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Nonlinear optical nanomaterials in integrated photonic devices

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Nonlinear optical nanomaterials in integrated photonic devices

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Content NONLINEAR OPTICAL NANOMATERIALS
IN INTEGRATED PHOTONIC DEVICES

by
Vinh Mien Diep

____________________________________________

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
Materials Science

August 2018

Copyright © 2018 Vinh Diep
ii

To my family, who stressed the importance of education, a privilege that was stripped
from them by war.
iii
Acknowledgments
The past five years here at USC has been an incredible journey that I will
assuredly look back upon with fond memories. Five years is a long stretch of time by any
standard, but I can honestly say that my time here has flown by, likely due to what they
say about how time behaves when you are having fun. Much of that fun is due to the
many people who have helped me in many ways along the way.
First and foremost, I must thank my advisor, Professor Andrea Armani, for her
guidance and mentorship in my development as a scientist. She made the decision to
come to USC an easy one, and it has been a pleasure to be a part of the Armani Lab. Your
passion for research and bringing USC to new heights knows no bounds, and I know you
will achieve all of your lofty goals.
I have also had the privilege of meeting many amazing professors at USC who
have taught me so much. In particular, I want to thank the members of my qualifying and
dissertation committees: Professor Jayakanth Ravichandran, Professor Paulo Branicio,
Professor Wei Wu, and Professor Pin Wang. Additionally, thank you to Professor Mike
Sailor and Dr. Michelle Chen, who mentored me as an undergraduate at UC San Diego
and helped me develop a love for research. I also owe thanks to Dr. Jarred Collins, who
accomplished the impossible task of making calculus fun in high school and inspiring me
to pursue a PhD. Thank you to all of my teachers from the past 23(!) years of schooling.
To all the friends and labmates whom I’ve met throughout grad school, I
definitely could not have made it through without you by my side. From the happy hours
to the not so happy hours, there are so many memories that I cherish with each and every
one of you. In no particular order, thank you to Alexa Hudnut, Victoria Sun, Michele
iv
Lee, Andre Kovach, Hyungwoo Choi, Erick Moen, Mark Harrison, Kelvin Kuo, Rene
Zeto, Soheil Soltani, Xiaoqin Shen, Rigoberto Castro-Beltran, Sam McBirney, Ashley
Maker, Eda Gungor, Lili Lash-Rosenberg, Tushar Rane, Abian Bentor-Socorro, Amanda
Cordes, Akshay Panchavati, Arsenii Epishin, Cecilia Lopez, Rasheeda Hawk, Maria
Chistiakova, Simin Mehrabani, Ce Shi, Xiaomin Zhang, Leah Tsui, Tara Assi, Brock
Hudnut, Danny Amchin, Linda Xu, John Lazzeroni, Lea Fang, Martin Siron, Sam
Kushner-Lenhoff, Gumi Sethi, Julie Strickland, Garrison Crouch, Max Reynolds, Emma
Meinke, and Nishita Deka. Special thanks to Teresa Estrella and Omar Garcia for putting
up with me as your mentor!
Outside of school, I want to thank all of my training partners at Westside Training
Center. I am so fortunate to have stumbled upon a top-notch academy for Brazilian jiu-
jitsu and kickboxing that has given me a lifelong passion. Thank you especially to Duke
Sutton and Damaris Armas, who have created a welcoming and warm atmosphere that
has helped me through more tough times than I care to admit. Thank you to instructors
Isaac Doederlein, Jose Diaz, Tino Morales, Will Candelario, Ram Ananda, Ryan Stiles,
and Kaiyana Rain for sharing your vast knowledge with all of us. Thank you to all of my
friends and family who have supported me throughout my time in grad school and helped
me maintain my sense of adventure and love of food. Special shout out to Bryce Caputo
for always convincing me to sneak off on camping or snowboard trips and helping me out
with MATLAB.
Last but not least, I want to thank my parents, brother, and sister-in-law. They
have been my continued source of stability, humility, and tranquility. In my moments of
neuroticism, they are always there to keep me grounded. Having them nearby in San
v
Diego has been a blessing, with their home cooked meal care packages saving me
countless times. No matter the problem I faced or will face, I know that I can always turn
to them for guidance. Mom and Dad... I know you understand almost none of what’s
written in this dissertation, but I hope that I’ve made you proud. I will continue to do my
best.

“One day, in retrospect, the years of struggle will strike you as the most beautiful.”
-Sigmund Freud
vi
Table of Contents

Acknowledgements............................................................................................................iii
Table of Contents................................................................................................................vi
List of Figures.....................................................................................................................iv
Abstract...............................................................................................................................xi
Chapter 1: Overview............................................................................................................1
1.1 Motivation..........................................................................................................1
1.2 Chapter Overview..............................................................................................3
Chapter 1 References...............................................................................................6
Chapter 2: Background......................................................................................................10
2.1 Integrated Photonics.........................................................................................10
2.2 Whispering Gallery Mode Resonators.............................................................12
2.2.1 Quality Factor...................................................................................13
2.2.2 Free Spectral Range..........................................................................15
2.2.3 Evanescent Field...............................................................................16
2.2.4 Fabrication........................................................................................17
2.2.5 Optical Testing of WGMRs..............................................................20
2.2.5.1 Quality Factor Determination............................................21
2.2.5.2 Emission Measurements and Threshold Calculation.........23
2.3 Nonlinear Optics..............................................................................................25
2.3.1 Kerr Effect........................................................................................28
2.3.2 Four Wave Mixing............................................................................30
2.3.3 Stimulated Raman Scattering............................................................33
2.3.4 Brillouin Scattering...........................................................................35
2.4 Dispersion........................................................................................................36
2.5 Frequency Combs............................................................................................39
Chapter 2 References.............................................................................................41
Chapter 3: Dispersion-Compensated Frequency Combs with Calcium Fluoride
Nanocrystals on Whispering Gallery Mode Resonators....................................................49
3.1 Introduction and Background..........................................................................49
3.2 Calcium Fluoride Crystals in Silica Sol Gel....................................................51
vii
3.2.1 Methods: Synthesis and Material Characterization..........................51
3.2.2 Methods: Optical Characterization...................................................56
3.3 Chemical Co-Precipitation Synthesis of Calcium Fluoride.............................57
3.3.1 Methods: Synthesis and Material Characterization..........................57
3.3.2 FEM Modeling..................................................................................61
3.3.3 Numerical Calculations.....................................................................64
3.3.4 Methods: Optical Characterization...................................................70
3.3.5 Results: Quality Factor.....................................................................71
3.3.6 Results: Threshold............................................................................73
3.3.7 Results: Comb Generation................................................................75
3.4 Conclusions......................................................................................................82
Chapter 3 References.............................................................................................84
Chapter 4: Gold Nanoparticle-Enhanced Frequency Comb Generation............................89
4.1 Introduction and Background..........................................................................89
4.2 Methods: Synthesis and Material Characterization.........................................91
4.3 Methods: FEM Modeling.................................................................................94
4.4 Results: Optical Testing...................................................................................96
4.5 Conclusions....................................................................................................103
Chapter 4 References...........................................................................................105
Chapter 5: Zinc Oxide Nanotetrapod-Based Flexible Fluorescent Material...................109
5.1 Introduction and Background........................................................................109
5.2 Methods: Synthesis and Material Characterization.......................................112
5.3 Results: Optical Properties.............................................................................119
5.4 Results: Modeling..........................................................................................124
5.5 Conclusions....................................................................................................125
Chapter 5 References...........................................................................................127
Chapter 6: Future Work...................................................................................................133
6.1 Enhanced Stimulated Brillouin Scattering.....................................................133
6.1.1 Methods...........................................................................................133
6.1.2 Preliminary Results.........................................................................134
6.2 Frequency Comb Enhancement via Simultaneous Dispersion and Kerr
viii
Coefficient Engineering...........................................................................135
6.3 Nonlinear Optical Phenomena in Carbon Nanotubes....................................136
Chapter 6 References...........................................................................................138
Appendix 1: Enhanced Stimulated Anti-Stokes Raman Scattering with Functionalized
Gold Nanorods.................................................................................................................140
A1.1 Methods: Gold Nanorod Synthesis and Microresonator Fabrication..........140
A1.2 Results: FEM Modeling..............................................................................141
A1.3 Results: Numerical Calculations.................................................................142
A1.4 Results: Optical Testing..............................................................................143
A1.5 Conclusions.................................................................................................145
Chapter A1 References........................................................................................147
Appendix 2: Magnesium Fluoride Nanocrystal Coated Whispering Gallery Mode
Resonator.........................................................................................................................149
A2.1 Methods: Nanocrystal Synthesis.................................................................149
A2.2 Methods: Microrsonator Fabrication and Coating......................................151
A2.3 Preliminary Results.....................................................................................151
Chapter A2 References........................................................................................154
Appendix 3: UV Lasing in Zinc Oxide Nanowire Coated Whispering Gallery Mode
Resonators........................................................................................................................155
A3.1 Methods: ZnO Nanocrystals Pre-Seeding...................................................156
A3.2 Methods: Hydrothermal Synthesis..............................................................157
A3.3 Methods: Polymer Coating.........................................................................159
A3.4 Results: Optical Testing..............................................................................161
A3.5 Conclusion..................................................................................................162
Chapter A3 References........................................................................................163
Appendix 4: Organic-Silica Hybrid Whispering Gallery Mode Resonators for Selective
Four Wave Mixing and Raman Emission........................................................................166
A4.1 Methods: Synthesis.....................................................................................167
A4.2 Methods: Modeling.....................................................................................168
A4.3 Results: Optical Testing..............................................................................169
A4.4 Conclusions and Future Work.....................................................................171
Appendix 5: MATLAB Code for Resonance Peak Solver..............................................176

iv
List of Figures

Figure 2-1. Schematic depicting a WGM resonator on resonance (a) when the
circumference is equal to an integer number of wavelengths and constructive
interference is allowed. When off resonance (b), constructive interference does not
occur...........................................................................................................................13

