c:/phd research files electronics ali group/thesis/ut …...as well as proposal, design, and...

Silicon ring modulators for high-speed optical interconnects

by

Samira Karimelahi

A thesis submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering

University of Toronto

c© Copyright 2016 by Samira Karimelahi

Abstract

Silicon ring modulators for high-speed optical interconnects

Samira Karimelahi

Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering

University of Toronto

2016

This thesis presents research contributions in the area of ring modulator modeling, design,

and characterization. These include small-signal modeling of the intracavity and the coupling-

modulated ring modulators, optimization of intracavity ring modulator rib-to-contact distance

as well as proposal, design, and fabrication of PAM-N and QAM-N modulators.

Accurate modeling of the ring modulator small-signal response is essential for designing a

modulator. In this thesis, a closed-form expression for small-signal response of an intracavity

ring modulator is derived and verified by measurement results. The pole-zero representation

of the transfer function illustrates dependency of the ring modulator frequency response upon

parameters such as electrical bandwidth, coupling condition, optical loss, and sign/value of the

laser detunings.

Using the developed small-signal model and through measurement of the fabricated intra-

cavity ring modulators in IME A*Star process, electrical and optical trade-offs of rib-to-contact

distance are analyzed. Key parameters such as extinction ratio, insertion loss, transmission

penalty, and bandwidth are compared quantitatively. We show that at 4dB extinction ratio,

decreasing the high doped region distance to rib from 800nm to 350nm increases the bandwidth

by 3.8× while increasing the insertion loss by 8.4dB.

Small-signal response of the coupling-modulated ring resonator is also obtained and is com-

pared with the intracavity ring modulator response. Based on number of poles and zeros, it is

shown that unlike the intracavity ring modulator, the coupling-modulated ring resonator does

not have the optical bandwidth limitation.

Coupling modulation in a ring resonator is then used to present a new method for optical

PAM modulation. The response of this modulator is optimized in terms of linearity for both

ii

reverse and forward-biased cases. This modulator can operate for long haul communication

with its data rate only limited by the MZI bandwidth.

Lastly, a compact structure for DAC-free optical QAM modulation based on the coupling-

modulated ring resonator is proposed and fully analyzed where various key design considerations

are discussed. Output level linearity is also studied where we show that linearity among levels

is achievable with two segments in QAM-16 while an additional segment may be required in

QAM-64.

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Acknowledgements

The journey toward getting my PhD was not the easy one. I had to make one of toughest

decisions that one may encounter during her/his PhD and that was switching the direction of

research and my supervisor. Despite all warnings, I switched my research direction and started

over with a new supervisor, which turned out to be a really great decision.

I would like to express my sincere gratitude to my supervisor Prof. Ali Sheikholeslami. He

always believed in me and helped me figure out my strengths and weaknesses. I will always

appreciate his continuous support. His guidance helped me throughout my PhD study.

I am thankful to my thesis committee: Prof. Amr Helmy, Prof. J. Stewart Aitchison,

Prof. Harry E. Ruda, and my external examiner Prof. Lukas Chrostowski, for their insightful

comments and valuable feedback.

I would like to extend my sincere gratitude to Prof. Farid N. Najm and Prof. David Lie

for their support during my tough times in my PhD studies. I would also like to thank CMC

microsystems for technological support and workshops, and especially to Jessica Zhang and

Dan Deptuck. Some of the experiments in this thesis were carried out in Prof. Joice Poons lab

with the help of Jared Mikkelsento both of whom I am grateful. I would also like to thank Dr.

Naim Ben Hamida and Ciena for their support. I am also grateful to NSERC and OCE for

financial support.

I am thankful to all of my great friends in BA5000 especially I am thankful to Alif Zaman,

Sayeh Sharifimoghaddam, and Farhad Ramezankhani as their presences made the process of

taking courses more fun. I am thankful to Sadegh Jalali, Joshua Liang, Wahid Rahman, and

Behzad Dehlaghi for all the informative discussions we had.

Thank you to my kind friends Yue Yin, Sevil Zeynep Lulec, and Aynaz Vatankhah for

creating awesome memories during my PhD study. I will always remember the ISSCC trips.

I was lucky and blessed to have many great friends who were beside me and were like

family to me during my years of being away from home. I am particularly thankful to Maliheh

Aramoon for her kind presence during both the hard and the fun times. I am also thankful

to Safa Akbarzadeh, Hamideh Zakeri, Masoomeh Kalantari, Mona Sobhani, and all the friends

from UTDisqo for many years of friendship. You guys made Friday nights exceptional for me

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and I could get the energy for the whole week ahead.

My deepest gratitude goes to my special family for being supportive, encouraging, and

helpful.

Last but denitely not the least, I would like to extend my deepest appreciation to my

husband, Nima Zariean, for being so awesome, caring, smart, and kind. I really benefit from

our academic and non-academic discussions.

v

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Background 7

2.1 Optical interconnect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Electro-optic modulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Electrorefraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Electroabsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.3 Free carrier effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.4 Thermo-optic effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Silicon and III-V material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Free carrier effect in silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1 Carrier depletion-mode waveguide . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Silicon optical modulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5.1 Mach-Zehnder modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5.2 Ring modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 High capacity optical communication . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6.1 Wavelength division multiplexing . . . . . . . . . . . . . . . . . . . . . . . 25

2.6.2 Complex modulation formats . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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3 Ring modulator small-signal response 30

3.1 Intracavity ring modulator small-signal response . . . . . . . . . . . . . . . . . . 32

3.1.1 Small-signal response modeling . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.2 Experimental verification of the small-signal model . . . . . . . . . . . . . 39

3.1.3 Gain-bandwidth product as a figure of merit . . . . . . . . . . . . . . . . 43

3.1.4 Pole-zero location impact on small-signal response . . . . . . . . . . . . . 45

3.2 Coupling-modulated ring resonator small-signal modeling . . . . . . . . . . . . . 51

3.2.1 Small-signal response modeling . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3 Comparison and summary of results . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 Intracavity ring modulator design trade-offs 61

4.1 Motivation of studying rib-to-contact distance . . . . . . . . . . . . . . . . . . . . 62

4.2 Device description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 DC performance measurement and analysis . . . . . . . . . . . . . . . . . . . . . 65

4.4 Small-signal characteristics from measurement and simulation . . . . . . . . . . . 71

4.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5 Coupling-modulated ring resonator for intensity modulation 83

5.1 On-off keying (OOK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1.1 Modeling of MZIARM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1.2 Operation principles and simulation results . . . . . . . . . . . . . . . . . 87

5.2 Pulse amplitude modulation (PAM) . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.1 Device proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6 Coupling-modulated ring resonator for QAM signaling 99

6.1 Device proposal and theoretical model . . . . . . . . . . . . . . . . . . . . . . . . 100

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6.2 Active region segmentation in add-drop MZIARM . . . . . . . . . . . . . . . . . 104

6.3 Non-quasi static analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.4 Output level linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7 Conclusions and Future Directions 117

7.1 Summary of contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Bibliography 122

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List of Tables

2.1 Comparison between direct and external modulation. . . . . . . . . . . . . . . . . 8

2.2 Comparison between MZI modulator, intracavity ring modulator, and MZI-

assisted ring modulator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 Extracted optical parameters from the measured transmission spectra. . . . . . . 67

4.2 Summary of bandwidth, GBW, and f3dB-GDC penalty trade-off efficiency. . . . . 79

4.3 Comparison between ring modulators in terms of ER, IL, and f3dB at 4V applied

voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.1 Summary of PAM-4 operation principle using the proposed device. . . . . . . . . 92

6.1 Summary of INL and DNL for QAM-64 modulator. . . . . . . . . . . . . . . . . . 114

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List of Figures

1.1 IP traffic per year [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Electrical and optical channel responses as a function of data rate [3]. . . . . . . 2

1.3 Examples of optical interconnect applications [4]. . . . . . . . . . . . . . . . . . . 3

2.1 System diagram of an optical link (modified from [8]). . . . . . . . . . . . . . . . 8

2.2 Optical Transmitter utilizing an external modulator. . . . . . . . . . . . . . . . . 9

2.3 Mechanisms of intensity modulation in silicon, based on plasma dispersion effect:

Cross section of (a) pin carrier injection (b) pn carrier depletion (c) MOSCAP

(d) SISCAP silicon modulator (modified from [16,47]). . . . . . . . . . . . . . . . 16

2.4 A 3D view of a doped waveguide in the depletion mode. . . . . . . . . . . . . . . 17

2.5 Mach-Zehnder modulator in on- and off-states (modified from [52]). . . . . . . . . 19

2.6 Transmission versus ∆V for MZM [22]. . . . . . . . . . . . . . . . . . . . . . . . . 20

2.7 Intracavity ring modulator schematic and transmission spectrum versus wave-

length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.8 Electro-optical response of the ring modulator for various detuning frequencies [55]. 22

2.9 Coupling-modulated ring resonator schematic and transmission spectrum versus

wavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.10 Transmission of MZI modulator and MZI-assisted ring modulator versus normal-

ized ∆φ [57]. The required ∆φ of on-off switchings are indicated with arrows. . . 24

2.11 WDM link based on the ring modulator [3]. . . . . . . . . . . . . . . . . . . . . . 26

2.12 Constellation diagrams of various modulation formats. . . . . . . . . . . . . . . . 27

2.13 Methods for optical PAM-4 signaling based on (a) VCSEL, (b) MZI, and (c)

segmented MZI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

x

2.14 Typical IQ transmitter for QAM format [66]. . . . . . . . . . . . . . . . . . . . . 29

3.1 Intracavity ring modulator small-signal block diagram. . . . . . . . . . . . . . . . 32

3.2 (a) Pole-zero diagram of a ring modulator. Location of zero divided by −2/τl (b)

versus ∆ωτ , excluding ∆ωτ = 0, for three coupling conditions (c) versus τe/τl

at ∆ωτ = ±2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 DC gain for three coupling conditions versus ∆ωτ . . . . . . . . . . . . . . . . . . 38

3.4 (a) Cross section of the ring modulator waveguide in the active region. (b)

Optical microscope image of the fabricated ring modulator. . . . . . . . . . . . . 39

3.5 Measurement setup of the ring modulator. . . . . . . . . . . . . . . . . . . . . . . 40

3.6 (a) Measured optical power transmission spectra (resolution of 2.5 × 10−4nm)

at various bias voltages . Extracted (b) ∆α and (c) ∆neff from the measured

spectra shown in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.7 Normalized measured and simulated small-signal (a) electro-optical response ver-

sus modulation frequency, fm, for ∆ω of 1.15, 0.57, and 0.28(b) 3dB bandwidth

of the reverse-biased ring modulator. . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.8 Normalized GDC , f3dB, and GBW versus ∆ωτ for a constant τ . . . . . . . . . . 45

3.9 (a) Pole-zero diagram of a ring modulator. Simulated (b) GBW versus ∆ωτ

for several fRC (c) GBW maxima versus fRC/fQ (d) ∆ωτ corresponding to the

GBW maxima versus fRC/fQ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.10 (a) Simulated f3dB/fQ versus DC gain penalty for several fRC . (b) Trade-off

coefficient versus fRC/fQ for both positive and negative detunings. . . . . . . . . 47

3.11 (a) Pole-zero diagrams of the ring modulator when p3 = −24/τ and from left

to right τe = τl/2, τe = τl, and τe = 2τl. (b) corresponding Bode plots of the

pole-zero diagrams shown in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.12 (a) Ring modulator 3dB bandwidth (b) GBW versus ∆ωτ when τl = 80ps and τe

is equal to τl/2, τl, and 2τl. (c) Laser detunings corresponding to the maximum

GBW at positive detunings (d) GBW maximum versus τe/τl for τl = 80ps. . . . 49

3.13 Schematic of the ring modulator with an MZI as a coupler. . . . . . . . . . . . . 51

3.14 Coupling-modulated ring resonator small-signal block diagram. . . . . . . . . . . 52

xi

3.15 Normalized GDC|∆ω=0of the coupling-modulated ring resonator optical response

versus τe/τl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.16 Pole-zero diagrams of a coupling-modulated ring resonator for ∆ω = 0 and for

∆ω 6= 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.17 Small-signal response versus modulation frequency for coupling modulated-ring

at (a) ∆ω = 0 and (b) ∆ω = 1.4/τ . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.18 Pole-zero diagrams of a (a) coupling modulated (b) intracavity modulated ring. . 59

4.1 Doped waveguide cross section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2 (a) Effective refractive index change with respect to 0V versus bias voltage. (b)

Loss of pn doped region versus bias voltage. . . . . . . . . . . . . . . . . . . . . . 64

4.3 Carrier concentration under reverse bias voltage. . . . . . . . . . . . . . . . . . . 64

4.4 Chip layout with tested ring modulators indicated in the red dashed boxes to-

gether with the microscope image. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.5 Ring modulator optical microscope image and waveguide cross-section. . . . . . . 66

4.6 (a) Notch depth versus gap. (b) Color-coded figure showing coupling conditions

of the tested ring modulators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.7 (a) Measurement setup of the ring modulator. (b) Chip under test. . . . . . . . . 68

4.8 Measured optical power transmission spectra at various bias voltages for (a)

Ring A with d++ = 200nm, (b) Ring B with d++ = 350nm, (c) Ring C with

d++ = 550nm, (d) Ring D with d++ = 800nm. . . . . . . . . . . . . . . . . . . . 69

4.9 (a) Extracted τl shown with markers for Ring A-D with d++ from 200nm to

800nm together with the fitted curves shown with solid lines. (b) Extracted

additional loss as a function of d++.(c) Extracted ∆neff versus voltage for Ring

A-D with d++ from 200nm to 800nm. . . . . . . . . . . . . . . . . . . . . . . . . 70

4.10 (a) Extinction ratio, (b) insertion loss, and (c) transmission penalty for voltage

swing from 0 to 3V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.11 (a) Measured maximum ER and (b) corresponding IL versus applied voltage. . . 72

4.12 Small-signal circuit model of a ring modulator. . . . . . . . . . . . . . . . . . . . 72

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4.13 Measured and simulated electrical S11 (a) magnitude (b) phase of Ring D with

d++ = 800nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.14 Schematic of the test bench used for small-signal electro-optical measurement. . . 74

4.15 Normalized simulated (line) and measured (marker) electro/optical response of

Ring B with d++ = 350nm at (a) negative and (b) positive detunings, Ring C

with d++ = 550nm at (c) negative and (d) positive detunings, and Ring D with

d++ = 800nm at (e) negative and (f) positive detunings. Here, fm is modulation

frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.16 Simulated (line) and measured (marker) (a) bandwidth of tested ring modulators

(b) DC gain penalty of Ring C with d++ = 550nm versus ∆ωτ . . . . . . . . . . . 77

4.17 Pole-zero diagrams of Rings B-D. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.18 Simulated (a) f3dB versus DC gain penalty and (b) GBW versus ∆ωτ at -1V

bias voltage for Ring B, C, and D with d++ = 350nm, d++ = 550nm, and

d++ = 800nm, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.19 (a) Extinction ratio and (b) IL versus f3dB for Ring B, C, and D with d++ =

350nm, d++ = 550nm, and d++ = 800nm, respectively. . . . . . . . . . . . . . . 80

4.20 Bandwidth and IL versus d++ for (a) ER = 4dB and (b) ER = 5dB at 4V

applied voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.1 Schematic of the OOK modulator using MZIARM. . . . . . . . . . . . . . . . . . 84

5.2 Transfer matrix formulation of MZIARM. . . . . . . . . . . . . . . . . . . . . . . 85

5.3 Transmission versus normalized ∆φ. . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.4 Transmission versus normalized ∆φ for various values of a. Diamonds are indi-

cating ∆φcritical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.5 Value of ∆φcritical/π versus a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.6 On-off keying modulation in an MZIARM. . . . . . . . . . . . . . . . . . . . . . . 89

5.7 Transmission of MZIARM at zero and non-zero detuning. . . . . . . . . . . . . . 90

5.8 Schematic of the proposed PAM-4 modulator using MZI-assisted ring. . . . . . . 91

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5.9 (a) Sample optical transmission spectra for 4 symbols in PAM-4 format for

binary-weighted scheme. (b) On-resonance transmission versus normalized ∆φ

for the same device. (c) T0 to T3 versus L2 to L1 ratio. (d) T0 to T3 correspond-

ing to each level in PAM-4 for various ratios of L2 to L1. The ideal case for the

same device is also plotted as a solid line. . . . . . . . . . . . . . . . . . . . . . . 94

5.10 (a) Sample optical transmission spectra for 4 symbols in PAM-4 format with

optimized L2 to L1 ratio. (b) On-resonance transmission versus normalized ∆φ

for the same device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.11 (a) Push-pull RZ PAM-4 random input sequence of ∆φ′(t). (b) RZ PAM-4 eye

diagram for the random sequence shown in (a), for optimized L2 to L1 ratio. . . 96

6.1 Schematic of the proposed QAM-16 modulator using two segmented add-drop

MZIARMs in IQ configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.2 On-resonance power transmission versus ∆φ of an MZI, and of an add-drop

MZIARM at the through and the drop ports. . . . . . . . . . . . . . . . . . . . . 103

6.3 Change in (a) effective index (b) pn junction loss versus reverse bias voltage. . . 105

6.4 (a) Amplitude of the field transmission at the output of the drop port (b) Peak

locations of |Tdr| (∆φ′peak) versus Lt. . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.5 A 2-segment MZIARM (a) optical power transmission spectra for the drop and

through ports, and (b) amplitude and phase of the field transmission at the

output of the drop port versus normalized ∆φ. . . . . . . . . . . . . . . . . . . . 106

6.6 Schematic of an add-drop coupling-modulated ring resonator. . . . . . . . . . . . 108

6.7 Phase accumulation differences through the active regions, cross coupling coeffi-

cient at the drop port, and power transmission at the drop port versus time. . . 109

6.8 Constellation diagram of QAM-16 for Lt = 500 µm. . . . . . . . . . . . . . . . . 110

6.9 QAM-16 constellation for Lt = 500 µm and for (a) r = 1.5, (b) r = 2.5, and (c)

r = 1.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

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6.10 (a) Field transmission at the drop port of the MZIARM plotted for each level

assuming binary-weighted and optimized ratio 3-segment case in depletion mode.

The ideal case is also plotted with a solid line. (b) QAM-64 constellation for the

3-segment IQ modulator with optimized segment lengths. . . . . . . . . . . . . . 113

6.11 (a) Field transmission at drop port of the MZIARM plotted for each level for

binary-/optimized-weighted 3-segment and for optimized-weighted 4-segment cases

assuming pin forward-biased RF section with Lt = 100 µm. (b) QAM-64 con-

stellation for the 3-segment IQ modulator with optimized segment lengths. (c)

Proposed 4-segment MZIARM which can be implemented in IQ configuration for

the properly aligned QAM-64 constellation. Encoder table for mapping a 3-bit

input to a 4-bit input is also shown. (d) QAM-64 constellation for the 4-segment

IQ modulator with optimized segment lengths. . . . . . . . . . . . . . . . . . . . 115

xv

List of Acronyms

CMOS: Complementary MetalOxideSemiconductor

FFE: Feed-Forward Equalization

DFE: Decision-Feedback Equalization

CW: Continuous Wave

FR4: Flame Retardant 4

M6: Metal on the 6th layer

WDM: Wavelength Division Multiplexing

DWDM: Dense Wavelength Division Multiplexing

FSR: Free Spectral Range

VCSEL: Vertical-Cavity Surface-Emitting Lasers

MZI: Mach-Zehnder Interferometer

MZM: Mach-Zehnder Interferometer Modulator

DML: Directly Modulated Laser

DAC: Digital-to-Analog Converters

SISCAP: Silicon-Insulator-Silicon Capacitor

MOSCAP: Metal-Oxide-Semiconductor Capacitor

CM: Coupling Modulation

MZIARM: Mach-Zehnder Assisted Ring Modulator

OOK: On-Off Keying

PAM: Pulse Amplitude Modulation

QAM: Quadrature Amplitude Modulation

BPSK: Binary Phase-Shift Keying

QPSK: Quadrature Phase-Shift Keying

MUX: Multiplexer

DEMUX: De-multiplexer

SSMF: Standard Single Mode Fiber

xvi

OMA: Optical Modulation Amplitude

ER: Extinction Ratio

IL: Insertion Loss

TP: Transmission Penalty

BER: Bit-Error-Rate

QCSE: Quantum-Confined Stark Effect

QW: Quantum Well

VOA: Variable Optical Attenuator

MMI: Multimode Interference

SE: Spectral Efficiency

PM: Polarization Multiplexing

NRZ: Non-Return-to-Zero

IM: Intracavity Modulation

SNR: Signal-to-Noise Ratio

xvii

Chapter 1

Introduction

1.1 Motivation

Network traffic is increasing due to the high data demanding applications such as video stream-

ing, on-line data storage services, the rise of social networking, and cloud computing. As shown

in Fig. 1.1, IP traffic is rising steadily every year reaching 1021 bytes in 2016, where most of

the traffic is from consumer usage. To address this, not only the traffic between user and data

centers should be handled, but also high speed and high capacity communication inside the

data centers among servers is needed. This would force the expansion of data centers utilizing

power efficient and cost efficient interconnects in intra chip, chip to chip, board to board, rack

to rack, and data center to data center communications.

Attenuation, dispersion, and crosstalk of the copper links limit the data communication

speed to 10 Gb/s [1]. Copper channel response is presented in Fig. 1.2 which shows that in

addition to increasing the link length, rising data rate also leads to a significant increase in

the channel loss. At a few tens Gb/s, wireline transceiver with an advanced equalization is

required for data recovery which adds to the circuit complexity and power consumption. To

resolve these issues, copper links are being replaced by high capacity optical fibers for rack

to rack and board to board applications. Optical fibers offer constant attenuation over data

rate ( Fig. 1.2), negligible cross talk, and high bandwidth. Also, for on-chip and chip to chip

connections integrated optical waveguide can be used to resolved the aforementioned limitations

from copper links. Figure 1.3 visualizes the applications of the optical interconnect in a less

1

Chapter 1. Introduction 2

Figure 1.1: IP traffic per year [2].

than a millimeter to a few meters distances (short reach).

Figure 1.2: Electrical and optical channel responses as a function of data rate [3].

Replacing the electrical interconnects to the optical interconnects leads to moving the per-

formance bottleneck from channel to other components in the link such as optical modulators.

Hence, in this thesis, we will focus on modeling and design of the high speed optical modulators

for short to medium reach links in Chapter 3, Chapter 4, and Chapter 5, and for long haul data

communication in Chapter 6.

The conventional method of optical data transmission is to modulate the amplitude of the


Figure 1.3: Examples of optical interconnect applications [4].

high-frequency optical carrier signal. This type of modulation which is called On-Off Keying

(OOK), is easy to detect. However, only one bit per symbol is transmitted. To address the

increasing demand for higher data rates, it is essential to increase the spectral efficiency of

the optical transmission systems. Therefore, OOK modulation format can be replaced with

a more advanced modulation formats. One of the prime modulation candidates is pulse am-

plitude modulation (PAM) where data is represented by different levels of signal amplitude.

Also, due to the advances in coherent detection, phase modulation can be added to the am-

plitude modulation. This will create more complex modulation schemes such as quadrature

amplitude modulation (QAM) which has been widely used for high-speed communication. An-

other technique to increase transmission capacity is wavelength division multiplexing (WDM)

where several modulated optical carriers are sent through one optical fiber. This decreases pin

numbers and increases the bandwidth further.

In optical interconnects, in addition to the modulation format, selecting the method of opti-

cal modulation has important effects on the overall link performance. There are two techniques

to convert electrical data to optical data: to directly modulate laser (DML) or to use an ex-

ternal modulator after the laser and drive it with the electrical data. The former method is

easy to implement and performs well for the short reach applications at a limited data rate.


However, due to the chirp generation, it fails to work for the medium to long haul optical com-

munications. On the other hand, external modulation is a good candidate for the short to long

haul transmission with the advantage of having a potential for a phase modulation. Also, in

external modulation, the optical source can be relatively inexpensive and a single light source

can feed multiple channels via individual modulators. More detailed comparison will be given

in Chapter 2.

There are several options for the base material of the external modulator and other optical

components in an optical interconnect. Among these candidates, silicon is among the most

favorable one as it is compatible with the well established CMOS process technology. Also,

dense integration of waveguides and other passive components in silicon is possible due to the

high confinement of light. Moreover, silicon photonics makes it easier to integrate the photonic

chip with electronic chip via monolithic or hybrid integration. The challenges though, are lack

of laser source and detector based on silicon.

In silicon photonics, the main candidates for the external light modulation are Mach-Zehnder

interferometer (MZI) and ring modulator. Each of these modulators have specific limitations.

Mach-Zehnder interferometer is a great candidate for long haul communication due to the

negligible chirp when driven in push-pull configuration. However, due to ring modulator smaller

size and lower driving voltage requirement, it is a better option for the short to medium reach

applications. The challenge is to stabilize the resonance wavelength of the ring modulator.

