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Optical simulation and development of novel whispering gallery mode microresonators

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Optical simulation and development of novel whispering gallery mode microresonators

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Content ㄱ
Optical Simulation and Development
of Novel Whispering Gallery Mode Microresonators
By
Dongyu Chen
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Electrical Engineering)
May 2021
Copyright 2021 Dongyu Chen
ii

Acknowledgments
The pursuit of a doctoral degree can never be a journey alone. Looking back upon the
incredible past five years at USC, I feel lucky and grateful to be accompanied by a group of
supportive people, professors, colleagues, friends and family. Without their help, support and
encouragement, it is impossible for me to finish this thesis. I want to use this opportunity to
express my sincerest thanks to these people.
First, I want to thank my advisor, Professor Andrea Armani. Thank you for building and
leading the Armani Lab and admitting me as a part of the lab. Your advisement and guidance
train me from a new graduate student to a researcher who is eager to solve challenging problems.
You always encourage us to explore our interests and unknown fields while you take the stress
and function as our backbone. I appreciate your support for the students that allows us to focus
on the projects and learning. Thank you for your devotion to the lab and guidance to us. I feel
extremely lucky to join the lab and spend the five year here. The supportive environment of the
lab makes the five-year journey a pleasant experience and also shapes me to be a better
researcher, writer, presenter and human.
I also want to express my thanks to other professors that have supported me throughout the
graduate school. Special thanks to my committee members, Prof. Alan Willner, Prof. Wei Wu
and Prof. Mark E. Thompson for their selfless devotion to help me finish this thesis. Supports
and teaching from Prof. Jayakanth Ravichandran, Prof. Chongwu Zhou, Prof. Yuji Zhao, Prof.
Tony Levi and Prof. Armand Tanguay give me a deeper understanding of my research area, as
well as a broader view of various fields.

iii

I am grateful for the support and joy I received from the Armani Lab. This is my second
home here with a lot of memorable moments. I want to thank all the previous and current
members of the lab; Dr. Alexa Hudnut, Dr. Victoria Sun, Prof. Xiaoqin Shen, Dr. Hyungwoo
Choi, Dr. Samantha McBirney, Dr. Soheil Soltani, Dr. Vinh Diep, Dr. Haijie Zuo, Dr. Yingmu
Zhang, Andre Kovach, Rene Zeto, Jinghan He, Kylie Trettner, Yasaman Moradi, Dr. Feifei Lian,
Debasmita Banerjee, Lexie Scholtz, Fakhar Singhera, Raymond Yu. We work together in the lab
as colleagues while also have fun together out of the lab as friends. It is a great honor and
pleasure for me to have this opportunity to know you all and work with you. Your advice,
support, discussing and sharing make the five-year journey easier and more enjoyable. I will
miss the time we spent in the lab, the lunch trips, as well as happy hours we had. I feel proud of
the achievements that you have made and I believe you all will have a bright future. I also want
to express thanks to my friends met outside of the lab. Especially I want to thank Wenyuan Li.
Your accompany and support make the whole graduate school experience and my life different.
Last but not least, I want to thank my parents. This thesis would definitely be impossible
without you. Your belief in education brings me from a small coastal village to a university on
the other side of the Pacific Ocean. Thank you for always standing back of me and supporting
whatever decisions I make. You are always the source of my courage, confidence and power.
The graduate school was not easy. Thank you for encouraging me while also not pushing me
when I ran into failures and letting me know I can always go back home and take a rest. I am
really proud of you, and I hope I can be your proud too.

iv

Table of Contents

Acknowledgments ……………………………………………………………………………ii
List of Figures ……………………………………………………………………………….vii
Abstract ……………………………………………………………………………................xi
Chapter 1. Overview ............................................................................................................. 1
1. 1. Abstract .................................................................................................................... 1
1. 2. Introduction ............................................................................................................. 3
1. 2. 1. Motivation ....................................................................................................... 3
1. 2. 2. Chapter overview ............................................................................................. 5
1. 3. References ............................................................................................................... 7
Chapter 2. Background ........................................................................................................ 12
2. 1. Whispering Gallery Mode (WGM) Optical Microresonators ............................... 12
2. 1. 1. Introduction ................................................................................................... 12
2. 1. 2. Modes and quality factors of WGM resonators ............................................ 14
2. 1. 3. Different WGM resonator structures ............................................................. 18
2. 1. 4. Different material systems for WGM microresonators ................................. 20
2. 2. Nonlinear optics in WGM microresonators .......................................................... 22
2. 2. 1. Introduction ................................................................................................... 22
2. 2. 2. Raman amplification ..................................................................................... 24
2. 2. 3. Four-wave mixing (FWM) ............................................................................ 26
2. 3. Optical Simulation Methods .................................................................................. 28
2. 3. 1. Introduction ................................................................................................... 28
2. 3. 2. Maxwell equations ......................................................................................... 29
2. 3. 3. Boundary conditions and evanescent field .................................................... 30
2. 3. 4. FEM and FDTD methods .............................................................................. 33
2. 4. References ............................................................................................................. 36
Chapter 3. Silicon oxynitride microresonators .................................................................... 46
3. 1. Introduction ........................................................................................................... 46
3. 2. Silicon oxynitride deposition ................................................................................. 49
3. 3. Material properties of silicon oxynitride ............................................................... 51
3. 3. 1. Oxygen and nitrogen ratio ............................................................................. 51
3. 3. 2. Refractive index ............................................................................................. 53
3. 3. 3. Material dispersion ........................................................................................ 55
3. 3. 4. Surface properties .......................................................................................... 57
v

3. 4. Silicon oxynitride microtoroid fabrication ............................................................ 58
3. 5. Silicon oxynitride microtoroid characterization testing setup ............................... 62
3. 5. 1. Tapered fiber coupler .................................................................................... 62
3. 5. 2. Testing setup .................................................................................................. 64
3. 6. Silicon oxynitride microring fabrication ............................................................... 66
3. 7. Silicon oxynitride microring characterization ....................................................... 69
3. 8. Summary ................................................................................................................ 72
3. 9. References ............................................................................................................. 73
Chapter 4. Characterization and Applications of Silicon Oxynitride Microresonators ...... 79
4. 1. Introduction ........................................................................................................... 79
4. 2. Environmental stability of silicon oxynitride microtoroids ................................... 81
4. 2. 1. Quality factor stability ................................................................................... 82
4. 2. 2. Fluorescence microscopy .............................................................................. 86
4. 3. SiOxNy microtoroids based Kerr frequency combs ............................................... 90
4. 3. 1. Kerr frequency combs ................................................................................... 90
4. 3. 2. Dispersion ...................................................................................................... 92
4. 3. 3. Frequency combs from SiOxNy microtoroids with normal dispersion ........ 100
4. 4. Summary .............................................................................................................. 109
4. 5. References ........................................................................................................... 110
Chapter 5. Modeling and Simulation ................................................................................ 116
5. 1. Introduction ......................................................................................................... 116
5. 2. Enhanced anti-Stokes Raman scattering from metal-doped silica toroids .......... 118
5. 2. 1. Theory .......................................................................................................... 119
5. 2. 2. Experimental results .................................................................................... 121
5. 2. 3. Summary ...................................................................................................... 124
5. 3. Optical diagnostic for malaria ............................................................................. 125
5. 3. 1. The diagnostic system ................................................................................. 126
5. 3. 2. Modeling ...................................................................................................... 128
5. 3. 3. Data analysis ................................................................................................ 133
5. 3. 4. Summary ...................................................................................................... 137
5. 4. UV-C disinfection system ................................................................................... 138
5. 4. 1. Modeling ...................................................................................................... 140
5. 4. 2. Experimental results .................................................................................... 145
5. 4. 3. Summary ...................................................................................................... 148
vi

5. 5. References ........................................................................................................... 149

vii

List of Figures
Figure 2-1 (a) Tiantan whispering gallery in Beijing. (b) Simplified light trajectory inside a
WGM resonator. ............................................................................................................................ 13
Figure 2-2 (a) A broad scan of a WGM resonator. Demonstrating the modes and FSR of the
resonator. (b) Transmission of a WGM resonator mode. Linewidth of the mode peak is linear to
the Q factor of the mode. ............................................................................................................... 15
Figure 2-3 Measured loaded quality factors at different coupling percentages of a WGM
resonator. The intrinsic quality factor of this device is the y-intercept at 2.1x108. ...................... 17
Figure 2-4 (a) Microscope image of an optical micorsphere. SEM image of a (b)
microdisk45, (c) microtoroid, (d) microring. ................................................................................ 19
Figure 2-5 Energy level diagram of (a) Rayleigh scattering, (b) Stokes Raman scattering and
(c) anti-Stokes Raman scattering. .................................................................................................. 25
Figure 2-6 Energy level diagram of (a) Rayleigh scattering, (b) Stokes Raman scattering and
(c) anti-Stokes Raman scattering ................................................................................................... 27
Figure 2-7 Illustration of electric field on boundary of WGM resonator and surrounding
material. ......................................................................................................................................... 31
Figure 2-8 (a) Illustration of a mesh of microtoroid at cross section. (b) Illustration of a Yee
lattice. ............................................................................................................................................ 34
Figure 3-1 Some examples of wafers with different materials and different layer structures. 50
Figure 3-2 Results of the EDX point and line scans for silicon oxynitride films with oxygen
to nitrogen ratios of (a) 12.7:1 and (b) 4:1 .................................................................................... 52
Figure 3-3 Measured refractive index of two silicon oxynitride wafers with different oxygen
to nitrogen ratios and a silica wafer. .............................................................................................. 54
Figure 3-4 Calculated material dispersion of SiO1.7N0.13 and SiO2. ................................... 56
Figure 3-5 Illustration of the silicon oxynitride microtoroid fabrication process at different
steps. (a) After patterning and BOE etching. (b) After XeF2 dry etching to generate microdisks.
(c) After CO2 laser reflow to generate microtoroids. .................................................................... 59
Figure 3-6 A SEM image of a silicon oxynitride microtoroid. ............................................... 61
Figure 3-7 A picture of the taper puller setup. ........................................................................ 63
Figure 3-8 (a) Rendering of the testing setup. Inset: top view of a toroid coupled with a
tapered fiber. (b) A picture of the testing setup covered by a plastic box to reduce the
contamination. ............................................................................................................................... 65
Figure 3-9 (a) A SEM image of the SiOxNy waveguides fabricated using positive resist and
metal mask. High roughness on the sidewall can be observed. (b) A SEM image of the SiOxNy
waveguides fabricated using negative resist with improved sidewall roughness. ......................... 67
Figure 3-10 A top view SEM image of a SiOxNy ring with a diameter of 200 µm coupled
with a bus waveguide. ................................................................................................................... 68
Figure 3-11 A picture of the testing setup for microring resonators with the key components
identified and marked. ................................................................................................................... 69
Figure 3-12 (a) Transmission of a SiOxNy ring under a broadband scan. (b) A observed
resonance peak with mode splitting. ............................................................................................. 70
Figure 4-1 Transmission spectrum of silica toroids on day 1 of testing at (a) 765 nm and (b)
1300 nm. Measured loaded quality factors are 5.7 × 10
7
and 1.3 × 10
7
, respectively.
Transmission spectrum of silicon oxynitride toroids on day 1 of testing at (c) 765 nm and (d)
1300 nm. The loaded quality factors are 8 × 10
7
and 5 × 10
7
, respectively. Reprinted with
viii

permission from Chen, Dongyu, et al. ACS Photonics 4, 2376-2381 (2017). Copyright 2017
American Chemical Society. ......................................................................................................... 83
Figure 4-2 Quality factors of the SiO2 and SiOxNy devices at 765 nm and 1300 nm over 14
days. (a, b) Intrinsic quality factors of SiO2 toroids over 14 days at 765 nm and 1300 nm. The
quality factors rapidly decreased and stabilized to a value in the order of 10
7
due to the
absorption of water molecules to the surface. (c, d) Intrinsic quality factors of SiOxNy toroids
over 14 days at 765 nm and 1300 nm. Quality factors of these devices were stable and didn’t
change over the time period. Reprinted with permission from Chen, Dongyu, et al. ACS
Photonics 4, 2376-2381 (2017). Copyright 2017 American Chemical Society. ........................... 84
Figure 4-3 Schematic of the surface functionalization process with (a−c) SiO2 and (d−f)
SiOxNy devices. The number of the initial −OH groups on the surface is directly related to the
final number of attached fluorophores. Reprinted with permission from Chen, Dongyu, et al.
ACS Photonics 4, 2376-2381 (2017). Copyright 2017 American Chemical Society. .................. 87
Figure 4-4 Fluorescence images of SiO2 (a) toroid cavity and (c) disk cavity and SiOxNy (e)
toroid cavity and (g) disk cavity. (b, d, f, and h) Bright field images of the corresponding devices.
(i, j) Fluorescence intensity maps of the toroids and disks taken at the dashed lines in the
fluorescent images. Zero position of the horizontal axis indicates the center of the toroids as
marked with a red + in (a), (c), (e), and (g). The fluorescence intensity of both SiO2 devices is
significantly higher than both SiOxNy devices, indicating the presence of a high density of
hydroxyl groups on the surface. Reprinted with permission from Chen, Dongyu, et al. ACS
Photonics 4, 2376-2381 (2017). Copyright 2017 American Chemical Society. ........................... 89
Figure 4-5 Simplified illustration of frequency combs with comb teeth equally spaced on
frequency domain. Inset: illustrations of degenerate and nondegenerate FWM. .......................... 91
Figure 4-6 Illustration of mode shifting caused by SPM and XPM. Dashed lines represent the
distribution of cold cavity modes with anomalous dispersion. Solid lines represent the shifted
modes that are equally spaced. ...................................................................................................... 92
Figure 4-7 A SEM image of a silicon oxynitride microtoroid. Major radius (R) and minor
radius (r) are indicated in the image. Reprinted with permission from Chen, Dongyu, et al.
Applied Physics Letters 115, 051105 (2019). ............................................................................... 94
Figure 4-8 Simulated dispersion of SiO1.7N0.13 microtoroids with different geometry
parameters. (a) Dispersion of the microtoroids with R = 60 μm and r = 2.5, 3, 3.5, 4, 4.5, and 5
μm, respectively. (b) Solid: Dispersion of the microtoroids with r = 2.5 μm and R = 20, 30, 40,
50, and 60 μm, respectively. Dashed: Dispersion of the microtoroid with the same dimensions of
R = 27 μm and r = 2.83 μm, which is the size of the toroid used in the experiments. Reprinted
with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105 (2019). ......... 95
Figure 4-9 (a) Measured refractive index of the silicon oxynitride wafer for ring resonators,
with the measured refractive index of silica and silicon nitride wafers for comparison. (b)
Calculated material dispersion of the silica, silicon oxynitride and silicon nitride wafers. .......... 96
Figure 4-10 Simulated overall dispersion of ring resonators with different height and width.
(a) Height of the rings are fixed at 1 μm and widths are 2 μm, 1.5 μm, 1 μm and 0.7 μm,
respectively. As the width increases, the overall dispersion shifts to anomalous dispersion. (b)
Width of the rings are fixed at 2 μm and heights are 0.7 μm, 1 μm, 1.5 μm and 2 μm,
respectively. As the height increases, the overall dispersion shifts to anomalous dispersion. ...... 97
Figure 4-11 Illustration of the testing setup used for dispersion measurement. ...................... 99
Figure 4-12 Measured FSRs of the SiO1.7N0.13 microtoroid. ................................................. 101
ix

Figure 4-13 Dispersion of microtoroids with different geometry. Dashed: Dispersion of the
microtoroid with the same dimensions as used in the experiment (R = 27 μm and r = 2.83 μm).
Stars: Experimentally measured dispersion values of the device. A zoomed-in view of the
experimental data is plotted on the right side. Reprinted with permission from Chen, Dongyu, et
al. Applied Physics Letters 115, 051105 (2019). ........................................................................ 102
Figure 4-14 (a) Type-I frequency combs generated from SiO1.7N0.13 microtoroid with initial
sideband located one FSR away from the pump. (b) Type-II frequency combs generated from the
SiO1.7N0.13 microtoroid with initial sideband located nine FSRs away from the pump. Reprinted
with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105 (2019). ....... 104
Figure 4-15 Comb generation at different pump wavelengths with the initial sideband fixed at
1541.5 nm as indicated by the red stars. Reprinted with permission from Chen, Dongyu, et al.
Applied Physics Letters 115, 051105 (2019). ............................................................................. 105
Figure 4-16 Power of the idler signal recorded on Optical Spectrum Analyzer as a function of
the input power coupled into the resonator. The threshold is estimated to be around 280 μW.
Reprinted with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105
(2019). ......................................................................................................................................... 106
Figure 4-17 The spectrums of the frequency combs generated on (a) day 1, and (b) day 9
after the fabrication. ..................................................................................................................... 107
Figure 4-18 The relationships between the comb span and the input power measured at both
Day 1 and Day 9 after the fabrication of the device. The combs are shown in Figure 4-17.
Reprinted with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105
(2019). ......................................................................................................................................... 108
Figure 5-1 (a) SRS and (b) SARS power as a function of the coupled power into the devices,
and (c) relationship between SARS and SRS power from various devices. Reprinted from Choi,
Hyungwoo, et al. Photonics Research 7, 926-932 (2019) under Open Access Publishing
Agreement. Copyright 2019 OSA. .............................................................................................. 121
Figure 5-2 (a) Threshold and (b) efficiency values of SRS, and (c) threshold and (d)
efficiency values of SARS from various devices. Reprinted from Choi, Hyungwoo, et al.
Photonics Research 7, 926-932 (2019) under Open Access Publishing Agreement. Copyright
2019 OSA .................................................................................................................................... 122
Figure 5-3 Schematic of the portable diagnostic system with the axes indicated in the figure.
..................................................................................................................................................... 127
Figure 5-4 Examples of particles’ movement in x and y directions. ..................................... 130
Figure 5-5 Preliminary results for tests with β-hematin with different concentrations in (a) –
(c) 10% PEG and (d) – (f) 15% PEG. Experimental results are solid lines and mathematical
results are dashed lines. ............................................................................................................... 133
Figure 5-6 Results for preliminary tests with β-hematin in 10% PEG. (a) Experimental and
mathematical results. Solid lines show experimental data and shaded regions show ranges
provided by mathematical modeling. Time on the x-axis refers to the total testing time. The
magnetic field is applied at t = 30s. (b) Working range of the diagnostic system for β-hematin
concentrations in 10% PEG. (c) Reproducibility of results with measurements performed
iteratively using the same setup. Reprinted with permission from McBirney, Samantha E, et al.
ACS sensors 3, 1264-1270 (2018). Copyright 2018 American Chemical Society. .................... 135
Figure 5-7 Results for tests with β-hematin in whole rabbit blood. (a) Experimental and
mathematical results. Solid lines show experimental data and shaded regions show ranges
provided by mathematical modeling. (b) Working range of the diagnostic system for β-hematin
x