Figure 2-2. Finite Element Method simulation of the optical mode circulating in a
spherical WGM resonator (D=120 µm). The mode is primarily located in the
resonator, but a portion extends beyond the resonator boundary. The right image is
the distribution of the mode intensity along the radial cross-section (green line in the
left image)...................................................................................................................17

Figure 2-3. a) Microsphere resonator fabricated from a stripped and cleaved SMF-28
optical fiber. b) Microtoroid resonator fabricated photolithographically using a
photomask with 150 µm circles..................................................................................18

Figure 2-4. Diagram showing the photolithography portion of toroid fabrication. Circular
silica pads are obtained from thermal oxide wafers (2 µm thick), which can then be
etched with XeF2 to yield suspended silica microdisks.............................................19

Figure 2-5. An artistic rendering depicting the resonator testing set-up used to
characterize whispering gallery mode resonators. Light from a tunable laser is
evanescently coupled into the WGM resonator. This signal is sent to a photodetector
(PD) and optical spectrum analyzer (OSA). Other components that are sometimes
used include the erbium doped fiber amplifier (EDFA) for 1550 nm light and the
electrical spectrum analyzer (ESA) for analyzing RF signals....................................21

Figure 2-6. Representative Q versus coupling plot used to determine the intrinsic Q factor
when coupling is equal to zero. The coupling is maintained below 30% to minimize
thermal effects. The inset shows a typical transmission spectrum used to determine
the loaded Q factor.....................................................................................................22

Figure 2-7. A typical transmission spectrum for a high Q factor device exhibiting thermal
broadening (broadening of the resonance peak, as traced in red) and mechanical
vibrations (the large fluctuation in transmission).......................................................23

Figure 2-8. Calibration curve used to convert the value of the voltage on the oscilloscope
to the power after the tapered optical fiber. This voltage is used to determine the
power that is coupled into the resonant cavity...........................................................25

Figure 2-9. Frequency comb formation from both degenerate and non-degenerate four-
wave mixing process..................................................................................................32

Figure 2-10. Energy level diagrams depicting Stokes and anti-Stokes Raman scattering
processes.....................................................................................................................34
v

Figure 2-11. Depiction of how the resonator modes shift as wavelength changes due to
dispersion. The gradual slippage between the resonator mode spacing and the comb
mode spacing, which remains constant, limits the span of a frequency comb...........38

Figure 3-1. (a) Diagram showing mainly homogeneous nucleation of crystals within a
bulk silica sol gel matrix. (b) When the crystals are grown in a thin film of silica sol
gel, the dominant process is heterogeneous nucleation on the substrate below the
film. (c) Bright field optical microscope image showing large crystals in a thin film
silica sol gel................................................................................................................54

Figure 3-2. (a) In most samples of the silica sol gel doped with CaF2 crystals, extensive
cracking was observed due to the increased stress within the silica matrix. (b) Dark
field image showing decrease in CaF2 crystal size upon increasing cooling rate
during the annealing process. The crystals seem to gather along streaks that form
during the spin-coating process..................................................................................55

Figure 3-3. Energy dispersive X-ray spectroscopy data for a broken microdisk fabricated
from a silica sol gel with CaF2 nanocrystals grown in the silica matrix. The inset is
the SEM image of the microdisk, with the red cross indicating the region and
nanocrystal being probed............................................................................................56

Figure 3-4. (a) Transmission spectrum near 980 nm used to calculate the Q factor for a
microtoroidal resonator fabricated from one layer of a CaF2 crystal in silica sol gel
deposited on a 1 µm thermal oxide wafer. (b) Dark field microscope image showing
a silica pad (before XeF2 etch) with large CaF2 crystals in the matrix, which lead to
high scattering loss when light is coupled into a fabricated device...........................57

Figure 3-5. (a) SEM image of CaF2 nanocrystals synthesized in solution, dispersed on a
silicon wafer. (b) SEM image of CaF2 nanocrystals that have been coated on the
surface of a microtoroidal resonator...........................................................................59

Figure 3-6. Energy dispersive X-ray spectroscopy spectrum for a CaF2 nanocrystal on the
surface of a silicon wafer. The inset shows the spot where the electron beam is
directed on the wafer..................................................................................................60

Figure 3-7. Dynamic light scattering data for CaF2 nanocrystals in ethanol showing two
prominent peaks at ~80 nm and ~9 µm......................................................................61

Figure 3-8. Schematic of the simulation design used in COMSOL Multiphysics.............62

Figure 3-9. (a) Finite element model of a cross section of the fundamental mode’s electric
field in a spherical microresonator (R=75 µm) without (top) and with (bottom) a
CaF2 particle on the surface (r=100 nm). (b) The electric field amplitude along a
radial cut line for each resonator in part (a). The dotted line represents the boundary
of the microresonator..................................................................................................63
vi

Figure 3-10. Chromatic dispersion plots for CaF2 and silica based on each material’s
respective Sellmeier Equation. Throughout this near-IR region, the refractive index
for CaF2 changes slower than for silica.....................................................................65

Figure 3-11. Numerical calculations based on the characteristic equation for resonance
peaks of a coated microsphere show the effect of CaF2 coatings on the rate at which
the FSR of a resonator changes for a spherical microresonator with a radius of 75
µm...............................................................................................................................68

Figure 3-12. Artistic rendering of the testing setup used to characterize optical
microresonators for frequency combs. A tunable laser couples light into the
resonator via a tapered optical fiber. The signal is then split to an optical spectrum
analyzer (OSA), a photodetector (PD) that connects to an oscilloscope (O-scope),
and an electrical spectrum analyzer (ESA)................................................................70

Figure 3-13. Transmission spectra for (a) an uncoated microtoroid and (c) CaF2
nanocrystal coated microtoroid. (b) and (d) show Q factor vs. coupling plots used to
determine the intrinsic quality factor (when coupling is 0%) for uncoated and coated
microtoroids, respectively..........................................................................................72

Figure 3-14. FWM threshold curves for coated and uncoated spherical resonant cavities
of varying diameter....................................................................................................74

Figure 3-15. (a) FWM threshold normalized by the square of the Q factor, showing the
R2 dependence. (b) Further normalization by R shows that the threshold is not
significantly affected by the presence of the CaF2 particles......................................75

Figure 3-16. Comb spacing for CaF2-coated microspheres of varying radius show the
spacing inversely proportional to the radius. The optical microscope images
corresponding to each comb are presented on the right, with the scale bar
representing 100 µm...................................................................................................76

Figure 3-17. (a) Subcombs form each comb line at high input powers, with spacing as
low as 0.02 nm. (b) Beat signal observed on the electrical spectrum analyzer at 2.43
GHz............................................................................................................................77

Figure 3-18. (a) Comb generation for an uncoated microsphere resonator as input power
increases. (b) Comb generation for a CaF2 nanocrystal-coated microsphere resonator
of similar radius to the one in part (a)........................................................................78

Figure 3-19. The widest spanning comb observed during testing of a CaF2 microsphere
resonator with a radius of 95 µm. The coupled power is 6.68 mW...........................80

vii
Figure 3-20. (a) Comb generation for an uncoated microtoroidal resonator (R=55 µm) as
input power increases. (b) Comb generation for a microtoroidal resonator of similar
size to the one in part (a)............................................................................................81

Figure 4-1. An artistic rendering of PEG-functionalized gold nanorods coated on a WGM
resonant cavity. The nanorods at the equatorial region interact with the circulating
optical field to form a hybrid surface plasmon polariton-whispering gallery mode..90

Figure 4-2. SEM images of (a) gold nanorods dispersed on a silicon wafer and (b) of a
spherical WGM resonator coated with gold nanorods...............................................92

Figure 4-3. UV-Vis absorption spectrum for gold nanorods dispersed in methanol. The
peaks at ~515 nm and ~845 nm correspond to the transverse and longitudinal surface
plasmon resonances, respectively...............................................................................93

Figure 4-4. a) Finite element method simulation of the circulating optical field in a
spherical resonator with a functionalized gold nanorod at the surface (15 nm
separation distance) showing the high intensity region in between the two interfaces.
b) The electric field amplitude along the cross section of the spherical resonator for a
device without (top) and with (bottom) a gold nanorod on the surface (15 nm
separation). c) Enhancement of the field relative to the intensity without a nanorod
present as the separation distance is varied................................................................95

Figure 4-5. Artistic rendering of the testing setup used to characterize the comb
generation of the WGM resonators. The comb spectra are recorded on the optical
spectrum analyzer, while the photodetector is connected to an oscilloscope to
analyze the transmission spectrum.............................................................................97