Coupling modulation in the ring resonator using MZI as a coupler [5] has been shown to

enable smaller switching voltage compared with MZI while solving the bandwidth limitation in

the intracavity ring modulator. The drawback, however, is the temperature sensitivity of the

cavity-based modulators.

To increase the capacity of the optical communication links, optical modulator design needs

to be optimized as the modulator is one of the main components of the optical communication

systems. Design optimization of an external modulator has been an active area of research.

One of the challenges in designing a silicon photonics modulator is the lack of a strong and

accurate system level opto-electrical simulator. Hence, there is a need to develop a model of the

modulator behavior to assess the modulator response in both time and frequency domain. Such

a modeling leads to gaining a better understanding of the modulator response and therefore


allows optimizing the modulator design.

Ring modulators are favorable in WDM links due to their small size, low power consumption,

and being narrow band. The main research focus is to design higher bandwidth, smaller, and

more power efficient ring modulator. To accurately predict the bandwidth, there is a need for

a complete modeling of the ring modulator small-signal transfer function. Part of this thesis is

dedicated to obtain a closed-form frequency response model of both intracavity ring modulator

and coupling-modulated ring resonator, and to compare the two responses. Furthermore, in

terms of the design trade-offs, one of the key design parameters in the intracavity ring modulator

is assessed through numerical modeling and experimental results.

To move to the complex modulation schemes such as PAM and QAM, it is desirable to

achieve phase and amplitude modulation optically to reduce the driver circuit design complexity.

There is a need to develop an efficient modulator design for generating complex modulation

formats. Hence, in this thesis, PAM and QAM signaling based on the coupling-modulated ring

resonators, which have the aforementioned advantages, are proposed.

1.2 Thesis objectives

The focus of this research is to model, design, and test high-speed optical modulators for OOK

as well as to propose and design new architectures for high-order modulation formats in silicon

photonics technology. The main objectives of this thesis are the followings:

• Derive a complete small-signal transfer function of a depletion-mode intracavity modu-

lated microring to accurately calculate the bandwidth of the device and gain a better

understanding of the device principle of operations.

• Derive small-signal transfer function of the coupling-modulated ring resonator and com-

pare the small-signal transfer functions of the intracavity and the coupling-modulated

ring resonators based on the pole-zero representation.

• Study the effects of the contact-to-rib distance on the optical and electrical characteris-

tics of the depletion-mode intracavity modulated microring to help design an optimum

modulator based on the targeted application. This is carried out using the developed


small-signal model and is verified by experiments.

• Propose and design a new method for PAM signaling based on coupling modulation of

a ring resonator to decrease the voltage requirement and size of the previously proposed

optical PAM modulator based on MZI.

• Model coupling modulation in an add-drop ring modulator and propose and design a new

configuration for QAM based on that.

1.3 Thesis outline

This thesis comprises 7 chapters. In Chapter 2, a general overview of the high speed inter-

connects is given. Also, the background work related to this research is reviewed and details

for electro-optical modulation techniques in III-V material and silicon, advantages of silicon

photonics, challenges and opportunities in silicon photonics, silicon-based optical modulator

for WDM link, and modulator for high order modulation formats are presented. In Chapter

3, a closed-form frequency response model of a carrier-depletion intracavity ring modulator is

given and verified by measurement results. The pole-zero representation of the obtained trans-

fer function is also discussed where the response of the ring modulator to detuning, coupling

condition, and electrical bandwidth are explained based on the pole-zero locations. Also, the

small-signal response of the coupling-modulated ring resonator is given and the results are com-

pared with the small-signal response of the intracavity ring modulator. In Chapter 4, the study

of decreasing rib-to-contact distance trade-offs is presented. The model presented in Chapter

2 together with the measurement results of several intracavity ring modulators fabricated in

IME A*Star process are used to compare the performances of each group of the modulators.

In Chapter 5, on-off keying modulation using coupling-modulated ring resonator is discussed

when an MZI is used as a coupler (MZIARM). Model of MZIARM is presented along with the

operation principles is presented and the PAM signaling using MZIARM is studied. In Chapter

6, MZIARM in add-drop configuration is assessed for QAM signaling where the complete for-

mulation and simulation results in static and dynamic modes are given. Chapter 7 concludes

thesis, summarizes the contributions, outlines the publications, and discussed the future work.

Chapter 2

Background

2.1 Optical interconnect

One of the primary motivations in using optical interconnects is the bandwidth offered by the

optical fiber as a channel. The conventional method of data transmission in an optical link

is on-off-keying (OOK) where the light intensity varies at the transmitter depending on the

input data. Figure 2.1 shows a typical optical link. At the transmitter, the driver sends the

electrical data to an electro-optical (E/O) converter where the electrical bits are transformed to

optical bits. The E/O converter could be the light source itself, usually referred to as directly

modulated laser (DML), or an external modulator after a continuous wave (CW) laser. Optical

data is then sent over the optical fiber. Optical amplification or regeneration may be required

before the receiver depending on the targeted distance due to loss, chromatic dispersion, modal

dispersion, or polarization mode dispersion. As shown in Fig. 2.1, at the receiver front-end a

photodetector converts the optical power to electrical current. The receiver electrical circuit

then converts the low current (a few hundred µA) generated by the photodiode to voltage and

amplifies it. The optical receiver usually consists of multi-stages where the first stage has a

high sensitivity and the second stage is used for further amplification [6, 7].

The electro-optical converter is one of the main building blocks in the optical link and there

are numerous research articles on the modulator performance optimization [9–15]. Although

the focus of this thesis is on external modulator design, here we will briefly discuss DML and

compare it with an external modulator. In DML, above a certain threshold, laser output inten-

7

Chapter 2. Background 8

Figure 2.1: System diagram of an optical link (modified from [8]).

Table 2.1: Comparison between direct and external modulation.Direct modulation External modulation

Simple implementation Cheaper CW laser source

Mostly multimode Single mode

High carrier induced chirp Low chirp when push-pull driven

Almost compact depends on the modulator

Limited extinction ratio Potentially larger extinction ratio

Short reach 100m @ 25 Gbps Medium to long reach

Medium temperature range depends on the modulator

sity is proportional to the drive voltage or current. Therefore, the output light can be turned

on or off by varying the driving electrical signal. Today, in short reach applications, directly

modulated vertical-cavity surface-emitting lasers (VCSEL) are widely used due to their imple-

mentation simplicity and ease of coupling to multimode fibers [16]. However, high performance

optical links targeting medium to long reach are mostly based on external modulation.

External modulation has some advantages over direct modulation such as higher speed,

using inexpensive laser source, feasibility of phase modulation, better extinction ratio, and

lower chirp [10]. The latter is essentially the unwanted frequency modulation along with the

intensity modulation. Table 2.1 shows a comparison summary between the two modulation

schemes. Some properties of external modulator such as size and temperature range depend on

the structure and will be discussed further in this chapter.

The main metrics of evaluating the performance of the modulator can be divided into three

categories of link metrics, cost metrics, and range metrics [17]. In terms of link metrics, modu-

lator design impacts overall link performance in terms of data rate, reach, power consumption,

and receiver design. Figure 2.2 shows an optical transmitter with an external modulator. When

the optical input power of Pin enters the electro/optical modulator, according to the electrical


input data, the driver will send an on-off signal to the optical modulator and as a result, the

output power switches between P1, corresponding to bit 1, and P0, corresponding to bit 0.

Based on Pin, P1, and P0, the following evaluation metrics are defined and categorized as link

metrics:

Figure 2.2: Optical Transmitter utilizing an external modulator.

• Optical modulation amplitude (OMA): is defined as a difference between transmitter

optical output power at bit 1 and at bit 0:

OMA = P1 − P0. (2.1)

• Average transmitted power is defined as:

Pavg =P1 + P0

2. (2.2)

• Extinction ratio (ER): is defined as a difference between P1 and P0 in dB:

ER = 10 log(P1

P0). (2.3)

• Insertion loss (IL): is defined as a drop of the output power at bit 1 with respect to the

input power:

IL = 10 log(Pin

P1). (2.4)


• Transmission penalty (TP): is defined as a ratio of OMA/2 to the input power:

TP = −10 log(P1 − P0

2Pin) = −10 log(

OMA

2Pin). (2.5)

Optical modulation amplitude and extinction ratio specify the difference or ratio of the

power levels, respectively. Therefore, to find an absolute quantity from the OMA or ER, we

need another term such as Pavg, P1, or P0 [18].

Considering the presence of loss and noise in the link, the larger the value of OMA, the easier

the task of the receiver in recovering the transmitted signal. In addition, the ratio of errors in

the detected bit sequence, bit-error-rate (BER), is also directly affected by OMA and would

benefit from large OMA. However, OMA would not show how efficiently the input laser power

is used. Transmission penalty is a metric to show how efficient the input power is translated

to OMA where for an ideal case TP will be -3dB [17]. Keeping the OMA constant (i.e. same

P1 and P0), one could increase ER by decreasing Pavg. In this case, insertion loss, which shows

an on-state loss, is traded for ER. Extinction ratio is a metric which remains constant at the

transmitter and receiver in the presence of linear channel loss.

Another important link metric of the modulator is bandwidth which affects the communi-

cation capacity. The main bandwidth constraints stems from the limited intrinsic speed of the

modulator due to optical or physical phenomenon inside the device and/or modulator electrical

bandwidth limitations [19].

In addition to link metrics, there are cost metrics determined by the optical modulator

design. These mainly include size, voltage, power, and fabrication.

In terms of range metric, chirp is an important factor as it could improve or worsen the effect

of dispersion and therefore ISI in an optical channel. Chirp is an unwanted carrier frequency

shift while modulating amplitude of the input light and manifests itself at rising and falling

edges of the intensity. Chirp is commonly quantified by Henry parameter α which is defined as

the amount of phase modulation normalized to the amount of intensity modulation produced

by the modulator [20]. When the Henry parameter is positive, the carrier frequency increases

on the rising edge and decreases on the falling edge, which leads to the pulse broadening during

propagation. When the Henry parameter is negative, the carrier frequency decreases on the


rising edge and increases on the falling edge, which leads to the pulse compression. This could

be beneficial as the negative Henry parameter may counteract the dispersion effect inside the

optical channel. When the Henry parameter is zero, the carrier frequency remains constant

throughout the intensity pulse.

Metrics of wavelength range, temperature range, and fabrication tolerance range are other

evaluation terms for an optical modulator [17]. The above-mentioned evaluation metrics will

be used in this thesis, specifically in Chapter 4, to assess the modulator response.

2.2 Electro-optic modulations

In certain materials, optical properties vary in the presence of the incident electric field and

therefore impact the propagation of light [21]. In such cases, applications of electric field to the

material changes the real or imaginary part of the refractive index allowing for the electro-optical

modulation. The variation in real part of refractive index, ∆n, occurs through electrorefraction,

whereas the variation in imaginary part or material loss, ∆α, is caused by electroabsorption.

These effects are extremely fast, with subpicosecond response times, and the speed limitation

of these types of modulators is mostly due to technological restrictions [22]. Other methods for

medium optical properties modulation could be based on either the carrier density variation,

which is called carrier plasma dispersion effect, or based on thermal effect, which is called

thermo-optic effect.

2.2.1 Electrorefraction

In Electrorefraction, the applied electric field changes phase of the traveling light. In this effect,

incident electric field induces a polarization density that contains parts which vary linearly with

the amplitude of the applied electric field and parts that vary nonlinearly. Consequently, the

refractive index of the material varies with electric field according to [23, 24]:

n = n0 +χ(2)E

2n0+

χ(3)E2

2n0, (2.6)


where E is the amplitude of the incident electric field, n0 =√1 + χ(1), and χ(n) is the nth order

nonlinear susceptibility.

The linear electro-optic effect govern by the first two terms of Eq. 2.6 is called Pockels

effect [21]. This effect occurs in crystals that do not have inversion symmetry including LiNbO3,

barium titanate (BaTiO3), and III-V semiconductors.

For the centrosymmetric materials, χ(2) is zero due to inversion symmetry. Hence, there is no

Pockels effect for liquids, gases, and certain crystals. In this case, electrorefraction occurs though

third order nonlinear dependency of the refractive index on electric field which is commonly

known as Kerr effect. Kerr effect can be found in all nonmetallic crystals [22].

2.2.2 Electroabsorption

In the electroabsorption effect, the applied electric field changes the absorption spectrum which

leads to direct intensity modulation of the incident light. This induced-absorption at the pres-

ence of applied electric field is as a results of the extension of electron and hole wavefunctions

in the bandgap which allows photon-assisted tunneling when the photon energy is lower than

the bandgap energy. As governed by the Kramers-Kronig relations, change in absorption re-

sults in refractive index variation. Therefore, there will be a phase modulation accompanying

intensity modulation. Electroabsorption can be carried out through Franz-Keldysh Effect or

Quantum-Confined Stark Effect (QCSE) effect.

2.2.3 Free carrier effect

In free carrier effect or plasma dispersion effect, changes in carrier density varies the absorption,

which in turn causes an index change through Kramers-Kronig relations [22]. Plasma dispersion

effects involving carrier injection to the guiding medium have speed limitations due to the carrier

lifetime of a few nanosecond for pure silicon and III-V semiconductors. This can be overcome

by operating in depletion mode where carriers are depleted instead of recombined but at the

price of higher switching voltage [25].


2.2.4 Thermo-optic effect

Thermal variation in most of the materials leads to absorption and refractive index change via

changing the properties such as band gap and carrier concentration. Application of temperature

variation for phase modulation of the electric field is called thermo-optic effect. Although this

method results in a large refractive index change with a relatively small applied power, it is

fairly slow (on the order of millisecond). Therefore, whenever operation speed is not a concern,

thermo-optic effect is used as low-speed modulators and switches or used to bias the optical

devices.

2.3 Silicon and III-V material

III-V semiconductors are compounds of group III and group V elements in the periodic table.

These compounds such as InP and GaAs have direct band-gaps whereas silicon has indirect

band-gap in telecommunication band. Also, in III-V materials, the quadratic electro-optical

properties are mush stronger than silicon and the linear electro-optic effect is non-zero. There-

fore, it is feasible to build lasers, modulators, and detectors based on III-V semiconductors.

The disadvantages of III-V materials is the complications in integration of components on the

same substrate which leads to fabrication difficulties and performance degradation [22,26]. Sil-

icon has been the dominant material for fabricating microelectronics for decades. One of the

prime motivation of silicon photonics is its compatibility with the mature silicon IC manufac-

turing and low cost of silicon wafers [27]. Also, silicon can make the monolithic integration of

photonic and electronic components possible. Moreover, silicon has high thermal conductivity

(≈ 10× higher than GaAs) and high optical damage threshold (≈ 10× higher than GaAs) [27].

However, in silicon, the main electro-optic effects are not applicable. Unstrained silicon does

not exhibit Pockels effect due to centrosymmetric crystalline. Also, Kerr and Franz-Keldysh

effects were shown to be weak in silicon. In near IR, a refractive index variation as small as

∆n ≈ 10−5 for the Franz-Keldysh effect, and ∆n ≈ 10−8 for the Kerr effect can be achieved for

a relatively large applied field of 105 V/cm [28]. Although there have been tremendous research

on silicon-based modulators based on the aforementioned effects [29–33], the most effective way

of light modulation in silicon is the plasma dispersion (free carrier) effect.


2.4 Free carrier effect in silicon

In plasma dispersion effect, carrier concentration variation as a function of voltage modifies

absorption based on Drude-Lorenz model [22], and therefore varies the imaginary part of the

refractive index. This loss modulation, ∆α, results in change in the real part of the refractive

index, ∆n, through the Kramers-Kronig relation. Using the measured absorption spectra of sili-

con, Soref and Bennett obtained expressions for ∆n and ∆α as a function of carrier density [34].

At 1550nm wavelength, we have [10, 35]:

∆n = ∆ne +∆nh = −(8.8× 10−22∆Ne + 8.5× 10−18∆N0.8h ), (2.7)

∆α = ∆αe +∆αh = 8.5× 10−18∆Ne + 6× 10−18∆Nh.

Here, ∆Ne (cm−3) is the change in free electron concentration and ∆Nh (cm−3) is the change

in free hole concentration. Also, ∆ne (∆nh) and ∆αe (∆αh) are the change in refractive index

and loss due to electron (hole) concentration variation, respectively.

Speed of carrier density modulation is very important. Also, overlap of the carrier concen-

tration variation region with the optical mode is important in determining the amount of the

effective index change of the waveguide. The efficiency of electro-optical modulation is com-

monly expressed in terms of Vπ ·L which shows the required voltage to induce π phase shift in

a phase shifter length of L.

Various structures in silicon have been proposed and demonstrated for optical modulation

using plasma dispersion effect. The mostly used ones are carrier injection pin diode [36, 37],

depletion-mode pn diode [14], MOS Capacitor (MOSCAP) [38,39], and silicon-insulator-silicon

capacitor (SISCAP) [40,41]. Figure 2.3a-d show cross sections of various types of silicon-based

modulators using plasma dispersion effects. Carrier injection type modulator (Fig. 2.3a) is

one of the earliest proposed structures in which, carriers are injected to and depleted from the

intrinsic silicon region through applying a forward bias voltage. The advantage of this method

is a large effective refractive index variation of up to few 10−3. The operation speed of this

type of modulator is limited by the long minority carrier life time. The bandwidth is limited

to 500 MHz-1GHz and drivers with pre-emphasis are required to gain higher bandwidth.


In carrier depletion pn diodes shown in Fig. 2.3b, the applied voltage modulates the depletion

region width of the reverse-biased pn junction. The interaction region of light and carrier density

variation region is narrower compared to the carrier injection case. In the former, light is only

partially confined at the depletion region whereas in the injection type, the light exist in the

whole injection region. Therefore, the effective index variation is smaller and is in the order of

10−5-10−4. A Typical Vπ · L is 2 V · cm [16]. The advantage of this type of structure is that it

is based on majority carrier movement and it does not suffer from the bandwidth limitation in

the injection type. The speed of index modulation with this scheme can reach over 50Gb/s [42].

To improve the effective index variation over voltage, instead of lateral pn junction, vertical

pn junction [43] can be implemented. Therefore, depletion region and optical mode have better

overlap but with the disadvantage of higher capacitance compared with lateral pn junction.

Another configuration is also proposed and demonstrated based on the interleaved pn junction

with improved capacitance compared to vertical junction while having a good mode overlap

with depletion region [44,45] at the cost of dopant diffusion. Also, depletion capacitance is still

higher compared to lateral junction [46].

In MOSCAP-type structures shown in Fig. 2.3c, a thin layer of oxide is implemented in

the waveguide (MOS capacitor) which allows carrier accumulation as well as depletion around

the oxide layer. This structure mostly operates through carrier accumulation (forward bias)

as it has higher efficiency than depletion mode. The applied voltage across the junction de-

termines the amount of carrier accumulation around the insulator and therefore the effective

index change. Here, accumulation is based on majority carriers rather than minority carriers

and therefore, modulation speed is not limited by the carrier lifetime. Nevertheless, the large

capacitance usually limits the bandwidth. Other drawbacks are optical loss from poly-Si and

small confinement factor.

In Fig. 2.3d, SISCAP structure is shown which was first proposed by Cisco [15]. In SISCAP

structure, a thin layer of SiO2 (about 20 to 24 angstroms) sandwiched between two silicon

electrodes: p-doped polysilicon on top and n-doped silicon on bottom and the structure is

surrounded by SiO2. This creates a high index contrast waveguide which confines the light both

horizontally and vertically. Similar to MOSCAP, SISCAP works through carrier accumulation

and therefore its operation speed depends on the majority carriers dynamics and parasitic


Figure 2.3: Mechanisms of intensity modulation in silicon, based on plasma dispersion effect:Cross section of (a) pin carrier injection (b) pn carrier depletion (c) MOSCAP (d) SISCAPsilicon modulator (modified from [16,47]).

RC from the electrodes. The advantage of SISCAP over MOSCAP is that in SISCAP the

region of carrier concentration overlaps with the maximum optical mode amplitude. Hence,

this structure has very small Vπ · L of about 0.13V · cm. Also, in SISCAP, the contact metal

is located further from the optical mode and this improves the propagation loss compared to

MOSCAP. However, the propagation loss is still relatively high and values around 6.5 dB/mm

have been reported [48]. This is mostly due to the p-doped poly Si layer.

2.4.1 Carrier depletion-mode waveguide

As stated earlier, one of the mostly used electro-optic modulation techniques in silicon-based

modulators is carrier depletion effect in the lateral pn junction. Figure 2.4 shows a 3D view

of the doped waveguide. The optical mode profile inside the rib region is shown, where the

depletion region is also illustrated. The effective index variation arises from interaction of the

optical field and depletion region created by p and n doped silicon in the rib waveguide. In

order to create a low resistance contact, high doped region of p++ and n++ are implemented


in the slab regions of the rib waveguide for metal connections. Optical phase is modulated by

variation of the depletion width based on the input data.

As shown in the figure for the simple case of non-return-to-zero (NRZ), applied voltage

(vs(t)) is a train of pulses (p(t)) with amplitude sign determined by the input data (bk) added

to the DC voltage (VDC). This DC voltage is chosen to keep the pn junction reverse biased.

Here, length of the device is assumed to be much smaller than the operating wavelength of the

modulator. In this lumped element assumption, the applied voltage is considered to be the

same across the whole length of waveguide. This assumption is not valid when the length of

the device is large (i.e. millimeter) and therefore the driving voltage should be applied through

transmission lines.

Figure 2.4: A 3D view of a doped waveguide in the depletion mode.

The electrical circuit model of the doped waveguide is also included in Fig. 2.4. This circuit

model includes the junction capacitance cj due to the depletion region and series resistance

from p and n doped regions in the rib (Rrp, Rrn) and slab (Rsp, Rsn) [49]. As the depletion

width varies with applied voltage, cj , Rrp, and Rrn are functions of voltage.

In order to improve the performance of this type of phase modulator, there have been nu-

merous studies [11, 12, 17, 25, 42, 50, 51]. The major targeted figure of merits are bandwidth,


insertion loss, and Vπ · L. The main parameters that determine the modulator performance

are waveguide geometry, doping concentration, and locations of high doped and low doped re-

gions. There are several trade-offs involved for designing the waveguide geometry. For example,

waveguide height, slab height, doping levels, and waveguide length vary electrical characteris-

tics such as junction capacitance and/or resistance. At the same time, these parameters define

other important effects such as optical mode confinement, efficiency of the effective index mod-

ulation, etc. All these trade-offs should be considered when designing a modulator based on

the application requirements and practical fabrication limitations.

Selecting the aforementioned design parameters also depends on the configuration of the

modulator. The interference- and resonance-based modulators may have different requirements

and trade-offs which should be considered when designing the doped waveguide. In Chapter 4,

we will assess the effects of the distance between the highly doped region to the waveguide edge

on DC and small-signal responses of the intracavity ring modulator.

2.5 Silicon optical modulators

Effective index variation as a result of the plasma dispersion effect leads to phase variation

of a traveling electric field. Converting effective index modulation to intensity modulation of

an optical signal can be done by utilizing interferometers or resonant devices. Structures that

have been widely used as a silicon optical modulators are Mach-Zehnder interferometer and

ring modulator [10]. Below, we will briefly describe each of these types of modulators.

2.5.1 Mach-Zehnder modulator

One of the most common methods to achieve intensity modulation is to use Mach-Zehnder

modulator (MZM) as an interferometer. The operation principle of an MZM is illustrated

in Fig. 2.5 in both on- and off-states. The MZM consists of an input Y-branch, two phase

control regions, and an output Y-branch. The beam splitter and combiner can be also based

on directional, adiabatic, or multimode interference (MMI) couplers. As shown in the figure,

in an MZM, the input light splits into two beams with ideally the same amount of power using

Y-junction, which are coupled into two phase control sections. The divided electric fields will


then travel through two arms of the MZM in which phase can be controlled through any of the

methods described in 2.4. Depending on the length, refractive index, and absorption at the

arms, each beam accumulates a different amount of phase and undergoes a certain amount of

loss. At the end, using another Y-junction, the two beams are recombined and coupled to the

output waveguide.

As shown in Fig. 2.5, in an on-sate, electric fields at the end of the top and the bottom arms

of MZM are in-phase and therefore, interfere constructively. In an off-state, the output electric

fields are out of phase and the interference is destructive where the combined beam results in

a radiative mode rather than a guiding mode. Therefore, the phase modulation between two

Figure 2.5: Mach-Zehnder modulator in on- and off-states (modified from [52]).

arms of MZM transform to intensity modulation. The output power of an MZM can be written

as:

Pout = Pin cos2(∆φ

2), (2.8)

where ∆φ is the phase difference between two arms. Here, it is assumed that the beam splitter

and combiner are an ideal 3dB divider. Also, we neglected loss mismatches (both passive and

active losses) between two arms. Assuming a linear relation between ∆φ and differential applied

voltage to two arms (∆V ), power transmission is shown in Fig. 2.6 versus ∆V where Vπ is also


indicated.

Figure 2.6: Transmission versus ∆V for MZM [22].

