion 88

7.2 Future work: polarization rotator-splitters

The performance of the PRS designs in Chapters 3 and 6 are promising, but widespread application of the designs will require performance improvements and optimization. Two

important properties of the PRS designs that require further investigation are the polarization crosstalk and the diﬀerential group delay between the two PRS outputs. The crosstalk was < −13 dB over a 50 nm bandwidth for the Si PRS and < −19 dB

over a 80 nm bandwidth for the Si3N4-on-Si PRS. Crosstalk values < −30 dB have been

reported with Si polarization splitters and Si3N4-on-Si rotators [32], which suggests that optimized versions of our PRS designs may achieve similar performance. Reducing the polarization crosstalk is important in polarization diverse PICs for wavelength-division multiplexing since the multiplexing and demultiplexing devices are polarization sensitive and residual TM light may be converted into inter-channel crosstalk. Improving the mode conversion eﬃciency using non-linear taper shapes [128,129], increasing the device length, and replacing the blunt tips at the beginning of the adiabatic couplers in Figs. 3.1(a) and 6.1(a) with waveguide arcs are straightfoward paths towards polarization crosstalk reduction.

As improved PRS designs with lower polarization crosstalk are fabricated, an improved measurement method may be necessary to accurately measure the crosstalk. The measurement setup used for our PRS crosstalk measurements in Chapters 3 and 6 may be limited by collection of the minor field components of the TE0 and TM0 modes from the edge couplers as explained in [130]. This effect leads to a lower bound in the polarization crosstalk that can be measured. Modifications to our free-space measurement setup or the use of a fiber-based measurement setup may reduce this effect. The difference in group indices between the TE0, TM0, and TE1 modes throughout the PRS leads to a differential group delay between the two PRS outputs. This delay impacts the performance of polarization diverse receiver PICs since pulses in the two paths will be detected at different times and cause timing jitter. In principle, the dif- Chapter 7. Conclusion 89

ferential group delay can be eliminated by adding additional lengths of waveguides on the two outputs, but dispersion engineering of the additional waveguide lengths may be necessary to ensure the delay is balanced over a broad bandwidth. Characterizing and, if necessary, balancing the delay between the two PRS outputs will be an important step

towards the adoption of our PRS designs as fundamental building blocks in Si photonic platforms.

7.3 Future work: silicon nitride on silicon photonic

platform

The Si3N4-on-Si platform in Chapter 4 demonstrated eﬃcient coupling between Si3N4 and

Si waveguides as well as a a new class of devices based on composite Si3N4-Si waveguides, but futher work is required to extend the functionalities of the platform beyond those of conventional Si photonic platforms. In this section, three paths for extending the

Si3N4-on-Si platform are identiﬁed: integration of Si electro-optic modulators and Ge

photodetectors, optimization of the Si3N4 waveguide losses, and integration of additional

Si3N4 layers.

The integration of electro-optic modulators and photodetectors into a Si3N4-on-Si platform was demonstrated in [30, 109], and similar integration in our Si3N4-on-Si platform would enable us to demonstrate transmitter and receiver PICs. Integration of modulators and detectors is one of the objectives of future fabrication runs planned for this project, and the processing steps will have to ensure that the Si3N4 deposition occurs before the deﬁnition of modulators and detectors since the high temperature of the LPCVD are incompatible with doped Si and Ge.

The Si3N4 waveguide losses in our platform are lower than typical Si waveguide losses but roughly an order of magnitude larger than state-of-the-art waveguide losses for high conﬁnement Si3N4 waveguides (4.2 dB/m [105]). Reducing the Si3N4 waveguide losses Chapter 7. Conclusion 90

can be accomplished by optimizing the LPCVD and etching processes to reduce the

sidewall roughness of the waveguides and reduce the hydrogen content in the Si3N4.In addition to improving the insertion loss of PICs, reducing the Si3N4 waveguide losses will open up the possibility of integrating Si3N4 ring or disk frequency combs with active Si components for line-by-line pulse shaping [131,132].

Finally, the fabrication process for our Si3N4-on-Si platform is scalable to multiple

Si3N4 layers (i.e., by repeating steps 2 and 3 in Fig. 4.1). Additional waveguide layers may increase the density of waveguide routing since waveguides may pass directly over

each other. Also, similar to the new functionalites achieved with multilayer Si3N4-Si devices in Chapters 5 and 6, device designs using multiple Si3N4 layers and possibly the Si layer may lead to unique performance characteristics unavailable in today’s Si or

Si3N4-on-Si photonic platforms. Appendix A

Analysis of microring resonator modulators

In this appendix1, we present a dynamical analysis of ring resonator modulators to show the modulation bandwidth limitations of coupling and intracavity modulation. The resonator modulator conﬁguration we shall focus on is shown in Fig. A.1: a continuous-wave (CW) incoming optical wave is modulated by varying certain physical parameters of the microring resonator. In principle, three parameters can be varied to achieve modulation: 1. the intracavity refractive index of the microring, 2. the intracavity loss of the microring, and 3. the coupling strength between the microring and the bus waveguide. Experimentally, most demonstrations of microring modulators have relied on intracavity modulation of the index of the microring waveguide [55,74,133,134]. This appendix is organized as follows. In Section A.1, we will describe a time- dependent model of the microring. We will then analyze the modulation characteristics of the microring when the intracavity loss (Section A.2), intracavity refractive index (Section A.3), and waveguide-ring coupling (Section A.4), is varied. To gain a better intuitive understanding of the resonator modulation characteristics, we will derive small

1c OSA. Reprinted, with permission, from [64]

91 Appendix A. Analysis of microring resonator modulators 92

signal limits from our complete model. Our dynamical model reveals that to achieve modulation rates beyond that imposed by the resonator Q and linewidth, the coupling coeﬃcient, not the intracavity refractive index or loss of the ring resonator waveguide, should be modulated.

A.1 Time-dependent microring transmission

In this section, we shall derive a general expression to describe the dynamics of the microring modulator illustrated in Fig. A.1. The electric ﬁeld at the various locations

in Fig. A.1 can be expressed as Eξ(t)=ξ(t)exp(iω0t), where ξ = B, C, D and is a

slowly varying amplitude, and ω0 is the frequency of the input optical wave. The input amplitude is constant, such that EA(t)=A exp(iω0t). In the presence of an index and/or loss modulation, the phase-shift, φ, and attenuation, a, experienced by a circulating wave at a frequency ω after each round-trip in the

resonator can be expressed by

ω t φ(t, ω)=ωτ + η(t)dt, (A.1a) n t−τ t 1 a(t)=a0 + γ(t )dt, (A.1b) τ t−τ

A B(t) κ, σ D(t) C(t)

Figure A.1: Schematic of a ring resonator modulator. Appendix A. Analysis of microring resonator modulators 93

where τ = nL/c is the resonator round-trip time, n is the eﬀective index, L is the ring circumference, and

ni(t)=n + η(t), (A.2a)

ai(t)=a + γ(t)(A.2b) are the instantaneous refractive index and attenuation coeﬃcient respectively. Each frequency component of C(t) propagates around the ring and experiences a

diﬀerent phase-shift, such that

a(t) ∞ D(t)= C˜(Ω) exp[−iφ(t, ω)] exp(iΩt)dΩ, (A.3) 2π −∞

where Ω = ω − ω0 and C˜(Ω) is the Fourier transform of C(t). To simplify Eq. (A.3),

we assume that φ(t, ω) ≈ φ(t, ω0)+Ωτ, which is equivalent to approximating that the change in the phase-shift of each frequency component circulating in the resonator due to the index modulation, the η(t) term in Eq. (A.1a), is the same or is negligible compared to Ωτ. This assumption is reasonable since typical index changes are on the order of ∼ 10−3. With this approximation, Eq. (A.3) simpliﬁes to

D(t)=a(t)exp[−iφ(t, ω0)]C(t − τ). (A.4)

To analyze the fundamental limitations imposed by the device structure itself, we remove any material specific dependencies and neglect the coupling between the refractive index and absorption through the Kramers-Kronig relations. This simplifying assumption allows us to isolate the effect of each resonator parameter. In this approximation, the instantaneous field amplitudes are

B(t)=σ(t)A + iκ(t)a(t)exp[−iφ(t)]C(t − τ), (A.5a) Appendix A. Analysis of microring resonator modulators 94

iκ(t)C(t)=σ(t)B(t) − A, (A.5b)

where φ(t)=φ(t, ω0)andκ(t)andσ(t) are the resonator-waveguide coupling and transmission coeﬃcients, and σ2(t)+κ2(t) = 1 for a lossless coupler.

Equation (A.5) gives steady-state or static transmission [135]:

B σ − a exp(−iφ) T ≡ = . (A.6a) ss A 1 − aσ exp(−iφ)

σ2 + a2 − 2aσ cos(φ) |T |2 = . (A.6b) ss 1+a2σ2 − 2aσ cos(φ)

2 We observe that a and σ are interchangeable in |Tss| . The situation when σ = a is referred to as critical coupling. At critical coupling, the wave in the bus waveguide destructively interferes with the wave coupled out of the ring to result in zero transmission [135, 136]. To have complete extinction of the input wave, the modulator must thus operate near the critical coupling condition. Moreover, to use small changes in the index, loss, or coupling to cause large changes in the output intensity, the Q of the resonator must be high and the linewidth of the resonator narrow (a, σ ≈ 1), so that a circulating wave can, in essence, experience any small changes in device parameters many times before being dissipated. For a general expression of the dynamical transmission, T (t), we eliminate C(t)in Eq. (A.5), to arrive at

B(t) κ(t) T (t) ≡ = σ(t)+ a(t)exp[−iφ(t)][σ(t − τ)T (t − τ) − 1]. (A.7) A κ(t − τ)

If a(t), κ(t), σ(t), and φ(t) are periodic with a period equal to τ,thenT (t)isequal to Tss but with the static parameters replaced by their time-dependent counterparts. Sinusoidally periodic modulation of the refractive index of ring resonators at the free spectral range (FSR) has been recently demonstrated in electro-optic polymers [137].

However, to solve Eq. (A.7) for general forms of modulation, we can express it as a Appendix A. Analysis of microring resonator modulators 95

Fredholm integral equation of the second kind, which possesses a Neumann series solution [138]. The Fredholm integral equation form of Eq. (A.7) is

κ(t) T (t)=σ(t) − a(t)exp[−iφ(t)]+ κ(t − τ) ∞ (A.8) κ(t + τ) − − − a(t + τ)σ(t )exp[ iφ(t + τ)]δ[t (t τ)]T (t )dt . −∞ κ(t )

In the following sections, we will use the Neumann series solution of Eq. (A.8) to model the modulation response of the microring resonator.