concentrations in rabbit blood. (c) Reproducibility of results with measurements performed
iteratively using the same setup. Reprinted with permission from McBirney, Samantha E, et al.
ACS sensors 3, 1264-1270 (2018). Copyright 2018 American Chemical Society. .................... 136
Figure 5-8 UV-C disinfection system. (a) Schematic of system. (b) Image of system before
application of reflective coating. (c) Example of several systems with reflective coating.
Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332 (2020) under
Open Access Publishing Agreement. Copyright 2020 OSA. ...................................................... 139
Figure 5-9 Schematic showing key variables used to calculate cumulative UV-C dose.
Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332 (2020) under
Open Access Publishing Agreement. Copyright 2020 OSA. ...................................................... 141
Figure 5-10 Cumulative UV-C dose delivered for a three minute exposure inside the UV-C
disinfection system. Three different wall reflectivity values are modeled: (a) 0%, (b) 25%, and
(c) 85%. (d) The dose at different heights for all three reflectivities modeled, measured in the
centered of the box x-y plane (e) Dose as a function of time for three different UV-C source
powers. This calculation is performed at the center of the bottom of the enclosure. The specific
coordinate based on the schematic in Fig. 2 is (39.4, 25.4, 0). For comparison, the requisite doses
to achieve three log reduction in growth for two bacteria and two viruses are also plotted.
Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332 (2020) under
Open Access Publishing Agreement. Copyright 2020 OSA. ...................................................... 143
Figure 5-11 Summary of results. (a) In both control samples, over 106 colony forming units
(CFUs) grew during the 24 hour incubation period. In contrast, the majority of the exposed
dishes were unable to support colony formation, indicating a 6 log reduction. (b) Control sample
of B. cereus not exposed to UV-C formed colonies after 24 hour incubation time. (c) In contrast,
this growth was dramatically eliminated after 1 minute exposure of identical sample preparations
to the UV-C. Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332
(2020) under Open Access Publishing Agreement. Copyright 2020 OSA. ................................ 147

xi

Abstract
Optical whispering-gallery mode resonators are a type of resonators with circular
enclosed structure, where light can circulate for a long period of time. The high confinement of
light greatly enhances the optical field inside the resonators, which makes these devices an ideal
platform for nonlinear optics like Raman lasing and Kerr frequency combs. Optical Kerr
frequency combs attract special attention recently due to its wide range of application in areas
like spectroscopy, Lidar, communication and optical atomic clocks. To realize these applications,
different materials are explored and examined aiming for higher quality factors, higher nonlinear
coefficient and higher modulation ability. Currently silica and silicon nitride are the two
materials that dominate the field. While silica has very low materials loss, which enables high
quality factor, it has a relatively low nonlinear coefficient and lacks the ability to realize a fully
integrated system. It also suffers from the limitation that the surface of silica is unstable in
atmosphere environment. On the other hand, while silicon nitride can easily achieve a fully
integrated system and has higher nonlinear coefficient, devices made from silicon nitride have
much lower quality factors as a result of higher material loss.
In this thesis, we explored another material, silicon oxynitride, for the whispering-gallery
mode resonators. The silicon oxynitride wafers are deposited in the lab and the basic material
properties are characterized. Optical microtoroids are fabricated from these wafers, which
achieved ultrahigh quality factors. The environment stability of these devices is characterized
with both optical methods and fluorescent microscopy. Comparing to silica microtoroids, silicon
oxynitride microtoroids are more stable in ambient atmosphere. Kerr frequency combs are also
demonstrated from these devices with normal dispersion. In the device design and data analysis,
optical modeling and simulation play an important role. In this thesis, the modeling and
xii

simulation on the whispering-gallery model resonators are also discussed. Besides that, we also
discussed the modeling on two other projects. One is the modeling for the optical malaria
diagnostic system, and the other one is for the UV-C disinfection system. In both projects, the
modeling helps the understanding and analysis of the experimental data and agrees well with the
observed result.

1

Chapter 1. Overview
1. 1. Abstract
Optical whispering-gallery mode resonators are a type of resonator with a circular
enclosed structure, where light can circulate for a long period of time
1-5
. The high confinement of
light greatly enhances the optical field inside the resonators, which makes these devices an ideal
platform for nonlinear optics like Raman lasing
6-10
and Kerr frequency combs
11-13
. Optical Kerr
frequency combs attract special attention recently due to its wide range of application in areas
like spectroscopy
14-16
, Lidar
17
, communication
18
and optical atomic clocks
19
. To realize these
applications, different materials
20-27
are explored and examined aiming for higher quality
factors
13, 26, 28
, higher nonlinear coefficient
29
and higher modulation ability
21
. Currently silica and
silicon nitride are the two materials that dominate the field. While silica has very low material
loss, which enables high quality factors, it has a relatively low nonlinear coefficient and lacks the
ability to realize a fully integrated system. It also suffers from the limitation that the surface of
silica is unstable in an ambient atmosphere environment
13, 28, 30, 31
. On the other hand, while
silicon nitride can easily achieve a fully integrated system and has higher nonlinear coefficient,
devices made from silicon nitride have much lower quality factors as a result of higher material
loss.
In this thesis, we explored another material, silicon oxynitride, for the fabrication of
whispering-gallery mode resonators. The silicon oxynitride wafers are deposited in the lab and
the basic material properties are characterized. Optical microtoroids are fabricated from these
wafers, which achieved ultrahigh quality factors. The environment stability of these devices is
characterized with both optical methods and fluorescent microscopy. Comparing to silica
2

microtoroids, silicon oxynitride microtoroids are more stable in ambient atmosphere
32
. Kerr
frequency combs are also demonstrated from these devices with normal dispersion
33
. In the
device design and data analysis, optical modeling and simulation play an important role. In this
thesis, the modeling and simulation on the whispering-gallery model resonators are also
discussed
7
. In addition, we also discuss the modeling on two other projects. One is the modeling
for the optical malaria diagnostic system
34
, and the other one is for the UV-C disinfection
system
35
. In both projects, the modeling helps the understanding and analysis of the experimental
data and agrees well with the observed results.
3

1. 2. Introduction

1. 2. 1. Motivation
Whispering gallery mode (WGM) optical microresonators have attracted a lot of attention
in both scientific research and technological applications. Ultrahigh quality factors have been
observed from WGM optical microresonators
1, 26, 36-39
, which makes these devices a desired
platform for applications like sensing
2, 40, 41
, Raman lasing and frequency comb generation. The
high confinement of light inside the resonators greatly enhances the optical field, which enables
the nonlinear behavior that requires high optical intensities to occur. Among these applications,
Kerr frequency combs have attracted special attention due to its wide range of applications in
areas like spectroscopy, Lidar, telecommunication and optical atomic clock.
Since the first demonstration of Kerr frequency combs using a silica microtoroid
13
,
various materials and structures have been explored to optimize the WGM resonators for
frequency comb generation. While silica devices have achieved ultrahigh Q, which greatly
decreases the threshold for the nonlinear process, they suffer from the difficulty in fully
integrating the system and in the low environmental stability of the devices. On the other hand,
the silicon nitride devices are stable in the air and easy to integrate, but the material loss of
silicon nitride limits the quality factors of the devices. In this thesis, we explored another
material, silicon oxynitride, for its potential in fabricating WGM resonators as well as generating
frequency combs from the devices. Both toroids and rings are fabricated from this material and
the high environmental stability of the fabricated devices is characterized. We also observed the
generation of Kerr frequency combs from the silicon oxynitride microtoroids with ultra-low
threshold, as well as broad bandwidth.
4

Besides the device fabrication and characterization, optical modeling and simulation are
also a key part in the research, which can help the device and experiment design, data
understanding and analysis. In this thesis, we will also discuss the optical simulation performed
on the WGM resonators for calculating specific parameters, as well as the optical modeling done
for other projects, like understanding the signal of an optical malaria diagnostic system and
calculating the intensity distribution of the UV-C disinfection system.

5

1. 2. 2. Chapter overview
Chapter 2 provides a background overview of the WGM optical microresonators with
different material and structures as well as a detailed discussion on the basic parameters of the
resonators, like quality factor and free spectral range. It also gives a brief introduction to the
nonlinear processes occurring in the WGM resonators. Different numerical optical simulation
methods are also discussed in this chapter.
Chapter 3 discusses the deposition of silicon oxynitride wafers and characterization of
basic material properties of these wafers, like oxygen and nitrogen ratio, refractive index and
material dispersion. It then discusses the fabrication of silicon oxynitride microtoroids as well as
the testing setup used for charactering the devices, followed by the discussion of the fabrication
of silicon oxynitride microring resonators.
Chapter 4 explores the detailed characterization and applications of the silicon oxynitride
microtoroids. Environmental stability of the devices is characterized by both monitoring the
quality factors and using fluorescent microscopy. The silicon oxynitride devices are proven to
have higher stability than the silica devices. Kerr frequency combs are also demonstrated from
these silicon oxynitride microtoroids with normal dispersion. Dispersion of the devices and the
threshold of the parametric oscillation are characterized. The stability of the generated combs is
also studied by monitoring the combs for several days.
Chapter 5 outlines three projects where we use modeling and simulation to understand
the experimentally observed results. Intensity of the anti-Stokes Raman scattering is calculated
analytically. Some conclusions are drawn from the analytical results and experimental
observations. A model is also developed for the optical diagnostic system for malaria, which
helps the understanding and analysis of the experimental data. Another model is built for
6

calculating the optical intensity distribution from fixed light sources, which is designed for the
UV-C disinfection system.

7

1. 3. References

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11. Kippenberg, T. J.; Holzwarth, R.; Diddams, S. A., Microresonator-based optical
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9

20. Jung, H.; Tang, H. X., Aluminum nitride as nonlinear optical material for on-chip
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10

29. Surya, J. B.; Guo, X.; Zou, C.-L.; Tang, H. X., Efficient third-harmonic generation in
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11

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12

Chapter 2. Background
2. 1. Whispering Gallery Mode (WGM) Optical
Microresonators
2. 1. 1. Introduction
Optical microresonators or microcavities are a group of optical structures where light is
confined and resonate inside the cavity. Among these structures, Fabry–Pérot (FP) cavities are
widely used in lasers
1, 2
. In FP cavities, light is reflected by the reflecting faces on the two sides
of a spacer layer or optical medium. They are called standing wave cavities because a standing
wave forms inside the FP cavities. Unlike the FP cavities, whispering gallery mode (WGM)
cavities are traveling wave cavities
3-6
. These cavities are usually circular structures. Light travels
inside the cavity and is reflected by the sidewall of the cavity. Because of total internal
reflection, light can be confined inside the cavity for a long period of time, thus the optical loss
of these cavities can be very low, which makes these cavities useful in many areas
3, 7
, like
lasing
8-13
, chemical and biomedical sensing
4, 14-17
, telecommunication systems
18-21
, and nonlinear
optics
22-24
.
The name “whispering gallery mode” comes from the acoustic whispering galleries, which
can transmit the acoustic waves along the circular wall over a long distance. Figure 2-1(a) is the
whispering gallery at Tiantan in Beijing. When someone speaks to the wall of the whispering
gallery, other people along the wall can clearly hear the sound although they might be very far
away from the speaker. WGM optical resonators operate in a similar way by trapping the light
inside the cavity through total internal reflection. However, unlike acoustic whispering galleries,
13

sizes of dielectric WGM resonators operating in the near-IR wavelength range are usually around
or less than hundreds of micrometers. Figure 2-1(b) shows a simplified scheme of the light
traveling inside a WGM resonator. Due to the total internal reflection and smooth surface, light
can travel inside the cavity for many roundtrips with a long lifetime, which would greatly
enhance the optical field inside the cavity.

Figure 2-1 (a) Tiantan whispering gallery in Beijing. (b) Simplified light trajectory inside a
WGM resonator.

14

2. 1. 2. Modes and quality factors of WGM resonators
Like any other optical resonators, WGM resonators support specific modes inside the
cavities. The modes are selected by the structure’s optical and physical properties. When
circulating inside the cavity, the waves would interfere with each other. As a result, constructive
interference waves add up and form modes, while destructive interference waves cancel each
other and are filtered out by the cavity. To satisfy the constructive interference conditions, the
circumference of the cavity should be N times that of the wavelength, and N should be an
integer
5
. Thus, the frequency of the modes can be written as
𝑓 =𝑁
𝑐
2𝜋𝑅𝑛
(2.1)

where N is an integer, c is the speed of the light, n is the refractive index of the cavity and R
is the effective radius of the resonator, which is close to the radius of the cavity. The spacing in
frequency between the two successive modes is called the free spectral range (FSR)
𝐹𝑆𝑅 =
𝑐
2𝜋𝑅𝑛
(2.2)
Figure 2-2(a) shows an example of a broad scan transmission of a WGM resonator. The
distance between the modes is the FSR of the resonator.
15

Figure 2-2 (a) A broad scan of a WGM resonator. Demonstrating the modes and FSR of the
resonator. (b) Transmission of a WGM resonator mode. Linewidth of the mode peak is linear to
the Q factor of the mode.

Quality (Q) factor is another important parameter used to characterize the modes inside
the cavity. It evaluates the cavity’s ability to confine photons, and Q is directly related to the
lifetime of photons inside the resonator
𝑄 =𝜔𝜏 (2.3)
where 𝜔 is the frequency of the mode (photon) and 𝜏 is its lifetime. Since photon lifetime is
determined by the loss of the cavity, quality factor for a dielectric cavity can also be calculated as
a summation of the optical losses as
25

𝑄
!"
=𝑄
#$%
!"
+𝑄
&.&.
!"
+𝑄
()*+
!"
+𝑄
,$+
!"
+ 𝑄
()-./0*1
!"
(2.4)
Here 𝑄
#$%
is determined by the radiation loss or bending loss which is generated due to the
curvatures. 𝑄
&.&.
is related to the scattering loss due to the inhomogeneities on the surface of the
resonator. 𝑄
()-*+
considers the loss caused by the interaction of the light with the contaminants
on the surface of resonator. 𝑄
,$+
denotes the material loss which generated by the interaction of
the light with the molecules of the material. Previous four losses are intrinsic for a device, we
16

also call 𝑄
0*+#0*&0(
!"
=𝑄
#$%
!"
+𝑄
&.&.
!"
+𝑄
()*+
!"
+𝑄
,$+
!"
as the intrinsic quality factor of the device.
Besides the intrinsic loss, we also have 𝑄
()-./0*1
for a system, which is determined by the
coupling loss between the device and the coupled taper or waveguide. As the most fundamental
and important parameter for a WGM resonator, quality factor is directly related to the ability for
a resonator to confine light, thus the ability to enhance the optical field inside the cavity. Larger
quality factor also enables smaller emission linewidth as is shown in Figure 2-2(b), which
improves the lasing quality. By fitting the transmission curve shown in Figure 2-2(b) with a
Lorentzian, we can get the full width at half maximum (FWHM) of the peak. By dividing the
wavelength of the resonance by the FWHM, we can experimentally determine the quality factor
of the WGM resonators. Increasing the quality factors of WGM resonators has been an important
part of WGM resonator research
26-30
.
The intrinsic quality factor of the devices is a property purely related to the quality of the
devices, while the loaded quality factor also includes the external coupling loss. Measuring the
intrinsic quality factor is of great interest in device characterization. However, in experiments,
we can only measure the loaded quality factor, because coupling light into the cavity is necessary
for performing the measurements, while this coupling would bring coupling loss to the system
unavoidably. One method to get the intrinsic quality factor is to measure the loaded quality
factors under different coupling percentages, then perform a linear fit to obtain the quality factor
at zero coupling, which is the intrinsic quality factor by definition. Figure 2-3 shows a typical
linear fit of the loaded Q ~ coupling percentage. They y-intercept is the intrinsic Q of the device.
17

Figure 2-3 Measured loaded quality factors at different coupling percentages of a WGM
resonator. The intrinsic quality factor of this device is the y-intercept at 2.1x108.

18

2. 1. 3. Different WGM resonator structures
The first whispering gallery mode optical cavities were fabricated from liquid droplets
31-
34
. Since then, many different structures have been developed and studied for different types of
research and applications, like sphere
10, 11, 18, 26, 35-37
, disk
38-40
, toroid
17, 27, 28, 41
, and ring
42-44
.
Among these devices, spheres are relatively easier to fabricate. They are usually made from
liquid droplets or by melting the dielectric materials to form spherical structures as is shown in
Figure 2-4(a). Fabrication of disks and toroids is more complicated. These two structures are
supported by pillars with air cladding. The function of pillars is to separate the main structure
where light travels from the substrates, which usually have higher refractive index that would
cause leakage. As is shown in Figure 2-4(b) and (c), the difference between a disk and a toroid is
that the top part of a disk is a circular pad with wedged edge while a toroid has a donut structure.
The majority of spheres, disks and toroids require external coupling fiber or waveguide for
getting the light into the devices. However, optical microrings are designed with coupling
waveguide integrated on the chip already as is shown in Figure 2-4(d). Because the device is
fabricated directly on the substrate surface, the optical microrings should be fabricated from
materials with higher refractive index than substrates.
19

Figure 2-4 (a) Microscope image of an optical micorsphere. SEM image of a (b)
microdisk45, (c) microtoroid, (d) microring.

Besides the structures mentioned above, other types of devices are studied by different
researches and groups, like WGM optical cylinder, microbubble, microbottle etc. Usually
different device structures are designed for specific applications or for being compatible with
specific material systems.