One of the advantages of MZM is its large bandwidth which is not limited by optical

properties of the device but rather its electrical characteristics. Also, MZM is temperature

insensitive. The main drawbacks of an MZM is the size of the phase shifter and required

driving voltage. For example, depletion type silicon MZM requires a long interaction length

in the order of a few millimeters for a complete transition between maximum and minimum

of the optical transmission. This not only hinders high-speed performance but also leads to

higher insertion loss, cost, and power consumption. The phase shifter length can be decreased

if an electro-optical modulation scheme with more efficient refractive index modulation is used.

As an example, MZM based on SISCAP scheme is shown to have smaller footprint compared

with other modulation techniques with around 500µm phase shifter length as opposed to a few

millimeters in the depletion type [41].

2.5.2 Ring modulator

Another method to transform effective index modulation to intensity modulation is to use a

resonant device. The widely used silicon-based resonant optical modulator is ring modulator.

Two methods of intensity modulation are possible using ring modulator. We could either

modulate the effective index of the waveguide forming the ring resonator or we could apply

index modulation to the ring-to-bus coupler and modulate the coupling coefficients. The former

is referred to as a intracavity ring modulator and the latter is called coupling-modulated ring


resonator.

Intracavity ring modulator

The majority of ring modulators used today are operated based on modulation of the intracavity

parameters. In the intracavity ring modulator, the ring resonator waveguide (excluding coupling

region) is doped and the round-trip parameters such as phase accumulation (φ) and transmission

(a) are modulated through plasma dispersion effect. Therefore, the circulating light experiences

different φ and a depending on the applied voltage to the doped region. When the phase

accumulation in a round-trip is an integer multiple of 2π, the circulating light constructively

interferes with the incoming light coupled from the bus waveguide and therefore light resonances

inside the cavity. Changing the refractive index of the ring resonator waveguide results in the

resonance wavelength shift.

Schematic of the intracavity ring modulator and the output power versus wavelength are

shown in Fig. 2.7. As shown in the figure, at the laser wavelength, the amount of transmitted

light in the bus waveguide depends on the location of resonance wavelength which is modulated

with an applied voltage representing input data. Extinction ratio and insertion loss are also

indicated in the figure.

This type of intensity modulation needs to deplete the light from the ring resonator in

on-state and to inject the light into the resonator in off-state. Therefore, the switching speed

between on- and off-states depends on how fast the cavity can respond. If quality factor of the

cavity (Q) is high, the cavity life time is longer and therefore, rise and fall times of the field

amplitude takes longer. Hence, the operation bandwidth is limited by the cavity linewidth [53].

The lower the photon life time and electrical time constant are, the higher the bandwidth will

be. However, lower photon life time means lower Q and therefore modulator requires higher

driving voltage to achieve a certain ER.

In addition to the optical bandwidth constraint in an intracavity ring modulator, there is

also electrical bandwidth limitation mostly arising from the junction capacitance and series

resistance. There is a widely used relation between the bandwidth of the device (f3dB) and

optical (fQ) and electrical bandwidth (fRC) which is 1/f23dB = 1/f2

Q + 1/f2RC [13]. However,

this formula is not accurate as it does not consider the effect of input wavelength detuning


Figure 2.7: Intracavity ring modulator schematic and transmission spectrum versus wavelength.

with respect to the resonance wavelength [54, 55]. As shown in Fig. 2.8, by increasing the

distance between the input laser wavelength and resonance wavelength, a peak appears in

modulator frequency response at high frequency which would increase the bandwidth [54–56].

The observed peak in the frequency response, which was called modulation resonance in [53],

occurs due to constructive interference between the frequency detuned through-coupled input

laser and the cross coupled light pre-existing inside the ring resonator and oscillating at its

natural frequency [54–56]. In Chapter 3, a complete closed-form formula of the intracavity ring

modulator small-signal transfer function will be presented from which the modulator bandwidth

can be accurately calculated.

Figure 2.8: Electro-optical response of the ring modulator for various detuning frequencies [55].


Coupling-modulated ring resonator

Another more recently-proposed ring modulator is the coupling-modulated (CM) ring resonator.

In this kind of modulator, the intracavity parameters are kept constant while the cross (κ) and

through (t) coupling coefficients are modulated. Figure 2.9 shows the schematic of the CM-ring

modulator together with the output power in on- and off-states. By variation of the coupling

coefficient between ring and bus waveguide, ring modulator is brought in and out of critical

coupling condition (t = a, a is the ring transmissivity) which causes the notch depth to vary at

around resonance wavelength and therefore creates intensity modulation. To make this more

clear, the ring modulator transmission at the resonance (Tres) is written as [5]:

Tres = (a− t)2 × (1

1− at)2. (2.9)

For high finesse cavity where we have at → 1, ( 11−at)

2 is a large value, hence deviation from the

critical coupling condition (t = a) leads to a large variation in the transmitted light at the bus

waveguide.

Figure 2.9: Coupling-modulated ring resonator schematic and transmission spectrum versuswavelength.

Coupling-modulated optical switch was first proposed by Yariv [5]. Later, MZM was used

as a tunable coupler to modulate the coupling coefficient by modulating the phase difference

between two arms, ∆φ, (Eq. 2.8) [57, 58]. This type of modulator can be called an MZI-

assisted ring modulator and was shown to have a bandwidth beyond the linewidth of the ring


resonator [58]. This will be further assessed in Chapter 3 based on pole-zero representation of

CM-ring resonator small-signal transfer function. The only bandwidth limitation in coupling

modulation arises from the MZM response [58, 59].

Improvement of bandwidth compared to intracavity ring modulator arises from the fact that

here, the circulating light does not need to be completely depleted from the cavity as in the case

of intracavity modulation. Also, it was theoretically shown that this type of modulation does

not cause chirp when push-pull driven [58]. Compared with MZM, CM-ring resonator enables

much smaller switching voltage than Vπ by taking advantage of the resonance enhancement.

Figure 2.10 shows the transmission of the MZM and MZI-assisted ring modulators where the

aforementioned improvement is clearly observable for a = 0.99. The amount of improvement in

general depends on the amount of the loss in the ring resonator. This will be further investigated

in Chapter 5.

Figure 2.10: Transmission of MZI modulator and MZI-assisted ring modulator versus normal-ized ∆φ [57]. The required ∆φ of on-off switchings are indicated with arrows.

Table 2.2 summaries the differences between MZI, intracavity ring, and MZI-assisted ring

modulators. In terms of reach, due to chirp generation in intracavity ring modulator, reach is

limited to medium distances while the other two types could be used in longer distances when

driven in push-pull. The resonance enhancement in either type of ring modulators allow for

more compact designs compared to the large footprint MZI modulators. The drawback with


the resonant nature, however, is higher sensitivity of these devices to temperature and wave-

length. Mach-Zehnder assisted ring modulator has relatively low free spectral range (FSR), and

therefore not suitable for wavelength division multiplexing (WDM). In terms of the bandwidth

limitations, MZI modulator is limited by the electrical characteristics of the doped waveguide

loaded with transmission line. Ring modulator bandwidth is mostly limited by photon life time

and it is also affected by the electrical response of the doped waveguide. MZI-assisted ring

modulator bandwidth is mostly limited by the electrical response of the MZI. Another limita-

tion in MZI-assisted ring modulator is the high-pass filtering behavior when operated at data

rates much higher than the cavity linewidth [58].

Table 2.2: Comparison between MZI modulator, intracavity ring modulator, and MZI-assistedring modulator.

MZI modulator Ring modulator MZIARMReach Long Medium Theoretically longTemperature range Wide Narrow NarrowOptical wavelength (working spectrum) Wide Narrow NarrowSize Large Compact MediumPotential for WDM Yes Yes for short to medium reach Currently noMain bandwidth limitation factor Electrical response Photon life time Electrical response

2.6 High capacity optical communication

Increasing capacity of the optical communication could be achieved by several methods such as

wavelength division multiplexing, mode division multiplexing, space division multiplexing, and

high order modulation format. Here, we will briefly review wavelength division multiplexing

and high order modulation formats.

2.6.1 Wavelength division multiplexing

Wavelength division multiplexing (WDM) takes advantages of the frequency independent loss

in optical fibers by modulating various data streams at different carrier frequencies and sending

them through a single fiber.

Intracavity ring modulators are great candidates for E/O conversion in short/medium-reach

WDM links due to their unique properties such as small footprint, low power consumption,

wavelength filtering, as well as being narrow band. However, one of the challenges with ring


modulator-based WDM links are to overcome the resonance wavelength change over tempera-

ture and process variation as well as keeping the laser source wavelength stable. A wavelength

stabilization feedback loop is required for each ring modulator to keep the operating wavelength

constant and avoid cross-talk between WDM channels [3].

Figure 2.11 shows a WDM link using ring modulators. Here, a four-wavelength laser output

is coupled into a silicon photonic chip. Four ring modulators with different resonance wave-

lengths share the same channel and each select a certain input wavelength to encode digital

data from their driver to the specific carrier wavelength. At the receiver, add-drop ring res-

onators are used as filters to select each one of these specific wavelengths and guide it to the

photodetector and receiver circuitry for decision making.

The design of the ring modulator as one of the main building blocks of WDM links is a

hot research topic. There is always a need for a faster, smaller and more power efficient ring

modulator. Hence, in Chapter 4, we fully assess the trade-offs of one of the design parameters

for intracavity ring modulator, which allows us to increase the device bandwidth.

Figure 2.11: WDM link based on the ring modulator [3].

2.6.2 Complex modulation formats

The simplest way of encoding data in digital communication is to use OOK format. In OOK, the

electrical zeros and ones are represented by absence or presence of the light. Spectral efficiency

(SE) of such a transmission is only 1 b/s/Hz. In order to increase the communication capacity,

one could increase SE by using more complex modulation formats. This could be achieved by

representing digital data on multiple amplitudes, phases, or a combination of the two as shown


in Fig. 2.12. In N-level pulse amplitude modulation (PAM-N), data is encoded into N levels

of light intensity corresponding to spectral efficiency of log2N b/s/Hz. It is also possible to

encode the data in phase rather than amplitude. Examples of phase modulation are binary

phase-shift keying (BPSK), differential phase-shift keying (DPSK), or quadrature phase-shift

keying (QPSK). As shown in Fig. 2.12, the distance between two symbols in BPSK/DPSK are

twice the distance in OOK which results in 3dB improvement in receiver sensitivity [60].

More complex modulation formats such as quadrature amplitude modulation (QAM) can

be realized by combined multi-level amplitude and phase modulation where QAM-N2 has SE

of N b/s/Hz. As can be seen from Fig. 2.12, while the spectral efficiency is increasing by

increasing number of bits per symbol, the distance between symbols decreases in PAM and QAM

modulation schemes limiting their reach. Also, increasing number of bits per symbol increases

complexity of the receiver circuit. Another technique to increase SE is to send the modulated

Figure 2.12: Constellation diagrams of various modulation formats.

data at two orthogonal polarizations. This method is called polarization multiplexing (PM)

and could double the spectral efficiency [61].

High order modulation transmitter power consumption, area consumption, cost, data rate,


and circuit complexity depend on the design of the electro-optical modulator. In this thesis we

focus on new designs for PAM and QAM modulators.

Previous work on PAM and QAM modulation

Figure 2.13 shows the most common methods for generating PAM-4 signaling which are ex-

tendible to PAM-N. As shown in Fig. 2.13a and b, multilevel optical intensity was achieved using

electrical digital-to-analog converters (DAC) to either drive directly modulated VCSELs [62],

or MZMs [63]. As mentioned earlier, there will be an imposed chirp in DML. Also, design of

a linear DAC operating at high frequencies could be challenging [64]. Another type of PAM

modulator is based on segmentation of an MZI [41] as shown in Fig. 2.13. Segmentation of the

RF section would relax the driver design without adding complexity in the optical modulator

design. In Chapter 5, a new configuration for PAM signaling will be presented to reduce the

size and voltage required by previously proposed methods.

Figure 2.13: Methods for optical PAM-4 signaling based on (a) VCSEL, (b) MZI, and (c)segmented MZI.

There are several possible configurations for QAM modulation. These are mainly based on

modulators requiring multi-level electrical signals. One of the widely used architectures is an

IQ optical modulator shown in Fig. 2.14. As shown in the figure, each of the I- and Q-arms of

the MZI consist of an MZM driven by multi-level electrical signals [61, 65].

There have been several proposed architectures for binary-driven QAM-16 such as quad

parallel MZM [67] and two cascaded IQ optical modulators [68]. Also, QAM modulator based

on segmentation of RF sections was demonstrated on SISCAP [69]. As MZM in general is large

and requires relatively high driving voltage, there is still room for the improvement of QAM

modulator as will be discussed in Chapter 6.


Figure 2.14: Typical IQ transmitter for QAM format [66].

2.7 Summary

In this chapter a general description of an optical link was given with a focus on electro-

optical modulators. We reviewed various schemes for electro-optic modulation techniques in

both III-V and silicon based materials. The benefits of silicon photonics as well as challenges

and opportunities in this area were described. Furthermore, the main mechanisms for optical

modulation in silicon together with an overview of silicon optical modulators were presented.

Methods of increasing optical communication capacity were evaluated. We mainly focused on

WDM links based on intracavity ring modulators as well as PAM and QAM modulators.

Chapter 3

Ring modulator small-signal

response

Among various silicon photonic modulator candidates, carrier-depletion ring modulators em-

ploying reverse-biased pn diode are one of the most favorable [11, 70–72] due to their small

footprint, high bandwidth, CMOS compatibility, low power consumption, and their suitability

to wavelength division multiplexing (WDM) [10, 73, 74]. In order to optimally design carrier-

depletion ring modulators in terms of power efficiency and bandwidth, it is essential to gain a

better understanding of the device performance and its design trade-offs.

One of the most important performance metrics of a ring modulator is the small-signal

electro-optical frequency response. It was shown recently that the widely used empirical formula

relating the bandwidth of the intracavity ring modulator (f3dB) to its optical (fQ) and electrical

(fRC) bandwidths (1/f23dB = 1/f2

Q +1/f2RC [13]) is not accurate because it neglects the impact

of other key parameters such as carrier wavelength and coupling condition [54,55]. For example,

when the input is detuned from the resonance wavelength, a peak may appear in the elector-

optical response of the ring modulator before the roll-off. This effect has been shown to increase

the bandwidth of the ring modulators [54–56].

Several studies on analyzing intracavity ring modulator small-signal frequency response

were published recently based on experimental and/or numerical results [53–55,75–78] and the

design trade-offs of the ring modulator were investigated [54, 55, 75]. The bandwidth and DC

30

Chapter 3. Ring modulator small-signal response 31

modulation efficiency (DC gain) of the ring modulator were extracted from the small-signal

response [54, 75, 76] as important design parameters. However, a closed-form expression for

electro-optical frequency response of a ring modulator considering both electrical and optical

characteristics as well as the loss modulation accompanying the index modulation is missing

to the best of our knowledge. Laser detuning was previously optimized based on DC gain [54,

55, 75], however, the widely used gain-bandwidth product (GBW) in electronics is a more

appropriate figure of merit (FOM) for ring modulators. This is because it includes both ring

modulator performance metrics of DC gain and bandwidth. Assuming a constant bandwidth,

decrease in DC gain of the device leads to increase in the power consumption. This could be

more critical for the link performance compared with data rate since data rate can be increased

by moving to higher order modulation scheme. GBW was considered in [79] as a FOM, but

limited analysis was presented.

As mentioned in Chapter 2, in addition to intracavity ring modulator in which OOK inten-

sity modulation is carried out via resonance wavelength shifting, there is another method for

OOK modulation utilizing ring resonator. This latter method uses coupling-modulated ring res-

onator and does not suffer from the bandwidth limitation set by cavity linewidth as discussed in

Chapter 2. Hence, it could be more favorable than intracavity ring modulator when high band-

width is required. Therefore, in order to gain a better understanding of the coupling-modulated

ring resonator and to compare it with intracavity ring modulator, it is important to obtain the

small-signal response of the coupling-modulated ring resonator as well. Small-signal response

of the coupling-modulated ring resonator was studied before [53,75]. However, loss modulation

accompanying the index modulation in plasma dispersion effect and electrical response of the

modulator were not considered.

In this chapter, we use first-order perturbation theory to obtain a closed-form frequency

response model of intracavity and coupling-modulated ring modulators. The model for intra-

cavity ring modulator is verified by the measurement results. Using the obtained models for

intracavity and coupling-modulation case, ring modulator response is assessed based on pole-

zero locations which depend on electrical bandwidth, coupling condition, optical loss, and laser

detuning. At the end, the small-signal response of both intracavity and coupling modulated

ring modulators are compared based on pole-zero diagrams in the case of zero and non-zero


laser detunings.

3.1 Intracavity ring modulator small-signal response

In this section, we aim to obtain a complete small-signal transfer function of a depletion-mode

intracavity modulated microring. This model will be verified by measurement results.

3.1.1 Small-signal response modeling

Driving a ring modulator with a small sinusoidal voltage of vin(t) = Vin cos(ωmt) in addition to

a DC voltage of VDC , the input voltage, vin(t), can be written as vin(t) = VDC +Re(Vinejωmt).

Here, Vin is the small-signal phasor, equal to amplitude of Vin, and ωm is the modulation angular

frequency. Under the small-signal assumptions, in response to this stimulus, the output optical

power Pout(t) oscillates at ωm. The output power is equal to PDC + Pout cos(ωmt+ φp) =

PDC + Re(Poutejωmt) where PDC is the DC optical power, φp is the phase delay with respect

to drive voltage, and Pout is a complex small-signal phasor. The total small-signal transfer

function of a ring modulator, Ht(ωm), is defined as [80]:

Ht(ωm) =Pout

Vin

. (3.1)

Figure 3.1: Intracavity ring modulator small-signal block diagram.

To obtain Ht(ωm), the response of the intracavity ring modulator to a small-signal driving

voltage can be divided into three parts of electrical (HE(ωm)), electro-optical (HEO), and


optical (HO(ωm)) responses as shown in Fig. 3.1. The small-signal equivalent circuit of a ring

modulator [11] is shown in Fig. 3.1 and it includes Cpad, Cj , and Cox as the capacitance between

the pads through the top dielectrics, the capacitance of the reverse-biased pn junction, and the

capacitance through the oxide layer, respectively. Also, Rin, Rj , and RSi are the input resistor,

the series resistance of the pn junction, and the resistance of the Si substrate. The electrical

response of a ring modulator can be modeled as a low pass filter by its dominant pole as:

HE(ωm) =1

1 + jωmReqCeq. (3.2)

The filtered AC voltage across the pn junction (Fig. 3.1), vj(t) is:

vj(t) = Vin |HE(ωm)| cos(ωmt+ φHE(ωm)), (3.3)

where φHE is the phase delay caused by the electrical circuit model of a ring modulator.

As illustrated in Fig. 3.1, due to the voltage-dependent effective index and electric field decay

time constant, both the resonance angular frequency, ωr, and the shape of the ring modulator

optical transmission spectrum are modulated. The effective index and the decay time constant

modulations can be lumped together as ωr(t) = Ωr cos(ωmt+φHE(ωm)), where Ωr is a complex

number equal to Vin × |HE(ωm)| ×HEO, and HEO is:

HEO = (−ωr

ng

∂neff

∂v|VDC

+j∂(1/τ)

∂v|VDC

). (3.4)

Here, ng is the group index, neff is the effective refractive index, and τ is the electric field

amplitude decay time constant.

So far, we have modeled HE and HEO. Instead of calculating the third transfer function

(Fig. 3.1), HO, we use the coupled mode theory [81, 82] to first find Pout and subsequently

Ht(ωm). From coupled mode theory, the optical behavior of microring can be modeled using


the following Eqs:

dA

dt= (jωr −

1

τ)A− jµSi, (3.5a)

St = Si − jµA, (3.5b)

where A is the energy amplitude circulating inside the ring and 1/τ = 1/τe + 1/τl, with τl and

τe being the amplitude decay time constants due to the intrinsic loss inside the cavity and due

to the ring to bus waveguide coupling, respectively. Also, Si and St are the CW input and time

varying transmitted waves, and µ is the mutual coupling coefficient between the ring and the

bus waveguide which is related to τe through µ2 = 2/τe. In the steady state domain and for a

harmonic input of Si = Si0ejωint, where ωin is the carrier angular frequency, A and St can be

calculated from Eq. 3.5a and 3.5b. Considering A = A0ejωint and St = St0e

jωint , we have:

A0 =−jµ

j∆ω + 1τ

Si0

St0 =j∆ω + 1

τ − 2τe

j∆ω + 1τ

Si0,

(3.6)

where ∆ω = ωin − ωr.

In the dynamic small-signal domain, we have ωr + ωr(t) where this small variation perturbs

the resonator resulting in alteration of A. Under small-signal assumptions, A can be expanded

as a Taylor series. Ignoring the higher order terms and considering the first order term, δA, first-

order perturbation theory can be used to solve Eq. 3.5a when A+ δA is substituted [55]. After

finding δA from Eq. 3.5a, St can be obtained using Eq. 3.5b and from |St|2, output power can

be calculated. Using this approach and assuming Ωr cos(ωmt+ φHE(ωm)) = Ωr

2 (ej(φHE+ωmt) +

e−j(φHE+ωmt)), Pout is found to be:

Pout = µejφHE

[ΩrA0S

∗t0

1τ + j(∆ω + ωm)

+Ω∗rA

∗0St0

1τ − j(∆ω − ωm)

]. (3.7)

By substituting A0 and St0 from Eq. 3.6 into Eq. 3.7 and after some manipulation, we arrive


at:

Pout =2µ2Pine

jφHE Re(Ωr)1τ2

+∆ω2×

[jωm(tan(φΩr)(

1τl− 1

τe)−∆ω)− 2∆ω

τl− tan(φΩr)(∆ω2 − 1

τ (1τl− 1

τe))

−ω2m + 2

τ (jωm) + ∆ω2 + 1τ2

], (3.8)

where Pin =∣∣S2

i

∣∣ and φΩr is the phase of Ωr. The ring modulator transfer function, Ht(ωm),

can now be found directly from Eq. 3.8 by replacing Ωr with Vin×|HE(ωm)|×HEO and dividing

Pout by Vin. Having tan(Ωr) = tan(φHEO), where φHEO is the phase of HEO in Eq. 3.4, Ht(ωm)

is found as:

Ht(ωm) =2µ2Pin(−ωr

ng

∂neff

∂v |VDC)

1τ2

+∆ω2

(tan(φHEO)(1τl− 1

τe)−∆ω)

1 + jωmReqCeq×

jωm −

2∆ωτl

+tan(φHEO)(∆ω2− 1

τ( 1

τl− 1

τe))

tan(φHEO)( 1

τl− 1

τe)−∆ω

−ω2m + 2

τ (jωm) + ∆ω2 + 1τ2

. (3.9)

The transfer function in Eq. 3.9 can be written in s-domain (jωm → s) as:

Ht(s) = GDC1

1 + s1

ReqCeq

[(− s

z + 1)ω2n

s2 + 2ζωns+ ω2n

](3.10)

where ωn =√∆ω2 + 1

τ2, ζ = 1/

√1 + (τ∆ω)2, and the DC gain, GDC = Ht(0), is:

GDC =2µ2Pin(

ωr

ng

∂neff

∂v |VDC)

ω4n

(2∆ω

τl+ tan(φHEO)(∆ω2 − 1

τ(1

τl− 1

τe))). (3.11)

Based on small-signal transfer function of a ring modulator in Eq. 3.10, for non-zero detuning,

ring modulator is a third-order system with a complex-conjugate pole pair, one real pole, and


a real zero at the following locations:

p1,2 = −1

τ± j∆ω,

p3 = − 1

ReqCeq,

z =2∆ω

τl+ tan(φHEO)(∆ω2 − 1

τ (1τl− 1

τe))

tan(φHEO)(1τl− 1

τe)−∆ω

.

(3.12)

Figure 3.2: (a) Pole-zero diagram of a ring modulator. Location of zero divided by −2/τl (b)versus ∆ωτ , excluding ∆ωτ = 0, for three coupling conditions (c) versus τe/τl at ∆ωτ = ±2.

A pole-zero diagram of Ht(ωm) is shown in Fig. 3.2a. As illustrated in the figure, the real

and imaginary parts of p1,2 depend on the photon life time and the value of the laser detuning,


respectively. However, as expected from Eq. 3.12, the location of the zero is more complicated.

