Advanced Silicon Photonic Device Architectures for Optical ... · Abstract...

Advanced Silicon Photonic Device Architectures for

Optical Communications: Proposals and Demonstrations

by

Wesley David Sacher

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering

University of Toronto

c© Copyright 2015 by Wesley David Sacher

Abstract

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 experimen-

tally 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 modula-

tion bandwidth vs. resonator linewidth trade-off of conventional intracavity modulated

microrings. We demonstrate a Si coupling-modulated microring with a small-signal mod-

ulation 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 in-

dependent 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 con-

version 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 stan-

dard 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

1.2 Fiber-to-chip coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Microring modulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Thesis contributions and organization . . . . . . . . . . . . . . . . . . . . 12

2 Coupling modulated microrings 14

2.1 Fabricated devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Small-signal modulation measurements . . . . . . . . . . . . . . . . . . . 18

2.3 PRBS modulation and eye diagram measurements . . . . . . . . . . . . . 21

2.4 Overcoming low frequency distortions in coupling modulation . . . . . . 25

2.5 Analysis of the modulation efficiency . . . . . . . . . . . . . . . . . . . . 27

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Silicon polarization rotator-splitters 32

3.1 Bi-level taper polarization rotator-splitter . . . . . . . . . . . . . . . . . . 33

3.1.1 Detailed polarization rotator-splitter design and operation . . . . 35

3.1.2 Polarization rotator-splitter measurements . . . . . . . . . . . . . 36

3.2 Polarization splitter-rotator with improved crosstalk . . . . . . . . . . . . 40

3.3 Polarization controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

v

4 Silicon nitride on silicon photonic platform 47

4.1 Si3N4-on-Si fabrication at IME . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Waveguide and transition characteristics . . . . . . . . . . . . . . . . . . 52

4.2.1 Propagation losses . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.2 Interlayer transitions . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2.3 Waveguide crossings . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5 Silicon nitride on silicon grating coupler 60

5.1 Device design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Integration example: 1 × 4 tunable multiplexer/demultiplexer . . . . . . 70

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6 Silicon nitride on silicon polarization rotator-splitters 75

6.1 Polarization rotator-splitter design . . . . . . . . . . . . . . . . . . . . . 76

6.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3 Polarization controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7 Conclusion 85

7.1 Future work: microring modulators . . . . . . . . . . . . . . . . . . . . . 86

7.2 Future work: polarization rotator-splitters . . . . . . . . . . . . . . . . . 88

7.3 Future work: silicon nitride on silicon photonic platform . . . . . . . . . 89

A Analysis of microring resonator modulators 91

A.1 Time-dependent microring transmission . . . . . . . . . . . . . . . . . . . 92

A.2 Intracavity loss modulation . . . . . . . . . . . . . . . . . . . . . . . . . 95

A.2.1 Small-signal approximation . . . . . . . . . . . . . . . . . . . . . 96

A.2.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

A.3 Intracavity index modulation . . . . . . . . . . . . . . . . . . . . . . . . 100



A.4 Coupling modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103



A.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

vi

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

B Coupling modulation for binary phase-shift keying 111

B.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

B.2 Experimental demonstration . . . . . . . . . . . . . . . . . . . . . . . . . 117

B.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 dop-

ing. 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . 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

about 450 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

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

ization 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. . . . . . . . . . . . . . . . 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 mea-

surement 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. . . . . . . . . . . . . . . . . . 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 show-

ing the resonance wavelength shift with increasing reverse bias (negative)

voltages applied to the PN diode. . . . . . . . . . . . . . . . . . . . . . . 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 μm on the die. . . . . . . 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

wavelength using the thermal tuners was achieved. . . . . . . . . . . . . . 18

ix

2.3 (a) Electro-optic S21 measurements of the reference MZI, coupling mod-

ulation, 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 ref-

erence 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 − 7 GHz). The

coupling modulation eye is open at 28 Gb/s, but the intracavity modula-

tion eye closes at bit rates greater than roughly 2× the linewidth. . . . . 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

remnants of the pre-emphasis are present in the optical output. . . . . . 24

2.6 Computed eye diagrams at several bit rates for (top) intracavity modula-

tion and (center) coupling modulation driven by an uncoded NRZ signal,

and (bottom) coupling modulation driven by a NRZ 8b/10b encoded sig-

nal. 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 mod-

ulation. 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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, of a 5 μm 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. . . . . 29

3.1 (a) Schematic of the polarization rotator-splitter (PRS). Widths are la-

beled in red and purple; lengths use green labels. (b) Schematic showing

the profiles of the modes with the first and second highest effective in-

dices (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. . . . . . . . . . . . . . . . . . . . 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), the bi-level taper, and (c), the end of the adiabatic coupler. . . . . . 36

3.3 Schematic of the experimental apparatus used for measurements of the

polarization rotator-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

facets and the measurement apparatus. . . . . . . . . . . . . . . . . . . . 38

3.5 Annotated optical micrograph of the polarization splitter-rotator (PSR)

with improved crosstalk. . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 di-

rectional coupler. (b) Optical micrograph of the polarizaton controller

fabricated in the IME-OpSIS process. . . . . . . . . . . . . . . . . . . . 43

3.8 Polarization controller measurement data. (a) Current-voltage character-

istics 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 se-

ries of deposition, planarizing, and patterning steps. Ge epitaxial growth

and ion implantation steps can be incorporated for the formation of pho-

todiodes and PN junctions. . . . . . . . . . . . . . . . . . . . . . . . . . 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

metals are omitted in this schematic. . . . . . . . . . . . . . . . . . . . . 51

xii

4.3 Measurements of the propagation losses of the Si3N4 and Si strip waveg-

uides 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 tran-

sitions 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. . . . . . . . . . . . . . . . 56

4.6 (a) Top-down view schematic of the Si3N4 waveguide crossing. The cross-

ing is designed for TE-polarized light in the C-band. (b) 3D-FDTD sim-

ulated profile of the optical power at λ = 1550 nm passing through the

crossing. The TE0 input is injected at y = 0 μm. (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. . . . . . . . . . . . . . . 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

next to the markers are the references. . . . . . . . . . . . . . . . . . . . 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 top cladding deposition). . . . . . . . . . . . . . . . . . . . . . . . . 68

5.6 Annotated optical micrograph of the Si3N4-on-Si grating coupler test struc-

ture. 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-Si dual-level grating coupler in Fig. 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

waveguides and the drop port is connected to a grating coupler. . . . . . 71

xiv

5.9 Fiber-to-fiber transmission measurements for the 1 × 4 tunable multi-

plexer/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). . . . . . . . . . . 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 μm and the Si

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

is on the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 interfer-

ence coupler. (b) Optical micrograph of the polarization controller. . . . 81

6.5 Polarization controller output polarization state measurements on the Poincare

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.1 Schematic of a ring resonator modulator. . . . . . . . . . . . . . . . . . . 92

xv

A.2 Modulation depths of a microring resonator with sinusoidal loss modu-

lation 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 mod-

ulation. φ0 = 0.039477 and φ′ = 0.005. The input is detuned from reso-

nance, with the modulation resonance frequency at 10 GHz. . . . . . . . 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.