20

2. 1. 4. Different material systems for WGM microresonators
Besides the varies structures, many different materials have also been explored and
applied in the area of WGM resonators. Staring from the dielectric liquid droplet
31, 32, 34
, like
glycerol, ethanol, the focus of research quickly moved to solid materials like polymer
45-48
and
COMS-compatible material systems like silicon
29, 49-52
, silica
27, 40, 53
and silicon nitride
42, 54-56
, as
well as materials like MgF2
57, 58
, CaF2
59-63
, diamond
44, 64
, lithium niobite
65-69
, AlN
70-72
, GaP
73
, and
AlGaAs
74-78
.
Among these materials, silica is one of the most popular and has been used for devices
like microspheres, microdisks and microtoroids. On one hand, silica has the advantage of easy
fabrication with well- established growing and etching techniques. On the other hand, silica has
very low optical loss in a wide range of wavelength, especially in near-IR, which has been the
focus of a lot of research. Because of the low loss, silica devices can achieve ultra-high quality
factors. For example, silica microsphere can have Q over 1 billion
26
, while silica disks and
toroids have demonstrated Q over 100 million
27, 40
. However, silica also has a relatively low
refractive index comparing to other materials, which makes these devices require air cladding.
As a result, silica devices are usually suspended in the air to prevent light leakage as shown in
Figure2-2. To overcome this and make a system with a higher degree of integration, materials
with higher refractive indexes are explored, like silicon nitride, diamond, lithium niobate, AlN,
GaP, and AlGaAs. To integrate the coupling waveguide into the system, these materials are
usually fabricated into microrings.
In this thesis, we explored another material, silicon oxynitride. On one hand, it has very
low optical loss and can be fabricated into disks and toroids with ultra-high quality factors. On
the other hand, it has a higher refractive index than silica, meaning that we can use silica as the
21

substrate and fabricate an integrated system from silicon oxynitride. There will be more
discussion and details about this material in future chapters.
22

2. 2. Nonlinear optics in WGM microresonators
2. 2. 1. Introduction
WGM resonators’ ability to confine and enhance the optical field inside the cavity makes
them a great platform for studying nonlinear optics. In linear optics, we consider the polarization
density of the material responds linearly to the electric field of the light. This assumption applies
to many materials under low electric field conditions. However, when the electric field gets high
enough, the polarization density is not linear to the electric field anymore. The relationship
between the dielectric polarization density and electric field can be written as
79

𝑷(𝑡)= 𝜀
2
(𝜒
(")
𝑬(𝑡) + 𝜒
(5)
𝑬
5
(𝑡) + 𝜒
(6)
𝑬
6
(𝑡)+⋯) (2.5)
here polarization density and electric field are both time dependent variables. In the equation,
𝜒
(*)
are the nth-order nonlinearity. The first term corresponds to the linear response of the
material, while the second and third terms are the second-order nonlinearity and third-order
nonlinearity, correspondingly. Usually, the higher the nonlinear order is, the smaller the
nonlinear coefficient would be. This is also the reason that we can ignore nonlinear behaviors
when the electric field is weak. However, in WGM resonators, the electric field intensity can
easily reach GW/cm
2
, which makes these nonlinear phenomena an important part of the WGM
resonator research.
Theoretically there can be infinite orders of nonlinearities, however, in reality we only
consider the nonlinearity up to third order in WGM microresonators, because fourth-order
nonlinearity and above are too weak to be observed in most cases. It is also worth noticing that
for many materials with centrosymmetry, like silica and silicon nitride, 𝜒
(5)
is zero
80-82
. Then for
these materials, we would only consider third-order nonlinearity. Though there seems to be only
23

one type of nonlinearity in these materials, there are multiple different phenomena all generated
to the third-order nonlinearity, like third-harmonic generation (THG), cross-phase and self-phase
modulation (XPM and SPM), four-wave mixing (FWM), and Raman amplification. All these
behaviors have been observed in WGM microresonators
83
. In this thesis, we focus on the Raman
amplification
41, 84
and FWM
22, 85
.
24

2. 2. 2. Raman amplification
Raman amplification is enabled by Stokes Raman scattering and anti-Stokes Raman
scattering, which are inelastic scattering of photons by the material. Unlike elastic scattering like
Rayleigh scattering, there is not only energy exchange between the matter and photon, but also
energy gain and loss in the Raman scattering. Raman effect was discovered and reported by C.
V. Raman and his coworkers during the investigations of “Molecular Diffraction of Light” in
1928, and Raman was awarded the Nobel Prize in 1930 for this work.
As the name “Molecular Diffraction of Light” suggests, Raman scattering reveals the
light-matter interaction. In this process, an important concept is the molecular vibration. A
molecular vibration is a periodic motion of the atoms of the molecule relative to each other,
while maintaining the center of the mass of the molecule unchanged. Molecules can be excited to
some vibrational states from the ground states. Specifically, in solids and some liquids, these
excitations are also called phonons.
Raman scattering is closely related to these molecular vibrational states. When a
molecule in its ground state is excited by a laser photon, which can also be described as
absorbing a photon, the molecule can be excited to a virtual electronic energy level, as is shown
in Figure 2-5(a) and (b). This imaginary state is unstable and the molecule reemits a photon. If
the reemitted photon has the same energy as the absorbed photon, we call it Rayleigh scattering,
which is an elastic scattering process. However, if the remitted photon has lower energy, and the
molecule jumps back to a vibrational state, we call this Stokes Raman scattering. Another
situation is that when the molecule absorbs the photon, it’s at a vibrational state already, then it
can jump back to ground state after the absorption and emit a photon with higher energy. We call
this anti-Stokes Raman scattering as is shown in Figure 2-5(c). Since anti-Stokes Raman
25

scattering requires that the molecule is already excited, it happens less frequently as compared to
Stokes Raman scattering.

Figure 2-5 Energy level diagram of (a) Rayleigh scattering, (b) Stokes Raman scattering and
(c) anti-Stokes Raman scattering.

The Stokes Raman scattering and anti-Stokes Raman scattering mentioned above are also
called spontaneous Raman scattering because they take place spontaneously in random time
intervals. For Raman amplification, or Raman lasing, we need to achieve stimulated Raman
scattering, which happens when there are some Stokes photons or anti-Stokes photons already in
the system. These photons can come from spontaneous Raman scattering (and remain in the
material) or be deliberately injected into the material with an external light source. For WGM
resonators, luckily because of its ability to confine photons inside the cavity, photons generated
by spontaneous Raman scattering remain inside the cavity and function as seeds for the
stimulated Raman scattering. Then Raman amplification or Raman lasing can happen inside
these WGM resonators.
26

2. 2. 3. Four-wave mixing (FWM)
Four-wave mixing is a third-order nonlinear phenomenon, where the interactions of two
wavelengths produce two new wavelengths, or the interactions of three wavelengths produce one
new wavelength inside the material. This is a parametric process, meaning that though there is
light-matter interaction, but there is no energy transfer. The energy of the incoming photons is
the same as the output photons. In the meanwhile, the momentums of the photons are conserved.
Energy and momentum conservations require the four-wave mixing to meet the phase matching
conditions. Efficiency of the FWM process is strongly affected by the phase mismatch.
In WGM resonators, we mostly study four-wave mixing which involves two input
photons and two new output photons. As is shown in Figure 2-6, two pump photons are
converted to one signal photon and one idler photon. Energy of the photons should satisfy the
conservation rule:
ℎ𝜈
"
+ ℎ𝜈
5
= ℎ𝜈
&
+ ℎ𝜈
0
(2.6)
The momentum conservation rule requires:
ℏ𝒌
"
+ ℏ𝒌
5
= ℏ𝒌
&
+ ℏ𝒌
0
(2.7)
here 𝒌 is the wave vector, with its value equals to 2𝜋/λ and direction in the photon’s propagation
direction.
Two types of FWM take place inside the WGM resonators: degenerate FWM and
nondegenerate FWM as shown in Figure 2-6 (a) and (b). The different between these two is that
in degenerate FWM, two pump photons have the same frequency (energy) while in
nondegenerate FWM, two pump photons have different frequencies.
27

Figure 2-6 Energy level diagram of (a) Rayleigh scattering, (b) Stokes Raman scattering and
(c) anti-Stokes Raman scattering
28

2. 3. Optical Simulation Methods
2. 3. 1. Introduction
Simulation plays an important role in optics and photonics, especially when device
fabrication is complicated and costly. On one hand, optical simulations can provide a guidance
for the device design and fabrication. On the other hand, simulations give us information to
understand the behavior of the devices.
Generally, there are two types of optics simulation, ray optics simulation and wave optics
simulation. The difference between these two types of simulations is that in ray optics, light is
viewed as rays and follows law of reflection and law of refraction, while in wave optics, light is
interpreted as waves and is guided by the Maxwell equations. Ray optics simulation is usually
applied to situations where the sizes of the objects are much larger than the wavelength of the
light, while the wave optics simulation is used where the sizes of the devices/objects are similar
or smaller than the wavelength of the light.
For WGM resonators, the sizes of the devices are usually in the order of micrometers,
and the active areas where light propagates in usually have the size of around 1 micrometer. So
here wave optics simulation methods are used for designing and studying the WGM resonators.
29

2. 3. 2. Maxwell equations
Maxwell equations are the most fundamental and important part of the wave optics
simulation. In wave optics, we use the electrical and magnetic waves and the electrical and
magnetic fields to represent the light propagation and distribution. Maxwell equations describe
how the electrical and magnetic fields are generated and how they change over time. So, solving
the Maxwell equations under different initial conditions and boundary conditions is the key part
in wave optics simulations. The Maxwell equations in differential form can be written as:
∇∙𝑬=
𝜌
𝜀
2
(2.8)

∇∙𝑩=0 (2.9)
∇×𝑬=−
𝜕𝑩
𝜕𝑡
(2.10)
∇×𝑩=𝜇
2
(𝑱 + 𝜀
2
𝜕𝑬
𝜕𝑡
) (2.11)
Equation 2.8 is based on the Gauss’s law, which describes the static electric field
generated by electrical charges. Equation 2.9 describes the Gauss’s law for magnetism. Since
magnetic charges don’t exist, the net outflow of the magnetic field should be 0 for any closed
surface. Equation 2.10 is Faraday’s law. It describes the generation of electric field as a result of
time-varying magnetic field. And equation 2.11 corresponds to Ampere’s law with Maxwell’s
addition, which describes the generation of magnetic field. It consists two parts, one is the
generation of magnetic field by electrical current (original Ampere’s law) and the other part
describes the generation of magnetic field by time-varying electric field.

30

2. 3. 3. Boundary conditions and evanescent field
Maxwell equations govern the behavior of electrical and magnetic waves and fields. For
WGM microresonators, there are no active electrical charges or electrical currents in the system,
so 𝜌 in equation 2.8 and 𝑱 in equation 2.11 are always 0. Meanwhile, at time zero, there should
be no electrical or magnetic field inside the resonator, which means the initial conditions for
these four equations at time 0 should also be 0. The key in simulating the optical fields in WGM
resonators lies in solving the Maxwell equations under different material and geometry systems,
which also creates different boundary conditions.
By applying Maxwell equations to the interface of the resonator and surrounding media,
we can derive boundary conditions. Figure 2-7 plots an illustration of the boundary, where we
use 𝑡 to represent the tangential component of the field and 𝑛 to represent the normal component.
𝜀
"
and 𝜀
5
are permittivity, 𝜇
"
, 𝜇
5
are permeability of two materials correspondingly. From
equation 2.8 – 2.11, we can get the following four boundary conditions:
𝜀
"
𝐸
"*
= 𝜀
5
𝐸
5*
(2.12)
𝐵
"*
= 𝐵
5*
(2.13)
𝐸
"+
= 𝐸
5+
(2.14)
𝐵
"+
𝜇
"
=
𝐵
5+
𝜇
5
(2.15)

31

Figure 2-7 Illustration of electric field on boundary of WGM resonator and surrounding
material.

Equations 2.12 – 2.15 shows that tangential component of 𝑬 and normal component of 𝑩
are continuous across the interface. Product of normal component of 𝑬 and permittivity,
tangential component of 𝑩 divided by permeability are also continuous across the interface.
However, in section 2.1, we discussed that WGM resonators can trap light inside the resonant
through total internal reflection, which means waves shouldn’t transmit to the surrounding
media. This inconsistence between the ray optics and wave optics can be explained by the
evanescent field.
Under total internal reflection, though the optical waves cannot transmit to the
neighboring media, there is still localized field near the interface, which is a result of the
32

continuous boundary conditions. The localized field is concentrated spatially and decays
exponentially with respect to the distance to the interface. It also doesn’t generate net energy
flow, which agrees with the total internal reflection in ray optics.
Thought the localized evanescent field has zero net flow of energy and doesn’t propagate
as an electromagnetic wave, it plays a critical role in terms of coupling light into the WGM
microresonators. When a coupler approaches the resonator and the evanescent field of the
coupler overlaps with the evanescent field of the resonator, the optical wave can be coupled in or
out of the resonator through the coupler. Coupling via the evanescent field can achieve efficiency
as high as 100%.

33

2. 3. 4. FEM and FDTD methods
The core of the wave optics simulation is solving the Maxwell equations. Though the
boundary conditions are easy to derive as demonstrated in the previous section, analytical
solutions are hard to get for most real world systems, including most of the WGM resonators. To
analyze these systems, numerical approaches are used for solving the Maxwell equations. Two
most commonly used methods are finite-element-method (FEM)
86
and Finite-Difference Time-
Domain (FDTD) method
87
. Though these two methods share some similarities like they both
solve the problem by dividing the space into small sections, fundamentally they are two different
approaches. FEM is a widely used method for numerical calculations in many areas, like
structural analysis, heat transfer, fluid flow and electromagnetic wave, while FDTD is a
technique developed specifically for electromagnetic problems.
FEM is widely used for numerically solving partial differential equations. To do so, it
subdivides the system into small sections, which are called finite elements, by constructing of a
mesh of the object. Each finite element is a domain for the numerical solution that contains a
finite number of points for calculating the values of interest. Figure 2-8(a) shows an example
mesh of a microtoroid at the cross section. The size of the mesh can be modified based on the
desired resolution. By constructing the mesh and boundary value problems in each finite
element, the problem of solving partial differential equations converts to solving a list of
algebraic equations, which can be solved numerically with a variety of methods.
34

Figure 2-8 (a) Illustration of a mesh of microtoroid at cross section. (b) Illustration of a Yee
lattice.

FDTD is developed specifically for electromagnetics, which solves the Maxwell
equations in time-domain. The method is also called Yee’s method, which is named after the
Chinese American mathematician Kane S. Yee. This method can be explained using the Yee
lattice as shown in Figure 2-8(b). The Maxwell equations are discretized to space and time
partial derivatives, which can be solved and updated iteratively. In Figure 2-8(a), the electric and
magnetic field components are discretized in space. At a given time, the electric field
components are solved, which updates the partial derivatives of the magnetic components. Then
in next instant of time, the magnetic field components are solved, which again updates the partial
derivatives of the electric fields. By doing the iteration, the time-evolving electric and magnetic
can be solved numerically.
Although in some cases both FEM and FDTD simulations work, they are good at
different user cases. FEM is based on the meshing in spatial domain, while FDTD relies on the
iteration in time domain. This is the most important difference for these two solutions in
35

electromagnetic calculations. Solving the Maxwell equations in time domain makes the FDTD
capable of coving a wide range of frequencies in one single simulation, which is impossible for
FEM. However, the time domain solution also makes FDTD unfriendly for cases where it takes a
long time before stabilization. Selecting the appropriate numerical method is important for the
simulations.
Both FEM and FDTD have very powerful software for implanting the numerical
methods. For example, COMSOL Multiphysics is useful for FEM simulation and have many
well established modules for different physics. Lumerical FDTD is good at FDTD simulations
and is widely used for FDTD simulations. For WGM microresonators mode analysis, the
COMSOL Multiphysics based on FEM is often used.

36

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46

Chapter 3. Silicon oxynitride microresonators
3. 1. Introduction
As discussed in Chapter 2, many different materials have been studied and applied for
fabrication of WGM microresonators
1-8
. One of the reasons that different materials are being
explored is that each material has different optical properties that make them particularly suited
for unique applications. However, they also have their own disadvantages. These limitations,
whether related to fabrication challenges or wavelength operating range, motivates the
development of new materials.
Silica is one of the most frequently used and successful materials for WGM resonators
due to its exceptionally low optical loss over a wide wavelength range. Silica microspheres can
be easily fabricated from silica fiber by melting the end of the fiber
9
. Because of surface tension,
the melted silica shrinks into spheres and forms solid microspheres at the end of the fibers after
cooling down. Silica microspheres can easily achieve quality factors over a billion. The ease of
fabrication and ultra-high quality factors make the silica microspheres popular for a variety of
research and applications, like studying the fiber-resonator coupling
10-12
and WGM modes
interactions
13, 14
, sensing
15-18
, and lasing
19-21
.
Though silica microspheres have successfully been demonstrated in many applications,
they suffer from the fact that the device is not integrated on chip, and it is difficult to precisely
control the sizes of the devices. To solve this problem, silica microdisks and microtoroids were
proposed and developed. Both devices can be integrated on silicon chip with pillar-supporting
structure. Though the sizes of the silica disks can be very precisely controlled in the fabrication
process, it is more difficult to achieve high quality factors for the disks because of the relatively
47

rougher surface generated in the etching process, as well as the smaller model confinement
region. This problem wasn’t solved until recently with the development of chemically etched
wedge-resonators from thick silica wafers
22, 23
. So, for a long time, silica microtoroids are the
powerhouse in the WGM resonator research. Silica microtoroids are fabricated from the
microdisks with an additional step of reflowing which can greatly decrease the surface
roughness, thus increasing the quality factors of the devices.
However, limitations also apply to silica microtoroids. As a material with relatively low
refractive index (1.444 at 1550 nm), air cladding is required for the mode confinement. Silica
microtoroids need to be suspended in the air with supporting pillar to satisfy this requirement.
This structure increases the fragility of the devices and the difficulty for integrating the coupling
waveguide to the system. Though there have been some efforts for integrating the coupling
waveguide into the system
24-26
, these approaches significantly increased the complexity of the
fabrication process. Another limitation of the silica microtoroid is that on the surface of silica,
there is a dense layer of hydroxyl groups, which is an intrinsic property of silica. These hydroxyl
groups would attract water molecules in the air
27-29
. Quality factors of the devices would
decrease over time because the attached water molecules can scatter the circulating light inside
the cavity.
Another very popular material for WGM resonators is silicon nitride
2, 30
. Unlike silica,
silicon nitride has a relatively higher refractive index (1.996 at 1550 nm), which allows the
devices to be integrated on chip. Silicon nitride rings with silica as cladding are commonly used.
Though silicon nitride has very low material loss, the overall loss of this type of device is
governed by scattering loss which is generated by the surface roughness introduced in the
etching process. As a result, silicon nitride rings usually have lower quality factors than silica
48

microtoroids and microspheres. The highest Q that has been achieved so far is on the order of
10
7
.
2, 31

To overcome the disadvantages of silica microtoroids, while also maintaining the low-
loss feature of the material, we studied another material, silicon oxynitride (SiOxNy)
32
. Although
SiOxNy is not a novel material and has been studied in some other areas
33-35
, not much research
had been done on investigating the performance of SiOxNy in WGM resonators. In this project,
we studied the fabrication of SiOxNy microtoroids and microrings, as well as potential
applications of these devices. It is worth noticing that because of the higher refractive index of
SiOxNy, we can use silica as the cladding for the SiOxNy microrings to achieve a fully integrated
system.

49

3. 2. Silicon oxynitride deposition
Silicon oxynitride films are deposited on substrate (silica or silicon) using plasma-
enhanced chemical vapor deposition (PECVD)
36
. In PECVD, plasmas are created by radio
frequency discharge between two electrodes. Chemical reactions occur after the creation of the
plasma of the reacting gases, and thin films are deposited on the substrate as the reaction product.
To deposit silicon oxynitride, the following gases are used: silane, nitrogen, ammonia and
nitrous oxide. Tuning the deposition recipe can change the ratio of the oxygen and nitrogen in
the film, thus changing the material properties of the SiOxNy, especially the refractive index.
This tunability provides another degree of freedom in the SiOxNy device fabrication. One
example recipe is that with 1000 sccm 2% SiH4 in N2, 60 sccm N2O and 20 sccm NH3, we can
get SiOxNy film with a refractive index around 1.7 at 1550 nm.
The SiOxNy films used in this thesis are deposited either at the Northrop Grumman or in
the cleanroom at USC. Though fabricated in two different labs, similar procedure and recipe are
used, so there are no significant differences in the wafers. Two types of different wafers are
deposited, one with silicon substrate and the other with silica on silicon substrate. The one with
silicon substrate can be used for fabricating the microdisks and microtoroids. Silicon pillars can
be formed by etching the substrate. The other type of wafer can be used for fabricating
microrings because the silica layer can function as the cladding for silicon oxynitride rings and
prevent the light from leaking into the silicon. The thicknesses of the SiOxNy layers are around
1.5 μm. This can also be modified easily in the deposition process by decreasing or increasing
the deposition time. Figure 3-1 shows some example wafers with different materials and
different layer structures. The silica on silicon wafer is commercially available while other
wafers are grown in the USC cleanroom.
50

Figure 3-1 Some examples of wafers with different materials and different layer structures.