The arrow close to −2/τl in Fig. 3.2a indicates that the location of z is in the vicinity of

−2/τl, where the distance depends on the coupling condition and on the value/sign of the laser

detuning. To make this more clear, z/(−2/τl) is plotted in Fig. 3.2b versus ∆ωτ , excluding

∆ωτ = 0, for three cases of strong over-coupled, τe = 0.1τl, critical-coupled, τe = τl, and strong

under-coupled, τe = 10τl, ring modulator. The ring modulator response at ∆ω = 0 will be

discussed later in this chapter. The zoomed-in view is also shown in inset of Fig. 3.2b. Here,

we assume to have τl = 80ps and tan(φHEO) = 0.04. In case of both under- and over-coupled

rings, because of the term in the denominator of the zero shown in Eq. 3.12, z approaches

infinity as ∆ω becomes equal to tan(φHEO)(1/τl − 1/τe). Also, as shown, in the over-coupled

case, z is farther from −2/τl compared with the critical- and the under-coupled cases. To see

the dependency of the z location on the coupling condition, z is calculated as a function of τe/τl

at ∆ω = ±2/τ and plotted in Fig. 3.2c. This detuning is equal to the resonator linewidth. For

large detuning, ∆ω >> tan(φHEO)(1/τl − 1/τe), z can be written as:

z =−2

τl− tan(φHEO)

∆ω(∆ω2 − 1

τ(1

τl− 1

τe)). (3.13)

As (1/τl − 1/τe) is negative for over coupling condition, 0 for critical coupling condition, and

positive for under coupling condition, deviation of z from −2/τl increases by moving towards

under-coupling condition. Another important point from Fig. 3.2c is that the location of zero

depends on the sign of laser detuning. According to Fig. 3.2c, moving from under coupling

condition to deep over coupling condition leads to farther zero locations for positive and negative

detuning. Consequently, from the transfer function point of view, it is clear that the frequency

response of the ring modulator will be different depending on the sign of the detuning where

this difference becomes more significant going towards over-coupling condition. The different

frequency response for positive and negative detunings was expected based on asymmetric

side-band generation [55].


It can also be seen from Eq. 3.9 and 3.10 that when ∆ω = 0, Ht(s) becomes:

Ht(s)|∆ω=0=−2µ2Pin(

ωr

ng

∂neff

∂v |VDC)

1τ3

tan(φHEO)(1τl− 1

τe)

1 + s1

ReqCeq

1

1 + s1

τ

, (3.14)

which is a second order system with two real poles at −1/ReqCeq and −1/τ when τl 6= τe.

Figure 3.3: DC gain for three coupling conditions versus ∆ωτ .

Normalized absolute value of DC gain (Eq. 3.11) is plotted versus ∆ωτ in Fig. 3.3 for three

aforementioned coupling conditions when τl = 80ps and tan(φHEO) = 0.04. Based on this

figure, the DC gain becomes very small for detunings close to zero. However, as shown in

Fig. 3.3, when τe 6= τl, GDC minimum shifts from ∆ω = 0 to positive and negative detunings

for under- and over-coupled cases, respectively. The DC gain minimum shift is larger for the

over-coupled case compared with the under-coupled case. According to Fig. 3.3 and Eq. 3.11,

in contrast to what was reported in [54], only for critically-coupled ring modulator, τl = τe, the

small-signal modulation is zero at ∆ω = 0. The fact that tan(φHEO) is non-zero in Eq. 3.11,

due to the loss modulation accompanying the index modulation, results in a non-zero small-

signal modulation at zero detuning for over- and under-coupled rings. Also, this results in the

coupling-condition dependent GDC maximum locations, as can be seen from Fig.3.3.


3.1.2 Experimental verification of the small-signal model

To verify the closed-form small-signal transfer function in the previous section, we characterize

an all-pass ring modulator fabricated in IME A*Star process [83]. The cross section of the

ring modulator waveguide in the high speed section and an optical microscope image of the

fabricated device are shown in Fig. 3.4a and b, respectively. The device is implemented on a

220nm Si on a 2µm buried oxide layer. The nominal doping concentration for low doped region

inside the waveguide is 3× 1017cm−3 for n and 5× 1017cm−3 for p, and for high-doped region

is 1020cm−3. The pn junction is positioned with 50nm offset with regards to the waveguide

center. The lateral pn junction is taking 75% of the ring circumference and is not covering the

coupling region. Radius of the ring is 10µm, waveguide width is 500nm, and gap between the

ring and the bus waveguide is 350nm.

Figure 3.4: (a) Cross section of the ring modulator waveguide in the active region. (b) Opticalmicroscope image of the fabricated ring modulator.

The photo of the measurement setup is shown in Fig. 3.5. We used a fiber array to vertically

couple laser light to the sample. Also shown, the DC probe to apply bias voltage to the RF

pads.

Transmission spectra at through ports of the ring modulator are shown in Fig. 3.6a under

reverse bias voltages of 0.5, 0, -0.5,-1, and -2V applied to the RF pads. Optical power loss,

α(V ), and through coupling coefficient, t, are extracted from the measured spectra at various

bias voltages based on the method presented in [84]. Figure. 3.6b shows the extracted ∆α


Figure 3.5: Measurement setup of the ring modulator.

in dB/cm versus voltage. From the extracted coupling coefficient and the voltage-dependent

power loss coefficient in 1/m, τl and τe are calculated [82]:

τl =2

vgα(v),

τe =2Lrt

vgκ2,

(3.15)

where vg is the group velocity, κ is the cross coupling coefficient (√1− t2), and Lrt is the

round-trip length. Also, ng, was extracted to be ≈3.9. As the coupling region in the ring is not

pn-doped, the change in τe by varying voltage is insignificant.

From Eq. 3.15, τl is calculated as a function of voltage and is fitted to a cubic polynomial.

τl and τe are found to be 82.2ps and 65.3ps, respectively, at VDC = 1.5V . Having τe < τl shows

that the ring is over-coupled as it was expected from notch depth-bias voltage dependency in

Fig. 3.6a. Also, ∂(1/τ)∂v |VDC

is calculated to be −2.7 × 108 1/s/V . Moreover, extracted neff as

a function of voltage is plotted in Fig. 3.6c together with the fitted quadratic curve with Eq

shown in the figure. From this,∂neff

∂v |VDCis calculated to be 2.35 × 10−5 1/V . Quality factor

of the ring is about 22,200 at VDC . In the small-signal circuit model, Rin is taken to be 50Ω,

and Cj and Rj are calculated based on the methods presented in [78] to be 11fF and 160Ω.

The calculated value for Cj closely matches the measured junction capacitance in [85] which is


Figure 3.6: (a) Measured optical power transmission spectra (resolution of 2.5 × 10−4nm) atvarious bias voltages . Extracted (b) ∆α and (c) ∆neff from the measured spectra shown in(a).


fabricated in the same foundry and has the same waveguide doping and geometry as here. The

Rj is also calculated based on the measured sheet resistance in [85]. Other circuit elements

(Cpad, RSi, and Cox) which are less important are assumed to be the same as [77] which has

similar waveguide cross section and metal. Based on these values, the electrical bandwidth of

the ring modulator, fRC = 1/2πReqCeq, is found to be 61.5GHz which is around 7× higher

than the optical bandwidth of fQ = 8.7GHz for this measured device.

Figure 3.7: Normalized measured and simulated small-signal (a) electro-optical response versusmodulation frequency, fm, for ∆ω of 1.15, 0.57, and 0.28(b) 3dB bandwidth of the reverse-biasedring modulator.

Substituting these parameters in Eq. 3.9, we simulated the electro-optical response of the

ring modulator at various laser detunings. The results for three laser detunings of 2π(−1.25GHz),

2π(−2.5GHz), and 2π(−5GHz) are shown in Fig. 3.7a. Frequency response of the ring mod-

ulator is also measured using a 40Gbps InP waveguide photodetector and a transimpedance

amplifier (TIA) photoreceiver referenced to a vector network analyzer (VNA) output. The mea-

surement results are also shown in Fig. 3.7a in circles which shows that our model is in excellent

agreement with the measurement results. All the curves are normalized with respect to their DC

values (200MHz). Figure 3.7a clearly illustrates the detuning-dependent frequency response of

the ring modulator. The observed peak in the frequency response occurs due to the constructive

interference between the frequency detuned through-coupled input laser and the cross coupled

light preexisting inside ring resonator and oscillating at its natural frequency [54–56]. Also,


3dB bandwidth, f3dB, calculated from our small-signal model is plotted in Fig. 3.7b together

with the measured f3dB at several detunings (circles). As shown in [53–56], by increasing laser

detuning, the device bandwidth increases due to the aforementioned peaking effect.

Due to their compact nature, any small changes in the ring modulators may lead to vast

changes in the device performance. Cross wafer characterization of the silicon photonics com-

ponents including ring modulator fabricated in this technology were studied earlier [86]. For

every tested device, the required parameters for the frequency response modeling need to be

extracted from DC measurements. We have tested the developed model at multiple design vari-

ations to confirm the model accuracy by way of comparing it to experimental results. However,

for the sake of consistency and brevity of the current manuscript, such results will be presented

elsewhere.

3.1.3 Gain-bandwidth product as a figure of merit

The small-signal transfer function of the ring modulator in Eq. 3.9 can be further simplified by

neglecting the loss modulation, as for a typical SOI process we have Im(Ωr)Re(Ωr)

<< 1 [55]. Based

on this assumption, the transfer function in the s-domain can be written as:

Ht(s) = GDC1

1 + s1

ReqCeq

( s2

τl

+ 1)ω2n

s2 + 2ζωns+ ω2n

, (3.16)

where GDC becomes:

GDC =2µ2Pin(

ωr

ng

∂neff

∂v |VDC)∆ω

(∆ω2 + 1τ2)2

2

τl. (3.17)

The laser detuning which maximizes the DC gain can be calculated by setting ∂GDC

∂∆ω = 0.

Based on this, at ∆ω = 1/(√3τ), DC gain is maximized. This is similar to what was shown

in [54, 55]. Also, it can be seen from Eq. 3.17 that at critical coupling (τe = τl) and for a

constant ∆ωτ , GDC is proportional to τ2. This can be qualitatively justified as follows: at the

same ∆ωτ , a transmission spectrum of the ring with higher quality factor, or τ , has higher

slope, and consequently higher GDC .

The ring modulator 3dB bandwidth can be calculated by setting |H(ωm)| equal to GDC/√2


in Eq. 3.16. In the case when 1/ReqCeq >> 1/τ and at critical coupling, f3dB is calculated to

be:

f3dB =1

2πτ

√3∆ω2τ2 +∆ω4τ4 +

√1 + 2∆ω2τ2 + 10∆ω4τ4 + 6∆ω6τ6 +∆ω8τ8. (3.18)

According to Eq. 3.18, for a constant ∆ωτ , f3dB is proportional to 1/τ and consequently fQ,

given that fQ = 1/πτ . This comes from the earlier assumption of 1/ReqCeq >> 1/τ which

neglects the bandwidth limitation arises from fRC . For the special case of ∆ωτ = 1, which

represents a detuning equal to the half of the resonator linewidth, f3dB will be around 1.4×fQ.

Here, we use the gain-bandwidth product, GBW = GDC×f3dB, as a FOM. For the simplified

case considered here, GBW is calculated from Eq. 3.17 and 3.18 to be:

GBW =Kτ∆ωτ

(∆ω2τ2 + 1)2×

√3∆ω2τ2 +∆ω4τ4 +

√1 + 2∆ω2τ2 + 10∆ω4τ4 + 6∆ω6τ6 +∆ω8τ8 (3.19)

where K = 2µ2Pinωr

πng

∂neff

∂v |VDC. Also, as expected from GDC and f3dB formulas, GBW is

proportional to τ . Hence, at the same ∆ωτ , the critically coupled ring with higher quality

factor has higher GBW.

In order to see the effect of detuning on DC gain, bandwidth, and GBW, ∆ω is swept while

the rest of the parameters are kept constant. Normalized GDC , f3dB, and GBW are plotted in

Fig. 3.8 versus ∆ωτ . In this figure, only positive detunings are shown as the plots are symmetric

around ∆ω = 0 due to the no loss modulation assumption. According to Fig. 3.8 top, increasing

∆ω beyond 1/(√3τ) to increase the bandwidth introduces a trade-off between GDC and f3dB

as was observed previously in [54, 75]. Figure 3.8 bottom shows that the product of GDC and

f3dB (FOM) reaches its maximum value when ∆ω = 1.129/τ .

The closed-form GBW formula (Eq. 3.19) for the simplified case helps develop an under-

standing of the ring modulator small-signal behavior. However, obtaining such a formula with

loss modulation, electrical bandwidth limitation, and for other coupling conditions is more com-

plicated. Therefore, in the following section, we will study GBW numerically using Eq. 3.10 as

a means to study the ring modulator frequency response.


Figure 3.8: Normalized GDC , f3dB, and GBW versus ∆ωτ for a constant τ .

3.1.4 Pole-zero location impact on small-signal response

We now study the effect of the ring modulator electrical behavior on GBW based on small-

signal transfer function. This is examined by sweeping ReqCeq in Eq. 3.10, so that fRC be equal

to m × fQ, m an integer value. The pole-zero diagram is shown in Fig. 3.9a where locations

of the poles/zero are indicated based on fQ and fRC when τl = τe = 80ps. Figure. 3.9b shows

GBW for several fRC values versus ∆ωτ . It is clearly shown that increasing fRC will result

in increasing GBW. However, the rate saturates as fRC increases above a certain value. To

observe this effect more clearly, maximum GBW for both positive and negative detunings are

plotted versus fRC/fQ in Fig. 3.9c. The plots show that up to fRC/fQ = 3 both curves initially

rise rapidly but then the rate decreases beyond this value and almost saturates at fRC/fQ > 11.

This occurs as for such large values of fRC , p3 is far apart from p1,2 and z, and therefore, its

effect becomes almost insignificant. Figure 3.9d shows the plot of (∆ωτ)max corresponding to

the GBW maximums for both positive and negative detunings versus fRC/fQ. According to

this figure, (∆ωτ)max also varies depending on p3 location. For large fRC (fRC/fQ = 100),

(∆ωτ)max becomes 1.134 for positive and 1.119 for negative detunings. These values are slightly

different from the predicted value of 1.129 obtained from Fig. 3.8bottom, as we had neglected

the loss modulation in obtaining the simplified GBW in Eq. 3.19.

It is well known that there is a trade off between bandwidth and DC gain (e.g. see Fig. 3.8).

The amount of penalty in DC gain caused by varying the laser detuning is defined as GDC


Figure 3.9: (a) Pole-zero diagram of a ring modulator. Simulated (b) GBW versus ∆ωτ forseveral fRC (c) GBW maxima versus fRC/fQ (d) ∆ωτ corresponding to the GBW maximaversus fRC/fQ.

divided by its maximum value achieved among all the detunings [54]. It is shown in [54] that

increasing fRC increases the trade-off efficiency between bandwidth and DC gain penalty. To

study this further, f3dB/fQ versus GDC penalty is plotted in Fig. 3.10a. This figure shows the

predicted increase in trade-off efficiency, however, there is a saturation point beyond which,

trade-off efficiency does not increase significantly. To make this more clear, slopes of these

curves, obtained by fitting a line to each, are calculated and plotted in Fig. 3.10b as a trade off

coefficient versus fRC/fQ for both positive and negative detunings. As shown, the saturation

point of fRC/fQ ≈ 11, observed in Figure 3.9c, is also clearly observable here. Also, according

to Fig. 3.10b, positive detuning, in this case of the critical coupling, reaches higher trade off

coefficient compared with the negative detunings. Although here we assumed critical coupling

condition, the result is the same for over- and under-coupling (e.g. in [54] the ring modulator

was assumed to be under-coupled).


Here, we assumed that the variation of the ring modulator electrical bandwidth (p3 location)

does not affect the other poles and zero locations. However, improvement of fRC may come at

the cost of excess optical loss which leads to variation of the entire pole-zero diagram. Therefore,

depending on the selected fRC improvement method, variation of p1,2 and z may need to be

taken into account.

Figure 3.10: (a) Simulated f3dB/fQ versus DC gain penalty for several fRC . (b) Trade-offcoefficient versus fRC/fQ for both positive and negative detunings.

Next, we study the effect of coupling condition on the ring modulator frequency response.

This is done by varying τe and keeping τl constant. This can be translated to various p1 and p2

locations with regards to z. First, we consider three cases of τe = τl/2 (over-coupled), τe = τl

(critical-coupled), and τe = 2τl (under-coupled) as shown in Fig. 3.11a. For simplicity, the

locations of z are shown to be at −2/τl and insensitive to the coupling condition as for this

range of τe/τl the walk-off is small (Fig. 3.2c). Here, it is assumed that fRC = 12 × fQ and

τl = 80ps for three cases studied here. As such, p3 is equal to −24/τ as shown in Fig. 3.11a,

and from left to right we have |Re(p1,2)| > |z|, |Re(p1,2)| = |z|, |Re(p1,2)| < |z|, respectively.

Figure. 3.11b shows Bode plots of each case presented in Fig. 3.11a, ignoring the third pole as

it is located far from other poles and zero. It is well known that when there is no resonant

peaking, Bode plot describes frequency response of a system with a pair of complex-conjugate

poles more accurately. This requires ζ > 0.707 and therefore |∆ωτ | < 1. In this regime, it is

easier to qualitatively describe the frequency response and compare the three aforementioned

cases. Also, considering the poles/zero configurations in Fig. 3.11a and given that τl is the same


in the three examples, it is clear that ωn1 > ωn2 > ωn3 for the same ∆ω. Here, indices 1, 2, and

3 are corresponding to over-, critical-, and under-coupled cases. According to Fig. 3.11b, in the

case of τe = τl/2 where z < ωn1, as the input frequency approaches z, the frequency response

magnitude starts increasing at a rate of 20dB/dec until ωn1 where the frequency response

amplitude start falling at a rate of -20dB/dec. For τe = τl where z = ωn2, the magnitude

rolls-off at the rate of -20dB/dec at input frequency equal to z and onward. When τe = 2τl, i.e.

z > ωn3, the magnitude rolls off at a rate of -40dB/dec at ωn3 until input frequency reaches z

after which the rate becomes -20dB/dec. Consequently, it is clear from Bode plots in Fig. 3.11b

that f3dB is higher for τe = τl/2 compared with the other two cases.

Figure 3.11: (a) Pole-zero diagrams of the ring modulator when p3 = −24/τ and from left toright τe = τl/2, τe = τl, and τe = 2τl. (b) corresponding Bode plots of the pole-zero diagramsshown in (a).

Breaking the assumption of ζ > 0.707 and sweeping ∆ω, f3dB of the ring modulators

with zero-pole diagrams shown in Fig. 3.11a are calculated from our model and are plotted

in Fig. 3.12a. As shown, the prediction based on Bode plots in Fig. 3.11b is also valid when

ζ < 0.707. This figure also shows that the rate of change in f3dB as a function of |∆ω| is higher

for τe = τl/2 than τe = τl and τe = 2τl. However, higher slope will result in more sensitivity

with respect to temperature variation since it leads to variation in ∆ω.


Figure 3.12: (a) Ring modulator 3dB bandwidth (b) GBW versus ∆ωτ when τl = 80ps andτe is equal to τl/2, τl, and 2τl. (c) Laser detunings corresponding to the maximum GBW atpositive detunings (d) GBW maximum versus τe/τl for τl = 80ps.

It has been shown that moving toward under coupling condition results in increasing DC

gain [54]. However, GBW plots versus ∆ωτ shown in Fig. 3.12b suggest that GBW is higher

for over-coupled ring than both critical- and under-coupled rings. Also, according to Fig. 3.12b,

contrary to the assumption made in [79], the location of peak is also shifting by changing the

coupling condition.

This is further investigated by sweeping τe/τl and simulating GBW. The τe/τl range is taken

to start from 0.3 to make sure the location of zero stays close to −2/τl (Fig. 3.11c) as our focus

here is to study the location variation of the complex-conjugate pole pair only. The optimum

laser detuning corresponding to the GBWmaximum at positive detunings is plotted versus τe/τl

which shows that moving from under- to over-coupling condition results in decreasing optimum

laser detuning. The GBW at this optimum detuning is illustrated in Fig. 3.12d. The figure


suggests a monotonous decay in GBWmax in the selected range of τe/τl, as poles move toward

z and closer to the imaginary axis. Consequently, higher GBW is achievable for over-coupled

ring modulator.

As shown above, the transfer function in Eq. 3.10 can be used to observe the response of

the ring modulator at various design conditions and therefore is useful to optimize the ring

modulator design in terms of the amount of peaking, bandwidth, temperature sensitivity, and

DC gain (GBW). To design a ring modulator, for the specific doping level and the doping

map of the waveguide, the value of τl, Req, and Ceq can be obtained. Then the rest of the

key design parameters such as τe and ∆ω can be swept to find the desirable response. The

pole-zero representation provide more insight to the response variations. As an example, the

complex pole and the value of ζ predicts the peaking, however, since the modulator response is

more complicated than a system with only a complex pole pair to predicts the exact response,

analysis and simulation based on Eq. 3.10 is required.

Please note that although GBW is a metric for the small-signal frequency response of the

ring modulator, other performance metrics should also be considered when choosing the laser

detuning. For example, extinction ratio and insertion loss are also dependent on the laser de-

tuning. Despite the high GBW for deep over-coupled ring modulator, the maximum achievable

extinction ratio decreases significantly which is not desirable for various applications.

The small signal response is obtained under the assumption of device linearity where the

device operates around a bias point. The results of small signal analysis show how much

attenuation is applied to each frequency component of the incoming modulation signal when

passing through the ring modulator. However, since the ring modulator has nonlinear behavior

in large-signal domain, the amplitude of the incoming modulation signal will affect the response

of the ring and therefore its bandwidth. To extend the applicability of this response to large-

signal behavior, we can define the bandwidth based on parameters such as the rise time of the

step response of the modulator


3.2 Coupling-modulated ring resonator small-signal modeling

Small-signal response of an intracavity ring modulator was derived in Section 3.1. In this

section, we aim to obtain a complete small-signal transfer function of a depletion-mode coupling-

modulated microring. The general procedure is similar to what was presented in Section 3.1.

However, the driving voltage modulates the coupling coefficient, contrary to the intracavity

modulation in Section 3.1.

As discussed earlier in Chapter 2, coupling modulation can be carried out using an MZI as

a coupler for the coupling modulation. Fig. 3.13 shows a schematic of such a device. We will

use this configuration for analysis of coupling-modulated ring resonator in this section. With

this assumption, the cross and through coupling coefficients can be written as αM cos(∆φ/2)

and αM sin(∆φ/2), respectively. Here αM is the transmissivity in MZI arms assuming equal

losses in both arms and ∆φ is the phase difference between two arms of the MZI.

Figure 3.13: Schematic of the ring modulator with an MZI as a coupler.

3.2.1 Small-signal response modeling

Similar to Section 3.1, the small-signal electro-optical transfer function of the coupling-modulated

ring resonator, Ht(ωm), can also be divided into HE(ωm), HEO, and HO(ωm), as shown in

Fig. 3.14. Similar to the intracavity case, small-signal equivalent circuit of a pn-doped region

is a low pass filter with the transfer function shown in Eq. 3.2. HEO describes the small-signal

relation between low pass filtered input voltage and mutual coupling coefficient (µ) to the ring

resonator. Mutual coupling coefficient is related to the cross coupling coefficient (κ) through

µ2 = κ2vg/Lrt, where vg and Lrt are the group velocity and ring round-trip length, respectively.

Therefore, HEO can be written as:

HEO =

√vgLrt

(∂αM

∂v |VDC

αMκ0 −

πLM

λ

∂neff

∂v|VDC

t0). (3.20)


Figure 3.14: Coupling-modulated ring resonator small-signal block diagram.

Here, LM is the MZI arm length and κ0 and t0 are the cross and through coupling coefficients

at bias voltage of VDC , respectively, where we have κ20 + t20 = α2M .

In Section 3.1, following the method presented in [55], first-order perturbation theory was

used to model the optical response of an intracavity ring modulator under small-signal as-

sumption. First-order perturbation theory can also be used in case of coupling modulation.

Small-signal variation of the mutual coupling coefficient will result in small-signal variation in

τe through τe = 2/µ2. Therefore, the mutual coupling coefficient can be written as µ + δµ(t)

from which 1/τe is found to be µ2/2 + µδµ(t). This results in a small change (δA) in energy

amplitude, A. Replacing A, µ, and 1/τ with A+ δA(t), µ+ δµ(t), and 1/τ +µδµ(t) in Eq. 3.5a

and neglecting second order terms we have:

dδA(t)

dt= (jωr −

1

τ)δA(t)− jµA(t)δµ(t)− jδµ(t)Si, (3.21)

Decomposing δA(t) into a slowly varying term and a time dependent term as δA(t) = δAe(jωr−1

τ)t,

Eq. 3.21 can be rewritten as:

dδA

dt= −µAδµ(t)e−(jωr−

1

τ)t − jδµ(t)Sie

−(jωr−1

τ)t, (3.22)

Considering the time varying mutual coupling coefficient δµ(t) as δµ cos(ωmt) = δµ/2(ejωmt +

e−jωmt) and A = A0ejωint in Eq. 3.22, we obtain:

dδA

dt=

δµ

2(−µA0 − jSi0)(e

(j(ωin−ωr+ωm)+ 1

τ)t + e(j(ωin−ωr−ωm)+ 1

τ)t). (3.23)


Therefore, we will find the following equation for δA(t):

δA(t) = −δµ

2(µA0 + jSi0)(

ej(ωin+ωm)t

j(ωin − ωr + ωm) + 1τ

+ej(ωin−ωm)t

j(ωin − ωr − ωm) + 1τ

). (3.24)

Using Eq. 3.5b and Eq. 3.24, we have:

St0 =Si0 − jµA0 +ejωmt

2(

jµδµ(µA0 + jSi0)

j(ωin − ωr + ωm) + 1τ

− jA0δµ)

+e−jωmt

2(

jµδµ(µA0 + jSi0)

j(ωin − ωr − ωm) + 1τ

− jA0δµ), (3.25)

From |St0|2, the phasor of the output power oscillating at the input frequency, Pout, can be

found:

Pout = St0B∗−ωm

+ S∗t0Bωm , (3.26)

where Bωm is the coefficient of eiωt/2 and B−ωm is the coefficient of e−iωt/2 in Eq. 3.25. By

substituting A0 and St0 from Eq. 3.6 and skipping algebra manipulations, Pout is found to be:

Pout =−2δµµ

∆ω2 + 1τ2

Pin[(∆ω2 +1

τ ′2)

jωm + 1τ

−ω2m + 2j

τ ωm +∆ω2 + 1τ2

+1

τ ′], (3.27)

where 1/τ ′ = 1/τl − 1/τe and Pin =∣∣S2

i

∣∣. The optical output of a coupling-modulated ring

resonator shown in Eq. 3.27 is somewhat similar to what was reported in [75]. However, in [75],

the approach was different from the method we used here. Also, loss modulation as well as

the electrical characteristic of the modulator were not considered. Therefore, the final transfer

function that will be presented below is more comprehensive.