Under-coupled: σ′ = 3.5 × 10−4 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

A.5 Device parameters (top) and the corresponding output intensities (bot-

tom) 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 mi-

croring, the input wavelength is on resonance for Δθ = 0; modulating

Δθ shifts the resonance wavelength. For the coupling-modulated micror-

ing, 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 de-

vice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 opera-

tion. 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 mod-

ulated 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. . . . . . . . . . . . . . . . . . . . . . 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 transmis-

sion 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, germa-

nium (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

Si substrate

BOX

Si

SiO2

Ge

Waveguide

Grating coupler Si modulator Ge photodetector

Via

220nm

150nm 90nm

500nm2μm

P++

P N

N++

ViaMetal layer 1

Metal layer 2

Figure 1.1: Cross-section schematic of a typical Si photonic platform consisting of three Sietch depths, metallization, Si doping, Ge deposition, and Ge doping. Typical thicknessesand 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 Simodulator doped regions are labeled in red, and the Ge photodiode doping is omittedfor 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-


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 sin-

gle 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


(a) (b)

300 400 500 6001.5

2

2.5

3

Waveguide width (nm)

Effe

ctiv

e in

dex

(nef

f)

TE0TM0Single−mode

Multi−mode

(c)

Figure 1.2: Characteristics of Si waveguides with SiO2 cladding. (a), (b) Computedmajor electric field components of (a) the TE0 mode and (b) the TM0 mode for a 220nm × 500 nm waveguide at a wavelength of 1550 nm. (c) Computed neff of 220 nmthick waveguides versus waveguide width at a wavelength of 1550 nm; the waveguide issingle-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 di-

mension variations is the integration of waveguides with lower refractive index contrasts.

Silicon nitride (Si3N4) is a CMOS compatible dielectric with a significantly lower refrac-

tive 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


1480 1510 1540 1570 1600−4

−3

−2

−1

0

Wavelength (nm)

Wav

egui

de lo

ss (

dB/c

m)

Figure 1.3: Our measurement of the waveguide loss of the TE0 mode in a 150 nm × 500nm 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 disadvan-

tage 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 birefrin-

gence 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


300 400 500 600

0.2

0.4

0.6

0.8

Waveguide width (nm)Bire

frin

genc

e (n

eff,T

E0−

n eff,T

M0)

220nm thick Si150nm thick Si

(a)

Optical inputfrom SMF Polarization

splitter

Photoniccircuit

Photoniccircuit

TE + TM

TE0

TM0

Polarizationrotator

TE0

Chip

Polarizationrotator

Polarizationcombiner

Optical outputto SMF

TE + TM

TE0

TM0

(b)

Figure 1.4: (a) Computed birefringence of 220 nm and 150 nm thick waveguides versuswaveguide width at a wavelength of 1550 nm. (b) Schematic of a polarization diversityscheme for coupling single-mode optical fiber (SMF) to a Si PIC. On-chip polarizationsplitters/combiners and rotators are used at the input and output and the separatedpolarization components are sent through nominally identical photonic circuits.


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


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 cou-

pling 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 effi-

ciency, 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.


…

BOX

Top SiO2 cladding

Fiber core

To PIC

Si

Si substrate

PinPup

Pdown

(a)

50 μm

Gratingcouplers

(b)

1500 1525 1550 1575 1600

−10

−5

0

Wavelength (nm)

Cou

plin

g ef

ficie

ncy

(dB

)

Δλ1dB

= 33 nm

−3.7 dB

(c)

0 20 40 60 80 100 120−5

−4

−3

−2

−1

0

40

43

51

41

47

44 49

5046

4248

4553

54

1−dB bandwidth (nm)

Pea

k co

uplin

g ef

ficie

ncy

(dB

)

Si3N

4 − only

Si3N

4 + back reflector

Si − onlySi + back reflectorSi − ≈ 50nm features

(d)

Figure 1.5: (a) Cross-section schematic of a typical Si grating coupler and a tilted andpolished single-mode fiber. (b) Optical micrograph of Si grating couplers connected by aSi waveguide fabricated at A*STAR IME. (c) Our measurement of the coupling efficiencyversus wavelength for a single grating coupler in the test structure in (b); the gratingused 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 efficienciesand 1-dB bandwidths) in the C-band. The numbers next to the markers indicate thereferences.


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 mea-

surements 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 op-

tical 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 there-

fore, low-loss and high quality factor, Q, microrings will have high modulation efficien-

cies. 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


Modulation section(e.g., PN diode)

Opticalinput

Modulatedoutput

Couplingregion

(a)

50 μm

(b)

1500 1520 1540 1560 1580

−15

−10

−5

0

Wavelength (nm)

Nor

mal

ized

tran

smis

sion

(dB

)

(c)

1556.6 1556.7 1556.8 1556.9

−15

−10

−5

0

Wavelength (nm)

Nor

mal

ized

tran

smis

sion

(dB

)

0 V−2 V −4 V

(d)

Figure 1.6: (a) Schematic of a typical microring modulator. (b) Optical micrograph of amicroring modulator with a PN diode fabricated at A*STAR IME. (c) Our measurementof the transmission spectrum of the microring in (b) showing multiple resonances withno voltage applied to the PN diode. (d) Our measurement of the transmission spectrumof the microring showing the resonance wavelength shift with increasing reverse bias(negative) voltages applied to the PN diode.


the linewidth is inversely proportional toQ, 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 cou-

pler 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 band-

width 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 conver-

sion 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].


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 nec-

essary 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 cou-

pler 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 mod-

ulation (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 increas-

ing Q [64]. Additionally, complete on/off modulation (0-100% transmission) requires the

stored intracavity optical energy be completely charged and depleted in each switch-

ing 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-

1 c©OSA. Reprinted, with permission, from [68]

14

Chapter 2. Coupling modulated microrings 15

b a Optical input Optical output

a(t) e–iφ (t)

c d

Optical input Optical output

κ (t)

σ (t)

Figure 2.1: Schematics of (a) an intracavity modulated microring and (b) a couplingmodulated microring that uses a 2 × 2 MZI-coupler as marked by the box. Opticalmicroscope images of the fabricated SOI (c) microring with the 2×2 MZI-coupler markedby the box and (d) the reference MZI. The reference MZI was nominally identical to theMZI-coupler in the microring. The microring and MZI were separated by 620 μm on thedie.