3.3 Material properties of silicon oxynitride
As a material that is not very commonly used in optics and photonics research, many of
the material properties of the silicon oxynitride are unknown. For example, as the formula
SiOxNy suggests, the ratio of oxygen and nitrogen can be adjusted in the deposition process and
varies for wafers deposited using different recipes. Different material characterization methods
can be used to study the properties of the SiOxNy. In this section, I mainly focus on the
characterizations of some very general and basic material properties like oxygen and nitrogen
ratio, refractive index and dispersion of the materials. There will be more discussion on the
device-related material properties in next chapter.

51

3. 3. Material properties of silicon oxynitride
3. 3. 1. Oxygen and nitrogen ratio
Although we can tune the oxygen and nitrogen ratio of silicon oxynitride in the
deposition process, but we cannot directly calculate the ratio from the deposition recipe. To
determine the ratio, we performed energy dispersive X-ray (EDX) measurements on the
deposited wafers.
EDX is a very commonly used characterization method for elemental analysis or
chemical characterization of a sample
37
. It relies on the different emission spectrum of different
elements under excitation. To stimulate the emission, a beam of X-rays is used to excite the
electrons in the sample atom. When an electron from a lower energy level (inner shell of the
atom) is excited and ejected from the shell, an electron from a higher energy level (outer shell of
the atom) would fill the hole created by the ejection and emit an X-ray because of the energy
difference between inner shell and outer shell. The X-ray emissions can be collected and
measured by an energy-dispersive spectrometer which can convert the X-ray energy into voltage
signals. Because of the unique atomic structures of different elements, we can distinguish
different elements from the signals received by the X-ray spectrometer.
In our experiments, we performed the measurements on a JSM-6610LV low-vacuum
SEM equipped with an energy dispersive X-ray spectrometer. The spectrometer has a Sapphire
Si(Li) detecting unit, 10 mm
2
detector crystal, and genesis software. Both point scans and line
scans were carried out on different locations on the wafers. Point scans give information on
relative abundances of atoms present on the sample surface, while line scans can confirm atomic
ratio uniformity across the wafers. As is shown in Figure 3-2, two example results were plotted
from two different wafers. Images on the top of both Figure 3-2 (a) and (b) show point scan
52

results and images on the bottom demonstrate the line scan results. The peaks in the point scan
correspond to the silicon, oxygen and nitrogen respectively as indicated in the figure. From the
line scan results, the atomic ratio distributions are fairly uniform across the example wafers.
From the EDX, the atomic ratios of oxygen to nitrogen can be determined. For the wafers
demonstrated as examples in Figure 3-2, the atomic ratios are 12.7:1 and 4:1, respectively. With
these ratios, we can calculate the x and y in the formula and rewrite the SiOxNy as SiO1.7N0.13 and
SiO1.4N0.35, respectively for these two wafers.

Figure 3-2 Results of the EDX point and line scans for silicon oxynitride films with oxygen
to nitrogen ratios of (a) 12.7:1 and (b) 4:1
53

3. 3. 2. Refractive index
Refractive index is one of the basic parameters for optical materials. It is the ratio of the
velocity of light at a specific wavelength in the vacuum to its velocity in the material studied.
The behavior of the light inside the material and between the interface of two materials is largely
decided by the refractive index of these materials. Measuring or looking up the refractive index
is fundamental in the optics and photonics research. For silicon oxynitride, the refractive index
changes as the ratio of oxygen to nitrogen changes. Measuring the refractive index of silicon
oxynitride is the first step in our study. It is also worth noting that refractive index of a material
is not a constant; instead, it is a variable which is a function of the wavelength of the light. So,
refractive index is always measured at specific wavelengths.
The refractive index of thin films on a substrate can be measured using an ellipsometer
38
.
When the light is incident on the sample at an angle, it will be reflected by the structure. The
ellipsometer measures the change in polarization by recording the amplitude ratio and phase
difference of the reflected light. By collecting the polarization changes at different incident
angles, the thickness and refractive index of the thin films can be calculated. By varying the
wavelengths of the incident light, the refractive index of the thin films at different wavelengths
can be measured, which is necessary for calculating the material dispersion.
In our experiments, we used a V-VASE ellipsometer from J.A. Woollam Co. for the
refractive index measurements. The measurements were performed in the wavelength range of
400-1700 nm. Three different angles of incident 65°, 70° and 75° were used in the experiment.
As a control, refractive indexes of a commercial silica wafer were also measured in the
experiment. The experimentally measured refractive indexes were fitted using Sellmeier
equation, which is a very commonly used empirical equation for the relationship between
54

wavelength and refractive index
39, 40
. The results are demonstrated in Figure 3-3 for the two
wafers described in the previous section in Figure 3-2, together with the results measured from a
silica wafer. By increasing the nitrogen ratio, the refractive index of the film also increases as
shown in the result, which agrees with the fact that silicon nitride has a higher refractive index
than silica.

Figure 3-3 Measured refractive index of two silicon oxynitride wafers with different oxygen
to nitrogen ratios and a silica wafer.

55

3. 3. 3. Material dispersion
The wavelength-dependence of refractive index is the origin of the material dispersion.
There are some different definitions for the dispersion based on the specific situation or area of
study. For example, in optics communication, the dispersion of interest is the chromatic
dispersion, which can be directly calculated using 𝑑𝑛/𝑑𝜆, here 𝑛 is the refractive index of the
material and 𝜆 is the wavelength of light
41-43
. In optical microresonators, we are more interested
in group velocity dispersion
44-49
, which is defined as
𝐺𝑉𝐷 =
𝑑
5
𝑘
𝑑𝜔
5
(3.1
)
here 𝑘 =𝑛(𝜔)𝜔/𝑐 is the frequency-dependent wavenumber, 𝑛(𝜔) is the frequency-
dependent refractive index, 𝜔 is the angular frequency, and c is the speed of light in vacuum.
The group velocity dispersion is often quantified by the group velocity dispersion parameter 𝐷,
which can be calculated in the following formula
𝐷 =−
𝜆
𝑐
𝑑
5
𝑛
𝑑𝜆
5
=−
2𝜋𝑐
𝜆
5
𝑑
5
𝑘
𝑑𝜔
5
=−
2𝜋𝑐
𝜆
5
𝐺𝑉𝐷 (3.2
)
From these formulas, it is obvious that the key for calculating the material group velocity is
to measure the wavelength/frequency-dependent refractive index of the material.
From the measured refractive index using ellipsometer, group velocity dispersion (GVD)
of the material can be calculated by taking second-order differential. As an example, in Figure 3-
4, GVD of two different wafers, SiO1.7N0.13 and SiO2 are demonstrated. The dispersion is
referred as normal dispersion when GVD is positive and anomalous dispersion when GVD is
negative. From Figure 3-4, dispersion of the SiO1.7N0.13 shifts a little bit to the normal dispersion
range comparing to the GVD of SiO2.
56

Figure 3-4 Calculated material dispersion of SiO1.7N0.13 and SiO2.
57

3. 3. 4. Surface properties
We are particularly interested in the surface properties of silicon oxynitride in our
research. As mentioned earlier, one of the disadvantages of devices fabricated from silica is that
the surface properties of silica are not ideal because of the existence of the dense hydroxyl
groups which could degrade the performance of devices. Past studies showed that on surface of
silicon oxynitride, many of the hydroxyl groups are replace by fluorine groups when etched by
xenon difluoride
27
, which are very stable in the air and decreased the chance of attracting water
molecules to the devices in ambient environment.
In our study, we also characterized the surface properties of silicon oxynitride. However,
different from the characterization of oxygen to nitrogen ratio and refractive index, the
characterization of the surface properties relies on the WGM devices. So we will discuss the
surface properties of silicon oxynitride in more details in next chapter, where we characterized
these properties using SiOxNy microtoroids and fluorescence microscopy.

58

3. 4. Silicon oxynitride microtoroid fabrication
Whispering-gallery model microtoroids were firstly demonstrated in 2003 using silica
1
.
The most important step in the fabrication is the reflow, which greatly improves the quality
factors by smoothing the surface of the devices. This step takes advantages of high absorption of
silica above 10 μm wavelength range and relatively low melting point of silica. Besides silica,
there are very few other materials that can be successfully reflowed. In this project, we firstly
studied the fabrication of microtoroids from silicon oxynitride. The results show that silicon
oxynitride microtoroids can be successfully fabricated from wafers whose oxygen to nitrogen
ratios are within a certain range. In the meantime, the fabrication process for silicon oxynitride
microtoroids is also slightly different from the silica microtoroids.
The silicon oxynitride microtoroids are fabricated from the wafers with the SiOxNy on
silicon structure in the USC cleanroom and optics lab of Armani Lab. The fabrication is
composed by four steps, photolithography patterning, wet etching, XeF2 etching to generate the
supporting pillar, and CO2 laser reflow.
The first step is to pattern the circular structure out of the silicon oxynitride film. Before
patterning photoresist on the cleaned wafers, the silicon oxynitride wafers are treated with
hexamethyldisilazane (HMDS, Sigma Aldrich) to improve the adhesion between the wafer and
the photoresist by spin-coating. However, in the traditional procedure for silica microtoroids, the
HMDS is vapor-deposited to the silica film. Then Shipley 1813 photoresist is spin-coated on the
wafers with spinning speed of 500 rpm for 5 seconds followed by 3000 rpm for 50 seconds. Then
wafers are soft baked at 95 °C for 2 minutes. The next step is using an aligner to pattern arrays of
circular pads on the wafers. Shipley 1813 is a positive photoresist, so the circular pads are coved
by the photolithography mask while the other areas are exposed to the UV light. The dose of UV
59

exposure used is 80 mJ/cm
2
and we have different masks for different diameters of the pads. The
diameters vary from tens of micrometers to hundreds of micrometers. Then Microposit MF-321
developer (DOW) is used to remove the exposed photoresist around the pads. This process takes
about a minute. After thoroughly washing with DI water and drying with nitrogen air gun, the
chips are baked at 120 °C for two minutes.
The next step is chemical wet etching to transfer the pattern into the silicon oxynitride
layer. Buffered oxide etchant (Transene Co.) is used to etch the silicon oxynitride. The SiOxNy
film is completely etched besides the circular pad covered by the photoresist. The etching stops
at the boundary of SiOxNy and silicon because BOE cannot etch silicon. A big difference in the
etching is that for SiOxNy, it takes about 4 minutes to etch the 1.5 µm thick SiOxNy layer while
the etching takes about 20 minutes for a 2 µm thick silica layer. After BOE etching, the
remaining photoresist on the wafer is cleaned by acetone, isopropyl alcohol and DI water. Figure
3-5(a) shows an illustration of what the chip looks like after the BOE etching. In the figure, the
orange circular pads are SiOxNy pads and the grey substrate is silicon.

Figure 3-5 Illustration of the silicon oxynitride microtoroid fabrication process at different
steps. (a) After patterning and BOE etching. (b) After XeF2 dry etching to generate microdisks.
(c) After CO2 laser reflow to generate microtoroids.

60

After BOE etching, pulsed XeF2 dry etching is used to etch the silicon substrate to
undercut the SiOxNy. This step is the same as the step used in silica microtoroids fabrication.
Before the process, the samples are cleaned and dried to avoid any contamination, especially
water, because water can react with XeF2 and produce HF, which can etch the SiOxNy or silica.
The etching pressure is 2800 mTorr. Each XeF2 pulse lasts for 80 seconds. The total number of
pulses is adjusted according to the number and size of samples loaded into the chamber. After
the XeF2 dry etching, the samples look like the illustration in Figure 3-5(b), which are actually
silicon oxynitride microdisks.
The previous three steps are all conducted in the cleanroom to prevent any contamination.
The last step is to smooth the surface of the devices with a high power CO2 laser (SYNRAD 48-
2KAM) which is done in the optics lab. CO2 laser is chosen because silicon oxynitride and silica
both have high absorption at the CO2 laser emission wavelength of 10,600 nm. The maximum
output power of the laser is 25 W. In order to get smooth surfaces for SiOxNy devices, the output
of the laser should be increased gradually from 0 to around 25% of the maximum output power.
However, for silica cavities, we can either increase the power gradually or set the output power
to a certain amount and hit the cavity directly with high power. Another important difference
worth noticing is that it is extremely difficult to reflow SiOxNy disks with high nitrogen ratio. In
our experiments, we fabricated SiOxNy toroids from films with refractive index of 1.5. In the
attempts to reflow disks with refractive index of 1.65, we observed bubbles forming on the
surface of the devices, which destroyed the Q. Similar to silica devices, the diameter of the
cavity is reduced by the reflow process. For a microdisk with a diameter of 150 µm, the diameter
of the toroid after reflow is usually around 110 µm with a minor diameter around 8 µm. But the
device can further be reduced by decreasing the size of the supporting pillar, increasing the CO2
61

laser power and/or reflow time. Figure 3-5(c) shows the illustration of microtoroids after reflow.
In the fabrication process, multiple arrays of pads are patterned at the same time. The chip can be
diced into smaller ones with single array of devices on each chip after the patterning or etching
as shown in Figure 3-5. This can greatly increase the fabrication efficiency. This also guarantees
that we have enough functional devices for experiments even though some defects might destroy
some of the devices. Figure 3-6 is a SEM image of a silicon oxynitride microtoroid.

Figure 3-6 A SEM image of a silicon oxynitride microtoroid.

62

3. 5. Silicon oxynitride microtoroid characterization
testing setup
3. 5. 1. Tapered fiber coupler
One key part in characterizing WGM resonators is coupling light in and out of the
cavities. While some systems have coupler integrated on chip, like ring resonators, many others
still need external coupler for injecting light into the cavity. Prisms
50-52
and tapered fibers
53
are
two very commonly used couplers. In our experiments, we use tapered fiber coupler as it can be
connected through fibers and avoid too many free space operations.
Tapered fibers are fabricated from normal optical fibers by applying heat and mechanical
pulling at the same time. Depending on the wavelength of the light, different types of fibers are
selected. Figure 3-7 is a picture of the taper puller setup. After stripping the coating from the
fiber, it is placed and held on a fiber holder which has two movable ends. A hydrogen flame is
placed underneath the fiber to heat and melt the fiber, while the two movable ends are guided
and moved by two electrical-controlled mechanical moving stages. In this process, the fiber gets
thinner and thinner as the two stages move far apart from each other. In order to achieve the best
coupling efficiency, the fiber shall be pulled to single mode to achieve the phase matching
between the device and tapered fiber. This can be achieved by monitoring the transmission of the
fiber while the fiber is being pulled. The fiber becomes single mode when the transmission
becomes stable after a series of strong oscillation. Another empirical indicator of single mode is
that the color of the tapered fiber becomes greenish under microscope. Figure 3-7 shows the
taper puller setup in the optics lab.
63

Figure 3-7 A picture of the taper puller setup.

64

3. 5. 2. Testing setup
The tapered fiber is transferred to the testing setup after pulling, and functions as part of
the setup. It is used for coupling light into and collecting light out of the resonator. Besides the
tapered fiber, the testing setup also contains components like laser for input light, fine-tune
stages for holding and moving the samples, and other units for measuring the output
transmission.
Figure 3-8 shows a picture and a simplified rendering of the testing setup. Light from the
laser is coupled into the tapered fiber and its transmission is collected by a photodetector. A
nano-stage holding the chip is brought close to the central area of the tapered fiber. The stage is
movable in three axes. By controlling the positions of the stage, we can change the gap between
the devices and the tapered fiber, which changes the coupling conditions between the device and
fiber. This is useful in measuring the intrinsic quality factors of the devices. Inset in Figure 3-
8(a) shows a top-view image of toroid and tapered fiber. Signal from the photodetector is sent to
an oscilloscope or a computer with oscilloscope card installed. For the purpose of searching or
recording the resonant peaks, a 100 Hz modulation can be applied to the laser while it is
scanning. The setup can also be modified to fit for other measurements. For example, we can
split the transmission of the tapered fiber and send them to photodetector and optical spectrum
analyzer (OSA) if we are interested on the spectrum information in the output signal. This
measurement can be useful for studying nonlinear behaviors of the microresonators, like Raman
lasing and frequency comb generations, where light with new wavelengths are generated.
65

Figure 3-8 (a) Rendering of the testing setup. Inset: top view of a toroid coupled with a
tapered fiber. (b) A picture of the testing setup covered by a plastic box to reduce the
contamination.

66

3. 6. Silicon oxynitride microring fabrication
Besides the microtoroids, microrings can also be fabricated from the silicon oxynitride
wafers. For the rings, we need to use silica as cladding which can provide the contrast in
refractive index to confine the mode inside the silicon oxynitride. As a result, for silicon
oxynitride ring fabrication, we use wafers that have the silicon oxynitride – silica – silicon
structure.
First step of the fabrication is patterning. Unlike toroid, where we use photolithography
for the pattering, EBeam lithography (EBL) is required for the ring fabrication because of the
high resolution needed. The gap between the integrated coupling waveguide and ring is usually
below 1 µm. This resolution is hard to achieve for the aligners that we have in the cleanroom. To
prepare for the EBL, resist is spin coated on the wafer firstly. Two types of resists are commonly
used, positive resist and negative resist. For the positive resist, areas that are exposed to the
ebeam would be soluble in developer, which will be washed away. In contrast, the negative resist
becomes crosslinked or polymerized when exposed, which makes them difficult to dissolve in
developer. As a consequence, areas that are not exposed to the ebeam would be washed away by
the developer for the negative resist. For the ring resonator fabrication, areas with the
ring/waveguide structures are exposed to reduce the EBL writing time and improve the
efficiency, which means for the positive resist, metal deposition after developer combined with
metal liftoff after etching is required to provide the protection of the structure. This additional
metal deposition and liftoff increased the complexity of fabrication and introduced more
roughness to the waveguide sidewalls as shown in Figure 3-9(a). On the side hand, the negative
resist can function as the protector during the etching directly, which makes the metal deposition
unnecessary and improves the roughness a lot as shown in Figure 3-9(b). However, since the
67

resist is easier to be etched than the metal, the metal protector has a higher etching selectivity
ratio, making it easier to fabricate waveguides with large thickness. In the fabrication of silicon
oxynitride ring resonators, negative resist ma-N 2405 is used for the EBL.

Figure 3-9 (a) A SEM image of the SiOxNy waveguides fabricated using positive resist and
metal mask. High roughness on the sidewall can be observed. (b) A SEM image of the SiOxNy
waveguides fabricated using negative resist with improved sidewall roughness.