To obtain Ht(ωm), δµ in Eq. 3.27 is replaced by Vin ×HE(ωm)×HEO, and Pout is divided

by Vin. From this, Ht(ωm) is found to be:

Ht(ωm) =−2κ0Pinvg

(∆ω2 + 1τ2)Lrt

1

τ ′(∂αm

∂v |VDC

αmκ0 −

πLM

λ

∂neff

∂v|VDC

t0)1

1 + jωmReqCeq×

((jωm + 2

τl)(jωm + τ ′∆ω2 + 1

τ )

−ω2m + 2j

τ ωm +∆ω2 + 1τ2

), (3.28)


In s-domain (jωm → s), the transfer function in Eq. (3.28) can be written as:

Ht(s) = GDC1

1 + s1

ReqCeq

[( sz1

+ 1)( sz2

+ 1)ω2n

s2 + 2ζωns+ ω2n

], (3.29)

where ωn =√∆ω2 + 1

τ2, ζ = 1/

√1 + (τ∆ω)2, and the DC gain, GDC = Ht(0), is:

GDC =−2κ0Pinvg

(∆ω2 + 1τ2)2Lrt

(∂αm

∂v |VDC

αmκ0 −

πLM

λ

∂neff

∂v|VDC

t0)2

τl(∆ω2 +

1

ττ ′). (3.30)

Based on small-signal transfer function in Eq. (3.29), for non-zero detuning, coupling-

modulated ring resonator has a complex-conjugate pole pair, a real pole, and two real zeros at

the following locations:

p1,2 = −1

τ± j∆ω,

p3 = − 1

ReqCeq,

z1 = − 2

τl,

z2 = −(τ ′∆ω2 +1

τ).

(3.31)

From Eq. 3.31, locations of p1,2 depend on the laser detuning. Location of z2 also varies

with laser detuning when ring resonator is under- or over-coupled whereas for critical coupling

condition z2 goes to infinity. Also, in addition to GDC in Eq. 3.30, none of the poles-zeros

locations in Eq. 3.31 depend on the sign of detuning, hence, the frequency response will be

symmetric with respect to detuning. Aside from p3 which models the electrical response of

the ring modular, the other poles and zeros are generated due to the optical response of the

modulator.

Coupling-modulated ring resonators are usually operated at zero detuning, i.e. ∆ω = 0. In

that condition, Eq. 3.28 will become:

Ht(ωm)|∆ω=0=−2κ0Pinvg

1τ2Lrt

1

τ ′(∂αm

∂v |VDC

αmκ0 −

πLM

λ

∂neff

∂v|VDC

t0)1

1 + jωmReqCeq(jωm + 2

τl

jωm + 1τ

),

(3.32)


where in s-domain (jωm → s) we have:

Ht(s)|∆ω=0= GDC|∆ω=0

1

1 + s1

ReqCeq

(sz1

+ 1sp′1

+ 1), (3.33)

which is a second order system with two real poles at −1/ReqCeq and p′1 = −1/τ and one real

zero at z1 = −2/τl. Also, GDC|∆ω=0is:

GDC|∆ω=0=

−2κ0PinvgLrt

(∂αm

∂v |VDC

αmκ0 −

πLM

λ

∂neff

∂v|VDC

t0)2τ3

τ ′τl. (3.34)

Neglecting (∂αm∂v

|VDC

αmκ0 − πLM

λ∂neff

∂v |VDCt0) in GDC|∆ω=0

and considering only the contribution

from the optical response of the ring resonator, normalized GDC|∆ω=0is plotted in Fig. 3.15.

Here, we assumed τl = 100ps. This figure suggests that the DC gain of the coupling-modulated

ring resonator optical response is highest when the ring is under-coupled and is zero at critical

coupling condition. This coupling condition dependent GDC will be more discussed in Chapter 5

where intensity modulation using this type of modulator is explained.

Figure 3.15: Normalized GDC|∆ω=0of the coupling-modulated ring resonator optical response

versus τe/τl.

To gain a better understanding of the ring response, pole-zero diagrams of Ht(s) are shown

in Fig. 3.16 for zero and non-zero laser detuning (∆ω) and also for under- and over-coupling

conditions. As shown in Fig. 3.16, the coupling condition determines the placement order of

pole-zero with respect to the imaginary axis. The effect of this will be clearly seen further in


this chapter.

Figure 3.16: Pole-zero diagrams of a coupling-modulated ring resonator for ∆ω = 0 and for∆ω 6= 0.

3.2.2 Simulation results

Assuming τl = 100ps and τe = τl/2, τe = 3τl, normalized Ht is simulated at ∆ω = 0 and

∆ω = 1.4/τ , and the results are shown in Fig. 3.17. The electrical bandwidth is considered

to be 200GHz to enable clear observation of the ring optical behavior (|1/ReqCeq| > |1/τ |).

Nevertheless, at critical coupling (τe = τl), there is no small-signal modulation response at ∆ω =

0, so we have only plotted normalized Ht for under- and over-coupled cases. An interesting

observation based on optical pole-zero locations for ∆ω = 0 shown in Fig. 3.16 is that in

the under-coupled ring, zero is located farther from the imaginary axis compared to the pole.

Therefore, in Fig. 3.17a the response falls and then becomes flat until modulation frequency

approaches the second pole at −1/ReqCeq. As shown in Fig. 3.17a this behavior is different for

the over-coupled ring as according to Fig. 3.16 zero is closer to imaginary axis than the pole.

Also, when ∆ω 6= 0, due to the formation of a complex pole pair (Eq. 3.28), a resonant peaking

may appear as presented in Fig. 3.17b.

According to Fig. 3.16, for both cases of ∆ω = 0 and ∆ω 6= 0 and also regardless of the

coupling condition, number of poles and zeros in optical response are equal. Hence, the small-


Figure 3.17: Small-signal response versus modulation frequency for coupling modulated-ring at(a) ∆ω = 0 and (b) ∆ω = 1.4/τ .

signal response of the coupling-modulated ring eventually becomes flat before the roll-off due

to the electrical-response related pole at −1/ReqCeq.

The high-pass filter effect observed based on large-signal response is not observed in small-

signal frequency response of the coupling-modulated ring. This is due to the fact that in

large-signal domain, the large variation in coupling coefficients leads to depletion of circulation

light inside the ring if the modulation is slower than the photon life time. It is shown that

this high-pass filter behavior can be removed by using DC-balanced coding [58] or by using

differential ring modulator [87].

3.3 Comparison and summary of results

For both intracavity and coupling-modulated ring resonators, the electrical characteristic was

modeled as a first-order low pass filter. Also, electro-optical transfer function HEO, which

describes the small-signal relation between low pass filtered voltage and resonance angular fre-

quency in intracavity modulation (IM) case and mutual coupling coefficient in coupling modu-


lation (CM) case, were derived. Equation 3.35 summarizes HEO for both IM and CM cases:

HEO,IM = (−ωr

ng

∂neff

∂v+ j

∂(1/τ)

∂v)

HEO,CM =

√vgLrt

(∂αM

∂v

αMκ0 −

πLM

λ

∂neff

∂vt0). (3.35)

In the dynamic small-signal domain, to characterize the optical response of the ring modulator

in either IM and CM cases, we used first-order perturbation theory and applied it to the

coupled mode equations shown in Eq. 3.5a and 3.5b. In case of IM, variation in the complex

resonance angular frequency ωr(t) and in case of CM, variation in mutual coupling coefficient

µ(t) modulates the output optical power. To summarize, Ht(s) in both cases of IM and CM

are shown here:

Ht(s),IM = GDC,IM1

1 + s1

ReqCeq

[(− s

z + 1)ω2n

s2 + 2ζωns+ ω2n

](3.36a)

Ht(s),CM = GDC,CM1

1 + s1

ReqCeq

[( sz1

+ 1)( sz2

+ 1)ω2n

s2 + 2ζωns+ ω2n

]. (3.36b)

Here, GDC,IM and GDC,CM are taken from Eq. 3.11 and Eq. 3.30, respectively. Unlike the IM-

ring, in CM-ring, location of zeros (Eq. 3.36b) and therefore the transfer function are symmetric

with regards to the detuning sign. On the other hand, in Section 3.1, we showed that detuning

sign affects the location of zero and therefore symmetry of the electro-optical response of the

intracavity ring modulator.

For comparison, pole-zero diagrams of IM and CM cases are summarized in Fig. 3.18 for

∆ω = 0 and ∆ω 6= 0. The preferred detuning is zero for CM-ring [53] and non-zero for

IM-ring [54, 75, 88]. As shown in Fig. 3.18a, for both CM-ring and IM-ring there are no small-

signal modulations at critical coupling condition at ∆ω = 0. In critically-coupled CM-ring,

at ∆ω 6= 0, z2 goes to infinity and z1 moves to −1/τ as shown in Fig. 3.16. Aside from

this specific case and neglecting the pole at −1/ReqCeq, for CM-ring, number of poles and

zeros are generally equal for ∆ω = 0 and ∆ω 6= 0. This explains the former observation

in [53] that the optical properties of the coupling modulated-ring resonator do not limit the

bandwidth. However, in IM-ring, number of poles are one more than number of zeros resulting


in a low pass filter behavior from ring modulator optical response, which eventually limits the

modulation bandwidth. Therefore, as demonstrated experimentally [58], modulation beyond

the ring modulator linewidth is possible if utilizing coupling modulation.

Figure 3.18: Pole-zero diagrams of a (a) coupling modulated (b) intracavity modulated ring.

3.4 Conclusion

In this chapter, closed-form formulae were presented for ring modulator small-signal responses.

From these small-signal transfer functions, locations of poles and zeros were obtained and were

shown to vary with parameters such as electrical bandwidth, coupling condition, optical loss,

and laser detuning.

For intracavity ring modulator, the derived model was experimentally verified for a sample

ring modulator. We showed that for non-zero detuning, transfer function of the intracavity ring

modulator is a third-order system with one real pole, one zero, and a pair of complex-conjugate


poles. Through such a model, we showed that the well-known asymmetric frequency response

of the intracavity ring modulator arises from the different zero locations. At various pole/zero

locations, GBW was calculated as a ring modulator performance metric, and an optimum laser

detuning was obtained based on maximum GBW. We also assessed the frequency response at

zero detuning and showed that it is coupling-condition dependent.

For coupling-modulated ring, the DC gain was shown to be coupling condition-dependent

where maximum DC gain was shown to occur for an under-coupled ring. At zero detuning,

the small-signal transfer function was shown to have two poles and one zero while at non-zero

detuning, it has three poles and two zeros. Based on locations of poles-zeros, it was concluded

that the response is symmetric with respect to the detuning sign.

Also, comparison between intracavity and coupling modulation cases based on pole-zero

diagrams showed that unlike the intracavity case, in coupling modulation case, optical behavior

does not limit the bandwidth as the number of poles and zeros in optical domain is equal.

Chapter 4

Intracavity ring modulator design

trade-offs

One of the main design parameters of the ring modulator is bandwidth which is partially af-

fected by the design of the doped waveguide. Several studies are done to optimize the waveguide

geometry and doping profile of a pn doped waveguide [11,12,17,25,42,50,51]. A cross section of

doped waveguide is shown in Fig. 4.1. It was shown that electrical bandwidth of the depletion-

mode waveguide can be increased using the following methods: higher dopant concentration

for p and n to reduce series resistance, higher reverse bias voltage to decrease junction capaci-

tance [51], higher ratio of slab thickness to rib height, or smaller distance between highly doped

region, p++/n++, and the edge of the waveguide (d++) to decrease series resistance [25, 49].

Figure 4.1: Doped waveguide cross section.

61

Chapter 4. Intracavity ring modulator design trade-offs 62

4.1 Motivation of studying rib-to-contact distance

There are multiple trade-offs associated with each of the above-mentioned methods. Increasing

the dopant concentration not only increases the optical loss but also increases the junction

capacitance and therefore careful design of concentration is required for electrical bandwidth

improvement. Moreover, the available doping levels are limited to certain levels in each foundry.

Also, higher bias voltages and higher ratio of slab thickness to rib height would result in a lower

modulation efficiency. It was theoretically predicted that one optimum way to increase band-

width without sacrificing modulation efficiency is reducing the series resistance by decreasing

d++ in reverse-biased pn diode waveguide [49]. Although, too much reduction of d++ results

in the increase of the optical loss [49, 89] due to optical mode lateral extension to the highly

doped region [12] as well as the carrier diffusion to the waveguide. This additional loss is ex-

perimentally studied in IME A*Star process for a certain waveguide geometry [12]. However,

the quantitative influences of decreasing d++ on loss and bandwidth of the ring modulator are

little discussed. The main goal in many of the above studies were to optimize Mach-Zehnder

modulators (MZM) bandwidth and modulation efficiency and the results may not be applicable

for ring modulators. This is due to the more complex nature of the resonance in the ring mod-

ulator which couples optimization of optical and electrical parameters. As both cavity photon

life time and electrical bandwidth of the carrier-depletion ring modulator are affected by d++,

it is important to systematically study design trade-offs.

To accurately calculate the ring modulator bandwidth (f3dB), small-signal modeling has

been used, where in addition to optical (fQ) and electrical (fRC) bandwidths, carrier wavelength

and coupling condition are also considered [53–55, 77, 78, 90]. In Section 3.1 of this thesis, we

reported a closed-form frequency response model of a carrier-depletion ring modulators and

showed that for a non-zero detuning, small-signal electro-optical transfer function is a third-

order system with one real pole, one zero, and a pair of complex-conjugate poles. This model

was verified by comparing to the measurement results of a typical ring modulator in SOI process.

We will use this model in this work together with the measurements to better understand the

ring modulator performance.

In this chapter, we study the effects of decreasing d++ on the reverse-biased ring modulator


performance. Four groups of reverse-biased ring modulators with different values of d++ and

coupling gaps are studied. The key performance parameters such as extinction ratio, modulator

penalties, insertion loss, and ring modulator electrical and optical bandwidth were compared

at various d++ based on measurement and simulation results. Frequency response of the ring

modulator is simulated based on our model presented in Section 3.1 of this thesis to provide

additional insight into the frequency response trade-offs. Also, the rate of increase in bandwidth

gained at the price of decrease in DC gain are calculated based on the electro-optical frequency

response and compared across ring modulators with various d++. We show that d++ can also

be used as a tuning factor in changing the amount of trade-off between the frequency response

DC gain and bandwidth. Finally, performance of each of these ring modulators is compared

according to the device bandwidth, extinction ratio (ER) and insertion loss (IL).

4.2 Device description

To quantitatively assess the effects of d++ on the ring modulator performance, we characterize

all-pass ring modulators fabricated in IME A*Star process [83]. An optical microscope image

of the fabricated device and a cross-section of the ring modulator doped waveguide are shown

in Fig. 4.5. Ring modulators are fabricated on a Silicon on Insulator (SOI) wafer with top Si

layer of 220nm and 2µm thick buried oxide layer. The rib waveguide slab thickness is 90nm.

The doping concentration for low-doped region is 3× 1017cm−3 for n and 5× 1017cm−3 for p,

and for high-doped contact region is 1020cm−3. The doped section is taking 75% of the ring

circumference excluding coupling region. As shown in Fig. 4.5, pn junction has 50nm offset from

the waveguide center. As discussed in Chapter 2, holes induce more refractive index change and

less loss and therefore offsetting the pn junction with respect to the waveguide center could be

beneficial. The effective index change, ∆neff , and loss due to the pn doped region are simulated

and plotted in Fig. 4.2 for pn offsets of 0, 50nm, and 100nm. Based on this result which does

not include the process simulation, 100nm offset is slightly more efficient than 50nm offset while

the improvement of 50nm offset compared to 0nm offset is more significant. To consider the

effect of the process, using Sentaurus process and Sentaurus device simulator, the pn junction

carrier concentration is simulated when pn offset is 0nm and the results are shown in Fig. 4.3.


Figure 4.2: (a) Effective refractive index change with respect to 0V versus bias voltage. (b)Loss of pn doped region versus bias voltage.

According to the figure, for this process, the pn junction will not be located at the center of

the waveguide even at 0nm pn offset. Therefore, 50nm was selected instead of 100nm to avoid

moving the pn junction close to the edge of the waveguide where the optical mode is weak.

Figure 4.3: Carrier concentration under reverse bias voltage.

Twenty ring modulators in total are fabricated with various distances of highly doped region

to the edge of the waveguide, d++. The chip layout is shown in Fig. 4.4 where these twenty

rings are illustrated with dashed red boxes. Also shown is the microscope image of two of the

rings as an example. These include four groups of ring modulators with d++ of 200nm, 350nm,

550nm, and 800nm. In each group, gap between the ring modulator and the bus waveguide


ranges from 200nm to 400nm with a step of 50nm to enable finding the ring modulator at or

close to critical coupling condition. Radius and waveguide width of all the rings are 10µm and

500nm, respectively.

Figure 4.4: Chip layout with tested ring modulators indicated in the red dashed boxes togetherwith the microscope image.

4.3 DC performance measurement and analysis

In order to identify ring modulators closest to the critical coupling condition in each group, static

power transmission of all 20 ring modulators are measured when no DC voltage is applied. For

each group of ring modulators, the notch depths of power transmission spectra are measured and

plotted versus gap in Fig. 4.6a where data points are indicated with markers. The trend of rising

and falling in the notch depth indicates a transition in the coupling condition. For example,

for d++ of 350nm and 550nm, it is clear that ring modulators before and after maximum

notch depth are in different coupling conditions. Amplitude decay time constant due to ring-

to-bus waveguide coupling (τe) increases when the gap gets wider, whereas the other part of

the amplitude decay time constant arising from the intrinsic loss inside the cavity (τl) stays

constant. As such, ring modulators with d++ of 350nm and 550nm can be classified in terms

of coupling condition. However, modulators with the maximum notch depth needs optical

parameters extraction to verify coupling condition. Knowing that τl increases by increasing d++,


Figure 4.5: Ring modulator optical microscope image and waveguide cross-section.

coupling conditions of the ring modulators with d++ of 200nm and 800nm are also determined.

Figure 4.6b shows color-coded coupling conditions for each group of d++ where the over-coupled

and under-coupled rings are shown in orange and blue, respectively. Also, data points are shown

in cross markers. The boundary between under and over coupling conditions are shown with

shaded colors as it is uncertain due to resolution limitation of the gap tested here. According

to Fig. 4.6b, critical coupling condition is not reached for d++ = 200nm as loss is high and gap

smaller than 200nm is required. In the other three groups of d++, the closest ring modulators to

critical coupling condition are selected for further analysis. In this study, it is important to pick

the rings close to the critical coupling conditions as coupling condition status (i.e. deep under-

or over-coupling) changes dynamic response of the ring modulator [54,88,91]. Selected rings are

indicated with circles in Fig. 4.6b and are Ring B with d++ = 350nm and gap = 250nm, Ring

C with d++ = 550nm and gap = 350nm, and Ring D with d++ = 800nm and gap = 400nm.

In some comparison notes, for example ring loss, ring modulator with d++ = 200nm and

gap = 200nm called Ring A, is also included.

Transmission spectra at through ports are measured using the measurement setup shown

in Fig. 4.7a. The microscope image of the chip under test is shown in Fig. 4.7b. Transmission

spectra at through ports of the ring modulators A to D under reverse biased condition are also

shown in Fig. 4.8a to 4.8d, respectively. For Ring A due to the large quality factor, only the

results for 0V and -4V are shown, while for Rings B-D the results for 0V to -6V are plotted.

Notch-depth variation by increasing applied bias voltage indicates the coupling condition of


Figure 4.6: (a) Notch depth versus gap. (b) Color-coded figure showing coupling conditions ofthe tested ring modulators.

under-, under-, over-, and over-coupled for Ring A to D, respectively. Resonance wavelength

shift of about 7-8pm/V is observed. In this work, the aim was not to optimize modulation

efficiency as the available doping concentrations were limited and low. Efficiency of 24pm/V

could be achieved with about 10× higher concentration [11].

Optical parameters of the ring modulators are extracted by fitting the measured data to the

ring static transmission formula [92]. Table 4.1 summarizes the key optical parameters of τl,

τe, τ , cavity linewidth, Q, and coupling condition for Ring B to D at -1V bias voltage. Here, τ

is the electric field amplitude decay time constant and 1/τ = 1/τe + 1/τl. The parameters for

Ring A at 0V is also added in this table for comparison. Group index, ng, was extracted to be

3.86.

Table 4.1: Extracted optical parameters from the measured transmission spectra.Ring d++(nm) τl(ps) τe(ps) τ(ps) Linewidth(pm) Q Coupling Condition

Ring A,@ 0V 200 3.4 9.6 2.5 742.2 2,084 Deep under-coupled

Ring B,@ -1V 350 14.7 17.7 8 314.4 4,971 Slightly under-coupled

Ring C,@ -1V 550 71.2 59.1 32.3 77.4 20,068 Slightly over-coupled

Ring D,@ -1V 800 124 101.5 55.8 44.8 34,627 Slightly over-coupled

According to the table, by decreasing d++ from 800nm in Ring D to 200nm in Ring A,

τl decreases about 36× due to increase in optical losses. Decreasing d++ also lowers the ring


Figure 4.7: (a) Measurement setup of the ring modulator. (b) Chip under test.

quality factor which leads to a higher optical bandwidth. However, decreasing d++ too much

(i.e. 200nm) results in the impractical device due to very low quality factor (Q = 2, 084 in Ring

A).

From measured transmission spectra shown in Fig. 4.8a to 4.8d, τl as a function of voltage

is extracted and shown in Fig. 4.9a with circles for all four rings. Also shown is the quadratic

fit in solid line. Variation in τe over voltage is insignificant, as the coupling region is not doped.

From the extracted voltage-dependent τl, power loss coefficient in 1/m is calculated as [82]

α =2

vgτl, (4.1)

where vg is the group velocity. Based on this, additional optical loss with respect to d++ =

800nm is plotted in Fig. 4.9b. This additional loss is resulted by lateral mode expansion to

the high-doped region. According to Fig. 4.9b, additional loss rises rapidly with decreasing

d++ where, for example at d++ = 550nm the additional loss of 6.6dB/cm increases to over

300dB/cm at d++ = 200nm. The increase of loss by decreasing d++ depends on the lateral

confinement set by waveguide geometry such as the ratio of rib height to the slab thickness [12].

Refractive index change with respect to 0V, ∆neff , as a function of voltage was also de-

termined and plotted (Fig. 4.9c) for Rings B-D based on the ∆neff =ng∆λr

Fλrwhere ∆λr/λr


Figure 4.8: Measured optical power transmission spectra at various bias voltages for (a) RingA with d++ = 200nm, (b) Ring B with d++ = 350nm, (c) Ring C with d++ = 550nm, (d) RingD with d++ = 800nm.

is the normalized resonance shift and F is the ratio of pn junction length to the ring circum-

ference [17]. As expected, changing d++ does not alter modulation efficiency. Small changes

observed in this figure may arise due to the process variations from one ring to another.

In order to evaluate ring modulator performance based on the DC characteristics of the

tested devices, static ER and IL are calculated from transmission spectra shown in Fig. 4.8b

to 4.8c, for Rings B-D assuming voltage swing from 0V to 3V. Figure 4.10a and b show ER

and IL plots versus relative input wavelength to the resonance wavelength at 0V, respectively.

Although all three rings are close to critically coupled, due to the lower quality factor of Ring B,

the maximum achievable ER with 3V applied voltage is much smaller than Rings C and D, as

shown in Fig 4.10a. Also, due to the lower slope in the transmission spectra (wider transmission

spectrum), the rate of change in ER value versus relative wavelength is smaller when d++ is

smaller. Also, the corresponding IL in Fig. 4.10b is higher for smaller d++.