A.2 Intracavity loss modulation

We ﬁrst consider the case of loss modulation, where a(t) varies in time, but φ, σ,andκ are constant. The solution of Eq. (A.8) for the transmission with loss modulation, Ta(t), is

∞ n−1 −iφ n −inφ −iφ Ta(t)=σ − a(t)e + σ e σ − a(t − nτ)e a(t − mτ). (A.9) n=1 m=0

The ﬁrst two terms in the above equation are the “instantaneous” response of the resonator, while the summation represents the “memory” eﬀect of the resonator or the modulation prior to time t. Each prior round-trip is weighted by σe−iφ, so that for high

Q resonators, a large number of terms in the summation will be signiﬁcant to Ta(t). Equation (A.9) can account for arbitrary loss modulation in both magnitude and time, and, in general, must be solved numerically. However, to gain an intuition of the modulation characteristics, we can derive a small signal approximation to Eq. (A.9). Appendix A. Analysis of microring resonator modulators 96

A.2.1 Small-signal approximation

We begin by considering a sinusoidal loss modulation of the form a(t)=a0 + a cos(Ωmt),

where Ωm is the modulation frequency, and a /a0 1. The Fourier transform of a(t)is

a a˜(Ω) = a0δ(Ω) + [δ(Ω + Ω )+δ(Ω − Ω )]. (A.10) 2 m m

Substituting Eq. (A.10) into the Fourier transform of Eq. (A.7), gives

−i(φ+Ωτ) a −i(φ+Ωτ) iΩmτ −iΩmτ T˜ (Ω) 1 − a0σe − σe T˜ (Ω − Ω )e + T˜ (Ω + Ω )e a 2 a m a m −iφ a −iφ =(σ − a0e )δ(Ω) − e [δ(Ω − Ω )+δ(Ω + Ω )] , 2 m m (A.11)

where T˜a(Ω) is the Fourier transform of Ta(t). Since we consider a sinusoidal modulation,

T˜a(Ω) consists only of the Ω = 0 component and the harmonics of Ωm.

We solve T˜a(Ω) order by order in a . We obtain an approximate solution by keeping only the terms up to O(a) to ﬁnd that

− −iφ ˜ σ a0e Ta(0) = − δ(0), (A.12) 1 − a0σe iφ

which is simply the steady-state transmission coeﬃcient, and

−iφ ˜ − ˜ a e [σTa(0) δ(0)] Ta(Ωm)= − ( +Ω ) (A.13a) 2 1 − σa0e i φ mτ

−iφ ˜ − ˜ − a e [σTa(0) δ(0)] Ta( Ωm)= − ( −Ω ) . (A.13b) 2 1 − σa0e i φ mτ

We can neglect the higher harmonic terms since they are of higher orders of a.Eqs. (A.12) and (A.13) show that when the input wave is near resonance so that exp(−iφ) ≈ 1 and the modulation amplitude is small, the output intensity of the ring resonator is Appendix A. Analysis of microring resonator modulators 97

sinusoidal with the same frequency as the loss modulation but with a constant oﬀset determined by the static response of the resonator. Eqs. (A.12) and (A.13) can also be used to study the distortion of a signal and the linearity of the modulator by evaluating

the relative magnitudes and phases of Tã(±Ωm)andTã(0). Next, we will use Eqs. (A.12) and (A.13) to determine the modulation depth as a function of Ωm. The modulation depth of a signal is defined as

f(t) − f(t) Δ= max min , (A.14) f(t)max + f(t)min

where f(t)max and f(t)min are the maximum and minimum amplitudes of the signal. Comparing the Fourier transform of a sinusoidally modulated signal with Eq. (A.14), we ﬁnd, after some algebra, that

T˜∗(−Ω ) T˜(Ω ) Δ=2 m + m , (A.15) T˜∗(0) T˜(0) where T˜(Ω) is the Fourier transform of T (t). For loss modulation, substituting Eqs. (A.12) and (A.13) into Eq. (A.15), the modulation depth, Δa,is

−iΩmτ σ cos φ − a0 + σa0e (a0 cos φ − σ) Δ =2a(1 − σ2) . (A.16) a 2 2 2 2 −i2Ωmτ −iΩmτ (a0 + σ − 2a0σ cos φ)(1 + a0σ e − 2a0σ cos φe )

For Ωmτ 1, Eq. (A.16) shows that the modulation depth decreases with increasing

modulation frequency. By taking the derivative of Δa with respect to Ωmτ, we ﬁnd that for a, σ ≈ 1, there exists a special condition when the modulation depth is maximum:

φ +Ωmτ ≈ 2pπ,wherep is an integer, i.e. when one of the sideband frequencies is on resonance. We shall refer to this situation as a modulation resonance. The output distortion when the modulator operates close to a modulation resonance is dictated by the relative amplitudes and phase of the resonant and non-resonant sidebands. Appendix A. Analysis of microring resonator modulators 98

When the input wavelength is on resonance, for Ωmτ 1, the modulation depth simpliﬁes to

1 (1 − σ2) 1 2 (A.17) Δa,res =2a 2 2 , |σ − a0| (1 − a0σ) + a0σ(Ωmτ) with a 3 dB roll-oﬀ at a frequency

1 − a0σ 3 Ωa,3dB,res = . (A.18) τ a0σ

Ωa,3dB,res is higher for lower Q resonators with smaller values of a0 and σ. Therefore, for loss modulated microrings, the modulation bandwidth is limited by the resonator Q.

A.2.2 Numerical results

In this section, we compare our small signal approximation results with the exact Neu- mann series solution. For all calculations in this work, we take the ring radius to be 10μm and the waveguide index to be n = 3, resulting in a round-trip time of 0.628 ps.

For the summation in the Neumann series [Eq. (A.9)], we include terms up to O(10−5).

Figure A.2 shows the modulation depth as a function of Ωm calculated using the small signal approximation, Eq. (A.17), and the exact expression, Eq. (A.9), when the loss of

the microring is modulated between 2 dB/cm and 5 dB/cm (a0 =0.9975, a =0.0011) while σ =0.9928. The 3 dB roll-off frequency is 4.3 GHz, in good agreement with Eq. (A.18). Figure A.2(b) shows the presence of the modulation resonance when the input wavelength is detuned from resonance by fm. The ratio between the modulation resonance and Δa(Ωm = 0) is larger for an input wavelength that is greater detuned from resonance. As evidenced by the figures, there is good agreement between the small signal approximation and the exact equation at frequencies below the modulation resonance. At higher frequencies, higher order (harmonic) terms become more significant. Appendix A. Analysis of microring resonator modulators 99

0 10 ) a

−1 10

Modulation Depth (Δ series solution

−2 small signal solution 10 0 1 2 10 10 10 Modulation Frequency (GHz) (a)

−1 10 ) a

−2 10

−3 10 fm =10GHz, series solution

fm =10GHz, small signal solution Modulation Depth (Δ fm =40GHz, series solution

−4 fm =40GHz, small signal solution 10 0 1 2 10 10 10 Modulation Frequency (GHz) (b)

Figure A.2: Modulation depths of a microring resonator with sinusoidal loss modulation between 2 dB/cm and 5 dB/cm. a0 =0.9975, a =0.0011, and σ =0.9928. (a): The input is on resonance. (b): Detuned input, with the modulation resonance frequency at fm. Appendix A. Analysis of microring resonator modulators 100

A.3 Intracavity index modulation

We now proceed to consider the modulation of the refractive index, where φ(t) varies in time and a and σ are constant. The Neumann series solution of Eq. (A.8) for the transmission coeﬃcient, Tφ(t), is

∞ n−1 −iφ(t) n n −iφ(t−nτ) −iφ(t−mτ) Tφ(t)=σ − ae + σ a σ − ae e . (A.19) n=1 m=0

As in the case of loss modulation, the expression for Tφ(t) consists of an instantaneous response, which is given by the ﬁrst two terms, and a summation of memory terms where each preceding round-trip is weighted by σa.

A.3.1 Small-signal approximation

Similar to Section A.2.1, we shall ﬁnd the small signal modulation characteristics of the resonator transmission. The round-trip phase-shift can be expressed as

φ(t)=φ0 − φ cos(Ωmt). (A.20)

The phase-shift can be expanded into Bessel functions using the Jacobi-Anger identity:

∞ −iφ(t) −iφ0 n inΩmt e =e i Jn(φ )e . (A.21) n=−∞

For φ 1, only the J0 and J1 terms dominate and J0(φ ) ≈ 1andJ1(φ ) ≈ φ /2. Therefore,

−iφ(t) −iφ0 −iφ0 e ≈ e + iφ e cos(Ωmt). (A.22)

We substitute Eq. (A.22) into Eq. (A.7) and take the Fourier transform of the Appendix A. Analysis of microring resonator modulators 101

resulting equation to obtain

φ ˜ −i(φ0+Ωτ) −i(φ0+Ωτ) ˜ iΩτ ˜ −iΩτ Tφ(Ω)[1−aσe ] − i aσe [Tφ(Ω − Ωm)e + Tφ(Ω + Ωm)e ] 2 (A.23) φ =(σ − ae−iφ0 )δ(Ω) − i ae−iφ0 [δ(Ω − Ω )+δ(Ω + Ω )]. 2 m m

Equation (A.23) can be solved to ﬁrst order in φ . T˜φ(0) = T˜a(0) = Tss, which is the static response of the resonator, and

−iφ0 φ ae [σT˜φ(0) − δ(0)] T˜φ(Ωm)=i , (A.24a) 2 1 − σae−i(φ0+Ωmτ)

−iφ0 φ ae [σT˜φ(0) − δ(0)] T˜φ(−Ωm)=i . (A.24b) 2 1 − σae−i(φ0−Ωmτ)

Finally, the modulation depth, Δφ, can be found using Eq. (A.15) to be

− 2 σa(1 σ ) sin(φ0) × Δφ =2φ 2 2 σ + a − 2σa cos(φ0) 1 4 2 2 1+a − 2a cos(Ωmτ) 2 2 2 2 2 2 2 . (1 − σ a ) +4σ a [cos(φ0) − cos(Ωmτ)] − 4σa(1 − σa) cos(φ0)cos(Ωmτ) (A.25)

If the input is on resonance, Eq. (A.25) gives Δφ = 0. Intuitively, this is because the resonance wavelength is at the minimum of the static transmission spectrum. Thus, to first order in φ, there is no modulation in the transmission amplitude, and the microring operates as a phase modulator rather than an intensity modulator. As a, σ → 1, the 3 dB roll-off frequency decreases, so the modulation bandwidth is again Q limited. By taking the derivative of Eq. (A.25), we find that for high Q resonators where a, σ ≈ 1, a modulation resonance also exists for index modulation, with the modulation depth

reaching a maximum at φ0 +Ωmτ ≈ 2pπ,wherep is an integer. Appendix A. Analysis of microring resonator modulators 102

0 10 ) φ

−1 10

−2 10 a =0.9971, σ =0.9928, series solution

Modulation Depth (Δ a =0.9971, σ =0.9928, small signal solution a =0.9928, σ =0.9971, series solution

−3 a =0.9928, σ =0.9971, small signal solution

10 −1 0 1 2 10 10 10 10 Modulation Frequency (GHz)

Figure A.3: Modulation depths of a microring resonator with a sinusoidal index modulation. φ0 =0.039477 and φ =0.005. The input is detuned from resonance, with the modulation resonance frequency at 10 GHz.