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) and κ(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


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 coef-

ficient and resonance wavelength. The differential phase-shift between the MZI-coupler

arms changes κ(t) and σ(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 de-

vices. 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


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


1549.8 1550 1550.2 1550.4 1550.6-40

-30

-20

-10

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

1549.8 1549.9 1550 1550.1 1550.2

-30

-20

-10

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

critically-coupledover-coupledunder-coupled

a b

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


b

a

Figure 2.3: (a) Electro-optic S21 measurements of the reference MZI, coupling modula-tion, and intracavity modulation. The RF cables, RF adapters, and bias tees have beende-embedded. (b) Optical small-signal modulation responses of coupling and intracavitymodulation. Each curve is obtained by normalizing the electro-optic S21 of the microringto the S21 of the reference MZI and referencing to the value at 100 MHz. The microringwas biased near critical coupling, with a cavity linewidth Δν ≈ 6 GHz. The intracavitymodulation response for a ∼ 1.3 GHz detuning from resonance (blue) has a 3 dB band-width of 4.4 GHz, similar to the linewidth. A ∼ 5 GHz detuning produces a resonantsideband peak near the value of the detuning (red), and the 3 dB bandwidth is extendedto ∼ 13 GHz. The coupling modulation response (black) does not roll-off to 40 GHz(more than 6× the linewidth).


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 refer-

ence 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, are given by

Scm =S21,cm

S21,MZI,push−pull, (2.1a)

Sim =S21,im

S21,MZI,single, (2.1b)

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, and S21,im are as shown in Fig. 2.3(a).


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


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

linewidth as intracavity modulation. Since the PN diode phase-shifters were not opti-

mized 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 − 1 PRBS.

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


intracavity phase-shifters, except the MZI-coupler was driven in push-pull while the in-

tracavity 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 ≈ 0.2 and |κ|2 ≈0.08.

The reduction in maximum optical transmission at high data rates is not necessar-

ily a characteristic of coupling modulation. As discussed in Section 2.4 and [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 de-

pleted 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 demon-

strated microring should function beyond 28 Gb/s. The measurements were limited by

the instrumentation.


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 intracavitymodulation 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 ofthe reference MZI (right). No remnants of the pre-emphasis are present in the opticaloutput.

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 modu-

lation 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,


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


0

8b/10b Coupling Modulation

Uncoded Intracavity Modulation

0

1

0

1

1

Uncoded Coupling Modulation

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

Figure 2.6: Computed eye diagrams at several bit rates for (top) intracavity modulationand (center) coupling modulation driven by an uncoded NRZ signal, and (bottom) cou-pling modulation driven by a NRZ 8b/10b encoded signal. The calculations assume agroup index of 4.3, a NRZ PRBS 217 − 1 data signal, Δν = 5 GHz, a round-trip lengthof 250 μm, a resonant input for coupling modulation, and critical coupling for intracav-ity 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 encodedcoupling 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,


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 modu-

lation 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 circu-

lating 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 mod-

ulation. 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 substan-

tially 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 effi-

ciency 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.


We define an efficiency metric,

η =ΔφMZI

Δφring, (2.2)

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 com-

parison 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.


Figure 2.7: The coupling modulation efficiency, ηc, versus microring waveguide loss andcavity linewidth computed for several round-trip lengths, L. The calculations assume a8b/10b encoded drive signal, a 0-90% output swing, a group index of 4.3, a NRZ PRBS217 − 1 data signal, a resonant input, and critical coupling. The intracavity efficiency,ηi, of a 5 μm 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. Criticalcoupling is assumed. Coupling modulation becomes increasingly efficient over intracavitymodulation 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

modulation in cavities with the same F and phase-shifters when F � (kc/ki)2. 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


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 modula-

tion 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.


2.6 Summary

We have demonstrated experimentally that coupling modulation circumvents the con-

ventional 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 modula-

tion 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 mi-

croring 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 chal-

lenges, 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 demon-

strated 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


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.


50μm 50μm 300μm

Opticalinput Optical

outputsTE0,TM0

TE0 TE0

TM0 TE1 TE0

450nm 550nm

850nm 650nm 500nm

500nm200nm1.55μm

90nm Partiallyetched slab

220nm Si

200nmTE0,TE1

Bi level taper Adiabatic coupler

(a)

Mode 1TE0

Mode 1TE0

Mode 1TE0

Mode 1TE0

Mode 2TM0

Mode 2TE1

Mode 2TE1

Mode 2TE1

(b)

0(450) 125(475) 250(500) 375(525) 500(550)1.4

1.8

2.2

2.6

Partially−etched Si fin width (Si rib width) (nm)

n eff

TE0Mode 2Mode 3

TM0

TE1

TE1

TM0Hybridized

Hybridized

(c)

Mode 2 Mode 3

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 labeledin red and purple; lengths use green labels. (b) Schematic showing the profiles of themodes 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” referto supermodes of the composite waveguide. (c) Effective indices (neff ) along the firsthalf of the bi-level taper for modes 1 to 3 at a wavelength of 1550 nm. (d) Electric fieldcomponents (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.


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


100 m

Bi level taper Adiabatic coupler

(a)

50 m

(b)

50 m

(c)

Figure 3.2: (a) An optical micrograph of the polarization rotator-splitter fabricated inthe IME baseline process. Magnified optical micrographs are shown for (b), the bi-leveltaper, 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 dimen-

sions 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


Swept wavelengthtunable laser Detector

Broadband fiberpolarizationcontroller

Single modeoptical fiber

Fiber tofree spacecollimator

Chip

Couplinglens

Adjustablelinear

polarizer

Circularlypolarized light

Linearlypolarized light(TE or TM)

Chip output(TE+TM)

TE or TMcomponent of

output

Figure 3.3: Schematic of the experimental apparatus used for measurements of the po-larization 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


1500 1520 1540 1560 1580−60

−40

−20

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TE branch output

TE−>TETE−>TMTM−>TETM−>TM

(a)

1500 1520 1540 1560 1580−60

−40

−20

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TM branch output


(b)

1530 1540 1550 1560 1570 1580−3

−2

−1

0

1

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TE branch output (TE −> TE)

Raw dataFabry−Perot removed

(c)

1530 1540 1550 1560 1570 1580−3

−2

−1

0

1

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TM branch output (TM −> TE)


(d)

Figure 3.4: Measurement data for the PRS in Fig. 3.2. (a) Transmission spectra of thePRS 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 legendsin (a) and (b) indicate the settings of the input and output polarizers (i.e., TE→TMmeans 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 removeFabry-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 cou-

pler 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


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.