The resist is firstly spin coated on the wafer by pre-spin for 5 seconds at 500 rpm
followed by 3000 rpm for 45 seconds. Then the wafer is softbaked for 2 minutes at 120 °C on a
hot plate to reduce the remaining solvent content. Then EBL is used to write the desired pattern
on the wafer. For the EBL exposure, a recipe of 30 kV voltage and 150 µC/cm
2
exposure dose is
used. After the exposure, the unexposed resist is washed away by developer. Hard baking is
performed after the development, which can increase the etch resistance. The development and
hard baking after exposure is similar to the procedure used in the photolithography.
After hard baking, the chip is etched using reactive ion etching (RIE) and the negative
resist functions as the protecting layer for the waveguides and rings during the etching. Unlike
the fabrication for microtoroids, dry etching is used here instead of wet etching because wet
etching is isotropic, which can result in angled sidewalls. For the silicon oxynitride film, CHF3,
Ar and CF4 gases are used with plasma power of 280 W and pressure of 30 mTorr. The gas flow
68

is optimized to 40 sccm CHF3, 10 sccm Ar and 10 sccm CF4. With this etching recipe, the
etching rate of silicon oxynitride is around 100 nm/min. After the etching, remaining resist can
be removed with acetone. Depending on the specific application, another layer of silica can be
deposited on the chip to cover the silicon oxynitride waveguides and rings to function as the
cladding. Without the silica deposition, air cladding on top would be used for the devices. The
fabricated devices can be further annealed to reduce the material loss and increase the quality
factors of the devices.

Figure 3-10 A top view SEM image of a SiOxNy ring with a diameter of 200 µm coupled
with a bus waveguide.
69

3. 7. Silicon oxynitride microring characterization
In general, characterization of the silicon oxynitride microrings is similar to the
characterization of microtoroids. The major difference is in the coupling. For the microtoroid,
external tapered fiber is used to couple light into the devices, while for the microring on chip, the
coupling waveguide is already integrated. To couple light into the waveguides, two lensed fibers
are used to guide the light into and out of the waveguide on both ends. Two piezo controlled
nanopositioning stages are used to fine-tune the positions of the lensed fibers to achieve the
optimized coupling. Figure 3-11 shows an image of the testing setup with the major components
marked and indicated.

Figure 3-11 A picture of the testing setup for microring resonators with the key components
identified and marked.

70

After light is coupled into the waveguide, the transmission is coupled out using another
lensed fiber and guided to the detecting units. A photodetector and OSA can be used for
monitoring the transmission and spectrum respectively, which is similar to the characterization
of the microtoroids.
Quality factors of the ring resonators can be characterized with this setup. By scanning
the laser quickly and recording the transmission, we can get a broadband transmission of the
device as is shown in Figure 3-12(a). The resonances are one FSR away from each other,
indicating the ring and waveguide are single mode.

Figure 3-12 (a) Transmission of a SiOxNy ring under a broadband scan. (b) A observed
resonance peak with mode splitting.

The loaded quality factors can be calculated from the resonances in the transmission as
discussed in Chapter 2. For the integrated ring resonators, the distance between the ring and
coupling waveguide is fixed, so the measured quality factor is the loaded quality factor, which
includes the coupling loss. For the silicon oxynitride ring resonators, quality factors are
measured in the order of 10
5
. Figure 3-12(b) shows an example of the resonance. Mode splitting
is observed in this resonance, which is caused by the splitting of the clockwise and
71

counterclockwise waves in the ring
54, 55
. The averaged quality factors for these two resonances is
3×10
5
.
Quality factors of the silicon oxynitride ring resonant can be further improved by
optimizing fabrication process. For example, by polishing the wafer before the fabrication can
reduce the top surface roughness of the devices. And by further optimizing the etching recipe,
the sidewall roughness can be improved as well.

72

3. 8. Summary
In this chapter, we discussed the deposition of silicon oxynitride films with different
oxygen and nitrogen ratios as well as the basic material properties of these films. Microtoroids
and microrings are fabricated from these wafers following different fabrication procedures.
Characterization methods for both types of devices are discussed, together with the primary
results from the silicon oxynitride ring resonators. In next chapter, there will be more detailed
discussions on the characterization and applications of these devices.

73

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79

Chapter 4. Characterization and Applications of
Silicon Oxynitride Microresonators
4. 1. Introduction
WGM microresonators have been used in a variety of applications, like sensing
1, 2
,
lasing
3-5
and frequency comb generation
6-8
. The research has been going on for decades with new
materials and new device structures being developed and optimized for different applications.
These continuous efforts by many researchers around the world push the research and
technology forward. In this process, new concepts and characterization methods are also
invented. In this chapter, we will discuss the characterization of the silicon oxynitride WGM
resonators and some applications demonstrated using these devices. Specifically, we will focus
on the characterization of the environmental stability of these devices and the demonstration
frequency comb generation.
When studying WGM resonators, some basic properties, like geometry and quality factor,
are characterized first after the fabrication of the devices. Typically sizes can be easily measured
with an optical microscope or scanning electron microscope (SEM), and quality factors can be
characterized using the methods discussed in previous chapters. In addition to these basic
properties, other characteristics are analyzed, depending on the target application. For example,
when studying Raman lasing, the Raman emission spectrum of the material is usually
characterized
5, 9
, and when generating frequency combs, dispersion of the devices is analyzed
10-
12
. In this chapter, we will focus on the characterization of the environmental stability of silicon
oxynitride devices. As a fundamental property of silica, the dense hydroxyl groups presenting on
the surface result in the gradual degradation of the optical performance of the silica devices
13-15
.
80

Because of this, we are interested in the surface property of silicon oxynitride. Potential
improvement on the surface properties can make the silicon oxynitride devices more stable in the
air and more suitable for various applications.
Besides characterizing the surface properties of silicon oxynitride devices, the overall
dispersion of the devices is also studied with both simulation and experimental measurement.
Dispersion of the WGM resonators is important for the generation of Kerr frequency combs,
which has been demonstrated from a variety of devices. Depending on the specific properties of
the comb, these systems have applications in optical atomic clocks
16
, LIDAR systems
17, 18
,
telecommunications
19
and high-precision spectroscopy
20-23
. After the characterization of
dispersion, optical frequency combs are generated using the silicon oxynitride microtoroids.

81

4. 2. Environmental stability of silicon oxynitride
microtoroids
One of the motivations for studying silicon oxynitride for WGM resonators is to
overcome the limitation imposed by the environmental instability of silica devices. Previous
research has demonstrated that the layer of hydroxyl groups present on the surface of silica
attracts water molecules, resulting in the optical performance of the devices being degraded over
time unless they are stored in a nitrogen purged box
8
or an integrated cover is used to isolate the
devices from air
24
. To overcome this limitation, we are particularly interested in the surface
property and stability of silicon oxynitride devices in ambient atmosphere. Two different
approaches are used for characterizing the surface properties and examining the performances of
the silicon oxynitride devices. One is monitoring the quality factors of silicon oxynitride
microtoroids over time to directly study the environmental stability of the optical performance of
these devices. The other approach is to use fluorescence microscopy to observe the surface of the
devices that have been processed for identifying the surface chemical groups. The observation
gives direct information on the chemical groups present. Both methods are used to examine the
silicon oxynitride and silica devices.

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4. 2. 1. Quality factor stability
One obvious indicator for the degradation in performance is the device’s quality factor,
because the water molecules on the surface of the device can absorb light, which causes the
quality factor to decrease. To study the performance of the silicon oxynitride microtoroids, we
used silica microtoroids as a comparison at the same time. Both types of devices were
characterized by monitoring the quality factors continuously for two weeks at two different
wavelengths, 765nm and 1300nm.
In the experiments, a series of SiOxNy and SiO2 devices are characterized. Light is
coupled into the resonators using two different tapered fiber waveguides depending on the
wavelength. Transmission spectra are recorded on an oscilloscope. Details of the testing setup
are described in Chapter 3. By changing the distance between the tapered fiber and the device,
we can couple different amount of power into the resonators, which corresponds to different
coupling percentage. From these measurements, we can calculate the intrinsic quality factors of
the devices using the method described in Chapter 2. In total, about 10 SiOxNy microtoroids and
over 40 SiO2 microtoroids are fabricated and tested. More silica devices are fabricated because
the fabrication yield of high-quality silica devices is lower than the fabrication yield for SiOxNy
devices.
Figure 4-1 shows some representative transmission spectra for both SiO2 and SiOxNy
microtoroids at around 765nm and 1300nm on the first day of testing. Here, we observed mode-
splitting from all these measurements, which is due to the high quality factors of the devices.
This behavior occurs in high-Q cavities because light couples into both the clockwise and
counter-clockwise optical modes of the resonator, and due to some small scatters on the surface
of the cavity, the clockwise mode and counter clock-wise mode have slightly different resonator
83

wavelengths
25-28
. For transmission spectra with mode-splitting, we can fit the spectra to a dual
Lorentzian, which gives us the FWHM of both peaks, as well as the resonant wavelengths of
both peaks. Then loaded quality factors of both peaks can be calculated from the transmission
curves.

Figure 4-1 Transmission spectrum of silica toroids on day 1 of testing at (a) 765 nm and (b)
1300 nm. Measured loaded quality factors are 5.7 × 10
7
and 1.3 × 10
7
, respectively.
Transmission spectrum of silicon oxynitride toroids on day 1 of testing at (c) 765 nm and (d)
1300 nm. The loaded quality factors are 8 × 10
7
and 5 × 10
7
, respectively. Reprinted with
permission from Chen, Dongyu, et al. ACS Photonics 4, 2376-2381 (2017). Copyright 2017
American Chemical Society.

We performed the Q factor measurements for both SiO2 and SiOxNy devices for two
weeks to monitor the performance of the devices, which can reflect the changes on the surface of
these devices. The results for the four devices with highest quality factors are plotted in Figure 4-
2 for both types of devices at both wavelengths.
84

Figure 4-2 Quality factors of the SiO2 and SiOxNy devices at 765 nm and 1300 nm over 14
days. (a, b) Intrinsic quality factors of SiO2 toroids over 14 days at 765 nm and 1300 nm. The
quality factors rapidly decreased and stabilized to a value in the order of 10
7
due to the
absorption of water molecules to the surface. (c, d) Intrinsic quality factors of SiOxNy toroids
over 14 days at 765 nm and 1300 nm. Quality factors of these devices were stable and didn’t
change over the time period. Reprinted with permission from Chen, Dongyu, et al. ACS
Photonics 4, 2376-2381 (2017). Copyright 2017 American Chemical Society.

The performance of the silica toroids agreed with past observations in literature
13, 14
,
where the intrinsic quality factors decreased over the two-week observation window as is shown
in Figure 4-2. On day1, all devices had very high Q factors of about 100 million, while finally all
stabilized to approximately 10 million. This behavior is related to the presence of a dense layer
of -OH groups on the surface of the devices, which leads to the formation of a monolayer of
water. The same trend observed at both wavelengths, which indicating that the change is related
to the devices themselves and is consistent over different wavelengths.
85

In contrast, as shown in Figure 4-2 (c) and (d), Q factors of SiOxNy toroids are very stable
over the two-week window. All of these devices demonstrated very high quality factors, around
or above 100 million, for both 765nm and 1300nm wavelengths, which also means that silicon
oxynitride has very low material loss. The stability in Q factors is only possible because the
presence of the nitrogen in the material inhibits the formation of the hydroxyl groups on the
surface, which reduces the attraction of water molecules to the devices, even though the devices
are stored in ambient atmospheres without any protection.

86

4. 2. 2. Fluorescence microscopy
Beside characterizing the devices optically, we also performed fluorescence microscopy
to observe the surface of the SiOxNy devices to examine the existence of hydroxyl groups. For
comparison, silica devices were also tested using the fluorescence microscope. Fluorescence
microscopy was chosen as the characterization method because of the difficulty in directly
observing the -OH groups using other surface spectroscopy methods like XPS. We first prepared
the devices by attaching fluorescent molecules to the devices connected by silane coupling
molecules that specifically attach to hydroxyl groups, which means the fluorescent molecules
wouldn’t be attached to devices if there are no hydroxyl groups present on the surface. With this
method, fluorescence observed under the microscope can be used as an indicator of the presence
and density of the hydroxyl groups.
We performed this measurement on both SiOxNy and SiO2 disks and toroids. Firstly,
surfaces of the devices are silanated using a chemical vapor deposition method for 8 minutes at
room temperature. The silane coupling agent is [4-(chloromethyl)phenyl]trichlorosilane (CPS)
(97%), which is purchased from Sigma-Aldrich and purified by distillation. This step results in a
grafted CPS layer on the surface and the CPS molecules are attached by -OH groups, if present.
Then a 4-(4-(1,2,2-Triphenylvinyl)phenyl)pyridine (TPPy) solution in chloroform is drop-casted
onto the chloromethylphenylene -grafted devices. The 4-(4-(1,2,2-
Triphenylvinyl)phenyl)pyridine was synthesized following the procedure reported in literature
29
.
After the drop-casting, the coated devices are heated to 110 °C under vacuum for 20 minutes.
After that, devices are cooled down to room temperature, followed by a thorough rinse with
dichloromethane to remove any unattached molecules. Then all devices are dried under vacuum
at 110 °C for one minute. After the second step, the fluorescent molecules, TPPy, would be
87

attached to any -OH groups present on the surface. Details of the surface functionalization
process is illustrated in Figure 4-3, in which (a)-(c) describe the process for silica devices, and
(d)-(e) describe the functionalization process for silicon oxynitride devices. The less dense the -
OH groups are, the less fluorescent molecules are attached to the devices.

Figure 4-3 Schematic of the surface functionalization process with (a−c) SiO2 and (d−f)
SiOxNy devices. The number of the initial −OH groups on the surface is directly related to the
final number of attached fluorophores. Reprinted with permission from Chen, Dongyu, et al.
ACS Photonics 4, 2376-2381 (2017). Copyright 2017 American Chemical Society.

After surface functionalization, we further compared devices made from these two
different materials by performing fluorescence microscopy. A Nikon upright fluorescence
microscope with a 20X objective was used for taking fluorescence and bright field images of the
devices. The excitation light had a wavelength of 430 nm, and the fluorescence emission images
were captured after a 510-550 nm band-pass optical filter. During all measurements, the
excitation source, as well as the imaging detector settings, were held constant to make sure the
comparison was reasonable and fair for all materials and devices. Figure 4-4 (a)-(d) plot the
fluorescence and bright field images of silica devices, where (a) and (b) correspond to silica
toroid, (c) and (d) correspond to silica disk. Figure 4-4 (e)-(h) plot the images taken using silicon
88

oxynitride disks and toroidal devices. From these images, it’s clear that silica devices show much
higher fluorescent intensity compared to silicon oxynitride devices.
Fluorescent intensity maps were plotted to quantitatively compare the difference in
emission from these devices. The intensity is mapped along a line bisecting the center of the
devices using the Nikon imaging software. The results were plotted in Figure 4-4 (i) and (j),
where (i) plotted the intensity from SiO2 and SiOxNy toroids and (j) plotted the intensity from
SiO2 and SiOxNy disks. In both figures, blue represented silica devices and red represented
silicon oxynitride devices. This comparison further demonstrated the difference between the
surface of silica and silicon oxynitride devices. It confirmed the assumption that there are much
less dense -OH groups on the surface of silicon oxynitride devices than silica devices and
explained the environmental stability of SiOxNy devices.
89

Figure 4-4 Fluorescence images of SiO2 (a) toroid cavity and (c) disk cavity and SiOxNy (e)
toroid cavity and (g) disk cavity. (b, d, f, and h) Bright field images of the corresponding devices.
(i, j) Fluorescence intensity maps of the toroids and disks taken at the dashed lines in the
fluorescent images. Zero position of the horizontal axis indicates the center of the toroids as
marked with a red + in (a), (c), (e), and (g). The fluorescence intensity of both SiO2 devices is
significantly higher than both SiOxNy devices, indicating the presence of a high density of
hydroxyl groups on the surface. Reprinted with permission from Chen, Dongyu, et al. ACS
Photonics 4, 2376-2381 (2017). Copyright 2017 American Chemical Society.

90

4. 3. SiO
x
N
y
microtoroids based Kerr frequency combs
4. 3. 1. Kerr frequency combs
An optical frequency comb is a coherent light source, which has a spectrum with a series
of discrete and equally spaced frequency lines. Frequency combs have been demonstrated from
many different systems enabled by different mechanisms, like using mode-locked laser by
stabilizing pulse train and using microresonators by four-wave-mixing. The initial demonstration
of frequency combs from mode-locked laser led to the Nobel Prize in Physics in 2005
30, 31
. As a
light source and measurement tool, frequency combs attracted a lot of attention because of its
wide range of applications, like atomic optical clock
16
, telecommunications
19
and spectroscopy
20-
23
.
Though a lot of efforts were devoted into the study of frequency combs enabled by mode-
locked laser, in 2007, WGM microresonators have been demonstrated for generating frequency
combs and attracted a lot of attention because of its significantly smaller footprint compared to
previous systems
8
. After the initial demonstration using silica microtoroids, many other materials
and device structures have been studied for frequency combs generation, like silicon rings
32
,
silicon nitride rings
11, 33-35
, silica disks
24, 36
, aluminum nitride rings
37, 38
, aluminum gallium
arsenide rings
39, 40
, lithium niobite rings
41-44
and diamond rings
45, 46
. These variety of attempts
have pushed forward the research on WGM resonator-based frequency combs and brought the
research closer to applications.
Optical frequency combs generated from WGM microresonators are based on the Kerr
effect, which are third-order nonlinear phenomena. These nonlinear processes take place inside
the cavity benefiting from WGM resonator’s ability to enhance the optical fields
7
. When pump
light is coupled into the resonators, degenerate and nondegenerate four-wave mixing convert the
91

pump light photons into signal and idler photons which have different frequencies. Basics about
four-wave mixing is discussed in Chapter 2. Figure 4-5 shows a simplified scheme of how
frequency combs look and the associated four-wave mixing processes that occur. The energy and
momentum conservation laws guarantee the comb lines are equally spaced for the same FWM
process. Besides the FWM, there are other Kerr effects, like self-phase and cross-phase
modulations happen in the cavity to assist the comb formation.

Figure 4-5 Simplified illustration of frequency combs with comb teeth equally spaced on
frequency domain. Inset: illustrations of degenerate and nondegenerate FWM.
92

4. 3. 2. Dispersion
As mentioned, energy and momentum conservations play a key role in the comb
generation and are responsible for the formation of precisely equally-spaced comb lines. At the
same time, to satisfy these laws, phase matching is critical, which requires the frequencies of
cavity modes to match the positions of the comb lines. However, because of the existence of
dispersion, it is impossible for a cavity to have equally spaced cold modes. Fortunately, self-
phase and cross-phase modulations (SPM and XPM) can shift the cavity modes to lower
frequencies, and if the shifted modes match the desired locations of the comb lines, then phase
match conditions are satisfied, and frequency combs can be generated. This process is
demonstrated in Figure 4-6, where solid lines represent comb lines and dashed lines represent
cold cavity modes. In order to have the modes equally spaced after red-shifting, anomalous
dispersion is desired for the cavities. So, one key part for generating Kerr frequency combs is to
engineer the dispersion of the WGM resonators to anomalous dispersion.