A.3.2 Numerical results

Figure A.3 shows Δφ versus the modulation frequency for a sinusoidally index modulated microring resonator. The ﬁgure compares the results of the small signal modulation depth from Eq. (A.25) and the exact solution from Eq. (A.19). For the calculations,

−5 φ0 =0.039477 and φ =0.005, which corresponds to an index change of 2 × 10 at a wavelength of 1.55 μm. The two sets of calculations in Fig. A.3 are identical except the values of a and σ are interchanged. The low frequency modulation depth is identical between the two cases and is therefore symmetric in a and σ, as can be seen in Eq. (A.25). However, at higher frequencies, the modulation depth is slightly larger for the over-coupled (σ

There is good agreement between the small signal approximation and the exact solution for low modulation frequencies. The modulation depth at the modulation resonance can be much greater than the low frequency modulation depth. At higher frequencies Appendix A. Analysis of microring resonator modulators 103

near and greater than the modulation resonance, the deviation of the small signal analysis from the series solution becomes more severe due to the presence of the higher order sidebands which can be near or on resonance at other frequencies. The presence of higher order harmonics distorts the output.

A.4 Coupling modulation

Finally, we consider the case where the coupling strength between the waveguide and the

resonator is modulated, while a and φ are constant in time. The solution of Eq. (A.8) for Tσ(t)is

∞ n −inφ − κ(t) −iφ a e Tσ(t)=σ(t) − ae + κ(t) − κ(t τ) =1 κ(t nτ) n (A.26) κ(t − nτ) n σ(t − nτ) − ae−iφ σ(t − mτ). κ(t − (n +1)τ) m=1

We can immediately note an important difference between Eq. (A.26) and Eq. (A.9) or Eq. (A.19). In Eq. (A.26), the memory terms embodied by the summation are multiplied by κ(t), the instantaneous value of the coupling coefficient – such a term is absent in Eq. (A.9) and Eq. (A.19). This, as we shall further demonstrate, implies that coupling modulation does not suffer from the same limitations as loss and index modulation.

A.4.1 Small-signal approximation

We now analyze a small amplitude sinusoidal modulation of the coupling strength to obtain a simpliﬁed expression for the modulation characteristics from Eq. (A.26). For simplicity, we assume that the resonator is high Q, such that κ 1andσ ≈ 1. We take the coupling coeﬃcient as

κ(t)=κ0 + κ cos(Ωmt), (A.27) Appendix A. Analysis of microring resonator modulators 104

2 2 where, |κ /κ0|1. For |σ(t)| + |κ(t)| =1toO(κ ), it follows that

σ(t)=σ0 + σ cos(Ωmt), (A.28)

where σ = −κ0κ /σ0 and |σ /σ0|≈κ κ0. Substituting Eq. (A.27) and (A.28) into Eq. (A.7) up to O(κ), and taking the Fourier transform results in κ κ2 ˜ −i(φ+Ωτ) ˜ −iΩmτ −i(φ+Ωτ) iΩmτ 0 κ0Tσ(Ω)[1 − aσ0e ]+ Tσ(Ω − Ωm) e − ae σ0e − 2 σ0 2 κ iΩmτ −i(φ+Ωτ) −iΩmτ κ0 + T˜σ(Ω + Ωm) e − ae σ0e − 2 σ0 2 −iΩτ −iφ κ −iΩτ κ0 −i(Ω−Ωm)τ −iφ = κ0[σ0e − ae ]δ(Ω) + σ0e − e − ae δ(Ω − Ωm) 2 σ0 2 κ −iΩτ κ0 −i(Ω+Ωm)τ −iφ + σ0e − e − ae δ(Ω + Ωm). 2 σ0 (A.29)

We can solve for T˜σ(0), T˜σ(Ωm), and T˜σ(−Ωm) in the same fashion as was done for

index and loss modulation. To O(κ ), T˜σ(0) = Tss, the static response of resonator. Using Eq. (A.15) to solve for the modulation depth, we obtain

2 −iΩmτ −iΩmτ (1 − a e )[σ0 − a cos φ + aσ0(a − σ0 cos φ)e ] Δ =2σ . (A.30) σ 2 2 2 2 −2iΩmτ −iΩmτ (σ0 + a − 2aσ0 cos φ)(1 + a σ0 e − 2aσ0 cos φe )

To simplify Eq. (A.30), we take the input wavelength exactly on resonance, such that exp(iφ) = 1, and Ωmτ 1toarriveat

1 2 2 2 2 2 (1 − a ) + a (Ωmτ) Δσ,res =2σ 2 2 2 . (A.31) (σ0 − a) [(1 − aσ0) + aσ0(Ωmτ) ]

Equation (A.31) shows that the frequency response of the modulator depends strongly on the relative magnitudes of a and σ0. At low modulation frequencies, Ωmτ (1 −

√ 2 aσ0)/ aσ0,Δσ,res is approximately constant and equal to 2σ (1 − a )/[|σ0 − a|(1 − aσ0)]. Appendix A. Analysis of microring resonator modulators 105

√ At high frequencies such that Ωmτ (1 − aσ0)/ aσ0, the modulation depth is also constant and equal to 2σ a/σ0/|σ0 − a|. Thus, there is no frequency roll-oﬀ to the modulation depth.

A.4.2 Numerical results

Figure A.4 compares the modulation depths for resonant and detuned inputs of two sinusoidally coupling modulated microring resonators: one under-coupled and the other over-coupled. The loss of the rings is taken to be 4 dB/cm, a =0.9971. The series solutions, Eq. (A.26), closely follow the predictions of Eqs. (A.30) and (A.31). The low frequency modulation depth is smaller than the high frequency value for over-coupled ring resonators and vice-versa for under-coupled resonators. In addition, the results show that

for both resonant and detuned inputs, the modulation depth is roughly constant at large frequencies. However, comparing Fig. A.4 (a) with Fig. A.4 (b), we can see that the input wavelength should be close to resonance to achieve large modulation depths. Fig. A.4 (b) also shows the existence of modulation resonance for coupling modulation with the input detuned from resonance.

We can understand the modulation characteristics by examining the amplitude of the waves that interfere to produce the output, B(t), in Fig. A.1. The modulation of the coupling constant, similar to index or loss modulation, generates frequency sidebands to

the input frequency, ω0, that also circulate in the microring. The amplitude of these sidebands diminish with increasing modulation frequency or increasing Q, which leads to the roll-oﬀ in the modulation depth for index and loss modulation. In contrast, for coupling modulation, as can be seen in Eq. (A.26), a factor of κ(t) is applied to any light that exits the cavity. Therefore, the output of the modulator is determined by the instantaneous modulation of the frequency components at ω0 and the sidebands.

At low modulation frequencies, both the sidebands and ω0 components are modulated simultaneously. However, there will be a modulation frequency range over which the Appendix A. Analysis of microring resonator modulators 106

0 10 ) σ

σ(t)

Modulation Depth (Δ σ(t) >a, series solution σ(t) >a, small signal solution

−1 0 1 2 10 10 10 10 Modulation Frequency (GHz) (a)

−1 10 ) σ

−2 10

σ(t)

Modulation Depth (Δ σ(t) >a, series solution σ(t) >a, small signal −3 10 −1 0 1 2 10 10 10 10 Modulation Frequency (GHz) (b)

Figure A.4: Modulation depths of a microring resonator with a sinusoidal modulation of the coupling strength. Over-coupled: σ =0.0013 and σ0 =0.9902. Under-coupled: −4 σ =3.5 × 10 and σ0 =0.999. The loss of the ring is 4 dB/cm, a =0.9971. (a): The input is on resonance. (b): The input is detuned from resonance, with the modulation resonance frequency at 5 GHz. Appendix A. Analysis of microring resonator modulators 107

sideband amplitudes diminish, leaving only the instantaneous modulation of ω0,which is independent of modulation frequency. The flat high frequency modulation responses in Fig. A.4 are due to this instantaneous modulation. The higher the Q factor is, the lower the modulation frequency needs to be for the modulator to reach the flat high √ frequency response, i.e. Ωmτ (1 − aσ0)/ aσ0 in Eq. (A.31). The flat low and high modulation frequency responses are the quasi-static and non-quasi-static operating modes, respectively, mentioned in Chapter 2.

A.5 Discussion

Intuitively, we may understand the lack of a modulation frequency roll-oﬀ for coupling

modulation as follows. Consider the static scenario in which a CW wave is input to the microring. Initially, κ = 0, which results in a certain transmission amplitude. If κ is suddenly reduced to zero, immediately, no light can exit or enter the resonator. This leads to an instantaneous change in the transmission that is not limited by the resonator Q, but only the response of the coupler. On the other hand, if the intracavity loss or index of the resonator is changed suddenly, light that was circulating inside the resonator can continue to escape from the resonator. The rate at which the amplitude of the light in the resonator decays is inversely proportional to the Q factor. In the steady-state intensity transmission, Eq. (A.6b), σ and a are interchangeable. Therefore, a static description of the resonator would not distinguish between changes in a and σ.Itisonly through a dynamical description of the resonator that the differences in the modulation rate limits can be revealed. To further illustrate the difference between coupling modulation and index/loss modulation, we shall briefly examine a “large” modulation of the input CW wave. Due to the complicated nature of the interference that occurs at the output when device parameters are modulated, it is unlikely that the output from an arbitrary modulation waveform Appendix A. Analysis of microring resonator modulators 108

would simply be a superposition of the small signal sinusoidal outputs presented earlier. Figure A.5 illustrates the outputs attainable with a Gaussian pulse modulation of the index, loss, and coupling calculated using Eqs. (A.9), (A.19), and (A.26). The full- width half-maximum widths of the modulating pulses are 42 ps, 21 ps, and 8 ps. The

output pulses generated from loss and index modulation suﬀer from distortion and time delays relative to the modulation waveform, which are considerably worse for smaller pulse widths. In addition, the amplitudes of the output pulses decrease signiﬁcantly with shorter index or loss pulse widths. In contrast, the output pulses in Fig. A.5(f) generated from coupling modulation do

not decrease in amplitude with shorter modulation pulse widths. However, the output pulses are shorter than the modulation pulses in Fig. A.5(c). This distortion is due to the low frequency limit of a coupling modulated microring resonator suppressing the tails of the Gaussian pulse. The Q of the resonator must be very large to produce pulses

that closely resemble the coupling strength pulse shape. This is the opposite requirement compared to loss or index modulation which suﬀer from high frequency limitations and thus require low Q resonators for undistorted output pulses. The modulation depth does not remain constant at arbitrarily high modulation fre-

quencies of the coupling strength. If the device parameters are modulated with a period- icity of τ in Eq. (A.7), the resonator output is identical to the low frequency response, neglecting any averaging of device parameters that occur as a result of Eq. (A.1). There- fore, the response of a coupling modulated microring resembles the low frequency response at modulation frequencies approaching the FSR of the resonator. However, for micror-

ing resonators, the FSR is on the order of ∼ 1 THz, suﬃcient for most communication applications. Moreover, throughout this analysis, we have neglected the frequency, amplitude, and phase response of the coupler itself. The ultimate modulation rate would be determined by the modulation response of the coupler, which need not be a resonant de-

vice. For example, state-of-the-art electro-optic polymer Mach-Zehnder interferometric Appendix A. Analysis of microring resonator modulators 109 )

1 0.016 t 1 ) t ( ( σ φ ) t

( 0.996 0.012

a 0.999 0.992 0.008 0.998 0.988 0.004 Ring Loss Ring Phase Shift

0.984 0 Coupling Strength 0.997 0 40 80 120 160 200 0 40 80 120 160 200 0 40 80 120 160 200 Time (ps) Time (ps) Time (ps) (a) (b) (c)

1 1 0.5 2 2 2 | | | 0.4 ) ) ) 0.9

t 0.75 t t ( ( ( a φ σ 0.3 T T T | | 0.8 0.5 | 0.2 0.7 0.25 0.1 Output Output Output

0.6 0 0 0 40 80 120 160 200 0 40 80 120 160 200 0 40 80 120 160 200 Time (ps) Time (ps) Time (ps) (d) (e) (f)

Figure A.5: Device parameters (top) and the corresponding output intensities (bottom) versus time for single-pulse modulated microring resonators. (a), (d): Loss modulation, σ =0.9928, and the input is resonant. (b), (e): Index modulation, φ0 =0.039477, σ =0.9928, and a loss of 4 dB/cm. (c), (f): Coupling modulation, the loss is 4 dB/cm, and the input is resonant. Appendix A. Analysis of microring resonator modulators 110

switches can operate at > 100 GHz [139,140]. A disadvantage of coupling modulation for data modulation is low-frequency distortion. The low-frequency content of the drive signal can deplete the optical energy stored in the microring and lead to signiﬁcant intersymbol interference. This is discussed in greater detail in Section 2.4 along with the potential solution of coding to reduce the low frequency content of the drive signal.