100 m

Directional couplerTE pass filters

Directional couplerTM pass filters

Directional couplerTE pass filters

PRS used as a polarization rotator

Directional couplerpolarization splitter

TE0 +TM0 TE0

TM0 TM0 TE1 TE0

TE0

TE0

Figure 3.5: Annotated optical micrograph of the polarization splitter-rotator (PSR) withimproved 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 inte-

grated 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 μm long

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


1500 1520 1540 1560 1580−80

−60

−40

−20

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TE branch output


(a)

1500 1520 1540 1560 1580−80

−60

−40

−20

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TM branch output


(b)

1530 1540 1550 1560 1570 1580−3

−2

−1

0

1

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TE branch output (TE −> TE)


(c)

1530 1540 1550 1560 1570 1580−3

−2

−1

0

1

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TM branch output (TM −> TE)


(d)

Figure 3.6: Measurement data for the PSR in Fig. 3.5. (a) Transmission spectra of thePSR 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 legendsin (a) and (b) indicate the settings of the input and output polarizers (i.e., TE→TMmeans we had a TE input and measured the TM component of the output). The redcurves in (c) and (d) have been post-processed to remove Fabry-Perot oscillations fromthe 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-


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-


PRS 3-dB DC

PIN diode(500 m)

PRS Input Output

3-dB DC

Thermal tuner(500 m)

PIN diode(500 m)


PIN diode(500 m)


PIN diode(500 m)


2 x 2 MZI controls amplitude ratio of TE and TM Controls phase between TE and TM

(a)

500 m

PRS PRS

PIN diode

3 dB DC

Thermaltuner PIN diode

Thermaltuner

3 dB DC

(b)

Figure 3.7: (a) Schematic of the polarization controller. “3-dB DC” is a 3 dB directionalcoupler. (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


wavelength was fixed at 1570 nm and the input was chosen to be TE-polarized for sim-

plicity. 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 con-

troller 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


0 0.5 1 1.5 20

25

50

75

100

Voltage (V)

Cur

rent

(m

A)

Thermal tunerPIN diode

(a)

0 90 180 270 360−40

−30

−20

−10

0

Output polarizer angle (degrees)

Nor

mal

ized

ou

tput

pow

er (

dB)

TM−45 deg.Circular

(b)

0 20 40 60−20

−15

−10

−5

0

Thermal tuner power (mW)

Nor

mal

ized

ou

tput

pow

er (

dB)

Total outTE outTM out

TE −> TETE −> TM

(c)

0 10 20 30 40−20

−15

−10

−5

0

Diode current (mA)

Nor

mal

ized

ou

tput

pow

er (

dB)

Total outTE outTM out

TE −> TETE −> TM

(d)

Figure 3.8: Polarization controller measurement data. (a) Current-voltage characteristicsof the top-left thermal tuner and PIN diode. (b) Normalized output power as the outputpolarizer was rotated. With a TE-polarized input, bias conditions were chosen to obtaina TM-polarized output (black curve), a -45◦ linearly-polarized output (blue curve), anda circularly-polarized output (red curve). (c) Normalized output power as the top-leftthermal tuner power was swept. (d) Normalized output power as the top-left PIN diodecurrent was swept. In (c) and (d), the output polarizer was set to pass either TE or TMor removed from the optical path (“Total out”). The optical output power curves werenormalized to the maximum value in each plot. The magenta labels and dashed linesindicate points where a TM or TE output was generated from the TE input (marked“TE→TM” and “TE→TE”, respectively).


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 × 2 MZI to

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

In this chapter1, 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, dis-

persion, and sensitivity to variations in waveguide dimensions. In addition, Si3N4 does

not suffer from two photon and free carrier absorption over the telecommunication wave-

length 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-

1 c©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-

peratures around 800oC 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


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 pro-

cesses 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


(1) Si layer patterning (2) SiO2 deposition + Planarization

(4) SiO2 deposition+ Planarization

+ Heater patterning

(5) SiO2 deposition + Via formation

(6) Contact metal patterning + Deep trench formation

BOX

Si substrate

Si

(3) Si3N4 deposition + Patterning

Si substrate

TiN

Si3N4

BOX

Si

Si substrate

BOX

SiSiO2 SiO2

Si3N4

Si substrate

BOX

SiSiO2 Si3N4

Si substrate

BOX

SiSiO2

TiN

Si3N4

Si substrate

BOX

SiSiO2

TaN + Al

TiN

Figure 4.1: Schematic of the fabrication flow for the Si3N4-on-Si photonic platform show-ing the integration of thermal heaters. The process consists of a series of deposition,planarizing, and patterning steps. Ge epitaxial growth and ion implantation steps canbe incorporated for the formation of photodiodes and PN junctions.


Si3N4

Si substrate

BOX

Si

SiO2

2 m

400nm 150nm

50nm

65nm

Figure 4.2: Cross-section schematic showing the layer thicknesses and waveguide geome-tries in the Si3N4-on-Si photonic platform. The heaters and contact metals are omittedin 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 germa-

nium (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


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


1480 1510 1540 1570 1600−4

−3

−2

−1

0

Wavelength (nm)

Wav

egui

de tr

ansm

issi

on (

dB/c

m)

Si3N

4Si

(a)

1260 1280 1300 1320 1340 1360−8

−6

−4

−2

0

Wavelength (nm)

Wav

egui

de tr

ansm

issi

on (

dB/c

m)

Si3N

4Si

(b)

Figure 4.3: Measurements of the propagation losses of the Si3N4 and Si strip waveguidesover (a) the SCL-bands (near λ = 1550 nm) and (b) the O-band (near λ = 1310 nm). TheSi3N4 waveguides had a height of 400 nm and a width of 900 nm, and the Si waveguideshad 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 propa-

gation 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


Lc

Si Si3N4

wSi,wg wSi3N4,wgwSi3N4,tip wSi,tip

800nm

Si tipSi3N4 tip

Figure 4.4: Schematic of the interlayer transition. The computed TE0 mode at variouswaveguide 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 layersduring fabrication are shown, and the nominal widths of these tips were 200 nm and 180nm, respectively. Lc is the length of the interlayer transition; wSi,tip and wSi3N4,tip arethe widths of the Si and Si3N4 waveguide tips, respectively. wSi,wg and wSi3N4,wg are thestandard routing waveguide widths (wSi,wg = 500 nm and wSi3N4,wg = 900 nm).