Figure 4-6. a) Threshold curves for the microspheres coated with various concentrations
of functionalized and non-functionalized gold nanorods. b) Threshold values in
terms of circulating intensity and power for each device tested in this study show a
decrease as gold nanorods functionalized with PEG are introduced. CTAB-
functionalized nanorods on the resonators did not decrease the thresholds as
effectively...................................................................................................................99

Figure 4-7. Comb spectra for (a) bare silica spheres, and PEGylated gold nanorod-coated
spheres at a concentration of (b) 0.070 M, (c) 0.080 M, and (d) 0.125 M with
increasing input power.............................................................................................101

Figure 4-8. Comb generation spectra for a spherical microresonator coated with CTAB-
functionalized gold nanorods at a concentration of 0.125 mM................................103

Figure 5-1. Zinc oxide is found in two polymorphs, with hexagonal wurtzite being the
more thermodynamically stable form.......................................................................109

viii
Figure 5-2. Scanning electron microscope image of a single ZnO NTP on silicon
substrate, showing the characteristic four legs at 109.5° from adjacent legs...........111

Figure 5-3. (a) Schematic rendering showing the chemical vapor transport (CVT) method
for synthesizing ZnO NTPs. (b) Photograph of the modified tube furnace used for
the CVT growth. The inset shows the gas line splitter before the inlet port. (c)
Photograph showing final product of ZnO NTPs on the surface of silicon wafers..113

Figure 5-4. (a) Non-uniform ZnO structure that resulted from a poor seal on the CVT
tube furnace. (b) When the oxygen mixture is left for 20 min at 50 mL/min, the
tetrapod structure is lost in many regions of the growth substrate. (c) With 7 min of
O2 flow at the same rate, the resulting structures are more tetrapod-like................114

Figure 5-5. (a) A zinc blende core is the initial nucleation site with alternating +c/-c
facets. Growth is favored in the +c facets over the –c facets. (b) SEM image showing
the tetrapod morphology and hexagonal basal plane. (c) SEM of ZnO NTPs as-
grown on the surface of a silicon wafer. (d) EDX spectrum and quantitative results
for a single ZnO NTP on a silicon wafer. The inset shows the spot where the electron
beam is aimed during the collection, marked with a yellow cross...........................115

Figure 5-6. (a) TEM images of a ZnO NTP leg showing lattice fringe spacing of 2.6 Å,
consistent with growth in the [0001] direction. (b) XRD pattern of ZnO NTPs
removed from the silicon substrate, confirming wurtzitic structure........................116

Figure 5-7. Schematic rendering demonstrating the inverse soft lithography method for
embedding the ZnO NTPs in the flexible PDMS substrate. The bottom right image
shows the composite material emitting green light under a UV lamp (λ=365 nm).118

Figure 5-8. a) SEM image of the fluffy white layer that results after the CVT growth. It
consists of an interconnected network of ZnO NTPs. b) After the film is sonicated in
the PDMS curing agent, the ZnO NTPs are homogenously distributed in the
elastomer, shown here under a 325 nm UV lamp....................................................119

Figure 5-9. Spectrofluorometer spectra (λexcitation=325 nm) of ZnO NTPs (a) as-grown
and (c) embedded in PDMS with corresponding dark-field microscope images in (b)
and (d).......................................................................................................................120

Figure 5-10. Fluorometry spectra for ZnO NTPs embedded in PDMS when flexurally
bent to radii of (a) 13.85 mm and (b) 6.42 mm, and (c-d) corresponding changes in
ratio of the area under the UV peak to the area under the green peak.....................121

Figure 5-11. When the growth density of ZnO NTPs was varied, a negative slope for the
ratio of the area under the UV peak to the area under the green peak was never
achieved, as seen in other studies. A negative slope would be indicative of an
increase in the concentration of defects within the ZnO NTPs................................123

ix
Figure 5-12. a) Fluorometry spectrum for a PDMS sample with ZnO NTPs
homogeneously distributed in the elastomer, with a UV peak at 380 nm and a green
peak at 493 nm. b) The ratio of the intensity of the UV peak to the intensity of the
green peak during 100 bending cycles to a bend radius of 6.42 mm.......................124

Figure 5-13. Finite element method model of the strain imparted on a PDMS slab when
bent to a radius of 5 mm and (b) corresponding cross section of the slab. In the
experiments, the ZnO NTPs are located at the top surface, where they are subjected
to tensile stress..........................................................................................................125

Figure 6-1. Optical spectrum when a) on resonance and b) off-resonance, showing strong
SBS near the pump line............................................................................................134

Figure 6-2. Optical spectrum near the pump line shows simultaneous FWM and SBS..135

Figure A1-1. FEM model shows the hybrid whispering gallery-plasmonic mode located
between the gold nanorod and the silica WGMR when 1550 nm light is circulating in
the cavity..................................................................................................................142

Figure A1-2. a) Dispersion for microsphere resonators of different radii. b) Zero
dispersion wavelength versus cavity radius for silica spheres.................................143

Figure A1-3. Optical spectra for a microsphere coated with functionalized gold nanorods
at a) 15 mW and b) 30 mW of input power..............................................................144

Figure A1-4. Anti-Stokes emission power versus Stokes emission power for a coated
microsphere resonator..............................................................................................145

Figure A2-1. Scanning electron microscope image of MgF2 nanocrystals in dried up salts
dispersed on a silicon wafer.....................................................................................150

Figure A2-2. a) Scanning electron microscope image of purified MgF2 nanocrystals
dispersed on the surface of a silicon wafer. b) EDX spectrum of a single MgF2
nanoparticle. The presence of silicon and oxygen lines is due to the penetration depth
and large size of the electron beam reaching the silicon substrate below the
nanoparticle..............................................................................................................152

Figure A2-3. Frequency comb generation in a silica microsphere resonator coated with
MgF2 nanocrystals as coupled input power increases.............................................153

Figure A3-1. SEM image of a silicon wafer that has been partially seeded with ZnO
crystallites from decomposed zinc acetate...............................................................157

Figure A3-2. SEM images of silica toroids with ZnO nanostructures hydrothermally
grown with solute concentrations of a) 25 mM and b) 10 mM................................159

x
Figure A3-3. A toroidal WGM resonator with ZnO nanostructures on its surface is coated
with PMMA. Though the Q is very low, the intact ZnO after spin-coating the
polymer onto the device is a positive step................................................................160

Figure A3-4. a) Q spectra for a silica microtoroidal cavity coated in ZnO nanostructures
and a thin coating of PMMA polymer. b) Top-view microscope image of a coated
toroid during testing shows a high degree of scattering loss when light is coupled
into the cavity...........................................................................................................161

Figure A4-1. Schematic showing the surface functionalization of the spheres tested.
Insets of each device show the unique surface chemistry of each sphere: bare sphere
(gray), CPS coated sphere (blue), and DASP coated sphere (red)...........................168

Figure A4-2. Finite element method simulation of the optical mode circulating inside a
spherical WGM resonator with an organic monolayer coating. The optical mode and
evanescent tail are not distorted by the presence of the ~2 nm thick layer..............169

Figure A4-3. Comb spectra for (a) bare sphere, (b) CPS-silica sphere, and (c) DASP-
silica sphere..............................................................................................................170

Figure A4-4. Threshold plots for the FWM process in a DASP-silica sphere and bare
sphere. The plot on the right is a zoomed view of the bare sphere data points on the
left.............................................................................................................................171

Figure A4- 5. Schematic showing the T-type isomerization of azobenzene (adapted from
Garcia-Amoros)........................................................................................................172

xi
Abstract

A frequency comb consists of a broad span of highly resolved and precisely
spaced spectral lines. These lines are a tool that has been utilized in a wide range of
applications requiring high-precision measurements, including atomic clocks, astronomic
spectrographs, and spectroscopy. The phenomena responsible for frequency comb
generation are based on nonlinear optical effects. However, these phenomena have
required the comb generators to be extremely bulky, complex, and power-intensive.
Micron-scale whispering gallery mode resonant cavities are an ideal candidate to
overcome these limitations, as they are capable of achieving large power buildups within
a small footprint. One strategy to further improve frequency comb generation in these
resonators is to utilize nanomaterial coatings to enhance nonlinear optical phenomena.
In this dissertation, various nanomaterial-based strategies are investigated for
enhancing different nonlinear optical effects with the aim of improving frequency combs.
First, fluoride nanoparticles coated on the surface of silica resonators are shown to
improve the span of frequency combs by favorably altering material dispersion. Next, a
plasmonic enhancement strategy based on gold nanorods and nonlinear optical polymers
is demonstrated, yielding lower thresholds for frequency comb generation. Finally, zinc
oxide nanomaterials are used to develop a flexible fluorescent nanocomposite material.
This work lays the foundation for future work that will utilize other nanomaterials and
strategies for generating frequency combs in integrated photonic devices.