Figure 4-6 Illustration of mode shifting caused by SPM and XPM. Dashed lines represent the
distribution of cold cavity modes with anomalous dispersion. Solid lines represent the shifted
modes that are equally spaced.
93

For a WGM resonator, dispersion comes from both material and geometry. The material
dispersion is already discussed in Chapter 3, which is an intrinsic property of the material and
cannot be engineered once the wafer is deposited. In contrast, geometric dispersion can be tuned
by changing the geometry parameters, like the major and minor radius for toroids or height and
width for rings. The total dispersion of the device is a combination of geometry and material
dispersion, though it’s not a simple sum of these two dispersions. To calculate the dispersion of
the cavities, optical simulations are preferred because of the difficulty in solving the eigenmodes
analytically, except for microspheres, which have analytical solutions because of the simple
structure. In our experiments, we use COMSOL Multiphysics for dispersion calculation. Details
about the simulations would be discussed in next chapter. Here, we focus on the results of the
simulations, specifically, the dispersion of the silicon oxynitride devices.
For a microtoroid, geometric dispersion is governed by the major and minor radius of the
device. Figure 4-7 shows a SEM image of a SiOxNy microtoroid with the major and minor radius
marked as R and r, respectively. Values of R and r are governed by two steps in the fabrication
process: one is the photolithography where we define the size of the circular pads, and one is the
final reflow step where more reflow results in smaller R and larger r.
94

Figure 4-7 A SEM image of a silicon oxynitride microtoroid. Major radius (R) and minor
radius (r) are indicated in the image. Reprinted with permission from Chen, Dongyu, et al.
Applied Physics Letters 115, 051105 (2019).

COMSOL simulations are conducted based on different major and minor radius to study
their impact on the dispersion of the devices. Before the simulation, we already studied the
refractive index of the material and material dispersion using the method described in Chapter 3
section 3. In this work, silicon oxynitride with the formula SiO1.7N0.13 is used for the toroids. All
the following simulation and experimental work on microtoroids are based on this oxygen and
nitrogen ratio. Results of the material dispersion are directly used as the input of the COMSOL
simulation, so the results of simulation are the combined dispersion which takes both material
and geometric dispersion into consideration. Results of the simulations are plotted in Figure 4-8,
where 𝐷
5
/2𝜋 characterizes the mismatch of FSR of the modes in the same mode family. In
Figure 4-8(a), the major radius R is fixed as 60 μm and the minor radius varies from 2.5 um to
5.0 μm. The overall dispersion changes from negative (normal dispersion) to positive
(anomalous dispersion) as the minor radius decreases. Figure 4-8(b) plots the device dispersion
while the minor radius is fixed at 2.5 μm. The major radius is increased from 20 μm to 60 μm,
95

and the dispersion changes from normal dispersion to anomalous dispersion as the major radius
increases. From the simulation results, we can learn that to achieve anomalous dispersion in
SiOxNy microtoroids, devices with larger major radius R and small minor radius r are desired.

Figure 4-8 Simulated dispersion of SiO1.7N0.13 microtoroids with different geometry
parameters. (a) Dispersion of the microtoroids with R = 60 μm and r = 2.5, 3, 3.5, 4, 4.5, and 5
μm, respectively. (b) Solid: Dispersion of the microtoroids with r = 2.5 μm and R = 20, 30, 40,
50, and 60 μm, respectively. Dashed: Dispersion of the microtoroid with the same dimensions of
R = 27 μm and r = 2.83 μm, which is the size of the toroid used in the experiments. Reprinted
with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105 (2019).

Dispersion of the SiOxNy rings can also be studied using similar simulation methods. For
the ring resonators, in order to confine the modes inside the rings, we deposited layers with
larger refractive index comparing to the layers used for the toroids. The material dispersion is
firstly characterized by measuring the refractive index using the ellipsometry as mentioned
previously. Figure 4-9 shows the measured refractive index and material dispersion of the wafer,
along with the results measured from silica and silicon nitride for comparison.
96

Figure 4-9 (a) Measured refractive index of the silicon oxynitride wafer for ring resonators,
with the measured refractive index of silica and silicon nitride wafers for comparison. (b)
Calculated material dispersion of the silica, silicon oxynitride and silicon nitride wafers.

The overall dispersion of SiOxNy rings is studied with COMSOL Multiphysics and the
results are shown in Figure 4-10. Here we play with the width and height of the rings to tune the
geometry dispersion. As is shown in Figure 4-10, the overall group velocity dispersion parameter
D as a function of wavelength for different width and height pairs is plotted. In Figure 4-10(a),
the height is fixed as 1 μm and in Figure 4-10(b), the width is fixed as 2 μm. The dispersion
profile tends to move to anomalous dispersion range when the cross-section gets larger.
Comparing to silicon nitride, it is relatively easier to deposit silicon oxynitride wafers with larger
thickness, which makes the dispersion engineering easier for silicon oxynitride rings.
97

Figure 4-10 Simulated overall dispersion of ring resonators with different height and width.
(a) Height of the rings are fixed at 1 μm and widths are 2 μm, 1.5 μm, 1 μm and 0.7 μm,
respectively. As the width increases, the overall dispersion shifts to anomalous dispersion. (b)
Width of the rings are fixed at 2 μm and heights are 0.7 μm, 1 μm, 1.5 μm and 2 μm,
respectively. As the height increases, the overall dispersion shifts to anomalous dispersion.

The dispersion calculated from the simulation gives us guidance on the device design
and fabrication for generating frequency combs. For the devices fabricated, we also need to
measure the dispersion of the cavities to verify the accuracy of simulations. For the resonators,
the dispersion can be interpreted as the change of FSR over different wavelengths, and this
change is usually very small compared to the resonator frequency and FSR. So, the key in a
dispersion measurement is to measure the resonance of the cavities in high resolution in order to
catch the small changes in FSR. Also, here we aim at high resolution instead of high precision
because FSR is the difference of resonant frequencies, so shifting the resonance together by a
same value wouldn’t impact the results, which means high accuracy is not required in this
measurement.
Dispersion of the device is characterized using swept-wavelength interferometry
47
. The
idea of this interferometry is mapping the transmission of a resonator and a Mach-Zehnder
interferometer (MZI) on the same timeframe, then use the dense peaks of the MZI as a ruler for
98

measuring the FSRs of the resonator. The frequency resolution of the MZI can be controlled by
changing the length difference between the two arms. The larger the difference is, the higher the
resolution would be. In order to characterize the frequency of MZI, a standard gas cell is used as
reference. In the experiments, this measurement consists of two steps, first step is to characterize
the MZI using a standard gas cell, and in the second step, the gas cell is replaced with the
resonator and FSRs of the resonator are characterized using the MZI. The characterization of the
MZI only needs to be done once, and the system can function and measure any resonators as
long as the MZI stays unmodified.
Figure 4-11 shows a scheme of the testing setup used in the experiments. A tunable laser
(Newport Velocity Widely Tunable Laser, 1550 nm – 1630 nm, TLB-6730) is split by a
50%/50% splitter. One laser signal is sent through a polarization controller and a tapered fiber to
couple into the resonator cavity (gas cell in the first step). The transmission is received by a
photodetector (ThorLabs PDA10CS). The other laser signal is sent to a MZI. The two arms of
the MZI have a 250-meter difference in length, which results in a ~0.8 MHz optical frequency
sampling resolution, which is high enough (small enough in value) for catching the changes of
FSRs. The MZI is calibrated using a standard gas cell (WavelengthReferences TRI-H(80)-
5/150/150-FCAPC) for compensating the dispersion of the MZI. The transmission signals from
the MZI and the cavity are recorded by a two-channel data acquisition device (DAQ, National
Instruments PCI-5114) simultaneously.
99

Figure 4-11 Illustration of the testing setup used for dispersion measurement.

When measuring the dispersion, the laser is scanned from a higher wavelength to a lower
wavelength at a speed of 10 nm/s to avoid thermal distortion of the optical modes. The
calibration and measurement are separated into two wavelength ranges: 1630 nm – 1580 nm and
1600 nm – 1550 nm because of the memory limitation of the DAQ. In the data analysis, the
sampling signal from the MZI is statistically analyzed as well as manually examined to remove
artifacts from laser scanning error like stage scanning jitter.

100

4. 3. 3. Frequency combs from SiOxNy microtoroids with
normal dispersion
We studied the generation of frequency combs from SiO1.7N0.13 microtoroids. From the
simulation results shown in Figure 4-9, devices with large major radius R while also maintaining
small minor radius r are desired for achieving anomalous dispersion, which are actually very
difficult to fabricate. This difficulty comes from the reflow step. For disks with large radius, we
need to fully reflow it to have a complete toroidal structure and smooth surface, which results in
large minor radius. In contrast, toroids reflowed from small disks have small minor radius but
also small major radius. Because of this, in our experiments, we studied SiO1.7N0.13 toroids with
normal dispersion instead of the anomalous dispersion as desired.
Dispersion of the SiO1.7N0.13 toroid is characterized using the setup described in Figure 4-
11. FSR of the toroid can be measured by counting the number of cycles of the calibrated MZI.
Figure 4-12 plots the measured FSRs of the SiO1.7N0.13 toroids with a major radius of 27 μm and
minor radius of 2.83 μm. Due to the limited range of the scanning laser (1550 nm – 1630 nm),
only six FSRs are identified and measured.
101

Figure 4-12 Measured FSRs of the SiO1.7N0.13 microtoroid.

Differences between the FSRs are the dispersion that we are interested in. Figure 4-13
plots the comparison between the experimentally measured dispersion and the simulation results.
Figure 4-13(a) shows the dispersion calculated from the simulation as plotted in Figure 4-8 (b),
where the dashed line is based on the geometry of the device used in the experiments. The stars
show the experimentally measured dispersion using swept-wavelength interferometry. On the
right side, a smaller range of wavelength is plotted to give a clearer comparison between the
simulation and experiments. The experimentally measured dispersion confirms the normal
dispersion predicated by the simulation, and the simulation and experimental results are very
close to each other.
102

Figure 4-13 Dispersion of microtoroids with different geometry. Dashed: Dispersion of the
microtoroid with the same dimensions as used in the experiment (R = 27 μm and r = 2.83 μm).
Stars: Experimentally measured dispersion values of the device. A zoomed-in view of the
experimental data is plotted on the right side. Reprinted with permission from Chen, Dongyu, et
al. Applied Physics Letters 115, 051105 (2019).

Though anomalous dispersion is desired for phase matching, which is critical in the comb
formation process, it is difficult to achieve anomalous dispersion for many devices because most
materials have normal dispersion over a wide range of wavelengths. This pushes the research on
mechanism and demonstration of combs generated from devices with normal dispersion.
Studies have shown that combs can also be generated from normal dispersion cavities
assisted by avoided mode crossing between modes from different mode families
11, 48-50
. Though
theoretically modes in the WGM resonators are orthogonal, but in real systems these modes can
interact with each other because of the existence of defects. When two modes from different
mode families have the same or very similar frequencies, as well as spatial overlap, the
interaction between the modes alters the resonant frequencies of the modes. This shift can
dramatically change the dispersion around that wavelength. Local anomalous dispersion can be
realized and modulational instability becomes possible because phase matching requirements are
met after the shifting. This avoided mode crossing mechanism enables the comb generation from
cavities with normal dispersion, like our SiO1.7N0.13 toroids. In the meantime, it is important to
103

notice that it’s hard to determine and control the modes of a cavity in the fabrication step, so
generating combs requires a lot of testing and searching for the right mode.
From the SiO1.7N0.13 toroids, we observed two types of frequency combs as are shown in
Figure 4-13. As the avoided mode crossing changes the local dispersion, phase matching would
be firstly satisfied around the frequency of the avoided mode crossing, and initial comb lines are
also formed at these locations. Depending on the relative positions of the pump and initial comb
lines, two types of frequency combs can be formed. Figure 4-14(a) shows a Type-I frequency
comb generated from the SiO1.7N0.13 toroids. The initial sidebands are located one FSR away
from the pump. In the cascaded FWM processes, the frequency spacings between the initial
sidebands and the pump are duplicated, and this forms a series of equally spaced comb lines with
a frequency spacing of one FSR. When the initial sidebands are multiple FSRs away from the
pump, Type-II frequency combs can be generated as shown in Figure 4-14(b). Cascaded FWMs
fill the gap between the pump and initial sidebands and finally frequency combs with one FSR
are formed. Both Type-I and Type-II frequency combs observed from SiOxNy toroids have spans
over a few hundred nanometers. Different formation dynamics can lead to different qualities, like
coherence, in combs performance.
104

Figure 4-14 (a) Type-I frequency combs generated from SiO1.7N0.13 microtoroid with initial
sideband located one FSR away from the pump. (b) Type-II frequency combs generated from the
SiO1.7N0.13 microtoroid with initial sideband located nine FSRs away from the pump. Reprinted
with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105 (2019).

We further investigate the Type-I frequency combs generated from the SiO1.7N0.13
toroids. Since the initial sidebands are always located where the avoided mode crossing happens,
we can generate different types of frequency combs by shifting the pump wavelength. Figure 4-
15 shows the experimental results where we shifted the pump wavelength by 2 FSRs from
1551.0 nm to 1570.3 nm. In this process, the initial sideband is fixed at around 1541.5 nm, and
the combs change from Type-I to Type-II. The fixed initial sideband is a clear indicator of the
avoided mode crossing.
105

Figure 4-15 Comb generation at different pump wavelengths with the initial sideband fixed at
1541.5 nm as indicated by the red stars. Reprinted with permission from Chen, Dongyu, et al.
Applied Physics Letters 115, 051105 (2019).

One of the advantages of generating frequency combs from microresonators is that the
required pump power is lower compared to other systems, which also allows the system to have
smaller footprint. We studied the threshold of the parametric oscillation of SiO1.7N0.13 toroids,
which is the power required for exciting the initial sidebands. Theoretically, the threshold can be
written as
𝑃
+7
≈1..54
𝜋
2

𝑄
8
2𝑄
9
𝑛
5
𝑉
𝑛
5
𝜆
:
𝑄
9
5
(4.1)
where 𝑄
8
and 𝑄
9
are the coupling and loaded quality factors, respectively. 𝑛 is refractive
index, 𝑉 is mode volume, 𝑛
5
is the second-order nonlinear refractive index and 𝜆
:
is the pump
wavelength
51
. To decrease the threshold of parametric oscillation, methods like increasing the
quality factor and nonlinear refractive index and decreasing the mode volume are being explored.
106

In our experiment, the SiO1.7N0.13 toroids achieved very low threshold as a result of the ultra-high
quality factors (above 100 million) of the devices.
To characterize the threshold of the parametric oscillation, power of the idler peak was
monitored while we increase the input power into the resonator. The results are shown in Figure
4-16, where the measured relationship between the input power and idler output power is plotted.
The inset shows a typical signal and idler pair around the input. Threshold of the parametric
oscillation is characterized with the dashed black line at around 280 μW. This result is
comparable to or lower than the threshold of most current advanced platforms for Kerr frequency
comb generation.

Figure 4-16 Power of the idler signal recorded on Optical Spectrum Analyzer as a function of
the input power coupled into the resonator. The threshold is estimated to be around 280 μW.
Reprinted with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105
(2019).

107

While it is important to achieve low threshold, the ability to maintain this threshold as
well as overall performance of the combs is also an important factor for Kerr frequency combs.
As we discussed in last section, SiO1.7N0.13 toroids have the advantage of being environmentally
stable. As part of this work, we studied the stability of the frequency combs shown in Figure
13(a). In the experiments, the device was tested right after fabrication and 9-days after under the
same coupling conditions. The devices are stored in ambient atmosphere in a gel-pak during the
9-day gap. The Q factors and frequency comb spectra are recorded on both days at similar input
power levels. Qs on both days are measured to be 1.3x10
8
, which agrees with our findings in
previous section. The comb spectra are plotted in Figure 4-17.

Figure 4-17 The spectrums of the frequency combs generated on (a) day 1, and (b) day 9
after the fabrication.

Spectra from day 1 at different input powers are plotted in Figure 4-17(a) and spectra
from day 9 are plotted in Figure 4-17(b). Though the input power on day 1 and day 2 are not
108

exactly the same, they are at similar levels, and the spectra from two days are very similar in
terms of shape and span. To further quantify the similarity between the combs from these two
sets of measurements, we plotted the relationship between the input power and span in Figure 4-
18. Here the red points and dash lines represent measured and fitted trend from day 1,
respectively, and the blue points and lines represent result from day 9. For both days, the span of
the frequency combs increases as the input power increase, and finally reaches maximum span,
which is governed by the dispersion profile of the cavity. The two sets of results agree well with
each other, indicating the performance of the generated combs is stable over the 9-day period,
even though the devices are stored in ambient environment without any special protection.

Figure 4-18 The relationships between the comb span and the input power measured at both
Day 1 and Day 9 after the fabrication of the device. The combs are shown in Figure 4-17.
Reprinted with permission from Chen, Dongyu, et al. Applied Physics Letters 115, 051105
(2019).
109

4. 4. Summary

In this chapter, more detailed characterizations are performed on the silicon oxynitride
microtoroids, together with the demonstration of possible applications. Environmental stability
of the devices is characterized with both fluorescence microscopy, which can visualize the
density of the hydroxyl groups on the surface, and quality factor monitoring, which is very
sensitive to any changes to the devices. Dispersion of the microtoroids is also simulated and
characterized. Kerr frequency combs are generated from silicon oxynitride microtoroids with
normal dispersion. Threshold of the parametric oscillation is characterized and very low
threshold is achieved because of the high quality factor of the microtoroids. The generated
frequency combs also show very high environmental stability, which is consistent with the
environmental stability characterization of the silicon oxynitride microtoroids.

110

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116

Chapter 5. Modeling and Simulation
5. 1. Introduction
Optical modeling and simulation are useful in device design, data analysis and
understanding. It is performed by designing a model based on a real-world system or a system in
concept, with the purpose of calculating specific parameters that are of interest. A couple of
equations are usually developed for the model based on the physical principles to convert the
problem into a mathematical problem. For optical modeling and simulation, Maxwell equations
are usually the fundamental rules of the models. Depending on the complexity of the system and
the equations to solve, analytical solutions or numerical calculations are selected for different
problems.
In previous chapters, we have discussed the simulation of WGM microresonators for
calculating dispersion. Optical numerical simulations are selected because of the difficulty in
analytically solving the equations for WGM microresonators. COMSOL Multiphysics is used for
the numerical simulations, which is based on finite element method (FEM), to solve Maxwell
equations. With the powerful calculation capability of the simulation software, it is easy to
calculate various parameters of the WGM microresonators, for example modal area, modal
volume, modal profile, effective refractive index and dispersion.
In this chapter, I will discuss some other projects that used this modeling approach. These
projects are in collaboration with other lab members, and I lead the modeling and simulation
component. These modeling and simulation are used for understanding the data collected in the
experiments, as well as for fitting the data and extracting more information from the results.
Depending on the specific problem, different techniques and physical principles are applied.
117

Results of the modeling and simulation agree well with the experimental results, which gives us
better insights into our experimental system, as well as helping the optimization of the
experiments.