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 = 15 μm for the SCL-bands, and 2) a 140 nm

wide Si tip, a 200 nm wide Si3N4 tip, and Lc = 15 μm for the O-band. The two types

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


0 10 20 30 40 50

−2.5

−2

−1.5

−1

−0.5

0

Lc (μm)

Tra

nsm

issi

on (

dB/tr

ansi

tion)

(a)

0 100 200 300−30

−25

−20

−15

−10

−5

Number of transitionsR

aw tr

ansm

issi

on (

dB)

1550nm, Lc=15μm, w

Si,tip=180nm

1310nm, Lc=15μm, w

Si,tip=140nm

Fits

(b)

1480 1510 1540 1570 1600

−0.15

−0.1

−0.05

0

Wavelength (nm)

Tra

nsm

issi

on (

dB/tr

ansi

tion)

(c)

1260 1280 1300 1320 1340 1360

−0.15

−0.1

−0.05

0

Wavelength (nm)

Tra

nsm

issi

on (

dB/tr

ansi

tion)

(d)

Figure 4.5: (a) The computed transmission of the interlayer transition as a function ofLc for λ = 1550 nm. (b) Examples of the measured raw transmission data of cutbackstructures as a function of the number of interlayer transitions at wavelengths of 1550nm and 1310 nm. Linear fitting yields the transmission per transition. (c), (d) Spectraof the loss per transition in (c) the SCL-bands and (d) the O-band extracted from linearfits of the transmission spectra vs. number of transitions.


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 fea-

tures) 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


23 m3.5 m

0.9 m

6 m

Single modewaveguide

Lineartaper

Lineartaper

Multimodeinterference

region

6 m

Single modewaveguide

(a)

40

20

0020 20

X ( m)

Y(m)

0.0

0.5

1.0

(b)

(c)

0 20 40 60 80−9

−8

−7

−6

−5

Number of crossings

Raw

tran

smis

sion

(dB

)

DataFit

(d)

1480 1510 1540 1570 1600−0.1

−0.08

−0.06

−0.04

−0.02

0

Wavelength (nm)

Tra

nsm

issi

on (

dB/c

ross

ing)

(e)

1480 1510 1540 1570 1600−80

−60

−40

−20

0

Wavelength (nm)

Raw

tran

smis

sion

(dB

)

ThruCrosstalk

(f)

Figure 4.6: (a) Top-down view schematic of the Si3N4 waveguide crossing. The crossingis designed for TE-polarized light in the C-band. (b) 3D-FDTD simulated profile of theoptical power at λ = 1550 nm passing through the crossing. The TE0 input is injected aty = 0 μm. (c) Optical micrograph of the waveguide crossing. (d) Measured raw fiber-to-fiber transmission of the crossing cutback structures at λ = 1550 nm. (e) Transmissionspectrum of a single crossing extracted from the cutback structures. (f) Measured rawthrough (thru) and crosstalk transmission spectra showing < -48 dB of crosstalk over a120 nm bandwidth.


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 multi-

mode 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 band-

widths < 50 nm, and wide bandwidth grating couplers (1-dB bandwidth > 65 nm) had

coupling efficiencies < −4 dB. In this chapter1, 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


60

Chapter 5. Silicon nitride on silicon grating coupler 61

0 20 40 60 80 100 120−5

−4

−3

−2

−1

0

40

43

51

41

47

4449

50

46 4248

45

53

54

1−dB bandwidth (nm)

Pea

k co

uplin

g ef

ficie

ncy

(dB

)

This work (Si3N

4−on−Si)

Si3N

4 − only

Si3N

4 + back reflector

Si − onlySi + back reflectorSi − ≈ 50nm features

Figure 5.1: Comparison of our Si3N4-on-Si dual-level grating coupler experimental resultwith 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 thereferences.

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 plat-

form 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 cou-

pler design, Section 5.2 describes our experimental demonstration of the grating coupler,

and Section 5.3 describes our 1 × 4 tunable multiplexer/demultiplexer demonstration.


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 compos-

ite 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) radia-

tion 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 directionali-

ties 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 limita-

tion 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


(a)

400nm

Si substrate

BOX

Top SiO2 cladding

Si3N4Si

150nm

50nm

65nm

Si3N4waveguide

Si stripwaveguide

Si ribwaveguide

Si3N4 on SOIgratingcoupler

2 m

1.5 m

TiN heater

(b)

Si3N4

Partiallyetched Si

…

775nm

425nm

875nm

200nmwSi

wSi3N4 g

L

wSi3N4 =wSi =g=L =

Si substrate

BOX

Top SiO2 cladding &index matching fluid

675nm400nm

725nm

350nm

700nm400nm700nm

325nm

700nm400nm700nm

350nm

700nm400nm700nm

350nm

725nm400nm700nm

325nm

700nm400nm725nm

275nm

700nm400nm725nm

225nm

825nm400nm550nm

125nm

950nm400nm275nm

50nm

21o

Fiber core

To PIC

z

y

x

(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 plat-form. (c) Cross-section schematic of the grating coupler and an input/output opticalfiber. The following parameters of each grating period are listed: Si3N4 grating toothwidth (wSi3N4), Si grating tooth width (wSi), gap between Si3N4 teeth (g), and the offsetbetween Si3N4 and Si teeth (L).


1460 1480 1500 1520 1540 1560 1580−4

−3

−2

−1

Wavelength (nm)

Cou

plin

g ef

ficie

ncy

(dB

)

ApodizedUniform

(a)

−300 −200 −100 0 100 200 3000.5

0.6

0.7

0.8

0.9

ΔL (nm)

Dire

ctio

nalit

y, D

(b)

Figure 5.3: (a) Simulated coupling efficiency versus wavelength for the apodized anduniform grating couplers. (b) Simulated directionality (D) versus variations in the offsetsbetween the Si3N4 and Si teeth from their apodized values (ΔL). ΔL = 0 nm correspondsto 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


on sets of two adjacent grating periods. Specifically, the period, wSi3N4, wSi, and L 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, on the

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


1460 1480 1500 1520 1540 1560 1580−5

−4

−3

−2

−1

Wavelength (nm)

Cou

plin

g ef

ficie

ncy

(dB

)

ΔL = 0 nmΔL = +50 nmΔL = −50 nm

0.2 dB

Figure 5.4: Simulated coupling efficiency versus wavelength with ±50 nm variations inthe 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 < 0.1 dB and < 1 nm,

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


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 is tapered down to a width of 900 nm using a 40 μm 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


20 m

(a)

8 m

(b)

6 m

(c)

Figure 5.5: (a) Optical micrograph of the fabricated Si3N4-on-Si dual-level grating cou-pler. (b) Scanning electron microscope (SEM) image of the Si grating teeth duringfabrication (i.e., after Si etching but before deposition of the SiO2 spacer layer betweenthe 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).

100 μm

Grating couplers

Si3N4 waveguide

Figure 5.6: Annotated optical micrograph of the Si3N4-on-Si grating coupler test struc-ture. Two nominally identical grating couplers are connected by a single-mode Si3N4

waveguide.


1460 1480 1500 1520 1540 1560 1580−5

−4

−3

−2

−1

Wavelength (nm)

Cou

plin

g ef

ficie

ncy

(dB

)

SimulationMeasurement

Δλ1dB

= 80 nm

−1.29 dB

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


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.