1
1 Overview

1.1 Motivation
Nonlinear optics is the study of phenomena that result from the interaction between light
and matter. It is a relatively young field of research that has only been able to be investigated
more thoroughly with the invention of the laser (1). This is mainly due to the fact that high
incident optical intensities are required before nonlinear optical effects are apparent. Numerous
nonlinear phenomena have been experimentally observed including sum frequency generation
(2-4), intensity dependent refractive index (5), stimulated Raman scattering (6, 7), and four wave
mixing (8-10).
Four wave mixing in particular is a nonlinear optical phenomenon of interest because of
its ability to generate frequency combs (11-13), a broad light source that consists of many
equidistant and highly resolved spectral lines. These equidistant lines can serve as an optical
“ruler” for various metrological applications. In just over two decades, frequency combs have
proven to be promising candidates in high precision spectroscopy (14, 15), optical
communication (16-18), and sensing, as well as many other applications.
Integrated optical devices, including whispering gallery mode (WGM) resonators, have
proven capable of exhibiting nonlinear optical effects at low input powers. Micrometer-scale
silica WGM resonators are capable of confining very specific wavelengths of light within their
cavities for long periods of time. Silica-based WGM resonators have been fabricated in
numerous geometries including microspheres (19-21), microtoroids (22, 23), and microdisks
(24). Silica in particular has many favorable properties, including low absorption loss (25), that
allow for silica WGM resonators to have quality factors (Q) in excess of 100 million. One of the
primary advantages of using silica is its compatibility with many fabrication and processing
2
techniques currently used in the integrated electronic circuits industry. Therefore, it is desirable
to explore strategies that will allow for enhancing nonlinear optical behavior without introducing
more complexity in fabrication.
For ultra high-Q devices such as silica microspheres and microtoroids, confinement of
light can result in a buildup of light that can reach circulating intensities of gigawatts/cm
2
with
mW of input power. By leveraging this built up power, broad-spanning frequency combs based
on four wave mixing have been demonstrated in WGM resonators fabricated from various
materials. However, the frequency comb span has been limited on a practical level due to high
input power requirements. In order to make frequency comb generation feasible in low power
integrated photonic devices, the requirements for achieving the nonlinear optical phenomena
responsible for generating the combs must be relaxed.
The main strategies for improving frequency comb performance have focused on
increasing Q factor and/or the nonlinear Kerr coefficient by altering fabrication methods and
materials (26-28). In this dissertation, alternative nanomaterials-driven strategies for enhancing
nonlinear optical phenomena in silica WGM resonators are explored. This dissertation focuses
on utilizing nanomaterials in several ways to enhance the nonlinear optical behavior of silica
WGM resonators. The first approach focuses on modifying the effective dispersion of the
resonant cavity to yield combs that span a wide frequency range at low input power. This
approach is explored in this dissertation with both experiments and modeling to show that the
nanomaterial enhances the frequency comb performance.
Beyond dispersion, the nonlinear refractive index plays a significant role in comb
generation. Though silica WGM resonators hold many favorable advantages such as ease of
fabrication in large quantities, silica itself has very weak nonlinear optical properties. One
3
approach that has been investigated in WGM resonators is plasmonic enhancement. In this
dissertation, the frequency comb enhancement by plasmonic nanostructures on the surface of
WGM resonators is investigated experimentally and with computational models.
Nanomaterials are not only valuable tools for modifying the optical behavior of WGM
resonators, but also in flexible fluorescent materials. Nanocomposite materials have played a
large role in improving performance in flexible sensors (29, 30), optoelectronics (31-33), and
biomedical devices (34). However, many challenges remain due to difficulty in synthesis and
integration with flexible substrates. In this dissertation, an improvement upon fabrication of a
flexible fluorescent material is explored by utilizing an inverse soft lithography approach, and
this material is characterized experimentally and computationally.

1.2 Chapter Overview

Chapter 2 is an overview of whispering gallery mode resonators and associated nonlinear
optical phenomena. Important features, figures of merit, and experimental set-ups for testing
WGM resonators are discussed. A number of nonlinear optical phenomena that are observed in
WGM resonators are also examined.
Chapter 3 discusses a dispersion-inspired approach to improving frequency comb
performance, which involves applying nanocrystal coatings on the surface of resonators.
Calcium fluoride nanocrystals are synthesized by a solution-based co-precipitation method and
coated on the surface of WGM resonators. By utilizing calcium fluoride nanocrystal coatings, we
experimentally show that frequency comb span improves in the near-IR. Finite element method
(FEM) simulations are also performed to show that the particles do not significantly affect the
optical mode, and mathematical models are utilized to show that the dispersion of the resonator
4
is modified with the presence of the fluoride layer. Further improvement in comb generation is
explored by using magnesium fluoride nanoparticle coatings to reduce stimulated Raman
scattering.
Chapter 4 explores a plasmonic approach to enhance frequency comb performance by
utilizing small molecule-functionalized gold nanorods on the surface of WGM resonators. A
seed-mediated growth is used for synthesizing the nanorods, and subsequently coated on the
resonator surface. Optical characterization reveals that the presence of the functionalized
nanorods on the WGM resonators decreases the four wave mixing threshold and increases the
comb span at low input intensities. Numerous FEM simulations were also performed to observe
the enhancement in the optical field at the resonator interface when excited in the near IR.
Chapter 5 introduces work performed with another nonlinear optical material in zinc
oxide nanotetrapods. Though zinc oxide nanomaterials exhibit nonlinear optical effects, this
study focuses on the development of a flexible fluorescent composite material. The synthesis of
the zinc oxide nanostructures and approach for embedding it in an elastomeric material are
outlined. Flexural testing is performed in the lab to test the stability of the material’s
fluorescence. FEM modeling is also performed to theoretically characterize the mechanical strain
within the structure when subjected to flexural bending.
Chapter 6 outlines potential future work that can be performed based on the projects in
this dissertation. This includes additional nanomaterial-driven and coating-based strategies for
enhancing frequency comb performance. Also discussed are strategies for combining multiple
approaches that have been investigated in the Armani lab to enhance frequency comb generation
in multiple ways simultaneously. Appendix 1 discusses a collaborative project that also utilizes
functionalized gold nanorods in order to enhance another nonlinear optical effect− Stimulated
5
Anti-Stokes Raman scattering. Appendix 2 discusses another dispersion compensation approach
for enhancing frequency comb generation using magnesium fluoride nanocrystals. Appendix 3
discusses research done with the goal of obtaining UV lasing using ZnO nanomaterials.
Appendix 4 outlines a collaborative project that utilized a nonlinear molecule on the surface of
resonators to preferentially obtain parametric nonlinear processes. Appendix 5 includes
annotated MATLAB code utilized in Chapter 3 to solve for resonance frequencies.

6
Chapter 1 References

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10
2 Background
This dissertation covers a wide range of topics related to nonlinear optical
phenomena and integrated photonic devices. This chapter will discuss the relevant
background in the scope of integrated photonics (namely whispering gallery mode
resonators) and nonlinear optics.

2.1 Integrated Photonics
As the age of information progresses, one trend that has not slowed down is the
ever-increasing amount of data being generated and consumed. Though early
computation and communication relied on electrical signals, optical methods have greatly
enhanced data transmission. Optical communication has allowed for data transfer to
occur at previously unimaginable speeds and efficiency. Rather than electrical signals,
which rely on electrons, photonic signals utilizing photons have the potential to transmit
information or signals at much faster speeds and with higher efficiency due to less
resistive heating. Optics and photonics have the potential to improve performance in a
multitude of technological sectors beyond communication.
The European Union has identified six Key Enabling Technologies that it believes
will have an impact in a broad range of industries and will help to solve grand challenges
around the world. Two of these include photonics and nanotechnology. The efforts in this
dissertation represent incremental steps in advancing technologies that rely on the
synergy between these two technologies. Research outlined in this dissertation will
specifically focus on strategies to obtain nonlinear optical phenomena by combining
these two technologies. We undertake this goal with an eye on manufacturability and low
11
power requirements, conditions that will be necessary if integrated photonic devices are
to thrive on a large scale. Successfully obtaining these nonlinear optical phenomena in
integrated photonic circuits will spell success not just in optical communication, but also
in a wide range of fields including spectroscopy, sensors, astronomy, and metrology.
Integrated photonics is a promising field of research that has the potential to
improve performance in many different applications. However, there are many obstacles
to overcome. The manipulation of light at the nanoscale that is required to obtain a
functional integrated photonic circuit is no easy feat, resulting in prohibitively expensive
photonic circuits. Currently, only components in very high-end systems contain optical
circuitry due to high cost. Thus, we must thoroughly investigate individual photonic
circuit components before they can be assembled into all-photonic chips and
manufactured at a reasonable cost.
One challenge that must first be surmounted is the miniaturization of optical
systems in order to keep pace with the miniaturization of consumer devices. Like
electronic circuits with their building block components like resistors, diodes, and
capacitors, photonic circuits have their own analogues including lasers, detectors, and
filters. Ideally, all of these components will fit seamlessly on a chip in order to build
complex photonic circuits that will be incorporated into devices. However, these optical
components are typically bulky, so their on-chip integration remains an ongoing
challenge that is partially addressed in this dissertation.

12
2.2 Whispering Gallery Mode Resonators
The fabrication techniques used in the integrated circuits industry have been
optimized for mass production over the past several decades. Therefore, it would be ideal
to be able to continue utilizing these well-established techniques and machinery in order
to manufacture photonic circuits. The photonic circuit building block that we primarily
focus on in the Armani Lab is the optical resonator, or more specifically the whispering
gallery mode resonator (WGMR). Whispering gallery mode resonators are circular
cavities that can be fabricated on-chip using existing integrated circuit techniques, and
integrated with other photonic building blocks. WGMRs can come in many different
geometries including spheres, microtoroids, microdisks, and microrings.
WGMRs get their name from a unique architectural feature where acoustic waves
in certain round rooms circulate, allowing whispers from one end of the room to reach the
opposite end. Similarly, optical WGMRs allow certain wavelengths of light to circulate
and interfere constructively within the cavity. These “resonance” wavelengths correspond
to an integer number of wavelengths that circulate along the perimeter of the device
(Figure 2-1a). When the wavelength does not correspond to an integer multiple of the
wavelength, it is off-resonance (Figure 2-1b).