A.6 Summary

In summary, we have presented a dynamical analysis of a microring modulator in which the intracavity loss, intracavity refractive index, or waveguide-ring coupling strength is

modulated. We extended our fully rigorous results to small signal approximations to show that when the waveguide-ring coupling coeﬃcient is modulated, the modulation bandwidth of the microring approaches the FSR. We compared pulse modulation of the loss, index, and coupling strength, to ﬁnd that variable coupling is the most promising for generating short pulses with minimal distortion. Coupling modulation has the potential

of leveraging the resonant nature of high Q microresonators to realize low loss, low power, and compact modulators which also possess a high modulation bandwidth. Our model can be extended to incorporate the dynamic eﬀects of the coupler and to analyze other properties of microring modulators, such as the chirp, linearity, and extinction ratio. Appendix B

Coupling modulation for binary phase-shift keying

In this appendix1, binary phase-shift keying (BPSK) based on coupling modulation of microrings is proposed and demonstrated. This method can be extended to more complex advanced modulation formats. First, we brieﬂy review BPSK and its conventional implementations.

Advanced modulation formats that involve optical phase modulation have become attractive alternatives to on-oﬀ keying (OOK) in optical communications because of their potential to increase the spectral eﬃciency and receiver sensitivity [142, 143]. The most simple phase modulation format is BPSK, where the data is encoded as 0 and

π radian phase-shifts on the optical carrier. BPSK offers a relative ∼3-dB boost in receiver sensitivity and a lower vulnerability to fiber nonlinearities compared to OOK [142, 143]. In differential binary phase-shift keying (DPSK), information is encoded as phase differences between successive bits. Optical BPSK signals can be generated either with a phase modulator or with a Mach-Zehnder interferometer (MZI) modulator as illustrated in Figs. B.1(a) and B.1(b). Driving a MZI in a push-pull manner through the

1c OSA. Reprinted, with permission, from [141]

111 Appendix B. Coupling modulation for binary phase-shift keying 112 zero transmission point causes a π radian phase flip [142,143]. The advantages of using a MZI over a phase modulator for BPSK are a chirp-free output (except at the phase flip), a π phase flip that is independent of the voltage swing, and an improved tolerance to drive signal imperfections (e.g., due to limited bandwidth or over/undershoot) [142,143].

Drive signal imperfections affect the intensity, but the fluctuations are compressed by the MZI nonlinear transfer characteristic when the ‘0’ and ‘1’ symbols are positioned near the transmission peaks as shown in Fig. B.1(b). Recently, BPSK modulation using a single microring was proposed [144] and demonstrated [145]. Using a microring-enhanced MZI, quadrature phase-shift keying modulation (QPSK) has also been proposed and demonstrated [146, 147]. In these works, the refractive index in an over-coupled microring was modulated to spectrally shift the resonance relative to the input wavelength [Fig. B.1(c)]. This intracavity modulation of the microring produces a time-varying phase-shift and achieves BPSK modulation analogous to a phase modulator. The optical output is continuously chirped, and compared to MZI modulators, is less tolerant to drive signal imperfections. Moreover, because near unity transmission requires strong over-coupling, hence large linewidths, there exists a fundamental trade-off between the efficiency and insertion loss.

In this chapter, we propose a microring BPSK modulator based on coupling modulation and demonstrate the concept in silicon-on-insulator (SOI). The purpose of this demonstration is to verify that coupling modulation can result in BPSK outputs. As discussed in Chapter 2 and Appendix A, in coupling modulation, the coupling coeﬃ- cient between the microring and the input/output bus waveguide is modulated rather than the intracavity index or loss [64, 65, 89]. Even though coupling modulation can circumvent the cavity linewidth limitation to the modulation rate of resonators, which was proven in Chapter 2, here, we focus on the “quasi-static” regime, where the modulation rate is within the cavity linewidth. As illustrated in Fig. B.1, the operation of the coupling-modulated microring for BPSK is analogous to that of a MZI. Thus, the Appendix B. Coupling modulation for binary phase-shift keying 113

Phase modulator Mach-Zehnder interferometer Im[T] Im[T] S'T T T ÷ť Re[T] Re[T]

S'T )

) 1 1 S S T/ T/ 0.8 0.8 '0' symbol 0.6 '0' symbol '1' symbol 0.6 and and 2 2 0.4 0.4 2 2 '1' symbol |T| 0.2 |T| 0.2 T/S T/S Output (|T| Output 0 (|T| Output 0 0 0.2 0.4 0.6 0.8 1 -1.5 -1 -0.5 0 0.5 1 1.5 'T/S 'T/S (a) (b)

Intracavity-modulated microring Coupling-modulated microring Im[T] T Im[T]

S'T Re[T] ÷ť Re[T]

T S'T

) 1 )

S 1

2 S 2 T/ |T| |T| T/

0.8 0.5 T/S T/S

and 0.6 and 2

0 2 '0' symbol '1' symbol 0.4 -0.5 0.2 '0' symbol '1' symbol Output (|T| -1 (|T| Output 0 -0.2 -0.1 0 0.1 0.2 -1 -0.5 0 0.5 1 'T/S 'T/S (c) (d)

Figure B.1: Illustrations of BPSK modulation using (a) a phase modulator, (b) a MZI modulator, (c) an intracavity-modulated microring, and (d) a coupling-modulated microring. The illustrations show the similarities between MZI modulators and coupling- modulated microrings, as well as the similarities between phase modulators and intracavity-modulated microrings. Constellation diagrams and output intensity (|T |2) and phase (∠T ) versus applied phase-shift (Δθ) are shown. For the intracavity-modulated microring, the input wavelength is on resonance for Δθ = 0; modulating Δθ shifts the resonance wavelength. For the coupling-modulated microring, the input wavelength is on resonance, and the drop port coupler is modulated; the ‘1’ and ‘0’ symbols correspond to the two critical coupling conditions. Appendix B. Coupling modulation for binary phase-shift keying 114

OpticalInput Thermaltuners V1 ThroughPort

3dB 3dB N coupler coupler 1 PNdiode Thermal V2(t) phaseͲshifters tuners

3dB 3dB N (t) Drop Port 2 coupler coupler (modulatoroutput)

Figure B.2: Schematic of a coupling-modulated microring for BPSK. The microring is in an add-drop conﬁguration with MZI-couplers at the through and drop sides. Either MZI-coupler can be modulated through its zero transmission point to achieve BPSK. Here, only the MZI-coupler at the drop side is modulated, and the MZI-coupler on the through side acts as a tunable coupler. This conﬁguration matches the experimentally demonstrated device.

beneﬁts of coupling-modulated microrings for BPSK over existing intracavity-modulated microrings are akin to the beneﬁts of a MZI for BPSK over a phase modulator (i.e., lower chirp and improved tolerance to drive signal imperfections).

B.1 Principle of operation

The operation of the proposed device is summarized in Fig. B.1(d) and the device

schematic is shown in Fig. B.2. The microring is in an add-drop conﬁguration where the waveguide-ring couplers for the “through” and “drop” ports are tunable 2 × 2MZI- couplers. In Fig. B.1(d) and the experimental demonstration in Section B.2, we focus on high-speed modulation of the drop port coupler, but our analysis below shows that

modulation of either the through or drop port coupler can result in BPSK modulation. Since the device will operate in the quasi-static regime, we can analyze its operation using the steady-state transmission coefficients. The field transmission coefficients at the Appendix B. Coupling modulation for binary phase-shift keying 115

drop and through ports of the microring are, respectively,

√ ∗ ∗ a exp(−iφ/2) Tdrop = κ1κ2 ∗ , (B.1a) 1 − aσ1 σ2 exp(−iφ)

σ1 − σ2a exp(−iφ) Tthru = ∗ , (B.1b) 1 − aσ1 σ2 exp(−iφ)

where σ1 and κ1 are respectively the field through- and cross-coupling coefficients between the bus waveguide and the microring on the through side, σ2 and κ2 are the through- and cross-coupling coefficients on the drop side, a is the round-trip field transmission coefficient of the microring waveguide, and φ is the round-trip phase-shift. In deriving

2 2 Eq. B.1, losses in the couplers are lumped into a,and|σ1,2| + |κ1,2| =1.

Intuitively, Tdrop in Eq. (B.1a) is simply the modulation of the coupling coeﬃcients,

κ1 or κ2, multiplied by the large circulating ﬁeld amplitude. If we use 2 ×2 MZI-couplers at the through and drop ports as in Fig. B.2 [75, 76], BPSK modulation of either MZI-

coupler results in a BPSK modulation of Tdrop with the same properties as a MZI. To describe this more rigorously, we write the through- and cross-coupling coeﬃcients of the push-pull driven MZI-coupler as

θ01,2 +Δθ1,2(t) θ01,2 +Δθ1,2(t) σ1 2(t)=i cos ,κ1 2(t)=i sin , (B.2) , 2 , 2

where Δθ1,2(t) is the modulation of the relative phase difference between the two arms of the MZI-coupler and θ01,2 is the bias phase difference. The modulation of the coupling coefficient in this manner does not change the resonance frequency of the microring. To maximize the stored energy in the ring near resonance and reduce the cavity losses, |σ1,2| is biased near 1 and |κ1,2| is biased near zero. Therefore,

2 Δθ1,2(t) Δθ1,2(t) σ1 2(t) ≈ i 1 − ,κ1 2(t) ≈ i , (B.3) , 2 , 2 Appendix B. Coupling modulation for binary phase-shift keying 116

From Eq. (B.1a), if either κ1 or κ2 changes sign while φ, a,andσ1,2 are constant, then the optical output at the drop port would exhibit a phase-ﬂip of π radians. This can be accomplished by modulating Δθ1 or Δθ2 in the MZI-coupler between positive and negative values such that κ1 or κ2 is driven through the zero transmission point. For

BPSK modulation, κ1 or κ2 should swing between two values of equal magnitude and opposite sign, and σ1 or σ2 would swing between two identical values. The drop port transmission is the highest when the intracavity ﬁeld amplitude is maximum, which is at the critical coupling condition, when Tthru = 0 on resonance, i.e., σ1 = aσ2. Therefore, for low insertion losses, κ1 or κ2 should be modulated between the two values that lead to critical coupling, i.e., the drop port MZI-coupler is modulated between κ2 = 2 2 2 2 ± 1 − σ1/a or the through port MZI-coupler is modulated between κ1 = ± 1 − a σ2 .