200 m

GCin GC1 GC2 GC3 GC4 GCthru

Ring 1 Ring 2 Ring 3 Ring 4

(a)

Si3N4 on SOIdual level

grating coupler

Thru port coupler

Drop portcoupler

Si microring

Si3N4 Siwaveguidetransition

150 nm thick Si65 nm thick SiSi3N4

(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 microringresonator in the multiplexer/demultiplexer without the TiN and contact metals. Themicroring is connected to Si bus waveguides and the drop port is connected to a gratingcoupler.


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


1510 1520 1530 1540 1550−45

−35

−25

−15

−5

Wavelength (nm)

Thr

u po

rt tr

ansm

issi

on (

dB)

Not tunedTuned

(a)

1510 1520 1530 1540 1550−45

−35

−25

−15

−5

Wavelength (nm)

Dro

p po

rt tr

ansm

issi

on (

dB)

Ring 1Ring 2Ring 3Ring 4

(b)

Figure 5.9: Fiber-to-fiber transmission measurements for the 1 × 4 tunable multi-plexer/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 afterthermal tuning (i.e., transmission from GCin to GC1 - GC4). “GC” refers to a gratingcoupler and “Ring” refers to a Si microring; the nomenclature is defined in Fig. 5.8(a).


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.


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 and Si layers is used to

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 evo-

lution. 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 character-

istics, 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


(a)

Mode 1TE0

Mode 2TM0

Mode 1TE0

Mode 1TE0

Mode 1TE0

Mode 2TE1

Mode 2TE1

Mode 2TE1

(b)

180 330 480 630 780 9301.5

1.75

2

2.25

2.5

Si width (nm)

n eff

TE0Mode 2Mode 3

TM0

TE1

Hybridized

Hybridized

TE1

TM0

(c)

Figure 6.1: (a) Schematic of the Si3N4-on-Si PRS. Lengths are labeled in green; widthsare labeled in red for the Si layer and in purple for the Si3N4 layer. (b) Mode profiles ofthe modes with the first and second highest effective indices (i.e., “mode 1” and “mode2”) along the PRS. (c) Modal effective indices (neff ) in the TM0-TE1 mode convertershowing hybridization of the TM0 and TE1 modes; the Si3N4 width is fixed at 1.4 μm andthe Si width is increased. The calculations in (b) and (c) were performed at a wavelengthof 1550 nm.


(a)

(b)

Figure 6.2: Optical micrographs of the Si3N4-on-Si PRS. (a) The whole PRS. (b) Thepoint where the Si3N4 terminates before the adiabatic coupler; a Si3N4-Si compositewaveguide 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


1500 1520 1540 1560 1580−60

−50

−40

−30

−20

−10

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TE branch output


(a)

1500 1520 1540 1560 1580−60

−50

−40

−30

−20

−10

0

Wavelength (nm)

Tra

nsm

issi

on (

dB)

TM branch output


(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 inFig. 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-componentof the output).


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 ±0.5 dB

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


PRS Input Output3-dB

MMI3-dB MMI

3-dB MMI

3-dB MMI PRS

(a)

300 m

PRS Si3N4 3 dBMMI

Heater 2

PRSSi3N4 3 dBMMI

Si3N4 3 dBMMI

Si3N4 3 dBMMI

Heater 3 Heater 4 Heater 5Heater 1

(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 con-

troller. 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 wave-

length was fixed at 1550 nm. The polarization controller insertion loss was < 4.5 dB.

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 Poincare 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


TE input

(a)

45o input

(b)

Figure 6.5: Polarization controller output polarization state measurements on thePoincare 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 2power, a sweep of the Heater 3 power was performed. Similarly, in (b), the Heater 2power was swept at different Heater 1 power settings. The heater numbering is definedin Fig. 6.4(b), and Px refers to the power dissipated in Heater x.


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

Poincare 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 Poincare 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 Poincare 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), ap-

plying 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 Poincare 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 sta-

bilization (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.


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 band-

widths. 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 de-

vices, 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 av-

enue 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 en-

ables 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 addi-

tion, 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 cou-

plers. 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 mod-

ulators (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 microcav-

ities. 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


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 fre-

quency 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 com-

plexity 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 simulta-

neously 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 de-

vice 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 perfor-

mance of the BPSK, coupling modulated microring modulator in Appendix B would be

drastically improved, and the demonstration of more complex advanced modulation for-

mats 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.


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 polar-

ization 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 im-

proved 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-


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 plat-

form 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 oc-

curs 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


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 res-

onator 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 modula-

tion: 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 characteris-

tics 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


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 attenua-

tion, a, experienced by a circulating wave at a frequency ω after each round-trip in the

resonator can be expressed by

φ(t, ω) = ωτ +ω

n

∫ t

t−τ

η(t′)dt′, (A.1a)

a(t) = a0 +1

τ

∫ t

t−τ

γ(t′)dt, (A.1b)

C(t)

B(t)A

D(t)

κ, σ

Figure A.1: Schematic of a ring resonator modulator.


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

D(t) =a(t)

2π

∫ ∞

−∞C(Ω) exp[−iφ(t, ω)] exp(iΩt)dΩ, (A.3)

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)


iκ(t)C(t) = σ(t)B(t)− A, (A.5b)

where φ(t) = φ(t, ω0) and κ(t) and σ(t) are the resonator-waveguide coupling and trans-

mission coefficients, and σ2(t) + κ2(t) = 1 for a lossless coupler.

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

Tss ≡ B

A=

σ − a exp(−iφ)

1− aσ exp(−iφ). (A.6a)

|Tss|2 = σ2 + a2 − 2aσ cos(φ)

1 + a2σ2 − 2aσ cos(φ). (A.6b)

We observe that a and σ are interchangeable in |Tss|2. 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

T (t) ≡ B(t)

A= σ(t) +

κ(t)

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

If a(t), κ(t), σ(t), and φ(t) are periodic with a period equal to τ , then T (t) is equal

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


Fredholm integral equation of the second kind, which possesses a Neumann series solution

[138]. The Fredholm integral equation form of Eq. (A.7) is

T (t) = σ(t)− κ(t)

κ(t− τ)a(t) exp[−iφ(t)]+

∫ ∞

−∞

κ(t′ + τ)

κ(t′)a(t′ + τ)σ(t′) exp[−iφ(t′ + τ)]δ[t′ − (t− τ)]T (t′)dt′.

(A.8)

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, and κ

are constant. The solution of Eq. (A.8) for the transmission with loss modulation, Ta(t),

is

Ta(t) = σ − a(t)e−iφ +∞∑n=1

σne−inφ[σ − a(t− nτ)e−iφ

] n−1∏m=0

a(t−mτ). (A.9)

The first two terms in the above equation are the “instantaneous” response of the res-

onator, 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).