Another metric to evaluate the ring modulator performance is transmission penalty [93]

defined as Tp = −10log(P1−P0

2Pin) where P1 (P0) is transmitted power at bit 1 (bit 0) and Pin


Figure 4.9: (a) Extracted τl shown with markers for Ring A-D with d++ from 200nm to 800nmtogether with the fitted curves shown with solid lines. (b) Extracted additional loss as a functionof d++.(c) Extracted ∆neff versus voltage for Ring A-D with d++ from 200nm to 800nm.

is the input power. Transmission penalties for Ring B to D are shown in Fig. 4.10c where

the minimum TP for Ring B and D are 14.8dB and 5.8dB, respectively. This means that the

amount of optical modulation amplitude with respect to the input power decreases significantly

when d++ is smaller. However, when a higher bandwidth is required, the relative wavelength

should increase which will result in a rapid increase in TP for Rings C and D. The bandwidth

dependency over working wavelength will be discussed in further details later in the chapter.

In Fig. 4.11a and b, maximum ER (ERmax) and the corresponding IL as a function of

applied voltage with respect to 0V (∆V ) are shown for Rings B-D. According to this, from 0V

to 6V, ERmax increases from 1.6dB, 5.8dB, and 12dB to 8.8dB,17.8dB, and 20dB for Rings


Figure 4.10: (a) Extinction ratio, (b) insertion loss, and (c) transmission penalty for voltageswing from 0 to 3V.

B-D, respectively. Also, from 0V to 6V, corresponding IL decreases from 17.4dB, 15dB, and

9.2dB to 12.4dB, 3.8dB, and 1.4dB for Rings B-D, respectively.

All these parameters are essential in designing functional ring modulator as will be discussed

later in the discussion section.

4.4 Small-signal characteristics from measurement and simula-

tion

The electrical response of the ring modulator at small-signal is modeled by the equivalent circuit

shown in Fig. 4.12 [11]. Here, Cpad, Cj , and Cox are the capacitance between the pads, the

capacitance of the reverse-biased pn junction, and the capacitance through the oxide layer,

respectively. Also, Rsj and RSi are the series resistance of the pn junction and the resistance

of the Si substrate. The electrical circuit elements are extracted by fitting the simulated S11

coefficients of the equivalent circuit to the measured S11 magnitude and phase. Measured


Figure 4.11: (a) Measured maximum ER and (b) corresponding IL versus applied voltage.

phase and magnitude of S11 for Ring D at -1V bias voltage are shown in Fig. 4.13a and 4.13b,

respectively. Also shown in dashed lines, the simulated S11 by ADS assuming 50Ω source

resistor. The extracted circuit elements are Cox = 10fF , RSi = 30kΩ, Cpad = 2fF , Cj = 12fF ,

and Rsj = 208Ω. S11 for Ring B and C are also measured, but for the brevity the figures are

not presented here. The circuit elements which varies by changing d++ is Rsj . Other extracted

circuit components stayed almost similar. The value of Rsj for Rings B and C are extracted

to be 125Ω and 154Ω, respectively. Considering 50Ω source impedance, fRC for Rings B-D are

computed at -1V to be 75GHz, 59GHz, and 51GHz which are 2×, 6×, and 9× larger than their

fQ, respectively.

Figure 4.12: Small-signal circuit model of a ring modulator.


Figure 4.13: Measured and simulated electrical S11 (a) magnitude (b) phase of Ring D withd++ = 800nm.

In order to simulate frequency response of the ring modulators, our model presented in

Section 3.1 of this thesis is used. From fitted curves to τl versus voltage shown in Fig 4.9a,

∂(1/τ)∂v |VDC

are calculated to be −4.4× 108 1/s/V , −2.4× 108 1/s/V , and −2.6× 108 1/s/V for

Rings B-D, respectively when VDC = −1V . Moreover, from fitted quadratic curves to ∆neff as

a function of voltage in Fig. 4.9c,∂neff

∂v |VDCare calculated to be 1.88×10−5 1/V , 1.95×10−5 1/V ,

and 2.38 × 10−5 1/V for Rings B-D, respectively. Using electrical circuit model of the ring

modulators together with optical parameters listed above, small-signal electro/optical response

of Rings B-D at various laser wavelength detunings with respect to resonance wavelength (∆λ)

are simulated. The results of this simulation at several negative and positive detunings are

shown with lines in Fig. 4.15a and 4.15b for Ring B, Fig. 4.15c and 4.15d for Ring C, and

Fig. 4.15e and 4.15f for Ring D. Each curve is normalized to its value at 200MHz.

Frequency response of the ring modulators are measured by a 20GHz lightwave component

analyzer (Agilent 8703A) under -1V bias voltage through the full spectrum range of interest.

Schematic of the test bench is shown in Fig. 4.14. The RF signal was fed to the device using


high speed SG probe. All the RF components such as cables, connectors, RF probe, and bias

tee were de-embedded from the frequency response. Tunable laser source was coupled to the

devices by fiber grating coupler. The temperature of the stage was kept constant at 25C. In

order to perform an error-free measurement of small-signal frequency response at both positive

and negative detuning, either the output power should be low to avoid self-heating effect or

keep the laser output power high and calibrate the measured results to remove the self-heating

effect [55]. The output power of the laser was at -7dBm and -10dBm for Ring C and D in order

to avoid self-heating. For Ring C, due to higher intrinsic loss, smaller slope of the spectrum,

and sensitivity limitation of the optical receiver, the measurement results at low input power

were noisy. Therefore, we measured the small-signal response of the ring at 6dBm input power

and we used the method presented in [55] to remove the effect of the self-heating by mapping

the measured detuning to real detuning.

Figure 4.14: Schematic of the test bench used for small-signal electro-optical measurement.

The measured electro/optical response (markers) are also added to the simulation results

(solid lines) shown in Fig. 4.15a to 4.15d. For all three rings at both negative and positive

detunings, the measured data are in good agreement with the simulation results. The expected

input wavelength-dependent frequency response of the ring modulators [53–56,88] can be seen

from both measurement and simulation results. The difference between frequency response at

positive and negative detuning is a result of loss modulation when modulating index of the

ring resonator [55, 88]. Comparing E/O responses of these three rings, the 3dB bandwidth


Figure 4.15: Normalized simulated (line) and measured (marker) electro/optical response ofRing B with d++ = 350nm at (a) negative and (b) positive detunings, Ring C with d++ =550nm at (c) negative and (d) positive detunings, and Ring D with d++ = 800nm at (e)negative and (f) positive detunings. Here, fm is modulation frequency.

improvements by decreasing d++ is clear.

To better quantize the improvement in the device bandwidth, f3dB of rings with various

d++ versus normalized detuning are calculated based on the small-signal E/O measurements


and simulations. Figure 4.16a shows the simulated f3dB as a function of ∆ωτ . Measured f3dB

are also added for Ring C and D in markers but as the minimum bandwidth of Ring B was close

to the bandwidth of the lightwave component analyzer, accurate bandwidth measurement was

not possible. Comparing these three rings, the 3dB bandwidth improvements by decreasing

d++ is obvious. Based on Fig. 4.16a, the minimum bandwidth increases from 2.8GHz in Ring

D to 17.2GHz in Ring B.

As shown previously [54,55,88], by increasing detuning, the bandwidth will increase mono-

tonically while the DC gain will only rise until a certain detuning (i.e. ∆ω = 1/(√3τ) when

neglecting the loss modulation) where DC gain is maximized. Beyond this detuning, DC gain

will decrease whereas bandwidth increases due to the peak generation in the frequency response

at high frequencies. The amount of penalty in DC gain caused by varying the laser detuning

is defined as GDC divided by its maximum value achieved among all the detunings [54]. This

could be used as a metric to evaluate the amount of reduction in frequency response value at low

frequencies with respect to the maximum GDC among all detunings. Figure 4.16b shows the

simulated penalty in GDC versus ∆ωτ in solid line for Ring C. Neglecting the loss modulation,

GDC penalty is only proportional to ∆ωτ[∆ω2τ2+1]2

[54, 88]. Here, GDC penalty versus normalized

frequency detuning (ωτ) are similar for all three rings even when considering loss modulation

as τl/τe for three rings is close to 1 [88]. Hence, only results for Ring C are shown. From the

measured E/O responses shown in Fig. 4.15c and 4.15d at 200MHz, GDC penalty is calculated

and shown with markers in Fig. 4.16b which follows the same trend expected from simulation

result.

In Section 3.1 of this thesis, we showed that for a non-zero detuning, the ring modulator

small-signal electro-optical response has one real pole, one zero, and a pair of complex-conjugate

poles. We also showed that the trade-off efficiency between f3dB and GDC penalty rises to a

limit when increasing the electrical bandwidth. We assumed that electrical bandwidth only

affects the location of the real pole and does not change the locations of zero and complex-

conjugate poles. Here, increasing fRC is done through decreasing d++ which also alters the

optical behavior of the ring modulators. To make this more clear, pole-zero diagrams of Rings

B-D are shown in Fig. 4.17. In this figure, 1/(ReqXCeqX) (X = B,C, and D) shows the

pole representing the electrical behavior of the ring modulator while a complex pole located


Figure 4.16: Simulated (line) and measured (marker) (a) bandwidth of tested ring modulators(b) DC gain penalty of Ring C with d++ = 550nm versus ∆ωτ .

at −1/τX ± j∆ωX and a real zero show the optical behavior of the ring modulator. Location

of zero with respect to a complex pole pair depends on the coupling condition [88]. As shown

in Fig. 4.17, all the pole and zero locations are affected by d++. As the quality factor and

therefore τ is different in the three rings studied here, throughout the chapter, we compared

ring modulators response at similar normalized detunings (similar ∆ωτ). This is indicated as

a dashed line in Fig. 4.17 along which the damping factor (ζ = 1/√1 + (τ∆ω)2) is similar in

Rings B-D while the natural frequency (ωn =√

∆ω2 + 1τ2) of Ring B is higher than Ring C

and D.

To study and compare the aforementioned trade-off efficiency, simulated f3dB are plotted

versus GDC penalty in Fig. 4.18a for positive ∆ω. According to this figure, smaller d++ not

only results in a higher bandwidth but also it results in a more efficient trade-off between GDC

penalty and f3dB. Consequently, d++ is shown to be a design parameter in tuning the efficiency

of the bandwidth and low frequency eye opening of the ring modulators.

The gain-bandwidth product (GBW ), defined as GDC × f3dB, for these three rings are


Figure 4.17: Pole-zero diagrams of Rings B-D.

plotted in Fig. 4.18b. This shows that, although Ring D has the lowest bandwidth, the GBW

of Ring D is the highest compared to the other two rings due to its steeper transmission spectra.

Figure 4.18: Simulated (a) f3dB versus DC gain penalty and (b) GBW versus ∆ωτ at -1Vbias voltage for Ring B, C, and D with d++ = 350nm, d++ = 550nm, and d++ = 800nm,respectively.

Table 4.2 summarizes the comparison between Ring B, C, and D in terms of fQ, fRC , f3dB,

maximum GBW , and trade-off efficiency between f3dB and GDC penalty. The latter is defined

as the slope of a fitted line to plots shown in Fig. 4.18a. As shown in this table, in terms of


the bandwidth, Ring B with the smallest d++ among all the rings, has both higher optical,

electrical, and consequently total bandwidth. Also, it has the most efficient trade-off between

bandwidth and DC gain. However, Ring D with largest d++ has the highest GBW.

Table 4.2: Summary of bandwidth, GBW, and f3dB-GDC penalty trade-off efficiency.

Ring d++(nm) fQ(GHz) fRC(GHz) f3dB(GHz) @ GBWmax GBWmax

f3dB-GDC penaltytrade-off efficiency

Ring B 350 39.6 75 44.9 1.1×106 5

Ring C 550 9.8 58 15.7 1.5×106 2

Ring D 800 5.7 51 10.5 1.8×106 1.3

4.5 Discussions

As shown above, d++ not only changes the optical behavior of the device but also impacts

the electrical characteristics of the ring modulators. In order to assess the ring modulator

performance, other metrics such as ER and IL should be taken into account in addition to the

small-signal frequency response. Although the static ER of the ring modulator may degrade

when driven at high frequency, it could still be used as a parameter to compare different ring

modulator efficiencies.

As shown in Fig. 4.11a, decreasing d++ decreases the maximum achievable ER over various

applied voltages. At the same time, according to Fig. 4.11b, this increases IL. On the other

hand, based on Fig. 4.15a to 4.15d and 4.16a, the bandwidth of the ring modulator increases

significantly by decreasing d++. The three metrics of ER, IL, and f3dB are dependent on laser

frequency detuning. According to Fig. 4.10a, increasing laser detuning beyond the detuning

corresponding to maximum ER, results in decreasing ER while based on Fig. 4.16a, it leads

to increase in f3dB. Hence, there will be a trade-off between ER and f3dB over laser detun-

ing. Another important parameter is applied voltage which determines ER and IL (Fig. 4.11a

and 4.11b).

In order to see these relations between ER and IL with f3dB more clearly, Fig. 4.19a and

4.19b, plot the ER and IL obtained from measured transmission spectra with voltage varying

between 0-4V as a function of f3dB computed at 0V. Here, we considered positive frequency

detunings. According to Fig. 4.19a, ER above 5.7dB is not achievable for Ring B. Also, con-


sidering ER above 4dB, the maximum f3dB achievable for Ring B, C, and D are 22.1GHz,

8.2GHz, and 5.8GHz, respectively. The minimum IL corresponding to these maximum f3dB

from Fig. 4.19b are 9.4dB, 2.5dB, and 1dB for Ring B, C, and D, respectively. These values

are summarized in table 4.3. At 4V applied voltage, to achieve 4dB ER, the bandwidth can

increase by 3.8× by decreasing d++ from 800nm to 350nm but at the price of 8.4dB extra IL.

Figure 4.19: (a) Extinction ratio and (b) IL versus f3dB for Ring B, C, and D with d++ = 350nm,d++ = 550nm, and d++ = 800nm, respectively.

Table 4.3: Comparison between ring modulators in terms of ER, IL, and f3dB at 4V appliedvoltage.

Ring d++(nm) ER(dB) IL(dB) f3dB(GHz)

Ring B 350 4 9.4 22.1

Ring C 550 4 2.5 8.2

Ring D 800 4 1 5.8

Figure 4.20a and 4.20b show f3dB and IL versus d++ for targeted ER = 4dB and ER = 5dB,

respectively, at 4V applied voltage. The rate of change over d++ is different for f3dB and IL. At

ER = 4dB, decreasing d++ from 350nm to 550nm and from 550nm to 800nm, f3dB decreases

0.37× and 0.7×, respectively, while IL decreases around 0.49×, in linear scales, for both cases.


Figure 4.20: Bandwidth and IL versus d++ for (a) ER = 4dB and (b) ER = 5dB at 4V appliedvoltage.

These rates of changes are similar when ER = 5dB. In this study, we selected wide range

of d++ values to observe the trend of variation in parameters such as loss, IL, fRC , fQ, and

f3dB. Based on this study, exponential increase in loss by decreasing d++ (Fig. 4.9b) results

in the photon life time, τl, playing the main role in improvement of bandwidth than electrical

bandwidth for small values of d++ (350nm and 200nm). This has a disadvantage of an increase

in IL. If IL needs to be kept in the certain range, then based on the trend of variation in τl and

Rsj given here, d++ can be selected accordingly. In other words, selecting the right value for

d++ depends on the link power budget, required bandwidth, available peak-to-peak voltage at

the driver, and required ER where here we quantify the amount of variation in these parameters.

Also, note that since free carrier absorption of electrons and holes are different [35] and also

due to the fact that the doping in the outer side of the ring modulator has longer interaction

length with optical mode than the doping in an inner side, the doped waveguide propagation

loss will be also asymmetric. Here we considered symmetric positioning of the high doped

regions as it is the most common configuration. However, d++ could be asymmetric in order


to add an extra handle for further optimization of the ring modulator performance, it could be

helpful to decrease the insertion loss while maintaining the same value of electrical bandwidth.

4.6 Summary

We performed simulations and DC and small-signal measurements of the reverse-biased ring

modulators fabricated in IME A*Star process with various high-doped region locations. The

model for small-signal frequency response of the ring modulator presented in Chapter 3 was

used to provide further insight into the device design and optimization. Based on the DC

and AC characteristics of the devices, we assessed optical and electrical properties of the ring

modulators based on the location of the high-doped region. Parameters such as additional

loss, ER, IL, TP, and optical and electrical bandwidths were compared among various ring

modulators.

Chapter 5


for intensity modulation

In Section 3.2 of this thesis, small-signal transfer functions of the intracavity and the coupling-

modulated ring resonators were compared based on the pole-zero representation. It was shown

that the optical response of the intracavity ring modulator has one more pole than zeros and

hence, it has a low pass filtering effect in its optical response. Therefore, the bandwidth of

the intracavity ring modulator is limited not only by its electrical bandwidth but also by

its cavity linewidth. In contrast, it was shown that the coupling-modulated ring resonator

optical response has the same number of poles and zeros and consequently, the bandwidth could

extend well beyond the cavity linewidth. As discussed in Chapter 2, coupling-modulated ring

resonator utilizing MZI as a coupler, also known as MZI-assisted ring modulator (MZIARM),

takes advantage of the resonance enhancement. Therefore, such a devices has a smaller size

and requires lower driving voltage compared with an MZM.

In this chapter, application of MZIARM at various modulation schemes will be discussed.

We will first discuss the MZIARM concept and model for on-off keying (OOK) intensity mod-

ulation. Then, the idea of multi-level intensity modulation using MZIARM will be proposed

and discussed in detail.

83

Chapter 5. Coupling-modulated ring resonator for intensity modulation 84

5.1 On-off keying (OOK)

Structure of an MZIARM is shown in Fig. 5.1. As shown, the MZM is utilized as a coupler

to couple light from the bus waveguide to the ring resonator and vice versa. The MZM arms

include an RF section which is doped to modulate the phase accumulation of the propagating

light and a DC section which is dedicated to thermally bias the phase difference between two

arms. By modulating the phase difference, the cross and through coupling coefficients will be

modulated. This would lead to intensity modulation at the output of the MZIARM.

Figure 5.1: Schematic of the OOK modulator using MZIARM.

5.1.1 Modeling of MZIARM

In order to model an MZIARM, we used the transfer matrix of each section in MZM together

with a resonator circulation formula. The transfer matrix of MZM is essentially the coupling

matrix to the ring resonator. The coupling matrix includes the transfer matrix of the first

coupler, the transfer matrix of propagation in the arms, and the transfer matrix of the second

coupler as illustrated in Fig. 5.2. Here, we assume directional coupler as splitter and combiner

in the MZI. Transfer matrix of the directional coupler is:

Tcoupler =

σ iγ

iγ σ

, (5.1)


where σ is the through coupling coefficient and γ is the cross coupling coefficient. The propa-

gation matrix through RF and DC sections can be written as:

TPropagation =

a1e−iφ1 0

0 a2e−iφ2

, (5.2)

where a1 (a2) and φ1 (φ2) are the transmissivity and phase accumulation in top (bottom) arm

of the MZM. In addition to the propagation loss caused by the passive waveguide and active

doped sections, loss from the coupler and other source of constant losses could be included in

a1 and a2.

Figure 5.2: Transfer matrix formulation of MZIARM.

Based on this transfer matrix formulation, the output electric field of B and C shown in

Fig. 5.2 are related to the input electric field of A and D via coupling matrix, M:

B

C

=

M11 M12

M21 M22

A

D

. (5.3)

The coupling matrix which is the transfer matrix of the MZM is:

M = Tcoupler2TPropagationTcoupler1. Assuming that the two directional couplers are identical,

the coupling matrix will be:

M11 M12

M21 M22

= e−i

φ1+φ22

a1σ2e−i∆φ

2 − a2γ2ei

∆φ2 iσγ(a1e

−i∆φ2 + a2e

i∆φ2 )

iσγ(a1e−i∆φ

2 + a2ei∆φ

2 ) a2σ2ei

∆φ2 − a1γ

2e−i∆φ2

, (5.4)

where ∆φ is φ1 − φ2.

The feedback from the ring resonator relates the output electric field, C, to input electric


field, D, via D = C×ae−iθ. Here, a is the field transmissivity of the ring resonator and θ is the

round trip phase accumulation. Using this and coupling matrix in Eq. 5.4, ratio of the output

electric field to input electric field is found from B/A to be:

B

A=

M11 − |M | ae−iθ

1−M22ae−iθ. (5.5)

In Eq. 5.5, |M | is the determinant of matrix M.

In the ideal case of 3-dB directional couplers and assuming a1 = a2 = aarm, the coupling

matrix in Eq. 5.4 becomes:

M11 M12

M21 M22

= e−i

φ1+φ22

−iaarm sin(∆φ2 ) iaarm cos(∆φ

2 )

iaarm cos(∆φ2 ) iaarm sin(∆φ

2 )

, (5.6)

In this case, B/A shown in Eq. 5.5 can be re-written as:

B

A= e−i

φ1+φ22

t− a2armae−iθ′

1− t∗ae−iθ′, (5.7)

where t = −iaarm sin(∆φ/2) is the through coupling coefficient between ring and bus waveguide.

Also, cross coupling coefficient, κ, is equal to iaarm cos(∆φ/2) and we have: κ2 + t2 = a2arm.

Moreover, in Eq. 5.7, θ′ is θ + (φ1 + φ2)/2. The transfer function of MZIARM, TMZIARM , can

be found from |B/A|2 to be:

TMZIARM =|t|2 − 2a2arma |t| cos(θ′) + a4arma2

1− 2a |t| cos(θ′) + |t|2 a2. (5.8)

On resonance, we have θ′ = 2mπ, m an integer, where Eq. 5.8 becomes:

TMZIARMres = (|t| − a2arma

1− |t| a )2. (5.9)


5.1.2 Operation principles and simulation results

The phase difference between MZM arms, ∆φ, includes a DC part, φ0, and a time-varying

phase accumulation, ∆φ′. Hence the coupling coefficients can be written as:

t = −iaarm sin(φ0 +∆φ′(t)

2),

κ = iaarm cos(φ0 +∆φ′(t)

2). (5.10)

From this, it can be clearly seen that by modulating ∆φ′ around the bias point at φ0, the

coupling coefficients are modulated. According to Eq. 5.9, the output power on resonance

varies between on-off states by modulating t through ∆φ′ variation. Theoretical zero output

power occurs when |t| = aarm sin(∆φ/2) = a2arma that corresponds to the critical coupling

condition. Also, the maximum output occurs when ∆φ = π, which in Eq. 5.9 will result in:

TMZIARMres = a2arm

∣∣∣∣1− aarma

1− aarma

∣∣∣∣2

= a2arm, (5.11)

which shows that the maximum power transmission will be a2arm. The required phase modula-

tion in OOK based on MZI is π while for MZIARM is π− 2 arcsin(aarma). The closer aarma to

1, the more efficient the OOK modulation with MZIARM will be.

Assuming aarm = 1 and a = 0.99, the on-resonance transmission versus ∆φ/π is shown

in Fig. 5.3. For comparison, the transmission of MZI is also shown. Critical, under, and

over coupling conditions are marked in the MZIARM transmission. In case of aarm = 1,

the distance between critical coupling to π is set by a, which basically sets the efficiency of

MZIARM compared with MZI. To make this more clear, the on-resonance transmission is

plotted and shown in Fig. 5.4 for various values of a. The transmission of MZI is also added for

comparison. When a = 0, the feedback from output of MZI to the input of MZI is broken and

therefore the MZIARM will be similar to an MZI. According to Fig. 5.4, as the amount of the

feedback transmissivity increases, ∆φ corresponding to critical coupling condition, ∆φcritical

indicated with diamonds in the figure, moves closer to the peak location. This results in a

smaller required ∆φ for on-off switching. The value of ∆φcritical/π needed for power modulation

between theoretical zero and one is plotted versus a in Fig. 5.5. This plot shows a nonlinear


Figure 5.3: Transmission versus normalized ∆φ.

Figure 5.4: Transmission versus normalized ∆φ for various values of a. Diamonds are indicating∆φcritical.

decrease of ∆φcritical/π by increasing the feedback transmissivity. When theoretically we have

a = 1, the required switching phase modulation is zero.

Concept of OOK modulation using an MZIARM is illustrated in Fig. 5.6 assuming ring


Figure 5.5: Value of ∆φcritical/π versus a.

resonator is on resonance. As shown, the steep under-coupled region is favorable to operate the

device to allow for small required voltage swing. Hence, the value of φ0 is set by the thermal

tuner shown in Fig. 5.2 to bias the device in the under-coupling condition where the response

is close to linear. The small variation in ∆φ is then converted to the large variation in output

power through the steep transfer function.

Figure 5.6: On-off keying modulation in an MZIARM.

In Section 3.2 of this thesis, it was shown that DC gain of the small-signal response is higher

for under-coupled ring than over-coupled ring. This can be clearly seen from the slope of the Pout


curve in Fig. 5.6. Moreover, it was shown that at critical-coupling, the small-signal response

is zero. This is also clearly observable from the zero slope of Pout curve at critical-coupling

condition in Fig. 5.6.