13

Figure 2-1. Schematic depicting a WGM resonator on resonance (a) when the circumference is
equal to an integer number of wavelengths and constructive interference is allowed. When off
resonance (b), constructive interference does not occur.

2.2.1 Quality Factor
A primary figure of merit for WGM resonators is the quality factor (Q). This
unitless quantity is a common metric for describing how well a system stores energy (1).
In the case of WGM resonators, it is directly proportional to the photon storage lifetime τ,
which describes how long a photon stays confined in the resonator. Ultra-high Q factors
correspond to higher specificity of the resonance wavelength that is confined within the
cavity. Experimentally, Q factor can be determined by the following definition:
!=!"=
!
Δ!

where ω is the resonance frequency, τ is the photon lifetime, λ is the resonance
wavelength, and Δλ is the full width at half maximum linewidth of the resonance peak.
Calculation via measuring the resonance wavelength and the full width half max
linewidth is called the linewidth method. The Q factor can also be calculated with a
cavity ringdown method, which directly measures τ. However, this method is much more
complex and costly to implement.
14
The Q factor is dependent upon many contributions, and for WGMRs is described
by the equation:

!
!"!#$
!!
=!
!"#$!"%!&
!!
+!
!"#$%&'%(
!!
=!
!"#
!!
+!
!!
!!
+!
!"#
!!
+!
!"#$
!!
+!
!"#$
!!

where Q
rad
is the radiation loss, Q
ss
is the surface scattering los, Q
mat
is the material loss,
Q
cont
is the contamination loss, and Q
coup
is the coupling loss and is the sole contributor to
the extrinsic Q. Radiation loss occurs when the size of the resonator is too small,
allowing for a portion of the light to tunnel out of the cavity when total internal reflection
occurs. This loss term becomes negligible when the resonator is made to be above a
certain minimum diameter threshold (~ >20 µm) (2). Surface scattering loss is due to
rough surfaces that cause light to scatter away from the resonator. The reflow process for
spherical and toroidal silica devices allows for this term to be negligible. However, since
much of the work in this dissertation involves coating nanomaterials on the WGMR
surface, the scattering loss must also be considered. Based on Rayleigh scattering
considerations, the term can be estimated by !
!!
=
!
!
!
!!
!
!
!
!
, where λ is the wavelength, d
is the cavity diameter, σ is the RMS size of the scattering site, and B is the correlation
length of the scattering sites (3). Contamination loss is caused by contaminants on the
surface of the devices following fabrication. This loss term is minimized by practicing
proper storage techniques and treating the surface with oxygen plasma to clean off
undesired dust or residue on the surface. Finally, the material loss is due to the resonator
material absorbing the light circulating within it. The material loss can be determined
analytically from the equation (4)
15
!
!"#
=
2!!
!""
!!
!""

where n
eff
and α
eff
are determined using a mixing rule according to the following
equations:
!
!""
= !!
!"#$%&'$!
+!!
!"#

!
!""
=!!
!"#$%&'$!
+!!
!"#

where β and γ are the fraction of the optical field that lie in the resonator and air,
respectively. These values can be determined using COMSOL Multiphysics Finite
Element Method models. In the case of as-fabricated silica WGM resonators, the main
source of loss comes from this term, and thus Q
total
~Q
mat
.

2.2.2 Free Spectral Range
Another important value is the free spectral range (FSR). This is the spacing
between fundamental resonance peaks, and can be visualized as the inverse round-trip
time for a photon in a resonant cavity (5). For WGM resonators, the FSR is given by
!"#=
!
!
!"#

where λ is the wavelength, n is the refractive index, and D is the diameter of the
resonator.
FSR is important because it dictates the spacing of frequency combs. Hence,
changing the diameter will change the FSR, and consequently the comb spacing.

16
2.2.3 Evanescent Field
Another very unique feature of these WGM optical resonators is that the optical
mode of the light circulating in the cavity extends beyond the physical boundary of the
cavity itself (Figure 2-2). Optical modes depict the intensity distribution of the light
propagating in a medium, and, in the case of WGM resonators, are solutions of the
Helmholtz wave equation (6). The portion of the optical field that extends outside the
resonator is called the evanescent wave, and decays exponentially with increasing
distance from the resonator boundary. The evanescent wave exists because the magnetic
fields and electric fields comprising the light cannot be discontinuous, and therefore have
to extend beyond the physical boundary of the resonator. Because of this wave, the
optical field is directly interacting with the surroundings via this evanescent field. The
interaction of this evanescent field with the environment is the basis of using these
resonators as sensors (7, 8). Furthermore, evanescent coupling is one of the most efficient
ways that the light is coupled into the WGMRs (9). It is also important to note that in the
studies outlined in this dissertation, the light is only able to interact with nanomaterials
via this evanescent field. Thus, the evanescent field is a vital feature that we exploit to
couple WGMRs and nanomaterials.
17

Figure 2-2. Finite Element Method simulation of the optical mode circulating in a spherical
WGM resonator (D=120 µm). The mode is primarily located in the resonator, but a portion
extends beyond the resonator boundary. The right image is the distribution of the mode intensity
along the radial cross-section (green line in the left image).

2.2.4 Fabrication
WGMRs come in many different geometries including microrings, microdisks,
microtoroids, and microspheres, among others (10). In the research described herein, we
mainly utilize microsphere and microtoroidal resonators, which exhibit ultra high quality
factors of up to 10
9
(4, 11). Both of these WGMR geometries also have the advantage of
being straightforward to fabricate.
Microsphere WGMRs are fabricated by stripping the polymer cladding off of an
optical fiber, cleaning it with isopropanol, cleaving the end to obtain a flat face, and
reflowing the tip under a CO
2
laser. The diameter of the resulting microsphere is on the
order of ~200 µm for SMF-28 optical fiber (Figure 2-3a). The diameter is dependent on
the initial diameter of the fiber, so the type of optical fiber used is important.
18
Additionally, optical fibers can be tapered using the taper puller to obtain smaller
diameter fibers and consequently, smaller diameter microspheres.

Figure 2-3. a) Microsphere resonator fabricated from a stripped and cleaved SMF-28 optical
fiber. b) Microtoroid resonator fabricated photolithographically using a photomask with 150 µm
circles.

Microtoroid WGMRs are fabricated photolithographically based on a well-
established method (12). First, a thermally grown 2 µm silicon oxide wafer is cleaned
with acetone, methanol, and isopropanol, in sequence and then dried on a hot plate. The
surface of the wafer is vapor treated with hexamethyldisilazane in order to promote
adhesion of the photoresist. A spinner is used to apply a layer of S1813 positive
photoresist, followed by a soft bake (95°C for 2 min) to evaporate solvent and promote
adhesion. A photolithography mask with circular patterns of the desired disk size is then
placed on the wafer and exposed to UV light. The wafer is then developed in MF-321
developer, yielding circular photoresist pads on the silica wafer surface. After a hard bake
to even out the circular photoresist pads (120°C for 2 min), the wafer is immersed in
buffed oxide etchant (BOE). The HF in the BOE etches the unexposed silica until only
circular silica circles (covered in photoresist) remain. The photoresist is washed away
with acetone and the wafers are transferred to the XeF
2
etcher. The photolithography
19
portion of the process is schematically diagramed in Figure 2-4. Next, the XeF
2
isotropically etches the silicon wafer, leaving the silica disks suspended on a silicon
pillar. Finally, the disks are reflowed with a CO
2
laser, a process in which the surface
tension of the melting silica results in a nearly atomically smooth torus elevated off the
silicon wafer surface (Figure 2-3b).

Figure 2-4. Diagram showing the photolithography portion of toroid fabrication. Circular silica
pads are obtained from thermal oxide wafers (2 µm thick), which can then be etched with XeF
2
to
yield suspended silica microdisks.

After fabrication of both microsphere and microtoroidal resonators, oxygen
plasma treatment is always utilized in order to clean off any contaminants on the surface
and to hydroxylate the resonator surface, resulting in a hydrophilic surface (13).

20
2.2.5 Optical Testing of WGMRs
The first step to characterizing WGMRs is to obtain a method for coupling light
into the cavity. Though there are many strategies for coupling (9, 14, 15), one of the more
straightforward and inexpensive methods is by utilizing a tapered optical fiber (16). A
stripped and cleaned optical fiber is placed on a mounting stage. A hydrogen torch is then
lit in close proximity to the fiber while the fiber is slowly stretched. The transmission
through the fiber is monitored on an oscilloscope and tapering is stopped when the signal
flattens out, indicating single mode operation. The tapered fiber is approximately 1 µm
in diameter, and has an evanescent field extending beyond the fiber when light
propagates through it. This method allows for efficient coupling of light into the
microresonators since phase matching between the fundamental taper mode and
fundamental WGM can be satisfied (9, 16-18).
Whispering gallery mode resonators, including toroidal and spherical resonators,
are characterized using a resonator testing setup (Figure 2-5). A resonator is placed on a
piezoelectric nanopositioning stage to control the coupling, and alignment is assisted with
side and top view cameras. Light from a fiber-coupled CW tunable laser is coupled into
the resonator using the tapered optical fiber waveguide and bringing it into close
proximity with the resonator equator (17). The wavelength of the laser is rastered across a
~50 pm range using a triangle wave from a function generator set at 100 Hz and 1 V
p-p
.
The laser output from the taper is then sent to a photodetector, which is visualized on a
digitizer/oscilloscope on a computer. Resonance wavelengths are found by scanning the
wavelength until drops in the transmission are observed, indicative of light coupling into
the device at that wavelength. In cases where higher power levels are required and the
21
1550 nm laser is being used, an erbium doped fiber amplifier (EDFA, Amonics AEDFA-
23-B) is utilized. A tunable filter (Santec OTF-350) is also used to suppress the
spontaneous emission from the EDFA.