Modulating κ2 between the two critical coupling values is illustrated in Fig. B.1(d). Similar to a MZI, drive signal imperfections would not aﬀect the phase-shift and the

output intensity would be more tolerant to the drive signal imperfections because the

transmission reaches local maxima at κ2 values for critical coupling.

When either MZI-coupler is driven between the two values for κ2 or κ1 that lead to critical coupling, the phase-shifts, Δθ1 or Δθ2, required for the modulation are reduced compared to that of the MZI-coupler modulator alone by factors of

2π π πF η1 = ≈ ≈ for a → 1, (B.4a) 2 2 Δθ1 2 1 − a σ2 4

2π π πF η2 = ≈ ≈ for a → 1. (B.4b) 2 2 Δθ2 2 1 − σ1 /a 4

η1 and η2 are, respectively, the reduction factors when the through and drop port MZIs

are modulated; and F is the finesse at the critical coupling condition. As evidenced by √ Eq. (B.4), the modulation efficiency of the coupling modulated microring scales with F , and for a and |σ1,2|→1, the microring modulation efficiency greatly exceeds the efficiency √ of MZI DPSK modulators. The efficiency scaling with F is similar to the efficiency Appendix B. Coupling modulation for binary phase-shift keying 117

scaling of the coupling-modulated microring intensity modulator we demonstrated in [68]. While coupling modulation is typically less eﬃcient than intracavity modulation in today’s silicon photonic platforms [68, 148], our coupling modulation scheme can bring the beneﬁts of a MZI to microring modulators.

As an aside, eﬃcient BPSK is not possible at the through port. From Eq. (B.1b),

Tthru depends on σ1,2 and not κ1,2, and from Eq. (B.3), σ1,2 does not change signs in microrings with reasonable ﬁnesse. To use the microring for DPSK modulation at the through port, the MZI-couplers would need to be biased at |σ1,2|≈0and|κ1,2|≈1, and thus, the energy stored in the microring and the modulator eﬃciency would be low.

B.2 Experimental demonstration

Figure B.3(a) shows an optical microscope image of the fabricated silicon coupling- modulated microring used for a proof-of-concept demonstration of the proposed design. The modulation drive signal is applied to the drop port MZI-coupler, and the through port MZI-coupler is only for tuning and is not compatible with high-speed modulation.

The device was fabricated in the IBM Silicon CMOS Integrated Nanophotonics process [83]. The coupling coefficients at the through and drop ports of the microring were biased using the thermal tuners in the 2 × 2 MZI-couplers, while PN diode phase-shifters were included only in the MZI-coupler at the drop port. The PN diode phase-shifters and thermal tuners were 200 μmand50μm long, respectively. The MZI-couplers enable the independent tuning of the resonance wavelength and coupling coefficients [66,68]. When the drop port was tuned to κ2 = 0 and the through port was tuned to critical coupling, the full-width at half maximum linewidth of the microring at the through port was about 19.6 GHz, resulting in a cavity quality factor of Q ≈ 104. The free spectral range of the microring was 92 GHz, so the finesse was about 5. Figure B.3(b) shows the measured Appendix B. Coupling modulation for binary phase-shift keying 118

Thermaltuners Input Through port

Drop PNdiode port phaseͲshifters

(a)

−5

−10

−15

−20

−25 Thru

Normalized transmission (dB) Drop −30 1533 1534 1535 1536 1537 Wavelength (nm) (b)

Figure B.3: (a) Optical micrograph of the fabricated device. The thermal tuners are 50 μm long, and the PN diode phase-shifters are 200 μm long. PN diode phase-shifters are only present in the MZI-coupler at the drop side. (b) Measured transmission spectra at the through (thru) and drop ports. The thermal tuners were set for critical coupling with a drop port transmission of 30% on-resonance relative to the oﬀ-resonance through port transmission. Appendix B. Coupling modulation for binary phase-shift keying 119

Afterdemodulator Afterdemodulator Beforedemodulator (destructiveport) (constructiveport)

5Gb/s

10Gb/s

Figure B.4: Measured eye diagrams of the DPSK microring modulator at 5 and 10 Gb/s before and after the fiber delay line interferometer demodulator. The open eye diagrams with large extinction ratios confirm DPSK operation. The drive signals were NRZ PRBS 231 − 1. The vertical scales differ between the 5 and 10 Gb/s eye diagrams and between the DPSK modulated and demodulated eye diagrams; accurate amplitude comparisons between the eye diagrams are difficult due to the different fiber paths and losses for each set of measurements.

through and drop port transmission spectra of the microring when κ1 and κ2 were tuned to critical coupling with 30% power transmission on-resonance at the drop port relative to the oﬀ-resonance through port power.

To demonstrate DPSK modulation, the PN diode phase-shifters were forward-biased at 0.25 V and driven in a push-pull conﬁguration. Non-return-to zero (NRZ) PRBS 231−1 voltage signals with a 16 - 18 dB single-tap pre-emphasis and maximum swings of 1.6 Vpp were applied to each of the PN diode phase-shifters. The optical input was TE-polarized,

resonant, and at a wavelength of about 1535 nm. The optical output from the drop port was demodulated using a ﬁber delay line interferometer. An interferometer with a delay of about 200 ps was used to demodulate the output at 5 Gb/s, and an interferometer with a delay of about 100 ps was used for the 10 Gb/s output. The DPSK modulated

and demodulated optical signals were amplified using an erbium doped fiber amplifier, bandpass filtered (0.8 nm full-width at half-maximum bandwidth), and detected by a digital communications analyzer with a 28 Gb/s optical module. Appendix B. Coupling modulation for binary phase-shift keying 120

Figure B.4 shows the eye diagrams before and after the demodulator. The purpose of these measurements is to conﬁrm DPSK modulation. The measured eye diagrams

are characteristic of NRZ-DPSK modulation using MZIs [142]. Because κ2 was driven through its zero transmission point, a lower rail is absent in the eye diagrams before the demodulator. The destructive port of the delay line demodulator produces the al- ternate mark inversion (AMI) [142]. The bottom rail is due to destructive interference of consecutive bits with the same phase, and the pulses are due to constructive interference of phase-flipped consecutive bits. In contrast, the eye diagrams of the demodulator constructive port have a top rail from constructive interference of successive bits of the same phase and a bottom rail from destructive interference of phase-flipped consecutive bits. Overall, the open eye diagrams at both demodulator outputs confirm that the coupling-modulated microring produced DPSK signals. Even with open eye diagrams at the demodulator outputs, phase errors may be present and the phase difference between the two DPSK symbols may not be exactly π radians. The extinction ratio of the constructive port eye diagram is an indication of the phase errors in the DPSK signal, i.e., a 0 bottom rail requires perfect destructive interference (π radian phase-shift) between consecutive bits. We can calculate an upper-bound on the phase error by assuming the finite extinction ratio at the constructive port is entirely due to phase errors in the DPSK signal, and not the finite extinction ratio of the demodulator or any optical intensity fluctuations. The constructive port eye diagrams in Fig. B.4 exhibit extinction ratios > 15 dB, which corresponds to a worst-case phase error of 0.11π radians between the two DPSK symbols. The phase error may be caused by a residual modulation of the resonance wavelength due to the nonlinear electrical response of the forward-biased PN diodes, which would result in deviation from ideal push-pull modulation. Reverse-biased PN junctions would provide more ideal push-pull modulation due to their more linear electrical response.

Due to the low ﬁnesse of the microring and the non-optimized PN diode phase-shifters, Appendix B. Coupling modulation for binary phase-shift keying 121

the swing in the optical power before the demodulator at 5 and 10 Gb/s was only about 30% and 10% of the oﬀ-resonance through port transmittance, respectively. The small swing is not an inherent characteristic of this microring DPSK modulator design. As

shown in Eq. (B.1), |Tdrop|→1 on-resonance as a and |σ1,2| approach unity. Reducing the size of the ring and the intracavity losses would increase the output transmission swing, since the drop port insertion loss decreases and the modulation efficiency increases with the finesse. An obvious approach to increase the finesse is to reduce the length of waveguide sections that do not contribute to modulation. First, the microring could be reconfigured to eliminate the long passive waveguide sections adjacent to the through port coupler in Fig. B.3(a). Second, the tunable through port coupler could be replaced with a significantly smaller, fixed, directional coupler. Tunability of the through port coupling may not be necessary if the device is designed carefully and the fabrication variation is not too large [25].

B.3 Summary

We have proposed a new type of BPSK/DPSK microring modulator that operates by the phase-ﬂip of the MZI-coupler. The proposed device was demonstrated in silicon and operated at 10 Gb/s. DPSK modulation was conﬁrmed by eye diagram measurements of the output signal before and after a delay line interferometer demodulator. The design can be extended to higher order phase modulation formats, such as quadrature phase-shift keying (QPSK), by inserting a coupling-modulated microring BPSK modulator into each arm of a MZI, with a relative phase-shift of π/2 radians between them. This concept can also be extended to lasers to produce coupling-modulated lasers with BPSK outputs [90].

The modulator demonstrated here is a proof-of-concept, and the performance was limited by the low cavity finesse and non-optimized PN diode phase-shifters. Future research on this modulator design should focus on improving the modulation efficiency, Appendix B. Coupling modulation for binary phase-shift keying 122 demonstrating modulation at rates beyond the resonator linewidth, and quantifying the chirp and drive-signal tolerance benefits relative to BPSK microring modulators based on intracavity modulation. Bibliography

[1] A. Biberman, S. Manipatruni, N. Ophir, L. Chen, M. Lipson, and K. Bergman. First demonstration of long-haul transmission using silicon microring modulators.

Opt. Express, 18(15):15544–15552, 2010.

[2]K.Goi,K.Oda,H.Kusaka,Y.Terada,K.Ogawa,T.-Y.Liow,X.Tu,G.-Q.Lo, and D.-L. Kwong. 11-Gb/s 80-km transmission performance of zero-chirp silicon Mach-Zehnder modulator. Opt. Express, 20(26):B350–B356, 2012.

[3] W. Green, S. Assefa, A. Rylyakov, C. Schow, F. Horst, Y. Vlasov, and M. Dinu. CMOS integrated silicon nanophotonics for exascale computing. In in Frontiers in Optics 2011/Laser Science XXVII, OSA Technical Digest (Optical Society of America, 2011), page FMB1, 2011.