Figure 5.7: Transmission of MZIARM at zero and non-zero detuning.

The small-signal operation of CM-ring at both zero and non-zero detunings was discussed

in Section 3.2 of this thesis. Also, it was shown in [59] that the DC gain is maximum at

zero wavelength detuning. To elaborate more on this, we are showing the transmission of

an MZIARM at ∆ω = 0 and ∆ω = 1/τ in Fig. 5.7 for a = 0.97. As shown, in this type

of modulator, shifting the input wavelength from the resonance wavelength would result to a

smaller OMA and a less steep transmission curve in under coupling condition and therefore ∆ω

of zero is the favorable operating detuning.

5.2 Pulse amplitude modulation (PAM)

The spectral efficiency of the optical transmission systems would increase by moving from OOK

to more advanced modulation schemes such as pulse amplitude modulation (PAM). The multi-

level intensity modulation has the advantage of direct detection over multi-phase modulation.

The previous methods of PAM modulator that were based on electrical DAC in the driver

of VCSEL [62] or MZM [63] are disadvantageous due to chirp generation in DML and design


complexity of a linear high-speed DAC [64]. These issues were addressed by proposing optical

DAC based on segmented MZI [41].

Inspired by the paper by Yariv [5], and follow up works by Sacher et al. [58, 94, 95], we

propose an optical PAM implementation by adding feedback to the segmented MZI. Having

feedback in the optical path leads to a much shorter RF length compared to the segmented MZI

in [41] using either SISCAP or the conventional lateral pn/pin junction. Similar to [41], use of

the small phase shifters leads to lower power consumption in electrical drivers as there will be no

need to drive power hungry transmission line terminations. Moreover, similar to conventional

MZI, push-pull driven MZIARM can operate for long haul communication purposes as it does

not cause chirp [58, 59].

5.2.1 Device proposal

The proposed device schematic for PAM-4 signaling using MZIARM is shown in Fig. 5.8. For

simplicity, a PAM-4 configuration is illustrated here, while the same concept can be extended

to PAM-N by using log2 (N) pn/pin phase shifter segments.

Figure 5.8: Schematic of the proposed PAM-4 modulator using MZI-assisted ring.

Assuming loss-less MZI in MZIARM, optical power transmission can be modulated from

theoretical 0 to unity by varying the phase difference in the MZI arms, ∆φ, between 2 sin−1(a)

and π for the direct connected feedback MZIARM with the ring transmissivity of a [5]. For

the case of a = 0.99, the required ∆φ is around π11 , which leads to a much smaller required RF

length and drive voltage compared to the conventional MZI.

By segmenting the length of the pn/pin phase shifter, L, into L1 and L2, where L = L1+L2


Table 5.1: Summary of PAM-4 operation principle using the proposed device.

arm1 arm2

b1b0 L2 L1 L2 L1 ∆φ′

00 −V2

−V2

V2

V2 ∆φ′

1

01 −V2

V2

V2

−V2 ∆φ′

2

10 V2

−V2

−V2

V2 ∆φ′

3

11 V2

V2

−V2

−V2 ∆φ′

4

and L2 > L1 (e.g. L2 = 2L1), multilevel optical modulation can be achieved. The segments

with length of L1 and L2 can be treated as lumped circuit elements without any requirement for

transmission line driver. Assuming a loss-less MZI, the through and cross coupling coefficients

(t and κ) from input port (A) in Fig. 5.8 to the output port (B) and to the ring (C), respectively,

are:

t = −i sin(φ0 +∆φ′(t)

2),

κ = i cos(φ0 +∆φ′(t)

2). (5.12)

Here, φ0 is the DC operating phase (that can be induced by the thermal tuner in Fig. 5.8 or

by a length difference between the two arms), and ∆φ′(t) = ∆φ′L1(t) +∆φ′

L2(t) where ∆φ′L1(t)

and ∆φ′L2(t) are the time-varying phase accumulation difference between the two arms of the

first and second pn/pin phase shifter segments, respectively. In the case where both segments

are driven in push-pull scheme, φ′1(t) = −φ′

2(t) = ∆φ′(t)2 where φ′

1(t) and φ′2(t) are the time-

dependent phase accumulation of the first and second arms.

A summary of the device operation principle is shown in Table 5.1 for push-pull drive where

L1 and L2 represent the segments with length of L1 and L2, respectively. The first column

shows the bit sequence for 2bits/symbol in PAM-4 case. The next four columns illustrate the

RF drive voltage for segments in each MZI arm, and the last column shows the corresponding

phase difference between MZI arms. L1 represents the least significant bit while L2 corresponds

to the most significant bit.


By substituting t from Eq. 6.1 into the power transmission from [96], the following can be

derived in the steady state for MZIARM:

Pout

Pin=

a2 − 2a∣∣∣−i sin(φ0+∆φ′

2 )∣∣∣ cosθ′ +

∣∣∣−i sin(φ0+∆φ′

2 )∣∣∣2

1− 2a∣∣∣−i sin(φ0+∆φ′

2 )∣∣∣ cosθ′ +

∣∣∣−i sin(φ0+∆φ′

2 )∣∣∣2a2

, (5.13)

where ∆φ′ takes any of the 4 values presented in Tabel 5.1. The static on-resonance transmission

which occurs when θ′ = 2mπ, m an integer, is:

(Pout

Pin)res =

(a−∣∣∣−i sin(φ0+∆φ′

2 )∣∣∣)2

(1− a∣∣∣−i sin(φ0+∆φ′

2 )∣∣∣)2

. (5.14)

The performance of the modulator on resonance strongly depends on a where lower loss in the

feedback leads to lower required modulation in the coupling coefficient.

L1 and L2 can be selected based on binary weighting or other schemes such as thermometer

weighting where (N − 1) pn segments for PAM-N implementation are needed [41]. Here we

follow the binary-weighted scheme where L2 = 2L1 which leads to linear phase steps with

respect to φ0. This assumption will be revisited later in the chapter.

5.2.2 Simulation results

The proposed modulator is electro-optically simulated to study the performance. A device

simulator from Lumerical Solution Inc. [97] is used with lateral pn junction parameters provided

by Institute of Microelectronics (IME) /A*STAR [83]. The wavelength-dependent effective

index is determined using a commercial mode solver. The MZI was considered to be loss-less

and a propagation loss of 2 dB/cm is assumed for the passive waveguides which corresponds to

a = 0.988. The total phase shifter length is 340µm with a loaded Q of 1.86 × 105 at 1.55µm

and a feedback length of 490µm. The RF voltage for reverse-biased pn junction is taken to be

2Vpp. The device is biased at φ0 = 3.01 radian which corresponds to the dc phase where the

on-resonance transmission in Eq. 6.9 reaches 0.5.

Figure 5.9(a) plots the transmission spectra for input bit sequences of 00, 01, 10, and 11

according to Eq. 5.13. An ER of about 11 dB between 00 to 11 is observed. This ER can


be increased further by increasing L or peak to peak RF applied voltage; however, here, the

optical modulation amplitude (OMA) is maximized to maximize the eye opening.

The on-resonance transmission versus normalized ∆φ given by Eq. 6.9 is shown in Fig. 5.9(b).

The biased phase (φ0), located in the most linear part of the transfer function, is also indicated

in the figure. The modulator is biased at an under-coupled condition where |t| at φ0 is greater

than a. Also shown are the values of the power transmission at the resonance wavelength,

indicated as T0, T1, T2, and T3. As illustrated in Fig. 5.9(b), despite the linear phase steps in

binary-weighted segments, due to the nonlinear nature of the transfer function, the power levels

are not distributed uniformly which may pose challenges for higher-order PAM signaling.

Figure 5.9: (a) Sample optical transmission spectra for 4 symbols in PAM-4 format for binary-weighted scheme. (b) On-resonance transmission versus normalized ∆φ for the same device.(c) T0 to T3 versus L2 to L1 ratio. (d) T0 to T3 corresponding to each level in PAM-4 for variousratios of L2 to L1. The ideal case for the same device is also plotted as a solid line.

To distribute the power levels more linearly, the ratio of L2 to L1 needs to be optimized.

Figure 5.9(c) shows how the power transmission of each level varies as a function of L2/L1


for the aforementioned parameters of the reverse-biased MZIARM. Note that T0 and T3 stay

constant independent of the ratio because L is constant, while T1 and T2 change in the opposite

directions. Also, according to Fig. 5.9(c), for the case where L2 = L1, the number of output

levels decreases from 4 to 3 as T1 = T2. The optimum ratio was found based on the minimum

root-mean-square error (RMSE) with respect to the line connecting T0 to T3 shown in solid

black line in Fig. 5.9(d). Also plotted are T1 and T2 for a few selected L2 to L1 ratios including

the optimum ratio of 1.71 marked by the red dotted box in the inset of Fig. 5.9(d). The

corresponding RMSE for each case is also indicated in the inset of the figure. Note that the

optimized L2 to L1 ratio may differ in the transient case as the power levels are slightly different

and device response is affected by memory effect distortion [59]. Nevertheless, the same method

can be applied to find the optimum ratio in the transient case.

In some applications where a higher linearity is desirable for power level distribution, the

number of segments can be optimized as well as their lengths. On the other hand, in an

optical link with dominant shot noise whose variance rises with square root of input power [98],

non-uniform power levels may be favorable to meet the desired BER for each level. Also,

binary-weighted segments might provide desirable power level distribution depending on the

signal-to-noise ratio (SNR) requirements in the optical links.

Figure 5.10: (a) Sample optical transmission spectra for 4 symbols in PAM-4 format withoptimized L2 to L1 ratio. (b) On-resonance transmission versus normalized ∆φ for the samedevice.

To decrease the length of the phase shifter further, one can use forward-biased pin junction


and take advantage of a much higher refractive index change as a function of the applied voltage

(around 8× 10−4 for 0 to 1 V). In this case, L can be decreased by about 19× compared to the

reverse-biased condition not only due to the stronger electro-optic modulation but also due to

the smaller required feedback length and as a result a higher a. The transmission spectra and

the on-resonance transmissions are shown in Fig. 5.10(a) and (b), respectively. The optimum

ratio of L2 to L1 is calculated to be around 1.68. The result of the segment length optimization

is more clear when comparing almost equally-spaced power levels in Fig. 5.9(b) with binary-

weighted case in Fig. 5.10(b). The RF length for forward-biased case is about 27× smaller

than what has been reported in [41] for segmented MZI in a SISCAP process with the same

applied voltage. Using pre-emphasis scheme to drive the device overcomes the modulation

speed limitations of the forward-biased diode [99] but it may add to the complexity of the

driver circuit limiting the achievable operation speed [3].

Figure 5.11: (a) Push-pull RZ PAM-4 random input sequence of ∆φ′(t). (b) RZ PAM-4 eyediagram for the random sequence shown in (a), for optimized L2 to L1 ratio.

It has been shown that MZIARMs, used for OOK modulation, do not impose any optical

bandwidth limitations other than the cavity FSR, and the upper limit for modulation speed is


determined by the MZI bandwidth [59]. In order to verify the low distortion PAM-4 modulation

in the non-quasi-static mode of operation in the cavity, transient simulations are performed.

The cavity response to a return to zero (RZ) PAM-4 driving phase is simulated based on the

following equations [59]:

B(t) = t(t)A+ κ(t)D(t)

C(t) = −κ∗(t)A+ t∗(t)D(t)

D(t) = ae−iθfbC(t− τ), (5.15)

where A is the amplitude of a continues-wave input and B,C, D are the time-dependent slow-

varying envelopes of the electric field at the locations shown in Fig. 5.8. Propagation time and

phase shift in the feedback are τ and θfb, respectively.

The modulator is considered to have a feedback length of 220µm and a waveguide loss of

2 dB/cm corresponding to a = 0.995. Loaded Q is 1.86 × 105 for 1550nm wavelength with

about 1GHz cavity linewidth. The effective refractive index at 1550nm is used and τ is about

3 ps. FSR is greater than 300GHz. An RZ-PAM-4 random Gaussian signal with a period of

20ps and a pulse duration of 7ps (FWHM), shown in Fig. 5.11(a), is used to drive the device

on the resonance frequency. In Fig. 5.11(a), the maximum and minimum values of the phase

modulation are optimized to have a maximum OMA between T0 and T3 and the middle values

of the phase modulation are selected according to the optimum L2 to L1 ratio for linearity

of the output power levels in the transient mode. The modulation frequency corresponds to

the maximum achieved data rate with MZI [42] in depletion mode and is well above the cavity

linewidth of 1GHz to study the non-quasi-static mode. However, for a more accurate estimation

of upper speed limit, the electrical constraints such as RC time constant of the MZI pn junction

and wiring should be taken into account.

The device is modulated after being operated in the steady state for a few cycles. The eye

diagram which corresponds to the aforementioned RZ input sequence is shown in Fig. 5.11(b).

Despite the memory effect distortion present in the under-coupled MZIARM [59], the eye is

completely open for non-quasi-static mode of 50-Gsymbols/sec (100Gb/s). Four transmission

levels can be observed in the eye diagram. As the modulator is on resonance, only a small


variation of about 0.15 radian in ∆φ is required to induce a large difference of 0.76 between the

highest and the lowest output transmission levels. This leads to a much smaller required drive

voltage compared with MZI which requires π phase shift.

As discussed in Chapter 2, MZIARM acts as a high-pass filter when driven at frequency

rates higher than the cavity linewidth. This effect degrades the eye opening when there is a long

sequence of 1s or 0s and when there is an NRZ signal. For PAM modulation or more complex

modulation formats such as QAM signaling, this could cause more errors in data recovery as in

these complex modulation formats, the eye opening is traded with data rate. It is shown that

this high-pass filter behavior can be removed by using DC-balanced coding [58] or by using

differential ring modulator [87].

5.3 Summary

We discussed the operation principles of the OOK modulation using MZIARM. Also, we pro-

posed a device to facilitate electrical DAC-free PAM-N modulation format which requires

shorter RF length and lower voltage compared with the segmented MZI. The proposed config-

uration can be designed to work under reverse or forward bias. Reverse-biased case is a better

candidate for high speed modulation but requires higher than 1Vpp which makes it challenging

for integration with sub-1V CMOS technology. The forward-biased case is a better candidate for

low-speed operation as it can be driven by less than 1Vpp which makes it feasible for integration

with advanced CMOS circuits.

Chapter 6


for QAM signaling

Advanced optical modulation formats have received more attention recently due to the rising

need for higher bandwidth and advances in coherent detection [100]. The higher spectral

efficiency of modulation formats such as quadrature amplitude modulation (QAM), compared to

on-off keying (OOK), makes them more suitable for translating electrical data to optical output

in a transmitter. In QAM signaling which has been widely used for high-speed communication,

multi-amplitude combines with multi-phase modulation.

There are several possible configurations for QAM modulator. These can be divided into

two main categories: 1- modulators requiring multi-level electrical signal and 2- modulators

requiring binary electrical signal. One of the widely used architectures that fits into the first

category is an IQ optical modulator where each of the I- and Q-arm of a Mach-Zehnder inter-

ferometer (MZI) consists of a MZI modulator driven by multi-level electrical signals [61, 65].

Another example that also needs multi-level driver signal is cascading an MZI modulator with

a phase modulator (PM) [61, 101]. However, due to the complexity of generating linear and

high-speed multi-level electrical signals, it is more desirable to generate multi-level amplitude

and phase, both in the optical domain.

There have been several proposed architectures for binary-driven QAM-16 such as quad

parallel MZI modulator [67] and two cascaded IQ optical modulators [68], but both schemes

99

Chapter 6. Coupling-modulated ring resonator for QAM signaling 100

require four (instead of two) modulators that add to the cost and complexity. Another binary-

driven architecture uses an IQ modulator with imbalanced power-splitting ratio couplers in the

input of both nested MZIs [102]. This requires two tunable MZIs instead of Y junctions and

increases the device size further. A more promising QAM configuration was demonstrated using

segmented MZIs in the silicon-insulator-silicon capacitor (SISCAP) [69]. Substituting an MZI

by an MZI-assisted ring modulator (MZIARM) leads to a much shorter RF length and lower

required driving voltage [5]. We recently proposed PAM signaling based on all-pass segmented

MZIARM [90]. Also, MZIARM in add-drop configuration was demonstrated recently to work

as a low-chirp binary phase-shift keying (BPSK) modulator [94]. In [94], π phase shift at the

output of the drop port was achieved by flipping sign of the cross coupling coefficient at the

drop port.

In this chapter, we propose M-ary QAM modulator that consists of two add-drop MZIARMs

with multi-segment RF region at the drop port in IQ configuration. We show that using add-

drop MZIARM with multi-segment active region in the drop port not only will induce the

π phase shift but also will generate the multi-level modulation pure optically and eliminates

the requirement for DAC in the electrical driver. The device is also fully analyzed in SOI

process [103]. The MZI in the MZIARM is considered to be lossy and phase and amplitude

modulation are analyzed accordingly. The impact of the imbalanced loss of MZI arms in

MZIARM on the phase modulation is taken into account for the first time to the best of our

knowledge. The proposed device operation is also validated by assessing transient response in

the non-quasi static mode of operation. Also, the on resonance optical transmission at the drop

port is considered and assessed for optimizing level linearity. Hence, the principle of operation of

a multi-segment add-drop MZIARM is provided together with the simulation results of QAM-

16 and QAM-64 constellations where in each case, the output level linearity is studied. In

addition, the number of segments in add-drop MZIARM is also optimized.

6.1 Device proposal and theoretical model

The proposed QAM-16 modulator schematic is shown in Fig. 6.1 in a push-pull driven scheme.

The modulator consists of an add-drop MZIARM in I-arm and another add-drop MZIARM


Figure 6.1: Schematic of the proposed QAM-16 modulator using two segmented add-dropMZIARMs in IQ configuration.

cascaded with a thermal tuner phase shifter targeted for π/2 phase shift, in the Q-arm of the

MZI. Each of the add-drop MZIARM consists of the 2-segment RF phase shifters for active

phase modulation and a thermal tuner to bias the device in the desired DC operating point

and maintain the resonance wavelength of the ring resonator. Although in add-drop MZIARM

the coupling coefficient modulation at either the through or drop ports can be used for phase

modulation, the drop port is selected here as it leads to a more efficient modulation [94]. Also,

in the through port of each of these add-drop MZIARMs, there are small thermally tunable

MZIs that work as couplers. However, these two MZIs could be replaced with simple directional

couplers if the design and fabricated coupling coefficient match. This configuration is easily

extendible to QAM-22N , N ≥ 2, by using minimum N active segments in each arm, where more

than N segments may be required for linearity, as will be discussed in Section 6.4.

Although the proposed device can be implemented by any free-carrier dispersion-based

configurations, e.g. pn/pin diode or SISCAP [69], here, for the proof of concept, simulations

are based on the parameters provided by Institute of Microelectronics (IME) /A*STAR [83] for

an SOI process [103].

To provide insight into the device operation, we first briefly describe the operation principle

of a single segment add-drop MZIARM. Assuming quasi-static mode of operation, the device

can be analyzed using the steady state model [59]. The non-quasi-static mode of operation will


be investigated later in section 6.3. The electric field transmissions at the through and the drop

ports of an add-drop ring resonator in the steady state are given by [24,94]:

Tdr = κ∗1κ∗2

√aringexp(−iθ/2)

1− aringt∗1t2exp(−iθ),

Tth =t1 − t2aringexp(−iθ)

1− aringt∗1t2exp(−iθ). (6.1)

where θ is the round-trip phase shift including the phase shift through the coupler, aring is

the ring transmissivity, and t1(κ1) and t2(κ2) are the through (cross) coupling coefficients

in the through and the drop ports, respectively. By employing an MZI as a tunable cou-

pler in the drop port, as shown in Fig. 6.1, t2 and κ2 can be calculated from C × P × C,

where C =

1/√(2) j/

√(2)

j/√

(2) 1/√(2)

is a transfer matrix for a 50-50 directional coupler and

P =

aMZIe−jφ1 0

0 aMZIe−jφ2

is the propagation matrix of the phase shifters in MZI arms,

assuming equal loss of aMZI . Here, φ1 and φ2 are the phase accumulation in the top and the

bottom arms. Based on this transfer matrix formulation, we have the following equations:

t2 = −iaMZI sin(∆φ

2),

κ2 = iaMZI cos(∆φ

2). (6.2)

Here, ∆φ = φ1 − φ2 = φ0 +∆φ′ is the phase difference between MZI arms, φ0 is the DC bias

phase, and ∆φ′ is the phase accumulation differences through the active region.

The static power transmissions of a silicon-based add-drop MZIARM at the drop and

through ports on resonance, θ = 2mπ, m an integer, are shown in Fig. 6.2. In this exam-

ple, the modulator is considered to have a round-trip length of 220 µm and propagation loss of

2 dB/cm corresponding to aring = 0.995, with |t1| taken to be 0.95 and assuming aMZI = 0.985

and neff = 2.44. Note that these parameters are merely to show device operation principles

and are not Representative of a real device (foundry-based examples will be presented in the

next sections). Considering that the device operates at Tdr null point (φ0 = π), a phase flip of π

at the output occurs when crossing the transmission minimum. This is due to the fact that κ2


switches sign as soon as the null point is crossed [94]. As shown in Fig. 6.2, modulator operation

between the two peaks of Tdr corresponds to phase change of 2∆φ′peak where

∣∣∣∆φ′peak

∣∣∣ is the

phase accumulation in the active region at Tdr peaks. This phase shift is much smaller than

that required in the MZI modulator (dotted line in Fig. 6.2) for BPSK for the same distance

between the constellation points. However, the maximum achievable transmission is higher for

the MZI modulator than the one in MZIARM at drop port.

Figure 6.2: On-resonance power transmission versus ∆φ of an MZI, and of an add-dropMZIARM at the through and the drop ports.

The locations of |Tdr| peaks can be calculated by solving ∂|Tdr|∂t2

= 0 which results in

|t2| = a2MZIaring |t1| and equivalently, κ2 = ±iaMZI

√1− a2MZIa

2ring |t1|

2. From Eq. 6.2, ∆φ′peak

is found to be∣∣π − 2 sin−1(aMZIaring |t1|)

∣∣ which shows that the closer aMZIaring |t1| is to 1,

the closer the two peak locations will be and consequently, the less required phase modulation

is. According to Eq. 6.1, transmission at the through port becomes zero at the critical coupling

condition which occurs when |t2| = |t1| /aring corresponding to the active region phase accumu-

lation of ∆φ′cr, which is equal to

∣∣π − 2 sin−1(|t1| /(aMZIaring))∣∣. Only for aMZIaring = 1, ∆φ′

cr

is equal to ∆φ′peak (Fig. 6.2). Here, the obtained equations for the single segment add-drop

MZIARM represent a more complete version of the formulae presented in [94]. In the current

model, we have taken the effect of MZI arm loss into account. The derived formulation shows

that this loss term leads to different effects compared to the ring resonator round-trip loss.


6.2 Active region segmentation in add-drop MZIARM

By segmenting the MZIARM active region into L1 and L2 corresponding to the least significant

bit (b0) and the most significant bit (b1), respectively, ∆φ′ in Eq. 6.2 can take four possible

values depending on the input bit sequence of b1b0 similar to PAM-4 [90]. However, here, due

to the symmetry around π, two out of four cases have the same absolute values but opposite

signs. The values of ∆φ′ can be calculated from:

∆φ′3

∆φ′2

∆φ′1

∆φ′0

=

∆φ′3

∆φ′2

−∆φ′2

−∆φ′3

=

r + 1

r − 1

−r + 1

−r − 1

×M × L1. (6.3)

Here, r = L2/L1, and M = 2π/λres ×∆neff (V ), where λres is the resonance wavelength and

∆neff (V ) is the refractive index change as a function of driving voltage (V).

Based on this, a 2-segment add-drop MZIARM is simulated electro-optically to study the

device performance. Loss and effective refractive index of the active regions as a function

of voltage are calculated using a commercial device and optical simulator [97] and passive

waveguide loss is considered to be 2 dB/cm. Figure 6.3a and b show the simulated change in

effective index and pn junction loss versus reverse bias voltage that are used here. Total loss

at 0 V is 7 dB/cm. The 2-segment add drop MZIARM is simulated using the transfer matrix

formalism of the MZI together with the ring round-trip equation. Breaking the assumption of

having equal losses in the MZI arms, the propagation matrix of MZI should be considered as:

P =

a1e−jφ1 0

0 a2e−jφ2

, (6.4)

where a1 and a2 are the losses in the top and the bottom arms of the MZI, respectively. Due

to the loss modulation accompanying the refractive index modulation in the plasma dispersion

effect, similar to four possible values of ∆φ′ in Eq. 6.3, there will be four slightly different

propagation losses at each arm of the MZI depending on the input bit sequence (b1b0). In

this case, a1 = [a11 a12 a13 a14] and a2 is a1 with the reverse order due to the push-pull


driven configuration. Fabrication imperfection will also add to this loss inequality in MZI

arms, however, due to the small size of the device it will be less probable. As a result of the

loss imbalance in the MZI arms, the through and cross coupling coefficient formalization and

therefore Tdr and Tth equations will be slightly different from what were presented in Eq. 6.2

and Eq. 6.1. The effect of this non-equal loss will be explained later in the chapter.