Figure 2-5. An artistic rendering depicting the resonator testing set-up used to characterize
whispering gallery mode resonators. Light from a tunable laser is evanescently coupled into the
WGM resonator. This signal is sent to a photodetector (PD) and optical spectrum analyzer (OSA).
Other components that are sometimes used include the erbium doped fiber amplifier (EDFA) for
1550 nm light and the electrical spectrum analyzer (ESA) for analyzing RF signals.

2.2.5.1 Quality Factor Determination
The quality factor of the device is measured at low input powers in order to avoid
nonlinear effects (such as thermal broadening) that may distort the Q factor. At low input
power and in the undercoupled regime, the resonance peak is recorded on the
oscilloscope and then fit to a Lorentzian (Figure 2-6, inset). The loaded Q factor is equal
to Q
loaded
= λ/δλ, where λ is the wavelength where the resonance peak is located, and δλ is
the full-width half-maximum linewidth value determined in the Lorentzian fit. The
22
Q
intrinsic
is determined experimentally by recording the Q at a range of coupling values in
the undercoupled regime. Extrapolating for the Q at zero percent coupling allows for
calculation of Q
intrinsic
(Figure 2-6).

Figure 2-6. Representative Q versus coupling plot used to determine the intrinsic Q factor when
coupling is equal to zero. The coupling is maintained below 30% to minimize thermal effects.
The inset shows a typical transmission spectrum used to determine the loaded Q factor.

When both coupling and Q factor are high, the circulating power causes the
refractive index to change due to the thermo-optic effect. This causes the resonance peak
to broaden with the scanning laser, due to the refractive index increasing as the laser
scans. This effect prevents an accurate Q factor from being measured. Additionally, the
high circulating power can cause mechanical vibrations to be introduced due to radiation
pressure exerted by the circulating light, seen as large fluctuations in the transmission
signal (Figure 2-7) (19). During testing when high input powers are required, these
thermal broadening and mechanical vibration phenomena are unavoidable for high Q
devices.
23

Figure 2-7. A typical transmission spectrum for a high Q factor device exhibiting thermal
broadening (broadening of the resonance peak, as traced in red) and mechanical vibrations (the
large fluctuation in transmission).

2.2.5.2 Emission Measurements and Threshold Calculation
For the majority of the studies outlined in this dissertation, emissions are recorded
on an optical spectrum analyzer (OSA, Yokogawa AQ6370C). In order to observe the
nonlinear optical phenomena that we are interested in, coupling must be efficient in order
to allow for high circulating power to build up within the cavity. Because light can be
coupled in efficiently using tapered optical fibers, it can also be coupled back into the
fiber efficiently (16). Thus, emissions from the resonant cavity can also couple back into
the tapered fiber and analyzed on the OSA. In order to observe emissions, we split the
output signal after the tapered region using a 90%/10% splitter (Newport F-CPL-B12351-
FCAPC). The 90% branch is connected to the OSA, while the 10% branch is connected
to the photodetector so that simultaneous monitoring of emissions and coupling is
possible.
24
Testing begins at maximum input power when the patch cable from the laser is
fully connected to the fiber spool. The voltage level on the photodetector is recorded for
each power level. Once the fundamental mode is found by scanning the laser, the comb
spectrum is recorded on the OSA while the transmission spectrum from the oscilloscope
is simultaneously recorded. Next, input power is decreased by loosening the patch cable
connector on the fiber spool or utilizing an optical attenuator. Comb spectra and
transmission spectra are recorded at many different power levels until only signal and
idler lines (the two lines adjacent to the pump) are left.
When only the signal and idler lines are left, the threshold of the four wave
mixing process can be calculated (20, 21). Additional OSA and transmission spectra are
acquired and saved at varying input power. Once all spectra are acquired, a calibration for
conversion of the voltage level on the photodetector to the power after the tapered optical
fiber is performed using a power meter (Thorlabs PM100D). From this curve, we can
covert the voltage of the baseline transmission for each spectrum to power (Figure 2-8).
The coupled input power is then calculated by multiplying this power by the percent
coupling, determined from how low the resonance peak in the normalized transmission
spectra.
25

Figure 2-8. Calibration curve used to convert the value of the voltage on the oscilloscope to the
power after the tapered optical fiber. This voltage is used to determine the power that is coupled
into the resonant cavity.

The emission threshold is calculated by plotting the signal and idler power versus
the coupled input power, similar to how threshold is determined in lasers (22-25). The
threshold for FWM is defined as the x-intercept of the region when the output power
increases rapidly, indicative of stimulated four wave mixing. The emissions before this
consist of spontaneous four wave mixing (26, 27).

2.3 Nonlinear Optics
Nonlinear optics (NLO) is the study of light-matter interaction where the matter is
a nonlinear medium. In classical optics, light is not influenced by other frequencies of
light. However, the light can interact with electrons in a nonlinear optical material to
generate new frequencies of light. Nonlinear optics is a relatively young field, with the
26
first experimental demonstration of NLO phenomena occurring in the 1960s, when
second harmonic generation was discovered. For years, the assumption of linearity
prevailed in the field of optics, as no electric field strengths were obtainable to compare
to that of the field strengths of atoms and molecules. While Kerr and Pockels observed
nonlinear phenomena in the late 19th century, the study of nonlinear optics did not
flourish until the invention of the laser, which allowed for high incident intensities to be
exploited in experiments. With the laser, behaviors that deviated from classical
estimations became more apparent experimentally.
In whispering gallery mode resonators, a few different kinds of nonlinear optical
effects can be observed. This is due to the high circulating intensities that are achieved
when light can constructively interfere within an ultra high Q factor cavity. The cavity
build up factor can be calculated by (28)
!
!"#!
!
!"#$%
=
!"
2!
!
!"

where λ is the resonance wavelength, Q is the quality factor, n is the refractive index, and
D is the cavity diameter. The circulating intensity is then defined as P
circ
/A
m
, where A
m

refers to the mode area. For example, in a silica microtoroidal resonator with a 50 µm
diameter, Q factor of 10
8
, mode volume of 650 µm
2
, input power of 1 mW, and mode
volume of 650 µm
3
, the circulating intensity is ~2.5 GW/cm
2
.
In order to understand some of the NLO phenomena important to this proposal,
we first start with Maxwell’s Equations in non-magnetic media with no free charges to
understand the interaction between light and matter (29, 30):
∇ ∙!= 0
∇ ∙!= 0
27
∇ ∙!=−
!!
!"

∇ × !=
1
!
!
!
!
!
!!
!
+!
!
!
!
!
!!
!

where ! is the displacement vector (!= !
!
!+!), ! is the electric field, ! is the
magnetic field, c is the speed of light, ! is the polarization of the medium, and !
!
is the
vacuum permittivity.
These equations reduce to the wave equation:
!
!
!
!!
−
1
!
!
!
!
!
!!
!
= !
!
!
!
!
!!
!

Here, the polarization ! is the driving term for the solution to the wave equation. For
clarity, we can also consider !=!
!
+!
!"
for the linear and nonlinear contributions to
the polarization term, respectively.
In dielectric materials, the expression for the polarization is given by:
!= !
!
(!
!
!+!
!
!!+!
!
!!!+⋯
where !
(!)
is the n
th
order susceptibility of the medium, a tensor of rank n + 1 that
indicates how much a material will polarize in response to the applied electric field. It is
also important to note that the refractive index != 1+!. Here it is clear that when
incident electric field is weak, the polarization is linearly proportional to the electric field:
!= !
!
!
(!)
! . However, when the incident electric field increases, the linear
approximation is no longer sufficient, and the nonlinear terms must be considered. This is
often the case with the high circulating intensities in ultra-high Q whispering gallery
mode resonators.
28
We will proceed by discussing the nonlinear optical phenomena that we observe
in WGM resonators, with a focus on the ones that contribute to frequency comb
formation.