118

5. 2. Enhanced anti-Stokes Raman scattering from metal-
doped silica toroids
As previously discussed in Chapter 2, Stokes and anti-Stokes Raman scattering are third-
order nonlinear phenomena that take place inside the WGM microresonators
1-3
. Raman lasing
has been demonstrated in WGM resonators as well. While Stokes Raman lasing can easily occur
in silica microtoroids, benefiting from their high quality factors and relatively board and large
Raman gain
4-6
, anti-Stokes Raman lasing is hard to achieve, because it requires the excitation of
photons on vibration states, which has a very low density
7-9
. Anti-Stokes Raman lasing can also
be explained using FWM between the pump photons and Stokes Raman photons, where the anti-
Stokes photon is generated through the FWM process which involves two pump photons and one
Stokes photon. There are two factors limiting the generation of the anti-Stokes Raman lasing in
this process. One is the phase matching requirement of the FWM, which means that the Stokes
mode and anti-Stokes mode should be equally spaced away from the pump mode in the
frequency domain. Phase mismatch can decrease the efficiency of this process. The other factor
limiting the generation of anti-Stokes Raman lasing is that the density of Stokes photon is
usually orders of magnitude lower than the pump photon, which makes the density of anti-Stokes
even lower. This inhibits the formation of lasing.
To overcome the first limitation, dispersion engineering is required to decrease the
mismatch and increase the efficiency. To address the second problem and enhance the intensity
of anti-Stokes lasing, one research effort investigated doping silica with metal, like Zr and Ti, to
enhance the Stokes lasing efficiency, which in turn will lead to a higher anti-Stokes efficiency
10
.

119

5. 2. 1. Theory
While theories on Stokes Raman lasing inside the microresonators are well developed
11
,
the theory on anti-Stokes lasing based on the microresonators is less developed. In this project, I
focused on developing the model and theory to understand anti-Stokes lasing inside WGM
resonators, especially deriving the functions for the lasing intensity, which is beneficial for
understanding the experimental data.
The generation of the anti-Stokes signal can be viewed as a third-order nonlinear process,
where the interaction between the pump photons and Stokes photons results in the generation of
anti-Stokes photons. Since the intensity of the anti-Stokes signal is usually orders of magnitude
lower than the Stokes and pump, here we can ignore the terms of self-phase and cross-phase
modulations in the couple mode equations. After the simplification, the coupled mode equation
describing the amplitude of the anti-Stokes amplitude under slowly varying envelope
approximation can be written as:
𝜕𝐴
;
𝜕𝑡
=2𝑖𝛾𝐴
:
𝐴
:
𝐴
<
∗
𝑒
0∆?+
(5.1)

where 𝐴
;
, 𝐴
:
, 𝐴
<
are the amplitude of the anti-Stokes field, pump field and Stokes field,
respectively. 𝛾 =
?
!
*
#
( ;
$%%
, where 𝜔
:
is the angular frequency of the pump, 𝑛
5
=2.2×10
!52
,
#
A
is
the second-order nonlinear refractive index of silica. 𝐴
BCC
is the effective mode area. ∆𝜔 =
2𝜔
:
−𝜔
<
−𝜔
;
, and 𝜔
<
, 𝜔
;
are angular frequencies of the Stokes and anti-Stokes waves,
respectively.
Equation 5.1 can be solved analytically by integrating over time, after considering the
initial condition at time 𝑡 =0, 𝐴
;
= 0. We can get
𝐴
;
=
2𝛾
∆𝜔
𝐴
:
𝐴
:
𝐴
<
∗
(𝑒
0∆?+
−1) (5.2)

120

From equation 5.2, we obtain the intensity of the anti-Stokes field by applying the rule
between the intensity (𝐼) and amplitude (𝐴) of a field: 𝐼 =
D
5
𝐴
5
. 𝜀 is the permittivity of the
medium. The intensity of the anti-Stokes wave is
𝐼
;
=
16
𝜀
5
𝜔
:
5
𝑐
5
𝑛
5
5
𝐴
BCC
5
𝐼
:
5
𝐼
<
a
sin(∆𝜔𝑡/2)
∆𝜔/2
e
5
(5.3)
Here 𝐼
;
, 𝐼
:
, 𝐼
<
are the intensity of the anti-Stokes mode, pump mode and Stokes mode,
respectively. From the equation, we can see the intensity of the anti-Stokes mode is a function of
the frequency mismatch ∆𝜔. If ∆𝜔 is close to zero, the last part in equation 5.3 equals to 𝑡
5

under approximation and the intensity equals to
"E
D
#
?
!
#
(
#
*
#
#
;
$%%
#
𝐼
:
5
𝐼
<
𝑡
5
. From this expression, it seems
like the intensity of the anti-Stokes mode would increase to infinity as time increases. However,
the result is achieved under the approximation that the intensity of the anti-Stokes mode is much
smaller than the Stokes mode. When the intensity of the anti-Stokes mode becomes larger, the
equations here would not fit any more, so it would not go to infinity as the equations suggest. In
our experiments, the approximation holds true which means equation 5.3 is appropriate for the
experimental data. When ∆𝜔 gets larger, the last part in equation 5.3 approaches zero, which
means that phase mismatch limits anti-Stokes generation.
In WGM resonators, previous study has shown that when Raman mode is excited (power
of the pump mode is above the threshold), the pump mode would be a clamped mode, which
means the power of the pump mode, 𝐼
:
, becomes a constant
11
. Finally, from equation 5.3, the
intensity of the anti-Stokes mode, 𝐼
;
, would be a linear function of the intensity of the Stokes
mode, 𝐼
&
.

121

5. 2. 2. Experimental results
Experiments are performed on the silica microtoroids coated by metal-doped silica solgel
to observe stimulated Raman scattering (SRS) and stimulated anti-Stokes Raman scattering
(SARS). Zirconium (Zr)-doped and titanium (Ti)-doped silica solgel are used
12
. Quality factors
of the coated silica microtoroids are in the order of 10
7
. Though it is a little bit lower than
microtoroids without solgel coating, it is still high enough to excite the Stokes and anti-Stokes
photons. Figure 5-1 shows the relationship between the SRS power, SARS power and coupled
power. With the Ti-doped and Zr-doped silica, the efficiencies of the SRS and SARS increase
dramatically comparing to the bare silica devices. In Figure 5-1(a), SRS power is linearly
dependent on the coupled power, which agrees with previous research. In Figure 5-1(b), the
SARS power is also linearly dependent on the coupled power, which is because the SARS power
is linearly dependent on the SRS power as equation 5.3 suggests and SRS power is linearly
dependent on coupled power. Figure 5-1(c) further confirms the linear dependency between the
SARS and SRS.

Figure 5-1 (a) SRS and (b) SARS power as a function of the coupled power into the devices,
and (c) relationship between SARS and SRS power from various devices. Reprinted from Choi,
Hyungwoo, et al. Photonics Research 7, 926-932 (2019) under Open Access Publishing
Agreement. Copyright 2019 OSA.

122

A comparison of the threshold and efficiency of SRS and SARS of different types of
devices is plotted in Figure 5-2. As is shown in Figure 5-2(a), the averaged SRS threshold values
are 573.67 ± 54.35 µW for undoped devices, 329.33 ± 24.95 µW for Zr-doped devices and
342.67 ± 56.98 µW for Ti-doped devices. The SRS efficiencies are 3.38% ± 0.17%, 36.22% ±
2.44% and 33.22% ± 4.72% for these three types of devices, respectively. Thus, the coating of
the metal-doped silica solgel decreases the SRS threshold by over 1.5x and increases the
efficiency of SRS by 10x.

Figure 5-2 (a) Threshold and (b) efficiency values of SRS, and (c) threshold and (d)
efficiency values of SARS from various devices. Reprinted from Choi, Hyungwoo, et al.
Photonics Research 7, 926-932 (2019) under Open Access Publishing Agreement. Copyright
2019 OSA

123

Figure 5-2(c) and (d) plot the similar comparison of the threshold and efficiency for
SARS. The averaged SARS threshold values are 1081.49 ± 92.51 µW for undoped devices,
604.37 ± 66.83 µW for Zr-doped devices and 603.12 ± 26.75 µW for Ti-doped devices. The SRS
efficiencies are (0.91 ± 0.31) × 10
-4
, (14.66 ± 0.40) × 10
-4
and (14.20 ± 2.42) × 10
-4
for these
three types of devices, respectively. For SARS, devices with metal-doped silica solgel coating
have threshold decreasing by 1.8 x and efficiency increasing by 15x. The change in the SARS
generation is mostly contributed from the improvement in the SRS generation. The increase in
the population of electrons on the vibrational state in the metal-doped devices allows more pump
photons to be absorbed and excites these electrons from the vibrational state to the second virtual
state
12, 13
. Anti-Stokes photons are emitted when these excited electrons fall back to ground
states.

124

5. 2. 3. Summary
In conclusion, with the metal-doped silica solgel, thresholds of both SRS and SARS
decrease and efficiencies of both SRS and SARS increase. The theory of the anti-Stokes is
studied and equations for the intensity of the anti-Stokes mode are developed. From the
experiments, we observed a linear dependency on the SARS and SRS power, which agrees well
with the results of the theory and equations.

125

5. 3. Optical diagnostic for malaria
Malaria is a life-threatening disease that has killed millions of people worldwide. Though
reliable treatment has been developed for treating the infected patients, malaria is still heavily
impacting the developing countries, with hundreds of millions of cases and near half a million
deaths per year
14-16
. The high infection rate and death is largely due to the lack of medical
resources in the developing world to identify the infection early, like reliable and accessible
diagnostic tools. In this section, we will discuss the development of a portable rapid diagnostic
system for malaria based on a variant of optical spectroscopy.

126

5. 3. 1. The diagnostic system
For a diagnostic system, the key part is the indicator which tells if a patient is infected or
not. In the blood of a malaria-infected patient, a small nanoparticle called hemozoin exists as a
byproduct of the parasite digesting red blood cells
17-20
. One unique feature of the hemozoin is
that it is a magnetic nanoparticle, and unlike all other naturally occurring materials in the blood,
hemozoin has strong paramagnetic properties. As a material specific to malaria, hemozoin is an
ideal biomarker and selected in this project as the disease indicator. Its paramagnetic properties
are used in detecting the existence of the hemozoin, which is directly related to the infection of
malaria. In the experiments, a hemozoin mimic, β-hematin, is used, which allows us to study
hemozoin without the need to handle malaria-infected samples. β-Hematin and hemozoin from
P.falciparum share the same unit crystal structure and the same magnetic and optical properties,
which makes β-hematin a standard hemozoin mimic used in the field
21-23
.
We designed, constructed, and validated a portable optical diagnostic system for malaria
detection based on differential optical spectroscopy. Figure 5-3 shows a schematic of the testing
setup. A 635 nm laser diode (ThorLabs, CPS635) is used as the input, whose light passes through
a transparent poly(methyl methacrylate) cuvette, which contains the testing sample. The
transmission light is received by a photodetector (ThorLabs, S120C). A magnet is mounted on a
linear motion stage which can be brought close to or away from the cuvette.

127

Figure 5-3 Schematic of the portable diagnostic system with the axes indicated in the figure.

To perform the detection, a pair of measurements is taken before and after the magnet is
brought in close proximity to the sample. By monitoring the change in the transmission power,
we are able to determine the existence and concentration of the β-hematin in the sample. This is
because the magnet pulls all the magnetic nanoparticles out of the beam path, which decreases
the scattering caused by the nanoparticles and increases the transmission power. Thus, the
change in the signals is directly related to the nanoparticle concentration. While some lab
members focused on the sample preparation, system design and construction, and testing, I
mainly focused on the modeling and data analysis in this project.

128

5. 3. 2. Modeling
The key part in the model is to analyze the movement of the nanoparticles in the x and y
directions. The axes are defined in Figure 5-3 using the yellow arrows. Movement in the z
direction is not taken into consideration because it generates minor effects on the transmission
power. For a single independent particle in the sample solution, the following forces must be
considered when analyzing its movement: gravity, viscous resistance, and magnetic force
generated by the magnet. As the diffusion coefficient is very small for nanoparticles with size
around 100 nm, the diffusion term can be neglected as the movement caused by the diffusion is
much slower than the movement caused by the magnetic field. Therefore, the pair of equations of
motion can be written as:
𝑚
𝑑
5
𝑥
𝑑𝑡
5
= 𝐹
F
− 𝐶
F
𝑑𝑥
𝑑𝑡
(5.3)

𝑚
𝑑
5
𝑦
𝑑𝑡
5
= 𝐹
G
− 𝐶
G
𝑑𝑦
𝑑𝑡
−𝑚𝑔 (5.4)

where 𝑚 is the mass of the particle, 𝐹
F
and 𝐹
G
are magnetic forces in the x and y directions,
𝐶
F
%F
%+
and 𝐶
G
%G
%+
are the frictional forces proportional to the speed of the particles. 𝐶
F
and 𝐶
G
are
linearly dependent on the dynamic viscosity while also related to the structure of the particles.
Based on the magnetic strength values provided by the manufacturer and assuming that
the magnetic force is linearly dependent on the distance from the magnet and is nearly parallel to
the x-axis, we can calculate the magnetic forces. Setting the starting point of the x-axis and y-
axis at the center of the magnet, 𝐹
F
and 𝐹
G
can be written as 𝐹
F
=𝐴𝑥−𝐵 and 𝐹
G
= 𝛾k𝐴−
H
F
l∗
𝑦. Here, 𝐴, 𝐵 and 𝛾 are parameters related to the magnetic field, which are determined by the
129

properties of the magnet. 𝐹
F
is negative, which means that the direction of 𝐹
F
is along the
negative x-axis while the direction of 𝐹
G
changes depending on the value of 𝑦.
The equation of motion in the x direction can be solved analytically:
𝑥(𝑡) =𝑃𝑒
I
&
+
+𝑄𝑒
I
#
+
+𝐵/𝐴 (5.5)
where
𝛿
"
=
−𝐶
F
+ o𝐶
F
5
+4𝑚𝐴
2𝑚
(5.6)

𝛿
5
=
−𝐶
F
− o𝐶
F
5
+4𝑚𝐴
2𝑚
(5.7)

𝑃 and 𝑄 can be determined by the initial conditions. Figure 5-4(a) shows an example of the
particle trajectory in the x direction versus time, with initial position 𝑥
2
= 10 mm; 𝑥
2
= 8 mm; 𝑥
2

= 6 mm, and initial velocity equals to zero. The speeds of the particles increase as they ger closer
to the magnet. However, the equation of motion in the y direction does not have a simple
analytical solution because 𝐹
G
is dependent on x. Figure 5-4(b) shows an example of the
numerical results in the y direction, with initial positions 𝑥
2
= 10 mm and 𝑦
2
= 7 mm; 𝑦
2
= 5
mm; 𝑦
2
= 3 mm, and initial velocity equals to zero.
130

Figure 5-4 Examples of particles’ movement in x and y directions.

This calculation is intended to provide guidance in the experimental design, and the
parameters used in this calculation are close estimated values of the experimental conditions.
Though the time scale does not exactly match the experiment, it is obvious that the particles’
movements in the y-direction slow down as they approach to the x-axis. In the experiments, the
observation window is a very small area (beam size of the laser) near the x-axis. Thus, particles’
movements in the y direction make a minor impact on the transmission as the particles move
much more slowly in the y direction compared to the x direction when they are in the
observation area. The transmission was mostly determined by the movements of particles in the
x direction.
From equation 5.3, we can calculate the trajectories of all the particles with different
initial positions. Meanwhile, initial positions of the particles in the observation window at any
time 𝑡 can be also determined using the equation. For a laser beam with width Δ𝑥, at time 𝑡, we
can get the initial width of the particles Δ𝑥
J
through a simple calculation:
131

Δ𝑥
J
=
𝛿
"
−𝛿
5
𝛿
"
𝑒
I
#
+
−𝛿
5
𝑒
I
&
+
Δ𝑥 (5.8)

Assuming that all particles are uniformly distributed in the solution before the magnet is
applied, decrease in the number of particles in x direction in the observation window can be
calculated. Since the change in the transmission is dominated by movements in the x direction,
this change in the number of particles dominates the change in the transmission power. Decrease
in the number of particles can be written as
Δ𝑛 ∝1−
𝛿
"
−𝛿
5
𝛿
"
𝑒
I
#
+
−𝛿
5
𝑒
I
&
+
(5.9)

In our experiments, the mass of the particles is small while the viscosity is high,
Therefore, from equation 5.4 and 5.5, we can get that 𝛿
"
is positive, 𝛿
5
is negative, and |𝛿
5
| ≫
|𝛿
"
|. So, the final expression for change in transmission power can be approximated as
Δ𝑃 =𝑓(𝜌)(1−
𝛿
"
−𝛿
5
𝛿
"
𝑒
I
#
+
−𝛿
5
𝑒
I
&
+
)≈𝑓(𝜌)(1−𝑒
!I
&
+
) (5.10)

Here, 𝑓(𝜌) is the maximum change of the transmission power and is a function of the density
of magnetic nanoparticles. 𝑓(𝜌) is determined using experimental data because the actual
relationship between number of nanoparticles and transmission power is complex.
Equation 5.8 provides the relationship between the transmission power and time, which
can be directly measured in the experiments. Experimental data is fit using this equation. For
each data set, there are two parameters to fit, 𝑓(𝜌) and 𝛿
"
. As 𝛿
"
is related to the mass of the
particle, magnetic forces and viscous resistance on each particle, it should be a constant for
measurements conducted using the same solution and the same particles. In the meantime, 𝑓(𝜌)
reveals the maximum change of the transmitting power, and it is dependent on the concentration
of the nanoparticles. So, for testing samples with higher concentration of nanoparticles, 𝑓(𝜌) is
132

larger. Furthermore, the relationship between 𝑓(𝜌) and 𝜌 can be fit using a sigmoidal curve
based on the sensing theory. This relationship is also verified by the experimental results.

133

5. 3. 3. Data analysis
Before performing measurements with whole blood sample, a series of experiments are
conducted using β-hematin in polyethylene glycol (PEG) solutions to validate the hypothesis and
optimize the system design parameters. Two different concentrations of PEG are used, 10% and
15%. The preliminary results are shown in Figure 5-5. Figure 5-5(a)-(c) shows the results of β-
hematin with different concentrations in 10% PEG, and Figure 5-5(d)-(e) shows the
corresponding results in 15% PEG. The results are split into three panels for each solution
because the concentrations of β-hematin range from 0.0087 µg/mL to 393.3 µg/mL. It is
impossible to fit all concentrations into one plot and still differentiate them from each other.

Figure 5-5 Preliminary results for tests with β-hematin with different concentrations in (a) –
(c) 10% PEG and (d) – (f) 15% PEG. Experimental results are solid lines and mathematical
results are dashed lines.