Figure 6.3: Change in (a) effective index (b) pn junction loss versus reverse bias voltage.

Figure 6.4: (a) Amplitude of the field transmission at the output of the drop port (b) Peaklocations of |Tdr| (∆φ′

peak) versus Lt.

As shown in Eq. 6.3, ∆φ′3 is determined for a selected total segment length (Lt) and applied

voltage. Larger ∆φ′3 leads to a higher maximum value of Tdr. One way of increasing ∆φ′

3 is to

increase Lt at the constant applied voltage. Figure 6.4a shows maximum |Tdr| as a function of

Lt for the applied voltage of 4.4 Vpp considering reverse-biased pn junction. For each value of


Lt, t1 is optimized to give the maximum |Tdr|. As shown in Fig. 6.4a, Tdr increases more sharply

at the smaller Lt while it nearly saturates at the larger Lt. This saturation is a consequence

of a loss increase as a function of length. Moreover, as shown in Fig. 6.4b, larger Lt leads to

∆φ′peak further away from π, resulting in a less steep transfer function which lowers modulation

efficiency. As such, choice of Lt is a trade off between the maximum Tdr and the efficiency.

Here, we have selected Lt = 500 µm for all the simulations of the reverse-biased device.

Figure 6.5: A 2-segment MZIARM (a) optical power transmission spectra for the drop andthrough ports, and (b) amplitude and phase of the field transmission at the output of the dropport versus normalized ∆φ.

Figure 6.5a shows the power transmission spectra of the drop and through ports of the


2-segment add-drop MZIARM assuming reverse biased-pn junction with r = 2, t1 = 0.94 and

Vpp = 4.4 V . These values result in modulation of |κ2| between 0.046 to 0.14. An ER of about

9 dB is observed between the maximum and minimum on-resonance transmission at the drop

port. Figure 6.5b shows the amplitude and phase of the on-resonance field transmission at the

drop port versus normalized ∆φ. The on-resonance field transmission amplitudes are indicated

as |Tdr0|, |Tdr1|, |Tdr2|, and |Tdr3|. According to Fig. 6.5b, the effect of the difference in loss of

the MZI two arms has negligible effect on |Tdr|. However, the imbalanced loss impact on the

phase of the field transmission at the drop port is more significant. Also, 6 Tdr deviates from

0 and π in vicinity of ∆φ/π = 1. In the case of non-equal loss in two MZI arms, t2 and κ∗2 in

Eq. 6.1 should be respectively replaced by:

t2 →1

2(a1 + a2)[

(a2 − a1)

(a2 + a1)cos(

∆φ

2)− i sin(

∆φ

2)] (6.5a)

κ∗2 → − i

2(a1 + a2)[cos(

∆φ

2) + i

(a2 − a1)

(a2 + a1)sin(

∆φ

2)], (6.5b)

where |(a2 − a1)/(a2 + a1)| << 1. If a1 = a2 = a, then Eq. 6.5a and 6.5b becomes the same as

the t2 and κ∗2 in Eq. 6.1. Close to ∆φ/π = 1, where the modulator is operating, Eq. 6.5a can be

approximated by −ia sin(∆φ/2). However, in this region, the term i(a2−a1)/(a2+a1) sin(∆φ/2)

in Eq. 6.5b will be comparable with cos(∆φ/2) and therefore κ∗2 becomes a complex number

rather than the pure imaginary value in Eq. 6.2. Consequently, modulation of ∆φ will not

result in the complete sign flip in Tdr and this will result in a phase error. As a1 and a2 have

four different values based on b1b0, there are four phase curves where two of them are clearly

observable (dotted box in Fig. 6.5b). In the current example, the maximum phase error is about

0.02π, but could be larger depending on the active region length and loss-voltage dependency.

The phase error will affect the QAM constellation as will be discussed in the next section.

6.3 Non-quasi static analysis

So far, we focused on the quasi-static mode of operation where closed-form forumlae can describe

the operation of the proposed QAM modulator. In order to show that the proposed device

operates in the non-quasi-static mode as well, we carried out a time domain simulation. For


simplicity, ring modulator self-heating effect due to the free-carrier absorption [104] is not

considered. Here, we consider QAM-16 which includes two 2-segment add-drop MZIARMs.

Figure 6.6 shows a simplified schematic of one of the MZIARMs where A is the amplitude of a

continues-wave input and B, C, D, G, H, and E are the time-dependent slowly-varying envelopes

of the electric field at the locations shown. The input at the add port, F, is zero. Also shown are

the coupling matrices at the through and drop port indicated as M and N, respectively. Similar

to previous sections, the MZI modulator is consider to be at the drop port. All the parameters

taken for this simulation are similar to those used in Section 2. The device is driven by a

4.4 Vpp pseudo random input bit stream at 30 Gb/s where the modulation frequency is about

10× higher than the cavity linewidth. At this rate, the quasi-static assumption is not valid,

which necessitates the current time domain simulation. The input bit stream is first filtered

by a 54 GHz low-pass RC filter based on the junction capacitance and series resistance in the

selected technology. Then, based on the voltage-dependent refractive index and loss shown in

Fig. 6.3, the time-dependent propagation matrix, P, is found. From this, M = C × P ×C is

calculated. At the thought port, the time-independent coupling matrix N is:

N =

t1 κ1

−κ∗1 t∗1

. (6.6)

Based on these coupling matrices, we have the following relations for the electric field envelops

in Fig. 6.6:

Figure 6.6: Schematic of an add-drop coupling-modulated ring resonator.


B(t)

C(t)

= M

A

D(t)

, (6.7a)

H(t)

E(t)

= N

G(t)

0

. (6.7b)

Also, considering round-trip propagation time of τ , the following additional equations hold:

G(t) = C(t− τ/2)√aringe

−j θ2 , (6.8a)

D(t) = H(t− τ/2)√aringe

−j θ2 . (6.8b)

Figure 6.7: Phase accumulation differences through the active regions, cross coupling coefficientat the drop port, and power transmission at the drop port versus time.

Based on Eq. 6.7a-6.8b, the electric field envelope at the drop port, E(t), and Tdr can be


calculated through an iterative method. Figure 6.7 shows the calculated ∆φ′, κ2 (N(1, 2)), and

Tdr as a function of time. The device is modulated after being operated in the steady state for

a few cycles. Four levels of ∆φ′ are illustrated in Fig. 6.7, as expected for 2-segment MZIARM.

This results in four levels of coupling coefficient at the drop port. As shown in Fig. 6.7, Tdr

has two levels of amplitude as it is expected from Fig. 6.5 in quasi-static domain. In order

to observe both phase and amplitude multi-leveling, constellation diagram is generated. Four

independent bit stream of 4000 bits are applied to each active region in the QAM modulator

shown in Fig. 6.1. Constellation diagram of QAM-16 for r = 2 is generated and shown in

Fig 6.8. Deviation of the constellation points from vertical and horizontal line is due the phase

error as a result of loss imbalance between two arms of the MZI modulator as discussed in

Section 2. Phase error also exist in QAM modulator that are using MZI due to imbalanced

arm losses and limited ER [105]. It will be shown in the next section that this deviation of

constellation occurs in the quasi-static simulations as well.

Figure 6.8: Constellation diagram of QAM-16 for Lt = 500 µm.

6.4 Output level linearity

Linearity of the QAM output levels can be studied through steady-state analysis. Even though

the transient respond could potentially slightly change the levels, the methodology applied here

is valid for exploring the effect of nonlinear curve of the add-drop MZIARM on the constellation


of QAM-16. As can be seen from Eq. 6.3, ∆φ′ and the level distribution can be modified by

adjusting the driving voltage and consequently ∆neff and/or the segment length ratio. Here, we

focus on optimizing the segment length ratio as adjusting the driving voltage for each segment

may add to the driver circuit complexity and becomes less practical compared with adjusting

the segment lengths.

For a fixed Lt of 500 µm, the QAM-16 constellations are plotted for r = 1.5 and 2.5 as shown

in Fig. 6.9a and 6.9b. According to the figure, the constellation map significantly changes with

variation of the segment ratio, r. Here, a certain r value can be found for an exact linear

level distribution. Given Tdr3 = −Tdr0 and Tdr1 = −Tdr2 (Fig. 6.5b), for a fixed Lt, the only

equation that should be satisfied to arrive at the linear levels is Tdr2 = Tdr3

3 . For the current

example of Lt = 500 µm, r is calculated to be around 1.9. This calculated value of 1.9 is close to

binary-weighted ratio of 2, as the region of operation is almost in the linear part of |Tdr|-∆φ/π

curve in Fig. 6.5b. The corresponding QAM-16 constellation is shown in Fig. 6.9c. The small

tilt that exist in all constellations shown in Fig. 6.9 is due to the aforementioned phase error.

Figure 6.9: QAM-16 constellation for Lt = 500 µm and for (a) r = 1.5, (b) r = 2.5, and (c)r = 1.9.

As shown here, linearly-spaced constellation can be achieved for QAM-16 using two RF

segments in each arm of MZI in each MZIARM. However, for QAM-22N , N ≥ 3, employing N

segments does not lead to complete level linearity. As an example, in QAM-64, ∆φ′ can be


calculated from the following equation:

∆φ′ =

∆φ′3

∆φ′2

∆φ′1

∆φ′0

−∆φ′0

−∆φ′1

−∆φ′2

−∆φ′3

=

r3 + r2 + 1

r3 + r2 − 1

r3 − r2 + 1

r3 − r2 − 1

−r3 + r2 + 1

−r3 + r2 − 1

−r3 − r2 + 1

−r3 − r2 − 1

×M × L1 (6.9)

where r2 = L2/L1, r3 = L3/L1. Now, consider ∆φ′

optto be the column vector including

8 desired phase differences to get linear amplitude distribution in the I/Q-arm of the MZI.

In order to achieve linearity, ∆φ′ from Eq. 6.9 should approach ∆φ′

opt, which results in 4

independent equations. However, embedding three RF segments in each arm of the MZI in the

add-drop MZIARM leads to only three variables of Lt, r2, and r3. This is clearly not enough to

get the exact linearly-distributed constellation. However, for a small dynamic range, where the

operation region is in the linear part of the |Tdr|-∆φ/π curve, such as in the current example

of reverse bias (Fig. 6.5b), the level distribution might be close to the ideal case. In Fig. 6.10a,

an ideal line connecting Tdr at Level 1 to Tdr at Level 8 for the 3-segment add-drop MZIARM

is plotted. Also shown with circles are the Tdr values for each level when r2 = 2 and r3 = 4 in

the binary-weighted case. These values are close to the ideal case.

In order to quantize the level nonlinearity, we use differential nonlinearity (DNL) and integral

nonlinearity (INL) as in [106]. In this case, DNL shows deviation of the actual level difference

(Tdrm+1− Tdrm , m be a level number) from ideal linear level difference (TLSB) in unit of the

least significant bit (LSB) and is defined as follows:

DNL =

∣∣∣∣Tdrm+1

− Tdrm

TLSB− 1

∣∣∣∣ . (6.10)

DNL errors accumulate to produce the integral nonLinearity (INL). INL quantizes the maximum

amount of deviation of the actual output levels, Tdrm , from a fitted line in unit of LSB and is


calculated from:

INL =Tdrm − Tdr1 − S × (m− 1)

TLSB, (6.11)

where S is the slope of the fitted line. For the binary-weighted case shown in Fig. 6.10a, the

value of INL and DNL are calculated to be 0.11 and 0.1 LSB, respectively.

In order to improve linearity, the optimized r2 and r3 are calculated such that the root-mean-

square error (RMSE) with respect to the ideal line (Fig. 6.10a), is minimized. The Tdr values

for this optimized case which occurs when r2 and r3 are around 1.96 and 3.72, respectively, are

plotted in Fig. 6.10a as squares. For this case INL and DNL are calculated to be 0.07 and 0.13

LSB, respectively. Therefore, linearity is improved to a small degree compared to the binary

weighting case. The results for INL and DNL for these two cases are summarized in table 6.1.

The QAM-64 constellation for this case is illustrated in Fig. 6.10b.

Figure 6.10: (a) Field transmission at the drop port of the MZIARM plotted for each levelassuming binary-weighted and optimized ratio 3-segment case in depletion mode. The idealcase is also plotted with a solid line. (b) QAM-64 constellation for the 3-segment IQ modulatorwith optimized segment lengths.

To increase distance between points in QAM constellation, it might be necessary to move

further up in |Tdr|-∆φ/π curve where the nonlinearity is more significant for this larger dynamic

range. To achieve this, in the current example, either Lt or the applied voltage should be

increased. Alternatively, an active region with smaller Vπ.L, such as forward- biased junctions,


could be chosen. To demonstrate how to achieve linearly-distributed levels when dynamic

range covers nonlinear section of the transmission curve, a QAM-64 signaling is examined using

forward-biased pin junction with Lt = 100 µm for 1 VPP . As the carrier injection is more

efficient to induce effective index change compared with carrier depletion [99], the device could

be smaller in size, but with the disadvantage of being bandwidth limited. The Tdr distribution

for the binary-weighted and the optimized-weighted 3-segments with r2 = 2 and r3 = 3.44

are plotted in Fig. 6.11a where the optimized case shows a clear improvement. The inset of

Fig. 6.11a shows the error which is defined as the distance between the ideal Tdr to the Tdr

achieved for each level number. The improvement of the optimized segment length to the

binary-weighted segment length is more clear. Also, INL decreases from 0.49 LSB in the binary

case to 0.37 LSB in the optimized case while DNL stays almost the same at around 0.4 LSB.

The results for INL and DNL for these two cases are also added in table 6.1. The QAM-64

constellation corresponding to this optimized case is also plotted in Fig. 6.11b, which shows

more improvement is required.

Table 6.1: Summary of INL and DNL for QAM-64 modulator.QAM-64 type INL DNL

Binary weighted 3-segment, reverse bias 0.11 0.1

Optimized weighted 3-segment, reverse bias 0.07 0.13

Binary weighted 3-segment, forward bias 0.49 0.4

Optimized weighted 3-segment, forward bias 0.37 0.4

To improve the linearity further and compensate the transmission nonlinearity in this dy-

namic range, similar to the segmented MZI [41], an extra segment can be added while keeping

Lt constant. Using this extra segment, another parameter is added as r4 = L4/L1 and the

aforementioned 4 equations from Eq. 6.9 can be solved for exact linearity. In this case, an en-

coder is required to map the 3-bit input of b2, b1 and b0 to 4 bits of e3, e2, e1 and e0 as shown in

Fig. 6.11c. The Tdr distribution for the calculated r2 = 1, r3 = 2.2, and r4 = 5.18 based on the

encoder equations shown in Fig. 6.11c, is plotted in Fig. 6.11a as diamonds which fall exactly

on the ideal line. This is more clear from the inset of Fig. 6.11a. The QAM-64 constellation for

this 4-segment add-drop MZIARM IQ modulator is plotted in Fig. 6.11d which demonstrates

perfect linearity.

From both constellations in Fig. 6.10b and Fig. 6.11d, it is clear that constellation points


Figure 6.11: (a) Field transmission at drop port of the MZIARM plotted for each level forbinary-/optimized-weighted 3-segment and for optimized-weighted 4-segment cases assumingpin forward-biased RF section with Lt = 100 µm. (b) QAM-64 constellation for the 3-segmentIQ modulator with optimized segment lengths. (c) Proposed 4-segment MZIARM which canbe implemented in IQ configuration for the properly aligned QAM-64 constellation. Encodertable for mapping a 3-bit input to a 4-bit input is also shown. (d) QAM-64 constellation forthe 4-segment IQ modulator with optimized segment lengths.

deviation from vertical and horizontal lines is due to the aforementioned phase error. The

maximum phase error in the forward bias case is about 0.12π, which is 6× larger than the

corresponding error in the reverse-bias case (due to a more severe loss modulation with voltage).

However, in the forward bias case, the larger distance between the points in constellation may

compensate for this larger phase error, resulting in the same bit error rate.


According to Fig. 6.4 and aforementioned discussions, the advantages of smaller footprint

and lower required driving voltage of the proposed QAM architecture compared with the ar-

chitecture using MZI are more significant when the loss and/or device length become smaller.

Hence, to obtain maximum efficiency of the proposed device, it is necessary to select a technol-

ogy with high efficiency in electro-optical modulation and with low loss in passive and active

regions. Here, we chose lateral pn/pin junction to show the proof of concept. Using SISCAP [41]

or interleaved pn junction [9] for implementing this device will lead to a smaller device with

lower drive voltage requirement due to their smaller Vπ.L compared with that of a lateral pn

junction. Although, the bandwidth of the device with interleaved pn junction may degrade

compared with the one with a lateral pn junction, it is still well above the forward-biased pin

device [46].

6.5 Conclusion

We proposed and analyzed a DAC-free pure optical QAM-22N modulator using two N-segment

MZIARMs in the conventional IQ scheme. The proposed modulator has the advantages of

being driven with binary signal, having small number of modulators, smaller size, and lower

required applied voltage compared to the devices previously proposed. The loss in MZI was

taken into account and we showed that loss imbalance in MZI arms generates phase error in

advance modulation formats such as QAM. The proposed QAM modulator transient response

was also assessed in non-quasi static mode of operation. The effect of the nonlinear transfer

function curve of the device was studied both for QAM-16 and QAM-64. The impact of various

design parameters on the constellation map was investigated. To achieve the properly aligned

constellation, number of segments and their length should be optimized.

Chapter 7

Conclusions and Future Directions

In this thesis, we explored various silicon based ring modulators for high capacity optical com-

munications. One method to more efficiently benefit from the high bandwidth of a single optical

fiber is to use WDM. In a WDM link, one of the main building blocks is the external modulator.

Intracavity ring modulators are one of the most favorable external modulators in such a link

due to their small footprint, low power consumption, and narrow band. In the first part of this

thesis, the small-signal response of the intracavity ring modulator was obtained and studied in

detail. This allowed us to optimize the design of the modulator based on the link metrics.

Using the developed small-signal model and measurement results of the fabricated intracav-

ity ring modulator, the electrical and optical trade-offs of rib-to-contact distance are studied.

This assessment shows the trend of improvement in the modulator bandwidth and degradation

in terms of extinction ratio and insertion loss by decreasing the rib-to-contact distance. Not

only does this study confirm the validity of the derived model over various design parameters,

it also quantitatively provides a detailed understanding of ring modulator design trade-offs for

high speed applications.

Moreover, small-signal response of the coupling-modulated ring resonator was obtained

where the results were compared with the closed-form small-signal transfer function obtained

for intracavity ring modulator. Based on pole-zero representation of the transfer functions for

both cases of ring modulators, it was shown that unlike the intracavity ring modulator, optical

response of the coupling-modulated ring resonator does not limit the total bandwidth as the

number of poles and zeros are equal. The insight provided by this model was used later to

117

Chapter 7. Conclusions and Future Directions 118

propose modulators based on coupling modulation in a ring resonator.

In addition to WDM, another method for increasing the capacity in optical communication

is to replace OOK modulation with a more complex modulation scheme such as PAM or QAM

signaling. As the coupling-modulated ring resonator does not show the bandwidth limitation

observed in intracavity ring modulator, in this thesis, new methods for PAM and QAM sig-

naling based on coupling-modulated ring resonator are proposed. It is shown that by using a

segmented MZI as a coupler for the ring resonator, a PAM modulator can be realized, which

takes advantage of the resonance enhancement, smaller device size, and lower required drive

voltage compared with the segmented MZI proposed before. Also, segmented MZI as a coupler

in the drop port of an add-drop ring resonator was studied as a phase and amplitude modulator.

Two of these modulators were implemented in an IQ configuration to create an optical QAM

modulator based on ring resonators. Both of the proposed devices were studied in detail and

design trade-offs for both forward- and reverse-biased operation and level linearity optimization

were investigated. Using the proposed devices in optical communication systems increases chan-

nel capacity with the potential of reduction in power consumption and complexities compared

to the previously proposed devices.

7.1 Summary of contributions

Below is a short summary of the major accomplishments in this dissertation.

• A closed-form formula was obtained for the intracavity ring modulator small-signal re-

sponse. This model allows accurate estimation of the modulator bandwidth. Also, we

showed that pole-zero representation of such a transfer function would help gaining a

better understanding of the impact of electrical bandwidth, coupling condition, optical

loss, and sign/value of laser detuning. This work is published in Optics Express [88].

The author is grateful for assistance with testing from Professor Joyce Poon and her PhD

students at University of Toronto.

• The effects of contact-to-rib distance on the optical and electrical characteristics of the

depletion-mode intracavity ring modulator are assessed using the developed small-signal

model and through measurement of the fabricated ring modulators in IME A*Star process.


This study allows designing an optimum modulator based on the targeted application.

Key parameters such as additional loss, ER, IL, TP, and optical and electrical bandwidths

were compared among intracavity ring modulators with various contact-to-rib distances.

This work is submitted to IEEE Journal of Lightwave Technology [107]. The author

would like to acknowledge the contributions of Mahdi Parvizi and Naim Ben-Hamida

from Ciena for providing the measurement equipment and also for their valuable feedback

on the results.

• We derived a complete small-signal transfer function for the coupling-modulated ring res-

onator. Based on the pole-zero diagram of the ring transfer function in case of intracavity

modulation (IM) and coupling modulation (CM), we showed that unlike the IM-ring, in

CM-ring, optical behavior does not limit the bandwidth as number of poles and zeros are

equal. This work is presented at the CELO 2016 conference [108].

• We proposed and designed a PAM-N modulator based on coupling modulation in a ring

resonator. The proposed configuration does not require an electrical DAC at the driver.

Also, the proposed configuration needs shorter RF length and lower voltage compared

with the segmented MZI. This work is published in Optics Letters [90].

• We proposed and analyzed a DAC-free QAM-22N modulator using two N-segment add-

drop MZIARMs in the conventional IQ configuration. The advantage of the proposed

configuration is that it requires binary signal at the driver. Also, having less modula-

tors, smaller size, and lower required applied voltage compared to the devices previously

proposed are other advantages of this configuration. This work is published in Optics

Communications [109].

7.2 Future directions

The work presented in this thesis has the potential for further explorations in the following

three categories: 1. small-signal modeling, 2. ring modulator design trade-offs, and 3. PAM

and QAM modulators. Below we will describe the future directions for each category.

1. Small-signal modeling


In Chapter 3 we derived small-signal transfer functions for both intracavity and cou-

pling modulations in the ring resonators. The small-signal models can be improved by

adding the effect of self-heating. At high input laser power, the light circulating inside

the ring resonator results in an increase in the temperature which leads to a resonance

shift. This effect will change the response of the modulator in both small-signal and

large-signal domains. Also, the parasitic capacitance and inductance from wire-bonding

could be added to the model to more accurately predict the modulator bandwidth by

considering packaging effects.

Moreover, in the developed small-signal transfer function of intracavity ring modula-

tor, it was shown that the location of zero varies with detuning sign whereas the amount

of this variation depends on the coupling-condition. This could be verified experimentally

with measurement of deep over- and under-coupled ring modulators.

2. Ring modulator design trade-offs

The design trade-offs of rib-to-contact distance in the intracavity ring modulators

were studied based on DC and small-signal responses in Chapter 4. The impact of such

design parameters could be studied in a large-signal domain in addition to the small-signal

domain. The large-signal eye opening at the desired modulation rate and BER could be

used as a figure-of-merit to evaluate key parameters in a ring modulators. Also, the

relation between detuning and asymmetric eye diagram could be investigated based on a

large signal modeling/experiment. This could be beneficial to extend the study presented

in this thesis to the link-level performance assessment.

Also, now that the design trade-offs of ring modulator are studied and we have an

small-signal model of the ring modulator, a more complex WDM system based on multiple

ring modulators can be designed and tested.

3. PAM and QAM modulators

In Chapter 5, we proposed a PAM-N modulator. The device has been fabricated

and preliminary measurements are carried out. Further experimental investigation of this

device is part of the future work for this thesis. The power consumption of the device


should be estimated considering not only the modulator and the driver circuit but also

the control loop stabilizing the ring modulator resonance wavelength. The wavelength

tuning and stabilization of the ring consumes significant amount of power and could add

about 0.5mW to the power consumption [3].

Also, It will be beneficial to study the performance of this type of modulator in the

system level by considering all the required circuits at the transmitter. Hence, the power

consumption, area consumption in both optical and electrical chips, voltage requirement,

and driver design complexity could be evaluated and compared with the equivalent case

using multiple OOK modulators. Such a study will provide useful information for selecting

N OOK modulators versus one PAM-2N modulator for various values of N .

We proposed and designed a QAM modulator based on coupling-modulated ring

resonator in Chapter 6. This device has been already fabricated. Measurement of such a

device is out of the scope of this thesis and it will be carried out by future student in our

group. This would help to further investigate the proposed QAM modulator advantages

and shortcomings compared to the QAMmodulator based on MZI at various fiber lengths.

Also, impact of loss mismatch, between MZI arms could be assessed in practice.

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