2.3.1 Kerr Effect
The nonlinear effects that we are mainly interested in arise from the nonlinear
Kerr effect, the variation of a material’s refractive index with an applied electric field.
For the nonlinear optical phenomena relevant to the experiments in this proposal, one of
the most important parameters to consider is the Kerr coefficient, n
2
. This value, known
as the nonlinear index or Kerr coefficient, provides a measure of a material’s
nonlinearity. If light propagating in the material is intense enough, it can serve as the
electric field to polarize the material, without the need for an externally applied field.
Because the electric field component of light is sinusoidal, consider the electric field to
be !
!
cos (!"), where !
!
is the wave amplitude. When inserted into the polarization
equation from the section above and considering only the terms involving !
!
and !
!
,
the polarization becomes
!≅ !
!
!
!
+
!
!
!
!
!
!
!
!
!
cos(!")
Here we can take the terms in the parentheses to equal the total susceptibility ! and let
!=!
!"#$%&
+!
!"!#$!%&'
=!
(!)
+
!
!
!
(!)
!
!
!
. Because !
!
= 1+! , the refractive
index n can be described by
!= 1+!
!"#$%&
+!
!"#$%#&'(
≈ 1+!
!"#$%&
1+
1
2!
!
!
!
!"#$%#&'(

29
=!
!
1+
1
2!
!
!
!
!"#$%#&'(

where !
!
represents the linear (intensity-independent) component of the refractive index.
Because !
!"#$%#&'(
only becomes significant at high powers, it is reasonable to assume
that !
!
!
= 1+!
!"#$%&
≫!
!"#$%#&'(
. By Taylor expansion, the (intensity-dependent)
refractive index becomes:
!=!
!
+
3!
!
8!
!
!
!
!
=!
!
+!
!
!
where the identity for intensity != !
!
!
has been applied. With this, we have
established the relation between the Kerr coefficient !
!
and third-order susceptibility
!
!
, as well as a full description of how the refractive index of a material is affected at
high incident powers.
The main method used to determine the Kerr coefficient n
2
of a material is the z-
scan technique, first established in 1989 (31, 32). A sample is moved along the focus of a
laser, and the beam radius is measured at a point beyond the sample. The beam radius
will increase or decrease due to the self-focusing or self-defocusing effect of the
nonlinear index of the material. The magnitude can be determined from the dependence
of the beam radius on the sample position.
Material and Symmetry Considerations
Note that in the derivation of the intensity-dependent refractive index above,
terms from ! that included !
!
were neglected. The second order susceptibility !
!
is an
important quantity in second order nonlinear optical processes including second harmonic
generation and sum-frequency generation. However, in centrosymmetric materials such
as silica, !
!
= 0 due to inversion symmetry. In fact, all even-ordered susceptibility
30
terms !
(!)
,!
(!)
,!"#. are equal to zero. In the polarization equation != !
!
(!
!
!+
!
!
!!+⋯), negative and positive values for ! would yield different values of !. This
imposes the constraint that the material must be structurally different in different
directions in order to satisfy this electric field sign dependence of the polarization. This
requirement is only satisfied in non-centrosymmetric crystalline materials, where
!
!
≠ 0 values are allowed. Though silica is an amorphous material, the spatial
arrangement of silicon and oxygen atoms gives it pseudo-centrosymmetric
characteristics. Thus, the lowest order nonlinear term in silica is in !
!
, which is
responsible for the nonlinear effects that permit the formation of frequency combs.

2.3.2 Four Wave Mixing
The primary third order process that allows for a frequency comb to be generated
is four-wave mixing (FWM). This is a parametric process where two photons interact to
produce two new photons of a different wavelength by the relation !
!
+!
!
=!
!
+!
!
.
In degenerate FWM !
!
=!
!
, yielding 2!
!
=!
!
+!
!
.
For FWM in WGMR, the threshold of the process is highly dependent on the Kerr
coefficient n
2
by the equation (33)
!
!!
≅ 1.54
!
2
!
!
+!
!!
2!
!!
!
!
!
!
!
!
!!
!

where !
!
and !
!!
are internal decay rates of the modes and external coupling decay rates,
respectively, n
2
is the Kerr coefficient, n
0
is the refractive index, ! is the mode volume, !
is the resonant wavelength, and Q is the quality factor. From this equation, it is clear that
the n
2
and Q factor are critical considerations in reducing the FWM threshold to
31
ultimately obtain frequency combs at lower input powers. Thus, it is understandable that
the majority of research has focused on increasing these quantities in order to obtain
frequency combs (34-38). In the case of silica, the n
2
is on the order of 10
-20
cm
2
/W.
Though this is lower than many other glasses, silica has relatively low absorption loss.
Thus, nonlinear optical phenomena can be observed in silica if the intensity of light is
high enough.
For a frequency comb to form, two initial photons from the pump laser are
annihilated to create a new pair of photons with frequencies of ω
s
and ω
i
, with indices s
and i indicating the signal (up-shifted frequency) and idler photons (down-shifted
frequency). When the two initial photons are of the same frequency (as in two pump
photons of the same frequency), this process is called a degenerate FWM process,
resulting in two sidebands adjacent and equidistant from the pump. In the FWM process,
the energy conservation condition must be obeyed, governed by the equation 2!
!"#!
=
!
!
+!
!
, which strictly constrains the signal and idler sidebands to be located equidistant
from the pump Δ!= !
!
−!
!
= !
!
−!
!
. It is this same conservation condition that
allows for emissions to be tunable, as in optical parametric oscillators (39, 40). The
generated signal and idler frequencies themselves can subsequently interact with each
other in additional (non-degenerate) mixing processes that allow for more equidistant
sidebands to be generated (41). This cascaded process is what allows for a frequency
comb to form (Figure 2-9). Stimulated Raman emission (discussed below) can also assist
in the frequency comb generation by contributing additional photons that can participate
in non-degenerate mixing processes with FWM photons. Stokes Raman photons can also
32
form their own combs via degenerate and non-degenerate FWM, yielding a comb with a
slight offset spacing due to different FSR caused by varying dispersion (42).

Figure 2-9. Frequency comb formation from both degenerate and non-degenerate four-wave
mixing process.

In order for FWM to be an efficient process, the additional consideration of phase
matching is also of great importance. There must exist a proper phase relationship among
all waves participating in the FWM process (pump, signal, and idler) in order for the
output waves to be generated in the direction of propagation. The condition of perfect
phase matching Δ!= 0 ensures the highest efficiency for the FWM process, ie. when the
detuning is minimized. The difficulty of achieving phase matching is due to dispersion,
which causes the Δ! of each wave to deviate from Δ!= 2!
!
−!
!
−!
!
(30, 43). In
order for FWM to lead to parametric gain necessary for frequency comb generation, the
detuning Δ! must be less than the parametric gain bandwidth Ω=
!!"#
!
, where !=
!!
!
!!
!""
,
c is the speed of light in vacuum, P is the circulating power within the cavity, n is the
33
refractive index, n
2
is the Kerr nonlinearity of the cavity material, and A
eff
is the effective
mode area of the optical field (41, 43).

2.3.3 Stimulated Raman Scattering
Another nonlinear optical effect that can be described by !
(!)
and is commonly
observed in silica whispering gallery mode resonators is Stimulated Raman Scattering.
Raman scattering is an inelastic scattering process that occurs when incoming photons
lose or gain energy equal to differences in vibrational states of the atoms in the Raman-
active material. Because of this, the response is time-delayed. This is a non-parametric
process, which is distinct from parametric processes like four wave mixing because non-
parametric processes involve energy transfer to the medium and is intrinsically phase
matched (10, 44). Upon excitation from the incident photon, a molecule’s polarization is
excited to a higher virtual energy state. When coupled to a vibrational resonance of the
molecule, the scattered photon will have a lower frequency or higher frequency than the
incident photon, corresponding to Stokes scattering and anti-Stokes scattering,
respectively, and equal to the vibrational Raman shift of the material (Figure 2-10). The
energy is transferred to an optical phonon, or a quantum of the lattice vibration. This
scattering process is spontaneous, occurring randomly in most cases. However, when the
intensity of incoming photons is high, the process becomes a stimulated process that can
also be described in terms of the third-order susceptibility !
!
(29, 30, 45). In WGM
resonators, the threshold of Raman lasing is described by the equation
!
!!
=
!
!
!
!
!!
!
!
!
!
!
!
!
!
!
!

34
where n is the refractive index, ξ is a coupling parameter, g
c
is the Raman gain
coefficient, Q
P
and Q
S
are quality factors for the cavity wavelength and Stokes
wavelengths !
!
and !
!
, ! is the cavity mode volume.
In silica, the Raman gain coefficient is low, with a value of ~10
-14
m/W near 1550
nm (46). However, in a WGM resonator such as a sphere or toroid, the high circulating
intensities makes it possible to observe stimulated Raman emission at very low input
powers (47). Raman emission lines appear at a frequency shift of ~14.3 THz,
corresponding to silica’s vibrational energy state. For wavelengths near 1550 nm, this
corresponds to a shift of approximately 115 nm. Raman gain has been observed in our lab
at thresholds as low as 157 µW for silica microspheres (48, 49).