[4] G. Masini, A. Narasimha, A. Mekis, B. Welch, C. Ogden, C. Bradbury, C. Sohn,

D. Song, D. Martinez, D. Foltz, D. Guckenberger, J. Eicher, J. Dong, J. Schramm, J. White, J. Redman, K. Yokoyama, M. Harrison, M. Peterson, M. Saberi, M. Mack, M. Sharp, P. de Dobbelaere, R. LeBlanc, S. Leap, S. Abdalla, S. Gloeckner, S. Hovey, S. Jackson, S. Sahni, S. Yu, T. Pinguet, W. Xu, and Y. Liang. CMOS

photonics for optical engines and interconnects. In Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page OTu2I.1, 2012.

123 Bibliography 124

[5] J. E. Cunningham, A. V. Krishnamoorthy, Ron Ho, I. Shubin, H. Thacker, J. Lexau, D.C. Lee, Dazeng Feng, E. Chow, Ying Luo, Xuezhe Zheng, Guoliang Li, Jin Yao, T. Pinguet, K. Raj, M. Asghari, and J.G. Mitchell. Integration and packaging of a macrochip with silicon nanophotonic links. IEEE J. Sel. Top. Quant. Elect.,

17(3):546 –558, 2011.

[6] C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. Holzwarth, M. Popovic, H. Li, H. Smith, J. Hoyt, F. Kaertner, R. Ram, V. Stojanovic, and K. Asanovic. Building

manycore processor to DRAM networks with monolithic silicon photonics. In IEEE Symposium on High-Performance Interconnects, page 2130, 2008.

[7] P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, and L. Fulbert. Towards foundry approach for silicon photonics: silicon photonics platform ePIXfab. Electron. Lett., 45(12):581–582, 2009.

[8]A.E.-J.Lim,J.Song,Q.Fang,C.Li,X.Tu,N.Duan,K.K.Chen,R.P.-C.Tern, and T.-Y. Liow. Review of silicon photonics foundry eﬀorts. IEEE J. Sel. Top. Quant. Electron., 20(4):1–12, 2014.

[9] www.opsisfoundry.org.

[10] P. De Dobbelaere, A. Ayazi, Y. Chi, A. Dahl, S. Denton, S. Gloeckner, K. Hon, S. Hovey, Y. Liang, M. Mack, G. Masini, A. Mekis, M. Peterson, T. Pinguet, J. Schramm, M. Sharp, C. Sohn, K. Stechschulte, P. Sun, G. Vastola, L. Ver- slegers, and R. Zhou. Packaging of silicon photonics systems. In Optical Fiber

Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page W3I.2, 2014.

[11] T. Barwicz, Y. Taira, T. Lichoulas, N. Boyer, H. Numata, Y. Martin, J. Nah, S. Takenobu, A. Janta-Polczynski, E. Kimbrell, R. Leidy, M. Khater, S. Kamla- purkar, S. Engelmann, Y. Vlasov, and P. Fortier. Photonic packaging in high- Bibliography 125

throughput microelectronic assembly lines for cost-eﬃciency and scalability. In Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page W3H.4, 2015.

[12] A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers. Electri- cally pumped hybrid AlGaInAs-silicon evanescent laser. Opt. Express, 14(20):9203– 9210, 2006.

[13] G.-H. Duan, C. Jany, A. Le Liepvre, A. Accard, M. Lamponi, D. Make, P. Kaspar,

G.Levaufre,N.Girard,F.Lelarge,J.-M.Fedeli,A.Descos,B.BenBakir,S.Mes- saoudene, D. Bordel, S. Menezo, G. de Valicourt, S. Keyvaninia, G. Roelkens, D. Van Thourhout, D.J. Thomson, F.Y. Gardes, and G.T. Reed. Hybrid III-V on silicon lasers for photonic integrated circuits on silicon. IEEE J. Sel. Top. Quant.

Elect., 20(4):158–170, 2014.

[14] Q. Xu, D. Fattal, and R. G. Beausoleil. Silicon microring resonators with 1.5-μm

radius. Opt. Express, 16(6):4309–4315, 2008.

[15] M. Khotoku, T. Kominato, Y. Nasu, and T. Shibata. New waveguide fabrication techniques for next-generation PLCs. NTT Tech. Rev., 3(7):37–41, 2005.

[16] David J. Robbins, Katarzyna Lawniczuk, Xaveer Leijtens, Jing Zhao, Valentina Moskalenko, Erwin Bente, Adrian Wonfor, Xuhan Guo, Meint Smit, and Mike Wale. Laser research on an InP-based generic integration platform. In Proc. SPIE, volume 9134, pages 91340M–91340M–8, 2014.

[17] D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman,

S. Verstuyft, K. De Mesel, and R. Baets. An out-of-plane grating coupler for eﬃcient butt-coupling between compact planar waveguides and single-mode ﬁbers. IEEE J. Quant. Elect., 38(7):949–955, 2002. Bibliography 126

[18] Y. A. Vlasov and S. J. McNab. Losses in single-mode silicon-on-insulator strip waveguides and bends. Opt. Express, 12(8):1622–1631, 2004.

[19] W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets. Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides. Opt. Lett., 32(19):2801– 2803, Oct 2007.

[20]T.Barwicz,M.R.Watts,M.A.Popovic,P.T.Rakich,L.Socci,F.X.Kartner, E. P. Ippen, and H. I. Smith. Polarization-transparent microphotonic devices in the strong conﬁnement limit. Nature Photonics, 1:57–60, 2007.

[21] H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi. Silicon photonic circuit with polarization diversity. Opt. Express,

16(7):4872–4880, 2008.

[22] D. A. B. Miller. Device requirements for optical interconnects to silicon chips.

Proceedings of the IEEE, 97(7):1166 –1185, 2009.

[23] A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and

P. De Dobbelaere. A grating-coupler-enabled CMOS photonics platform. IEEE J. Sel. Top. Quant. Elect., 17(3):597–608, 2011.

[24] L. Chen and Y.-K. Chen. Compact, low-loss and low-power 8x8 broadband silicon optical switch. Opt. Express, 20(17):18977–18985, 2012.

[25] J. C. Mikkelsen, W. D. Sacher, and J. K. S. Poon. Adiabatically widened silicon microrings for improved variation tolerance. Opt. Express, 22(8):9659–9666, 2014.

[26] W. Bogaerts, M. Fiers, and P. Dumon. Design challenges in silicon photonics. IEEE J. Sel. Top. Quant. Elect., 20(4):1–8, 2014. Bibliography 127

[27] T. Barwicz and H. Haus. Three-dimensional analysis of scattering losses due to sidewall roughness in microphotonic waveguides. J. Lightwave Technol., 23(9):2719– 2732, 2005.

[28] S. Selvaraja, P. De Heyn, G. Winroth, P. Ong, G. Lepage, C. Cailler, A. Rigny,

K. Bourdelle, W. Bogaerts, D. VanThourhout, J. Van Campenhout, and P. Absil. Highly uniform and low-loss passive silicon photonics devices using a 300mm CMOS platform. In Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page Th2A.33, 2014.

[29] J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers. Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding. Opt. Express, 19(24):24090–24101, 2011.

[30] L. Chen, C. R. Doerr, P. Dong, and Y.-K. Chen. Monolithic silicon chip with 10 modulator channels at 25 Gbps and 100-GHz spacing. Opt. Express, 19(26):B946– B951, 2011.

[31] M. Piels, J. F. Bauters, M. L. Davenport, M. J. R. Heck, and J. E. Bowers. Low- loss silicon nitride AWG demultiplexer heterogeneously integrated with hybrid III- V/silicon photodetectors. J. Lightwave Technol., 32(4):817–823, 2014.

[32] L. Chen, C. R. Doerr, and Y.-K. Chen. Compact polarization rotator on silicon for

polarization-diversiﬁed circuits. Opt. Lett., 36(4):469–471, 2011.

[33] L. Liu, Y. Ding, K. Yvind, and J. M. Hvam. Eﬃcient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process. Opt. Lett., 36(7):1059–1061, 2011.

[34] D. Dai and J. E. Bowers. Novel concept for ultracompact polarization splitter- rotator based on silicon nanowires. Opt. Express, 19(11):10940– 10949, 2011. Bibliography 128

[35] D. Vermeulen, S. Selvaraja, P. Verheyen, P. Absil, W. Bogaerts, D. Van Thourhout, and G. Roelkens. Silicon-on-insulator polarization rotator based on a symmetry breaking silicon overlay. IEEE Photon. Technol. Lett., 24(6):482–484, 2012.

[36] Y. Ding, H. Ou, and C. Peucheret. Wideband polarization splitter and rotator with

large fabrication tolerance and simple fabrication process. Opt. Lett., 38(8):1227– 1229, 2013.

[37] H. Yoda, K. Shiraishi, Akihiko Ohshima, T. Ishimura, H. Furuhashi, H. Tsuchiya, and C. S. Tsai. A two-port single-mode ﬁber-silicon wire waveguide coupler module

using spot-size converters. J. Lightwave Technol., 27(10):1315–1319, 2009.

[38] L. Chen, C. R. Doerr, Y.-K. Chen, and T.-Y. Liow. Low-loss and broadband

cantilever couplers between standard cleaved ﬁbers and high-index-contrast Si3N4

or Si waveguides. IEEE Photon. Technol. Lett., 22(23):1744–1746, 2010.

[39] F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets. Compact focusing grating couplers for silicon-on-insulator integrated circuits. IEEE Photon. Technol. Lett.,

19(23):1919–1921, 2007.

[40] C. R. Doerr, Long Chen, Y.-K. Chen, and L. L. Buhl. Wide bandwidth silicon nitride grating coupler. IEEE Photon. Technol. Lett., 22(19):1461–1463, 2010.

[41] L. He, Y. Liu, C. Galland, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and

M. Hochberg. A high-eﬃciency nonuniform grating coupler realized with 248-nm optical lithography. IEEE Photon. Technol. Lett., 25(14):1358–1361, 2013.

[42] S. K. Selvaraja, D. Vermeulen, M. Schaekers, E. Sleeckx, W. Bogaerts, G. Roelkens,

P. Dumon, D. Van Thourhout, and R. Baets. Highly eﬃcient grating coupler between optical ﬁber and silicon photonic circuit. In CLEO: 2009, page CTuC6. Optical Society of America, 2009. Bibliography 129

[43] D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens. High-eﬃciency ﬁber-to-chip grating couplers realized using an advanced CMOS-compatible Silicon-On-Insulator platform. Opt. Express, 18(17):18278–18283, 2010.

[44] X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang. Apodized waveguide grating couplers for eﬃcient coupling to optical ﬁbers. IEEE Photon. Technol.

Lett., 22(15):1156–1158, 2010.

[45] Z. Wang, Y. Tang, and L. Wosinski. High eﬃciency grating couplers for silicon- on-insulator photonic circuits. In European Conference and Exhibition on Optical Communication (ECOC), page P2.06, 2010.

[46] C. Kopp, E. Augendre, R. Orobtchouk, O. Lemonnier, and J.-M. Fedeli. Enhanced ﬁber grating coupler integrated by wafer-to-wafer bonding. J. Lightwave Technol., 29(12):1847–1851, 2011.