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(Ω) = a0δ(Ω) +a′

2[δ(Ω + Ωm) + δ(Ω− Ωm)]. (A.10)

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

Ta(Ω)[1− a0σe

−i(φ+Ωτ)]− a′

2σe−i(φ+Ωτ)

[Ta(Ω− Ωm)e

iΩmτ + Ta(Ω + Ωm)e−iΩmτ

]

= (σ − a0e−iφ)δ(Ω)− a′

2e−iφ [δ(Ω− Ωm) + δ(Ω + Ωm)] ,

(A.11)

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

Ta(Ω) consists only of the Ω = 0 component and the harmonics of Ωm.

We solve Ta(Ω) order by order in a′. We obtain an approximate solution by keeping

only the terms up to O(a′) to find that

Ta(0) =σ − a0e

−iφ

1− a0σe−iφδ(0), (A.12)

which is simply the steady-state transmission coefficient, and

Ta(Ωm) =a′

2

e−iφ[σTa(0)− δ(0)]

1− σa0e−i(φ+Ωmτ)(A.13a)

Ta(−Ωm) =a′

2

e−iφ[σTa(0)− δ(0)]

1− σa0e−i(φ−Ωmτ). (A.13b)

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


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 Ta(±Ωm) and Ta(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

Δ =f(t)max − f(t)min

f(t)max + f(t)min, (A.14)

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

Δ = 2

∣∣∣∣∣T ∗(−Ωm)

T ∗(0)+

T (Ωm)

T (0)

∣∣∣∣∣ , (A.15)

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 mod-

ulation depth, Δa, is

Δa = 2a′(1− σ2)

∣∣∣∣ σ cosφ− a0 + σa0e−iΩmτ (a0 cos φ− σ)

(a20 + σ2 − 2a0σ cosφ)(1 + a20σ2e−i2Ωmτ − 2a0σ cosφe−iΩmτ )

∣∣∣∣ . (A.16)

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, where p 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.


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

simplifies to

Δa,res = 2a′(1− σ2)

|σ − a0|[

1

(1− a0σ)2 + a0σ(Ωmτ)2

] 12

, (A.17)

with a 3 dB roll-off at a frequency

Ωa,3dB,res =1− a0σ

τ

√3

a0σ. (A.18)

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.


100

101

102

10−2

10−1

100

Mod

ulat

ion

Dep

th(Δ

a)

Modulation Frequency (GHz)

series solutionsmall signal solution

(a)

100

101

102

10−4

10−3

10−2

10−1


Mod

ulat

ion

Dep

th(Δ

a)

fm = 10GHz, series solution

fm = 10GHz, small signal solution

fm = 40GHz, series solution

fm = 40GHz, small signal solution

(b)

Figure A.2: Modulation depths of a microring resonator with sinusoidal loss modulationbetween 2 dB/cm and 5 dB/cm. a0 = 0.9975, a′ = 0.0011, and σ = 0.9928. (a): Theinput is on resonance. (b): Detuned input, with the modulation resonance frequency atfm.


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

Tφ(t) = σ − ae−iφ(t) +∞∑n=1

σnan[σ − ae−iφ(t−nτ)

] n−1∏m=0

e−iφ(t−mτ). (A.19)

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.


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:

e−iφ(t) = e−iφ0

∞∑n=−∞

inJn(φ′)einΩmt. (A.21)

For φ′ � 1, only the J0 and J1 terms dominate and J0(φ′) ≈ 1 and J1(φ

′) ≈ φ′/2.

Therefore,

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

We substitute Eq. (A.22) into Eq. (A.7) and take the Fourier transform of the


resulting equation to obtain

Tφ(Ω)[1−aσe−i(φ0+Ωτ)]− iφ′

2aσe−i(φ0+Ωτ)[Tφ(Ω− Ωm)e

iΩτ + Tφ(Ω + Ωm)e−iΩτ ]

= (σ − ae−iφ0)δ(Ω)− iφ′

2ae−iφ0 [δ(Ω− Ωm) + δ(Ω + Ωm)].

(A.23)

Equation (A.23) can be solved to first order in φ′. Tφ(0) = Ta(0) = Tss, which is the

static response of the resonator, and

Tφ(Ωm) = iφ′

2

ae−iφ0 [σTφ(0)− δ(0)]

1− σae−i(φ0+Ωmτ), (A.24a)

Tφ(−Ωm) = iφ′

2

ae−iφ0 [σTφ(0)− δ(0)]

1− σae−i(φ0−Ωmτ). (A.24b)

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

Δφ =2φ′[

σa(1 − σ2) sin(φ0)

σ2 + a2 − 2σa cos(φ0)

]×

[1 + a4 − 2a2 cos(Ωmτ)

(1− σ2a2)2 + 4σ2a2[cos(φ0)− cos(Ωmτ)]2 − 4σa(1− σa)2 cos(φ0) cos(Ωmτ)

] 12

.

(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, where p is an integer.


10−1

100

101

10210

−3

10−2

10−1

100


Mod

ulat

ion

Dep

th(Δ

φ)

a = 0.9971, σ = 0.9928, series solutiona = 0.9971, σ = 0.9928, small signal solutiona = 0.9928, σ = 0.9971, series solutiona = 0.9928, σ = 0.9971, small signal solution

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


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,

φ0 = 0.039477 and φ′ = 0.005, which corresponds to an index change of 2 × 10−5 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 < a) ring.

There is good agreement between the small signal approximation and the exact solu-

tion for low modulation frequencies. The modulation depth at the modulation resonance

can be much greater than the low frequency modulation depth. At higher frequencies


near and greater than the modulation resonance, the deviation of the small signal analy-

sis 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

Tσ(t) = σ(t)− κ(t)

κ(t− τ)ae−iφ + κ(t)

∞∑n=1

ane−inφ

κ(t− nτ)[σ(t− nτ)− κ(t− nτ)

κ(t− (n + 1)τ)ae−iφ

] n∏m=1

σ(t−mτ).

(A.26)

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.


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 � 1 and σ ≈ 1. We take

the coupling coefficient as

κ(t) = κ0 + κ′ cos(Ωmt), (A.27)


where, |κ′/κ0| � 1. For |σ(t)|2 + |κ(t)|2 = 1 to O(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

κ0Tσ(Ω)[1− aσ0e−i(φ+Ωτ)] +

κ′

2Tσ(Ω− Ωm)

[e−iΩmτ − ae−i(φ+Ωτ)

(σ0e

iΩmτ − κ20

σ0

)]

+κ′

2Tσ(Ω + Ωm)

[eiΩmτ − ae−i(φ+Ωτ)

(σ0e

−iΩmτ − κ20

σ0

)]

= κ0[σ0e−iΩτ − ae−iφ]δ(Ω) +

κ′

2

(σ0e

−iΩτ − κ20

σ0e−i(Ω−Ωm)τ − ae−iφ

)δ(Ω− Ωm)

+κ′

2

(σ0e

−iΩτ − κ20

σ0e−i(Ω+Ωm)τ − ae−iφ

)δ(Ω + Ωm).