134

In Figure 5-5, experimental data is shown as a solid line for each concentration while the
result from mathematical modeling is shown as a dashed line. From the modeling, 𝛿
"
equals
0.0056 for β-hematin in 10% PEG and 𝛿
"
equals 0.0038 for β-hematin in 15% PEG. 𝛿
"
decreases
as the concentration of PEG increases because the viscous resistance increases for higher
concentration of PEG. This relationship between 𝛿
"
and viscosity agrees with the modeling
previously discussed. Also, it is notable that the experimental data fits exceedingly well to the
modeling for every concentration.
To further analyze the experimental data and reproducibility of the experimental results, a
subset of the results in Figure 5-5(a)-(c) (10% PEG) is taken for a closer analysis. The results are
plotted in Figure 5-6. As expected, the signal is dependent on the concentration of β-hematin in
the solution. Even with β-hematin concentrations as low as 0.0087 µg/mL, there is still a sizable
increase in transmission upon application of the magnetic field as compared to the base noise
level. The slight fluctuation in the transmission is related to the random particle-particle
interactions, which is not possible to predict absolute values at any point in time. Instead of
fitting the experiment data to a single line, here a ± 15% bound around the model fitting results is
given as the lower and upper bound of the predicated signal. The experimental data and the
ranges provided by simulations have an excellent agreement. In Figure 5-6(b), 𝑓(𝜌), the
maximum change in the transmission signal is fit using a sigmoidal curve as previously
discussed. Figure 5-6(c) investigates the reproducibility of the system. Each sample was
analyzed three times to determine the reproducibility of the sensing signal generated. The results
confirmed that the system was able to reproducibly detect clinically relevant concentrations of β-
hematin in PEG solutions with minimal user input.
135

Figure 5-6 Results for preliminary tests with β-hematin in 10% PEG. (a) Experimental and
mathematical results. Solid lines show experimental data and shaded regions show ranges
provided by mathematical modeling. Time on the x-axis refers to the total testing time. The
magnetic field is applied at t = 30s. (b) Working range of the diagnostic system for β-hematin
concentrations in 10% PEG. (c) Reproducibility of results with measurements performed
iteratively using the same setup. Reprinted with permission from McBirney, Samantha E, et al.
ACS sensors 3, 1264-1270 (2018). Copyright 2018 American Chemical Society.

To further study the performance of the diagnostic system, a series of rabbit whole blood
samples were prepared with known concentrations of β-hematin doped. The blood samples are
prepared with ultrasound and only 500 µL of the sample is used for each measurement. The
results are shown in Figure 5-7. In Figure 5-7(a), β-hematin with concentrations as low as 0.0081
µg/mL can be detected with signal-to-noise ratio of 4.03. This concentration is a full order of
magnitude below clinical relevance. The experimental data and the range provided by
mathematical modeling agree very well. Figure 5-7(b) characterizes the working range of the
system and Figure 5-8(c) characterizes the reproducibility of the instrument. The results are
consistent over different cycles.

136

Figure 5-7 Results for tests with β-hematin in whole rabbit blood. (a) Experimental and
mathematical results. Solid lines show experimental data and shaded regions show ranges
provided by mathematical modeling. (b) Working range of the diagnostic system for β-hematin
concentrations in rabbit blood. (c) Reproducibility of results with measurements performed
iteratively using the same setup. Reprinted with permission from McBirney, Samantha E, et al.
ACS sensors 3, 1264-1270 (2018). Copyright 2018 American Chemical Society.

137

5. 3. 4. Summary
In conclusion, in this section, we studied the mathematical modeling for the optical
diagnostic system for malaria based on the differential spectroscopy. A series experiments are
performed with β-hematin in both PEG solutions (10% and 15%) and rabbit whole blood.
Samples with very low β-hematin concentration (an order of magnitude below clinical relevance)
can be detected with the system, and the results can be consistently reproduced. The
experimental results agree very well with the modeling results. The system is promising for the
quick detection of malaria infections in low resource environment.

138

5. 4. UV-C disinfection system
Highly infectious microbial and viral diseases are a major challenge to the world, which
can bring huge cost to global health, financial stability and security. The widespread COVID-19
pandemic has caused hundreds of thousand deaths globally and brought tremendous physical,
mental and financial suffering to the people around the world. While vaccines play a key role in
preventing the epidemics and pandemics, it takes long time for a vaccine to be developed, tested
and deployed. Once an outbreak has occurred, the implementation of personal protective
equipment (PPE) and disinfection measures to limit the spread becomes paramount. In this
section, we will discuss a home-built and portable disinfection system that is easy to build and
implement. This section is based on our publication “She, Rosemary C., et al. "Lightweight UV-
C disinfection system." Biomedical Optics Express 11.8 (2020): 4326-4332.”
24
.
There are many methods of disinfection that have been developed, like chemical,
radiation and thermal
25-30
. Among these methods, short-wavelength ultraviolet (ultraviolet C or
UV-C) light has gained favor due to its efficacy against a broad range of microbial and viral
agents in a variety of environments and on a wide range of surfaces
27, 31
. The UV-C light covers
the wavelength ranging from 100 nm to 280 nm, which overlaps with the peak absorption of
DNA and RNA. The disinfection is achieved by causing transcription errors to inactivate the
bacteria or virus from reproduction
32
.
Figure 5-8 shows an illustration and a picture of the disinfection system that is built at
home. It includes a plastic bin, UV-C light bulb, and standard light housing. To increase the UV-
C intensity, the interior of the enclosure is coated with a reflective coating.
139

Figure 5-8 UV-C disinfection system. (a) Schematic of system. (b) Image of system before
application of reflective coating. (c) Example of several systems with reflective coating.
Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332 (2020) under
Open Access Publishing Agreement. Copyright 2020 OSA.

140

5. 4. 1. Modeling
The most important element of the system is optical power delivered by the UV-C
source. As simple guidelines, the dose delivered by the UV-C source is dependent on the
distance the object is away from the source, the source wattage and efficiency, and the exposure
duration. In other words, a lower wattage source can be used in place of a higher wattage source,
if the exposure duration is increased. Given the access to components may be highly variable, it
is desirable to create a generalizable expression governing the UV-C intensity distribution inside
of the UV-C system. This expression can then be used to calculate the impact of different bulbs
on UV-C dose, accelerating re-design when needed.
As a starting point in creating the model, the UV-C bulb is treated like a linear light
source, where each point on the bulb is a point light source with isotropic radiation. The
cumulative UV-C dose created by the bulb is an integration of the dose generated by all the point
light sources on the bulb. As is shown in Figure 5-9, assuming we have an enclosure with length
L, width W and height H. The bulb is placed on the sidewall above the floor of the box by a
height of h, and it has an optically active length of ℓ and is centered on the wall horizontally.
Given this configuration, the location of any point source on the bulb can be expressed as (𝑋, 0,
ℎ), where 𝑋 ∈ w
9!ℓ
5
,
9Lℓ
5
y. For any detection point (x, y, z) in the box, the distance between the
point light source and the detection point is:
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = o(𝑋−𝑥)
5
+ 𝑦
5
+ (ℎ−𝑧)
5
(5.11)
141

Figure 5-9 Schematic showing key variables used to calculate cumulative UV-C dose.
Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332 (2020) under
Open Access Publishing Agreement. Copyright 2020 OSA.

Assuming the UV-C wattae power of the bulb is 𝑃 (unit: Watt), then the power of the
input source is 𝑃/ℓ. As the point source radiates isotropically in a sphere, the radiation intensity
on point (x, y, z) would be:
𝑃/ℓ
4 𝜋 ((𝑋−𝑥)
5
+ 𝑦
5
+ (ℎ−𝑧)
5
)
(5.12)

By integrating all the point sources on the bulb, we get the intensity generated by the whole
bulb:
𝐼 = }
𝑃/ℓ
4 𝜋 ((𝑋−𝑥)
5
+ 𝑦
5
+ (ℎ−𝑧)
5
)
9Lℓ
5
9!ℓ
5
(5.13)

The intensity calculated in the equation 5.13 is for the situation where there is no
reflection from the box. However, in the system deveoped in the present work, the interior is
coated with a reflective chrome paint. To simplify the reflection calculation and set a lower
bound on the intensity inside the enclosure, we only take the firat and second order of reflections
142

into consideration. The calculation of intensity generated by the reflection is similar to the
previous one with slight modification. To account for the reflection, a series of “virtual light
bulbs” with a power of 𝛼𝑃 for first order reflection and 𝛼
5
𝑃 for second order reflection, where 𝛼
is the reflection rate, are located on virtual walls mirrored by other walls in the ectended space.
There are 6 first-order mirrored light sources and 30 second-order mirrored light sources in total.
The intensity generated by each mirrored bulb can also be calcuated using the integration method
described above. The only difference is that the distance between point (x, y, z) amd the mirrored
bulb is different from the previous calculation. By adding the reflection caused by all the walls
(including ceiling and floor) together, we get the intensity of the UV-C light inside the box. The
intensity can be expressed in the following equation:
𝐼
M0+7 #BC/B(+0)*
= }
𝑃/ℓ∗𝑑𝑋
4𝜋 ((𝑋−𝑥)
5
+𝑦
5
+(ℎ−𝑧)
5
)
9Lℓ
5
9!ℓ
5
+
}
𝛼𝑃/ℓ∗𝑑𝑋
𝑁𝑒𝑤 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
9Lℓ
5
9!ℓ
5 C0#&+!)#%B#
#BC/B(+0)*
+ }
𝛼
5
𝑃/ℓ∗𝑑𝑋
𝑁𝑒𝑤 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
9Lℓ
5
9!ℓ
5
&B()*% !)#%B#
#BC/B(+0)*
(5.14)

In the system shown in Figure 5-8, L = 78.74 cm, W = 50.8 cm, H = 35.56 cm, h = 25.4
cm, and ℓ = 43.18 cm. The wattage of the UV-C light bulb is 15 W, and consideriing a 35%
conversion efficiency, the UV-C wattage 𝑃 =5.25 W. By putting all these parameters in the
equation, we can calculate the intensity at any point in the box (unit: W/cm
2
). To determine the
UV-C dose, this value should be multiplied by the time that the system is on.
Figure 5-10 (a)-(c) shows the results from a series of calculations for an exposure time of
3 minutes. The wall reflectivity varies from 0% (Figure 5-10(a)) to 85% (Figure 5-10(c)), which
covers the range of possible values that could be achieved in our system. The dose achieved
varies by severl orders of magnitude depending on the location within the enclosure and the
143

reflectivity of the walls. Figure 5-10(d) shows the dose at the center of the enclosure from the
very bottom to the top. As can be seen, even with modest wall reflectivity (25%), the enclosure is
able to achieve doses above 10 mJ/cm
2
throughout the space, which is sufficient to meet
guidelines for bacteria, and with reflectivities of 85%, doses are well-above 100 mJ/cm
2
, which
is sufficient to meet guidelines for viruses.

Figure 5-10 Cumulative UV-C dose delivered for a three minute exposure inside the UV-C
disinfection system. Three different wall reflectivity values are modeled: (a) 0%, (b) 25%, and
(c) 85%. (d) The dose at different heights for all three reflectivities modeled, measured in the
centered of the box x-y plane (e) Dose as a function of time for three different UV-C source
powers. This calculation is performed at the center of the bottom of the enclosure. The specific
coordinate based on the schematic in Fig. 2 is (39.4, 25.4, 0). For comparison, the requisite doses
to achieve three log reduction in growth for two bacteria and two viruses are also plotted.
Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332 (2020) under
Open Access Publishing Agreement. Copyright 2020 OSA.

To compare the effects of the power generated by different optical sources, the
calculation was run with two additional sources with lower and higher powers, and the dose in
144

the bottom-center of the box was determined for different exposure times. As can be observed in
Figure 5-10(e), with a different power sources, the exposure duration needed to achieve a
specific dose was dependent linearly on optical power. For context, the dose required to achieve
three log reduction of two bacteria and two viruses are included in Figure 5-10(e)
33-36
. However,
it is critical to note that this calculation does not consider thermal effects. For example, if high
enough powers are used with optically absorbing materials, some optical power will be lost to
thermal heating. Thermal heating is particularly deleterious when the system is being used for
PPE re-use as it can result in the degradation of the PPE.

145

5. 4. 2. Experimental results
The UV-C disinfection system was built at home with low cost materials. Using B. cereus
as a test organism and untreated plastic Perti dishes as a representative non-porous surface, the
efficacy is experimentally validated. B. cereus is an aerobic, rod-shaped, gram-positive bacteria
that can quickly multiply at room temperature. B. cereus can form endospores that can withstand
harsh conditions including UV exposure
37, 38
. Previous work demonstrated that a UV-C dose
between 35-140 mJ/cm
2
is required to achieve a 3 log reduction of B. cereus on non-porous
surfaces
39, 40
.
B. cereus previously isolated from routine clinical culture was selected for this study.
After subculture on sheep blood agar and overnight incubation at 35 °C, a 4.0 McFarland
suspension was prepared in sterile 0.45% saline solution. For analysis of UV-C irradiation of
plastic surface, 100 µL aliquots were dispensed onto sterile polystyrene Petri dishes (100 mm
diameter) to mimic face shield surfaces over an approximately 1 × 2 cm area, then allowed to
completely dry at 35 °C, up to 30 minutes. Exposure times of 1, 3, and 6 minutes were tested as
well as control different locations equally spaced on the bottom of the box (z = 0), including one
in the centern, as modelled in Figure 5-10(e), and one on either side (19.7, 25.4. 0) and (59.1,
25.4, 0).
Immediately after the UV-C radiation treatment, each Petri dish was flooded with 10 mL
of 0.45% saline and scraped to completely resuspend the film. For baseline counts, 100 µL of
1:100 and 1:10,000 dilutions were plated on sheep blood agar in duplicate. For UV-C irradiated
organism counts, 100 µL of neat, 1:100, and 1:10,000 dilutions of each sample were plated in
duplicate. After a 24 hr incubation of culture plates at 35°C in 5% CO2, individual colonies were
146

enumerated and the dilution resulting in the highest calculated mean organism concentration was
used for analysis.
For analysis of direct irradiation of agar media, sheep blood agar plates were inoculated
with 1 µL and 10 µL of the 4.0 McF suspension prior to UV-C exposure. Baseline counts were
obtained for each experiment and were prepared in the same manner as experimental samples.
As can be seen in Figure 5-11(a), the B. cereus samples that were not exposed to UV-C
readily formed colonies after 24 hour incubation time indicating that all preparation methods
were correct. The baseline counts of Petri dish organism films ranged from 1 to 3 x 10
6
colony
forming units (CFU). In contrast, this growth was dramatically eliminated when the samples
were exposed to the UV-C, even with only 1 minute exposure (Figure 5-11(a)).
At 1 minute of UV-C exposure, all organism counts were nil except for one of three
replicates in which 800 CFU remained. At 3 and 6 minute UV-C exposure times, organism
counts were reduced to undetectable levels except for one of three replicates in which 100 CFU
remained. Directly irradiated organisms on blood agar plates demonstrated no growth of
organisms at 3 and 6 minute exposure times but growth of 700 CFU/mL after 1 minute exposure,
whereas baseline count was >3 x 10
5
CFU/mL (Figure 5-11(b), (c)). As mentioned, previous
work demonstrated that a dose between 35-140 mJ/cm
2
of UV-C achieved a 3 log reduction of
vegetative B. cereus cells. Based on the analytical calculations presented in Figure 5-10(e), a 1
minute exposure in the center of the box should have provided a dose in excess of 200mJ/cm
2
.
Therefore, these findings align with the prior results
39, 40
.
147

Figure 5-11 Summary of results. (a) In both control samples, over 106 colony forming units
(CFUs) grew during the 24 hour incubation period. In contrast, the majority of the exposed
dishes were unable to support colony formation, indicating a 6 log reduction. (b) Control sample
of B. cereus not exposed to UV-C formed colonies after 24 hour incubation time. (c) In contrast,
this growth was dramatically eliminated after 1 minute exposure of identical sample preparations
to the UV-C. Reprinted from She, Rosemary C, et al. Biomedical Optics Express 11, 4326-4332
(2020) under Open Access Publishing Agreement. Copyright 2020 OSA.

In addition to achieving >3 log reduction, the exposure times compare favorably to
commercial UV-C disinfection systems which typically have disinfection protocols between 1-2
minutes. The alignment between the current portable, lightweight approach and the conventional
commercial systems is possible because the cumulative dose delivered is the same, as shown in
Figure 5-10. However, the proposed system offers numerous advantages. Specifically, the design
can be adapted to use any UV-C bulb length, it is easy to construct, and it is less expensive.

148

5. 4. 3. Summary

In conclusion, we have designed and validated a simple to construct UV-C disinfection
system. It uses readily available, inexpensive components to create the UV-C chamber. The
efficiency of the system is further improved by coating the interior with a reflective material. As
a result, the intensity of the UV-C optical field is amplified, allowing shorter exposure times to
be used. Over 3 log reduction in CFUs on a polystyrene (or non-porous) surface is confirmed
using B. cereus as a model bacteria. Future research efforts are focused on improving the
operational safety of the system by integrating pressure switches to automatically control the
UV-C source, on exploring alternative light sources, such as UV-C LEDs, to improve the
robustness and power management, and on optimizing UV-C for porous media disinfection,
notably mask re-use. This approach will find use during the current COVID-19 pandemic where
PPE, such as faceshields and masks, is in short supply as well as in the future in low resource
environments
41
.

149

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Abstract (if available)

Abstract Optical whispering-gallery mode resonators are a type of resonator with a circular enclosed structure, where light can circulate for a long period of time. The high confinement of light greatly enhances the optical field inside the resonators, which makes these devices an ideal platform for nonlinear optics like Raman lasing and Kerr frequency combs. Optical Kerr frequency combs attract special attention recently due to its wide range of application in areas like spectroscopy, Lidar, communication and optical atomic clocks. To realize these applications, different materials are explored and examined aiming for higher quality factors, higher nonlinear coefficient and higher modulation ability. Currently silica and silicon nitride are the two materials that dominate the field. While silica has very low materials loss, which enables high quality factors, it has a relatively low nonlinear coefficient and lacks the ability to realize a fully integrated system. It also suffers from the limitation that the surface of silica is unstable in an ambient atmosphere environment. On the other hand, while silicon nitride can easily achieve a fully integrated system and has higher nonlinear coefficient, devices made from silicon nitride have much lower quality factors as a result of higher material loss. ❧ In this thesis, we explored another material, silicon oxynitride, for the fabrication of whispering-gallery mode resonators. The silicon oxynitride wafers are deposited in the lab and the basic material properties are characterized. Optical microtoroids are fabricated from these wafers, which achieved ultrahigh quality factors. The environment stability of these devices is characterized with both optical methods and fluorescent microscopy. Comparing to silica microtoroids, silicon oxynitride microtoroids are more stable in ambient atmosphere. Kerr frequency combs are also demonstrated from these devices with normal dispersion. In the device design and data analysis, optical modeling and simulation play an important role. In this thesis, the modeling and simulation on the whispering-gallery model resonators are also discussed. Besides that, we also discussed the modeling on two other projects. One is the modeling for the optical malaria diagnostic system, and the other one is for the UV-C disinfection system. In both projects, the modeling helps the understanding and analysis of the experimental data and agrees well with the observed results.

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Asset Metadata

Creator Chen, Dongyu (author)

Core Title Optical simulation and development of novel whispering gallery mode microresonators

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 01/28/2021

Defense Date 12/07/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag frequency combs,Modeling,OAI-PMH Harvest,optical,photonics,silicon oxynitride,simulation,whispering-gallery mode microresonators

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Armani, Andrea Martin (committee chair), Thompson, Mark E. (committee member), Willner, Alan (committee member), Wu, Wei (committee member)

Creator Email cdyphy@gmail.com,dongyuch@usc.edu

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