[47] A. Mekis, S. Abdalla, D. Foltz, S. Gloeckner, S. Hovey, S. Jackson, Y. Liang,

M. Mack, G. Masini, M. Peterson, T. Pinguet, S. Sahni, M. Sharp, P. Sun, D. Tan, L. Verslegers, B. P. Welch, K. Yokoyama, S. Yu, and P. M. De Dobbelaere. A CMOS photonics platform for high-speed optical interconnects. In Photonics Conference (IPC), 2012 IEEE, pages 356–357, 2012.

[48] W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus. Cost-eﬀective CMOS-compatible grating couplers with backside metal mirror and

69% coupling eﬃciency. Opt. Express, 20(26):B238–B243, 2012.

[49] C. Zhang, J.-H. Sun, X. Xiao, W.-M. Sun, X.-J. Zhang, T. Chu, J.-Z. Yu, and Y.-D. Yu. High eﬃciency grating coupler for coupling between single-mode ﬁber and SOI waveguides. Chin. Phys. Lett., 30(1):014207, 2013. Bibliography 130

[50] C. Li, H. Zhang, M. Yu, and G.-Q. Lo. CMOS-compatible high eﬃciency double- etched apodized waveguide grating coupler. Opt. Express, 21(7):7868–7874, 2013.

[51] W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus, and J. Burghartz. Bridging the gap between optical ﬁbers and silicon photonic integrated circuits. Opt. Express, 22(2):1277–1286, 2014.

[52] X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang. Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical ﬁbers. Opt. Lett., 37(17):3483–3485, 2012.

[53] H. Zhang, C. Li, X. Tu, H. Zhou, X. Luo, M. Yu, and G.-Q. Lo. High eﬃciency silicon nitride grating coupler with DBR. In Optical Fiber Communication Con-

ference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page Th1A.4., 2014.

[54] Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant. Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces. Opt. Express, 22(15):18224–18231, 2014.

[55] Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson. Micrometre-scale silicon electro- optic modulator. Nature, 435(7040):325–327, 2005.

[56] W. A. Zortman, A. L. Lentine, D. C. Trotter, and M. R. Watts. Low-voltage diﬀerentially-signaled modulators. Opt. Express, 19(27):26017–26026, 2011.

[57]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(25):22484– 22490, 2009. Bibliography 131

[58] G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy. 25 Gb/s 1 V-driving CMOS ring modulator with integrated thermal tuning. Opt. Express, 19(21):20435–20443, 2011.

[59] X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu. 44-Gb/s silicon microring modulators based on zigzag PN junctions. IEEE Photon. Technol. Lett., 24(19):1712–1714, 2012.

[60] W. A. Zortman, D. C. Trotter, A. L. Lentine, G. Robertson, A. Hsia, and M. R.

Watts. Monolithic and two-dimensional integration of silicon photonic microdisks with microelectronics. IEEE Photonics Journal, 4(1):242 –249, 2012.

[61] J. C. Rosenberg, W. M. J. Green, S. Assefa, D. M. Gill, T. Barwicz, M. Yang, S. M. Shank, and Y. A. Vlasov. A 25 Gbps silicon microring modulator based on an interleaved junction. Opt. Express, 20(24):26411–26423, 2012.

[62] R. Soref and B. Bennett. Electrooptical eﬀects in silicon. IEEE J. Quant. Elect., 23(1):123–129, 1987.

[63] I.-L. Gheorma and R. M. Osgood. Fundamental limitations of optical resonator based high-speed EO modulators. J. Lightwave Technol., 14(6):795–797, 2002.

[64] W. D. Sacher and J. K. S. Poon. Dynamics of microring resonator modulators.

Opt. Express, 16(20):15741–15753, 2008.

[65] W. D. Sacher and J. K. S. Poon. Characteristics of microring resonators with

waveguide-resonator coupling modulation. J. Lightwave Technol., 27(17):3800– 3811, 2009.

[66]W.D.Sacher,W.M.J.Green,S.Assefa,T.Barwicz,S.M.Shank,Y.A.Vlasov, and J. K. S. Poon. Controlled coupling in silicon microrings for high-speed, high Bibliography 132

extinction ratio, and low-chirp modulation. In Conference on Lasers and Electro- Optics (CLEO), page PDPA8, 2011.

[67] W. Sacher, W. Green, S. Assefa, T. Barwicz, H. Pan, S. Shank, Y. Vlasov, and J. Poon. 28 Gb/s silicon microring modulation beyond the linewidth limit by coupling modulation. In Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page OM3J.2, 2012.

[68]W.D.Sacher,W.M.J.Green,S.Assefa,T.Barwicz,P.Pan,S.M.Shank,Y.A. Vlasov, and J. K. S. Poon. Coupling modulation of microrings at rates beyond the

linewidth limit. Opt. Express, 21(8):9722–9733, 2013.

[69] W. Sacher, T. Barwicz, and J. K. Poon. Silicon-on-insulator polarization splitter-

rotator based on TM0-TE1 mode conversion in a bi-level taper. In CLEO: 2013, page CTu3F.3, 2013.

[70] W. D. Sacher, T. Barwicz, B. J. F. Taylor, and J. K. S. Poon. Polarization rotator- splitters in standard active silicon photonics platforms. Opt. Express, 22(4):3777– 3786, 2014.

[71] W. D. Sacher, Y. Huang, G.-Q. Lo, and J. K. S. Poon. Multilayer silicon nitride-on- silicon integrated photonic platforms and devices. J. Lightwave Technol., 33(4):901– 910, 2015.

[72] W. D. Sacher, Y. Huang, L. Ding, B. J. F. Taylor, H. Jayatilleka, G.-Q. Lo, and

J. K. S. Poon. Wide bandwidth and high coupling eﬃciency Si3N4-on-SOI dual-level

grating coupler. Opt. Express, 22(9):10938–10947, 2014.

[73] W. D. Sacher, Y. Huang, D. Liang, T. Barwicz, J. C. Mikkelsen, B. J. F. Talyor, G.-

Q. Lo, and J. K. S. Poon. Polarization rotator-splitters and controllers in a Si3N4- on-SOI integrated photonics platform. Opt. Express, 22(9):11167–11174, 2014. Bibliography 133

[74] P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton. Polymer micro-ring ﬁlters and modulators. J. Lightwave Technol., 20(11):1968–1975, 2002.

[75] A. Yariv. Critical coupling and its control in optical waveguide-ring resonator systems. IEEE Photon. Technol. Lett., 14(4):483–485, 2002.

[76] W. M. J. Green, R. K. Lee, G. A. DeRose, A. Scherer, and A. Yariv. Hybrid InGaAsP-InP Mach-Zehnder racetrack resonator for thermooptic switching and coupling control. Opt. Express, 13(5):1651–1659, 2005.

[77] L. Zhou and A. W. Poon. Electrically reconﬁgurable silicon microring resonator- based ﬁlter with waveguide-coupled feedback. Opt. Express, 15(15):9194–9204, 2007.

[78] 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. Top. Quant. Elect., 16(1):45 –52, 2010.

[79] P. Dong, L. Chen, Q. F. Xu, and M. Lipson. On-chip generation of high-intensity short optical pulses using dynamic microcavities. Opt. Lett., 34(15):2315–2317, 2009.

[80] D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie. Internal bandwidth equalization in a CMOS-compatible Si-ring modulator. IEEE Photon. Technol. Lett., 21(4):200

–202, 2009.

[81] A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki. Surface acoustic wave opto-mechanical oscillator and frequency comb generator. Opt. Lett., 36(17):3338–3340, 2011. Bibliography 134

[82]S.Assefa,W.M.J.Green,A.Rylyakov,C.Schow,F.Horst,andY.A.Vlasov. CMOS integrated nanophotonics-enabling technology for exascale computing systems. In Optical Fiber Communication Conference (OFC/NFOEC), page OMM6, 2011.

[83] S. Assefa, S. Shank, W. Green, M. Khater, E. Kiewra, C. Reinholm, S. Kamla- purkar, A. Rylyakov, C. Schow, F. Horst, H. Pan, T. Topuria, P. Rice, D. M. Gill, J. Rosenberg, T. Barwicz, M. Yang, J. Proesel, J. Hofrichter, B. Oﬀrein, X. Gu,

W. Haensch, J. Ellis-Monaghan, and Y. Vlasov. A 90 nm CMOS integrated nanophotonics technology for 25 Gbps WDM optical communications applications. In IEEE International Electron Devices Meeting (IEDM), page 33.8, 2012.

[84] Q. F. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson. 12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators. Opt. Express, 15(2):430–436, 2007.

[85] W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov. Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator. Opt. Express, 15(25):17106–

17113, 2007.

[86] S. Manipatruni, Q. F. Xu, B. Schmidt, J. Shakya, and M. Lipson. High speed carrier injection 18 Gb/s silicon micro-ring electro-optic modulator. In The Annual

Meeting of the IEEE Lasers and Electro-Optics Society, pages 537 –538, 2007.

[87] M. A. Popovic. Resonant optical modulators beyond conventional energy-eﬃciency

and modulation frequency limitations. In Integrated Photonics Research, Silicon and Nanophotonics, page IMC2, 2010.

[88] H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala. Chem- ically etched ultrahigh-Q wedge-resonator on a silicon chip. Nature Photonics, 6(6):369–373, 2012. Bibliography 135

[89] W. D. Sacher and J. K. S. Poon. Microring quadrature modulators. Opt. Lett., 34(24):3878–3880, 2009.

[90] W. D. Sacher, E. J. Zhang, B. A. Kruger, and J. K. S. Poon. High-speed laser modulation beyond the relaxation resonance frequency limit. Opt. Express, 18(7):7047– 7054, 2010.

[91] M. R. Watts and H. A. Haus. Integrated mode-evolution-based polarization rota-

tors. Opt. Lett., 30(2):139–140, 2005.

[92] M. R. Watts, H. A. Haus, and E. P. Ippen. Integrated mode-evolution-based polarization splitter. Opt. Lett., 30(9):967–969, 2005.

[93] T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong. Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization. IEEE J. Sel. Top. Quant. Elect., 16(1):307–315, 2010.

[94]T.Baehr-Jones,R.Ding,Y.Liu,A.Ayazi,T.Pinguet,N.C.Harris,M.Streshin-

sky, P. Lee, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg. Ultralow drive voltage silicon traveling-wave modulator. Opt. Ex- press, 20(11):12014–12020, 2012.

[95] W. Yuan, K. Kojima, B. Wang, T. Koike-Akino, K. Parsons, S. Nishikawa, and E. Yagyu. Mode-evolution-based polarization rotator-splitter design via simple

fabrication process. Opt. Express, 20(9):10163–10169, 2012.

[96] D. Dai, Y. Tang, and J. E. Bowers. Mode conversion in tapered submicron silicon ridge optical waveguides. Opt. Express, 20(12):13425–13439, 2012.