(A.29)

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

index and loss modulation. To O(κ′), Tσ(0) = Tss, the static response of resonator. Using

Eq. (A.15) to solve for the modulation depth, we obtain

Δσ = 2σ′∣∣∣∣ (1− a2e−iΩmτ )[σ0 − a cosφ+ aσ0(a− σ0 cosφ)e

−iΩmτ ]

(σ20 + a2 − 2aσ0 cosφ)(1 + a2σ2

0e−2iΩmτ − 2aσ0 cos φe−iΩmτ )

∣∣∣∣ . (A.30)

To simplify Eq. (A.30), we take the input wavelength exactly on resonance, such that

exp(iφ) = 1, and Ωmτ � 1 to arrive at

Δσ,res = 2σ′[

(1− a2)2 + a2(Ωmτ)2

(σ0 − a)2 [(1− aσ0)2 + aσ0(Ωmτ)2]

] 12

. (A.31)

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 −aσ0)/

√aσ0, Δσ,res is approximately constant and equal to 2σ′(1− a2)/[|σ0− a|(1− aσ0)].


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.


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


10−1

100

101

102

10−1

100


Mod

ulat

ion

Dep

th(Δ

σ)

σ(t) < a, series solution

σ(t) < a, small signal solution

σ(t) > a, series solution

σ(t) > a, small signal solution

(a)

10−1

100

101

102

10−3

10−2

10−1


Mod

ulat

ion

Dep

th(Δ

σ)

σ(t) < a, series solution

σ(t) < a, small signal

σ(t) > a, series solution

σ(t) > a, small signal

(b)

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


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. It is only

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 mod-

ulation, 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


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, am-

plitude, 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


0 40 80 120 160 2000.984

0.988

0.992

0.996

1

Time (ps)

Rin

gLos

sa(t

)

(a)

0 40 80 120 160 2000

0.004

0.008

0.012

0.016

Time (ps)

Rin

gP

hase

Shift

φ(t

)

(b)

0 40 80 120 160 2000.997

0.998

0.999

1

Time (ps)

Cou

plin

gSt

reng

thσ(t

)

(c)

0 40 80 120 160 2000.6

0.7

0.8

0.9

1

Time (ps)

Out

put|T

a(t

)|2

(d)

0 40 80 120 160 2000

0.25

0.5

0.75

1

Time (ps)

Out

put|T

φ(t

)|2

(e)

0 40 80 120 160 2000

0.1

0.2

0.3

0.4

0.5

Time (ps)

Out

put|T

σ(t

)|2

(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.


switches can operate at > 100 GHz [139, 140].

A disadvantage of coupling modulation for data modulation is low-frequency distor-

tion. 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 com-

plex 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


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 demon-

strated [145]. Using a microring-enhanced MZI, quadrature phase-shift keying modula-

tion (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 reso-

nance 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 mod-

ulation 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 mod-

ulation 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


Re[T]

Im[T]Phase modulator

T

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

/

Out

put (

|T|2 a

nd

T/)

|T|2

T/

'1' symbol'0' symbol

(a)

-1.5 -1 -0.5 0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

/

Out

put (

|T|2 a

nd

T/)

|T|2

T/

'0' symbol

'1' symbol

Re[T]

Im[T]Mach-Zehnder interferometer

T

(b)

-0.2 -0.1 0 0.1 0.2-1

-0.5

0

0.5

1

/

Out

put (

|T|2 a

nd

T/)

|T|2

T/

'0' symbol '1' symbol

Re[T]

Im[T]Intracavity-modulated microring

T

(c)

-1 -0.5 0 0.5 10

0.2

0.4

0.6

0.8

1

/

Out

put (

|T|2 a

nd

T/)

|T|2

T/

'1' symbol'0' symbol

Re[T]

Im[T]Coupling-modulated microring

T

(d)

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


Optical Input Through Port

Drop Port(modulator output)

Thermal tuners

Thermaltuners

PN diodephase shifters

3 dBcoupler

3 dBcoupler

3 dBcoupler

3 dBcoupler

1

1

2(t)

2(t)

Figure B.2: Schematic of a coupling-modulated microring for BPSK. The microring isin an add-drop configuration with MZI-couplers at the through and drop sides. EitherMZI-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 thethrough side acts as a tunable coupler. This configuration matches the experimentallydemonstrated 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× 2 MZI-

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


drop and through ports of the microring are, respectively,

Tdrop = κ∗1κ

∗2

√a exp(−iφ/2)

1− aσ∗1σ2 exp(−iφ)

, (B.1a)

Tthru =σ1 − σ2a exp(−iφ)

1− aσ∗1σ2 exp(−iφ)

, (B.1b)

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

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

σ1,2(t) = i cos

(θ01,2 +Δθ1,2(t)

2

), κ1,2(t) = i sin

(θ01,2 +Δθ1,2(t)

2

), (B.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,

σ1,2(t) ≈ i

[1− Δθ21,2(t)

2

], κ1,2(t) ≈ i

Δθ1,2(t)

2, (B.3)


From Eq. (B.1a), if either κ1 or κ2 changes sign while φ, a, and σ1,2 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 =

±√1− σ2

1/a2 or the through port MZI-coupler is modulated between κ1 = ±

√1− a2σ2

2 .

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

η1 =2π

Δθ1≈ π

2√1− a2σ2

2

≈√

πF

4for a → 1, (B.4a)

η2 =2π

Δθ2≈ π

2√

1− σ21/a

2≈

√πF

4for a → 1. (B.4b)

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


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| ≈ 0 and |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 pro-

cess [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 μm and 50 μm 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


Thermal tuners

PN diodephase shifters

Input

Dropport

Throughport

(a)

1533 1534 1535 1536 1537−30

−25

−20

−15

−10

−5

0

Wavelength (nm)

Nor

mal

ized

tran

smis

sion

(dB

)

ThruDrop

(b)

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


Before demodulator After demodulator(destructive port)

After demodulator(constructive port)

5 Gb/s

10 Gb/s

Figure B.4: Measured eye diagrams of the DPSK microring modulator at 5 and 10 Gb/sbefore and after the fiber delay line interferometer demodulator. The open eye diagramswith large extinction ratios confirm DPSK operation. The drive signals were NRZ PRBS231 − 1. The vertical scales differ between the 5 and 10 Gb/s eye diagrams and betweenthe DPSK modulated and demodulated eye diagrams; accurate amplitude comparisonsbetween the eye diagrams are difficult due to the different fiber paths and losses for eachset 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.


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 interfer-

ence 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,


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,


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.

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