[97] N. G. Walker and G. R. Walker. Polarization control for coherent communications. J. Lightwave Technol., 8(3):438–458, 1990. Bibliography 136

[98] T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata, and K. Okamoto. Planar lightwave circuit polarization-mode dispersion compensator. IEEE Photon. Technol. Lett., 14(4):507–509, 2002.

[99] C. R. Doerr and L. Chen. Monolithic PDM-DQPSK receiver in silicon. In European

Conference and Exhibition on Optical Communication (ECOC), page PD 3.6, 2010.

[100] C. R. Doerr, N .K. Fontaine, and L. L. Buhl. PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls. IEEE Photon. Technol. Lett., 24(8):697–699, 2012.

[101] M. Dinu, F. Quochi, and H. Garcia. Third-order nonlinearities in silicon at telecom wavelengths. Appl. Phys. Lett., 82(18):2954–2956, 2003.

[102] K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman. Thermal and kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides. Opt.

Express, 16(17):12987–12994, 2008.

[103] R. Amatya, C. W. Holzwarth, F. Gan, H. I. Smith, F. K¨artner,R.J.Ram,and M. A. Popovic. Low power thermal tuning of second-order microring resonators. In Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science

Conference and Photonic Applications Systems Technologies, page CFQ5, 2007.

[104] G. Cocorullo, F. G. Della Corte, and I. Rendina. Temperature dependence of the thermo-optic coeﬃcient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm. Appl. Phys. Lett., 74(22):3338–3340, 1999.

[105] K. Luke, A. Dutt, C. B. Poitras, and M. Lipson. Overcoming Si3N4 ﬁlm stress limitations for high quality factor ring resonators. Opt. Express, 21(19):22829– 22833, 2013. Bibliography 137

[106] A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roelof- fzen, L. Zhuang, M. Burla, D. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. van Dijk, and R. M. Oldenbeuving. TriPleX waveguide platform: low-loss technology over a wide wavelength range. In Proc. SPIE, volume 8767,

pages 87670E–87670E–13, 2013.

[107] J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse,

R. G. Heideman, D. J. Blumenthal, and J. E. Bowers. Ultra-low-loss high-aspect-

ratio Si3N4 waveguides. Opt. Express, 19(4):3163–3174, 2011.

[108] J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, and J. E. Bowers. Silicon on ultra-low-loss waveguide photonic integration platform. Opt. Express, 21(1):544–555, 2013.

[109] L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca. Monolithically integrated 40-wavelength demultiplexer and photodetector array on silicon. IEEE

Photon. Technol. Lett., 23(13):869–871, 2011.

[110] A. M. Jones, C. T. DeRose, A. L. Lentine, D. C. Trotter, A. L. Starbuck, and R. A. Norwood. Ultra-low crosstalk, CMOS compatible waveguide crossings for densely integrated photonic interconnection networks. Opt. Express, 21(10):12002–12013, 2013.

[111] M. Sodagar, R. Pourabolghasem, A. A. Eftekhar, and A. Adibi. High-eﬃciency and wideband interlayer grating couplers in multilayer Si/SiO2/SiN platform for

3D integration of optical functionalities. Opt. Express, 22(14):16767–16777, 2014.

[112] Y. Huang, J. Song, X. Luo, T.-Y. Liow, and G.-Q. Lo. CMOS compatible mono-

lithic multi-layer Si3N4-on-SOI platform for low-loss high performance silicon photonics dense integration. Opt. Express, 22(18):21859–21865, 2014. Bibliography 138

[113] Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong. Ultralow power silicon photonics thermo-optic switch with suspended phase arms. IEEE Photon. Technol. Lett., 23(8):525–527, 2011.

[114] Q. Fang, T.-Y. Liow, J. F. Song, C. W. Tan, M. B. Yu, G.-Q. Lo, and D.-L. Kwong. Suspended optical ﬁber-to-waveguide mode size converter for silicon photonics. Opt.

Express, 18(8):7763–7769, 2010.

[115] S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, and D. L. Kwong. Low propagation loss SiN optical waveguide prepared by optimal low-hydrogen module. Opt. Express, 16(25):20809–20816, 2008.

[116] Y. Liu, J. M. Shainline, X. Zeng, and M. A. Popovi´c. Ultra-low-loss CMOS- compatible waveguide crossing arrays based on multimode Bloch waves and imag- inary coupling. Opt. Lett., 39(2):335–338, 2014.

[117] Y. Ma, Y. Zhang, S. Yang, A. Novack, R. Ding, A. E.-J. Lim, G.-Q. Lo, T. Baehr-

Jones, and M. Hochberg. Ultralow loss single layer submicron silicon waveguide crossing for SOI optical interconnect. Opt. Express, 21(24):29374–29382, Dec 2013.

[118] H. Chen and A. W. Poon. Low-loss multimode-interference-based crossings for silicon wire waveguides. IEEE Photon. Technol. Lett., 18(21):2260–2262, 2006.

[119] H. R. Stuart. Waveguide lenses with multimode interference for low-loss slab propagation. Opt. Lett., 28(22):2141–2143, 2003.

[120] W. D. Sacher, Y. Huang, L. Ding, B. J. Taylor, H. Jayatilleka, G.-Q. Lo, and J. K.

Poon. Ultra-eﬃcient and broadband dual-level Si3N4-on-SOI grating coupler. In CLEO: 2014, page STh3M.4, 2014.

[121] M. T. Wade, R. Kumar, K. Nammari, C. M. Gentry, J. Shainline, J. S. Orcutt, A. Tamma, R. Ram, V. Stojanovic, and M. A. Popovic. Unidirectional chip-to-ﬁber Bibliography 139

grating couplers in unmodiﬁed 45nm CMOS technology. In Conference on Lasers and Electro-Optics, OSA Technical Digest, page STh3M.5, 2014.

[122] M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Sto- janovic, and M. A. Popovic. 75% eﬃcient wide bandwidth grating couplers in a

45 nm microelectronics CMOS process. In Optical Interconnects Conference (OI), 2015 IEEE, pages 46–47, 2015.

[123] D. Vermeulen, Y. De Koninck, Y. Li, E. Lambert, W. Bogaerts, R. Baets, and G. Roelkens. Reﬂectionless grating couplers for Silicon-on-Insulator photonic inte-

grated circuits. Opt. Express, 20(20):22278–22283, 2012.

[124] Y. Li, D. Vermeulen, Y. De Koninck, G. Yurtsever, G. Roelkens, and R. Baets. Compact grating couplers on silicon-on-insulator with reduced backreﬂection. Opt. Lett., 37(21):4356–4358, 2012.

[125] J. Notaros and M. Popovic. Band-structure approach to synthesis of grating couplers with ultra-high coupling eﬃciency and directivity. In Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC), page Th3F.2, 2015.

[126] L. Moller. WDM polarization controller in PLC technology. IEEE Photon. Technol. Lett., 13(6):585–587, 2001.

[127] A. Kodanev and M. Orenstein. Charge-discharge digital/analog microring modulator with no intrinsic speed limitation. IEEE Photon. Technol. Lett., 26(15):1522– 1525, 2014.

[128] D. R. Rowland, Y. Chen, and A. W. Snyder. Tapered mismatched couplers. J. Lightwave Technol., 9(5):567–570, 1991. Bibliography 140

[129] T. Barwicz and Y. Taira. Low-cost interfacing of ﬁbers to nanophotonic waveguides: Design for fabrication and assembly tolerances. Photonics Journal, IEEE, 6(4):1– 18, 2014.

[130] J. Wang, J. C. Wirth, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi. Far-ﬁeld

polarization characterization of the fundamental modes of a strip silicon waveguide. Opt. Lett., 38(22):4785–4788, 2013.

[131] F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner. Spectral line-by-line pulse shaping of on-chip microresonator

frequency combs. Nature Photonics, 5(12):770–776, 2011.

[132] Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta. Octave-spanning frequency comb generation in a silicon nitride chip. Opt. Lett., 36(17):3398–3400, 2011.

[133] A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. G¨unter. Electro- optically tunable microring resonators in lithium niobate. Nature Photonics, 1:407 – 410, 2007.

[134] T. Sadagopan, S. J. Choi, S. J. Choi, K. Djordjev, and P. D. Dapkus. Carrier-

induced refractive index changes in InP-based circular microresonators for low- voltage high-speed modulation. IEEE Photon. Technol. Lett., 17(2):414–416, 2005.

[135] A. Yariv. Universal relations for coupling of optical power between microresonators and dielectric waveguides. Electron. Lett., 36(4):321–322, 2000.

[136] J. M. Choi, R. K. Lee, and A. Yariv. Control of critical coupling in a ring resonator- fiber configuration: application to wavelength-selective switching, modulation, am- plification, and oscillation. Opt. Lett., 26(16):1236–1238, 2001. Bibliography 141

[137] B. Bortnik, Y.-C. Hung, H. Tazawa, J. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman. Electrooptic polymer ring resonator modulation up to 165 GHz. IEEE J. Sel. Top. Quant. Elect., 13(1):104 – 110, 2007.

[138] B. Crosignani and A. Yariv. Time-dependent analysis of a ﬁber-optic passive-loop resonator. Opt. Lett., 11(4):251–253, 1986.

[139] D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi. Demonstration of 110 GHz electro-optic polymer modulators. Appl. Phys. Lett., 70(25):3335–3337, 1997.

[140] M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee. Broadband modulation of light by using an electro-optic polymer. Science, 298(5597):1401–1403, 2002.

[141] W. D. Sacher, W. M. J. Green, D. M. Gill, S. Assefa, T. Barwicz, M. Khater, E.Kiewra,C.Reinholm,S.M.Shank,Y.A.Vlasov,andJ.K.S.Poon.Bi-

nary phase-shift keying by coupling modulation of microrings. Opt. Express, 22(17):20252–20259, 2014.

[142] A. H. Gnauck and P. J. Winzer. Optical phase-shift-keyed transmission. J. Light- wave Technol., 23(1):115 – 130, 2005.

[143] K.-P. Ho. Phase-Modulated Optical Communication Systems. Springer, New York, 2005.

[144] L. Zhang, J.-Y. Yang, M. Song, Y. Li, B. Zhang, R. G. Beausoleil, and A. E. Willner. Microring-based modulation and demodulation of DPSK signal. Opt. Express, 15(18):11564–11569, 2007. Bibliography 142

[145] K. Padmaraju, N. Ophir, Q. Xu, B. Schmidt, J. Shakya, S. Manipatruni, M. Lipson, and K. Bergman. Error-free transmission of microring-modulated BPSK. Opt. Express, 20(8):8681–8688, 2012.

[146] L. Zhang, J. Y. Yang, Y. Li, M. Song, R. G. Beausoleil, and A. E. Willner. Mono-

lithic modulator and demodulator of diﬀerential quadrature phase-shift keying signals based on silicon microrings. Opt. Lett., 33(13):1428–1430, 2008.

[147] P. Dong, C. Xie, L. Chen, N. K. Fontaine, and Y.-K. Chen. Experimental demonstration of microring quadrature phase-shift keying modulators. Opt. Lett.,

37(7):1178–1180, 2012.

[148] B. Pile and G. Taylor. Small-signal analysis of microring resonator modulators. Opt. Express, 22(12):14913–14928, 2014.