Figure 2-10. Energy level diagrams depicting Stokes and anti-Stokes Raman scattering
processes.
Because the Raman threshold is often lower than the FWM threshold, Raman and
FWM often coexist simultaneously (44, 50). Raman emission and FWM are competing
nonlinear processes (51). Though the Raman gain in silica is low, it is higher than the
Kerr coefficient n
2
of silica (n
2
~10
-20
cm
2
/W). Various strategies have been studied to
favor one process over the other including engineering the cavity geometry (43, 52),
35
careful control of coupling (53, 54), precise laser detuning (53), and surface modification
with organic molecules (55).
Additionally, Anti-Stokes Raman scattering is also observable in WGM
resonators. In this process, the optical phonon that is generated in the Stokes Raman
scattering process is absorbed by the pump photon to generate a higher energy photon.
The primary distinction between Stokes and anti-Stokes scattering is the condition of
phase matching. For Stokes Raman scattering, the phase matching is intrinsically
satisfied due to the flat dispersion of optical phonons. However, for anti-Stokes Raman
scattering, the same intrinsic phase matching does not occur because the anti-Stokes
Raman process is parametric. Therefore, it must follow the phase matching condition
Δ!
!"
=!
!"
+!
!
−2!
!
, where ω
x
is the angular frequency for each of the photons
associated with the scattering process. From the schematic in Figure 2-10, it is apparent
that for the anti-Stokes scattering to occur, there must be enough Stokes photons at the
frequency !
!
=!
!
−!
!"#$%&"'(%)
. As a result, stimulated anti-Stokes Raman scattering
is much weaker than stimulated Stokes Raman scattering (56, 57). Enhancing the
stimulated anti-Stokes Raman signal therefore requires methods like seeding at the
Stokes Raman wavelength (58).

2.3.4 Brillouin Scattering
Besides interacting with optical phonons, incident light can couple to acoustic
phonons in what is referred to as Brillouin scattering. In this inelastic process, the electric
field variation of the incoming light induces acoustic waves in the medium by
electrostriction or radiation pressure (30). The light induces the acoustic wave in the
36
forward direction, and a Stokes-shift Brillouin wave in the backward direction. In silica,
stimulated Brillouin scattering can occur at very low thresholds due to its relatively high
Brillouin gain coefficient of ~10
-11
m/W, which is three orders of magnitude higher than
the Raman gain coefficient near 1550 nm. The threshold for stimulated Brillouin
scattering is described by (59)
!
!!
=
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

where g
B
is the Brillouin gain, Q
P
and Q
B
are the quality factors for the pump and
Brillouin wavelengths !
!
and !
!
, and ! is the mode volume. As both Brillouin and
Raman scattering are photon-phonon processes, their threshold equations are similar. For
silica, the Brillouin frequency shift is approximately 10.7 GHz, much lower than the
Raman scattering shift (14.3 THz) (60).

2.4 Dispersion
In order for the frequency comb to be formed via FWM, both momentum and
energy must be conserved. Momentum is intrinsically conserved through the relation
2ℓ
!
= ℓ
!
+ℓ
!
because the optical modes of a whispering gallery mode resonator are
angular momentum eigenvalues (43). However, energy conservation requirements
(2!
!
=!
!
+!
!
) cause dispersion to become a crucial consideration. Because
dispersion causes the phase velocity to change as the wavelength changes, higher orders
of four wave mixing may not be able to satisfy energy conservation requirements,
limiting the frequency comb span.
Dispersion is the wavelength (or frequency) dependence of the refractive index in
a material !(!) (or !(!)). Due to different contributions including material dispersion,
37
geometric dispersion, and modal dispersion, different wavelengths of light will take
different path lengths as they propagate through a medium. Dispersion is described by the
group velocity dispersion (GVD), !
!
=
!
!
!
!!
!
, where ! is the propagation constant of the
light equal to ! ! =
!!"(!)
!
!
. The positions of the resonance frequencies (or
wavelengths) are the only way to experimentally monitor the dispersion of the cavity,
given by
!
ℓ
=
ℓ ∙!
2! ∙! ∙!

where ℓ is the angular mode number, c is the speed of light, R is the resonator radius, and
n is the refractive index. As can be seen from this equation, the spacing of the resonance
frequencies Δ!
ℓ
(and the mode spectrum of WGMR) varies due to the frequency
dependence of n. Experimentally, the dispersion can be related to the change in free
spectral range by
!
!
=−
1
4!
!
!
∙
Δ(Δ!)
(Δ!)
!

where R is the cavity radius, Δ(Δ!) is the derivative of the FSR, and Δ! is the FSR.
The two most important contributions to dispersion in WGMRs are the material
dispersion and geometric dispersion. Because most materials, including silica, exhibit
normal dispersion
!"
!"
< 0 , cavity dispersion must be anomalous
!"
!"
> 0 in order to
equalize and allow for operation near a zero dispersion wavelength. At this zero-
dispersion wavelength, the whispering gallery modes are equidistant, allowing for the
FWM comb modes to align with the whispering gallery resonator modes (Figure 2-11).
38

Figure 2-11. Depiction of how the resonator modes shift as wavelength changes due to
dispersion. The gradual slippage between the resonator mode spacing and the comb mode
spacing, which remains constant, limits the span of a frequency comb.

For WGMRs, dispersion-compensating elements are often very difficult to add to
the system. This makes dispersion compensation much more difficult than in
conventional mode-locked laser based combs, which can be achieved by introducing
various optical components (61-64). One way to tune the zero dispersion wavelength is
by engineering the resonator geometry. The zero-dispersion wavelength in silica
resonators has been limited to >1300 nm until recently, when creative geometries have
been developed to shift the zero dispersion wavelength into the visible region (65-67). In
the case of silica microspheres, dispersion compensation is assisted by using silica
microspheres with diameters greater than 150 µm (52, 67). In silica microtoroids,
dispersion compensation is enhanced by shrinking the minor diameter such that D/d < 15,
where D is the major diameter and d is the minor diameter of the microtoroid (43). This
helps to decrease the effective mode area, which increases mode overlap with the
surroundings, in turn flattening dispersion. These geometry considerations are taken into
account when fabricating resonant cavities for obtaining frequency combs.
39

2.5 Frequency Combs
With the NLO phenomena discussed previously, frequency combs can be
generated via cascaded degenerate and non-degenerate processes. Frequency combs are
broad multiple wavelength light sources with spectral lines spaced at discrete intervals.
The strong potential of frequency combs lies in this precise spacing, which allows for the
comb to serve as highly accurate metrological “rulers”. The first iterations of frequency
combs were based on mode-locked femtosecond lasers in the frequency domain (68).
Later versions were based on comb generation in fiber (69, 70). More recently, there have
been many advances in microresonator-based comb generation based on CW lasers.
These advances represent a drastic reduction in both footprint and input power
requirements, as cavity build-up powers can reach higher within micrometer-scale path
lengths. Furthermore, comb spacing of more than 1 THz is possible in microresonator-
based combs due to the small cavity size, an impossible feat in mode-locked laser and
fiber-based systems with much longer cavity lengths.
Frequency combs have shown promise in a wide-ranging variety of applications
due to the very precise spacing of its spectral lines, with a uniformity of mode spacing
shown to be at a few parts in 10
17
(71). Despite the high cost and complexity, pulsed-laser
based systems have been utilized to perform many fundamental physics studies including
efforts to bridge the gap between the optical and microwave domains with frequency
combs (72-74). Frequency combs also played vital roles in refining the Rydberg constant
as well as the hydrogen atom Lamb shift (75).
40
With the high accuracy attainable with frequency combs, they have moved into
more applications, notably developing an all-optical atomic clock (76), improved optical
coherence tomography (77), astronomical spectrograph calibration (78), optical
communication (79), high-resolution spectroscopy (80-82), LIDAR (83-85), among many
others. In order for frequency combs to keep pace with the evolving technological
requirements, miniaturization of the system and reduction in operating power must be
reduced.

41
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49
3 Dispersion-Compensated Frequency Combs with Calcium Fluoride
Nanocrystals on Whispering Gallery Mode Resonators
3.1 Introduction and Background

Frequency combs are multiple wavelength optical sources consisting of multiple
spectral lines, where each line is discretely spaced from adjacent lines (1). As such, they
are very powerful tools, with the potential to make a lasting impact in many fields
including defense, spectroscopy, and medicine. To generate a frequency comb, a single
frequency of light is converted from a pump laser into a broad spectrum of coherent lines.
Currently, this process requires high input pump power due to the nonlinear optical
processes discussed in Chapter 2.
If frequency combs are to have a realistic chance of reaching their maximum
impact in integrated photonics and applications beyond, frequency combs will need to be
generated using on-chip laser sources. For this to be possible, power requirements for
comb generation the input power must be decreased by an order of magnitude, from tens
of mWs to approximately 5 mW. Planar integration of laser sources on-chip has been
difficult to achieve, and this 5 mW power level represents the approximate output power
limits of the current on-chip diode laser technology (2, 3). One method to achieve lower
input powers is to pair optical nanomaterials, such as calcium fluoride (CaF
2
)
nanocrystals, with microresonators to create novel platforms for frequency comb
generation. Since the invention of microresonator-based frequency combs (4), the input
power requirements for comb generation have dropped drastically from the earlier pulsed
laser (5) and fiber-based (6, 7) technology.
Though the majority of research has focused on increasing the Kerr coefficient to
improve frequency comb performance, one alternative approach that has been undertaken
50
is the use of low dispersion materials to fabricate ultra high-Q (Q~10
9
) monolithic
crystalline optical resonators, including calcium fluoride (8-11), magnesium fluoride (8,
12), barium fluoride (12, 13), and fused quartz (14). The ultra high-Q allows for high
circulating intensities to build up within the resonators and produce nonlinear optical
phenomena such as the four wave mixing required for comb generation. The favorable
flat dispersion behavior of many of these crystalline materials makes it possible to obtain
very wide spanning combs at input powers around 50 mW (8, 11). Though crystalline
resonators have allowed for lower power requirements, each monolithic resonator is
mechanically lathed and polished one at a time. Therefore, a significant limitation lies in
very low yields and limited production of the crystalline resonators. Furthermore, the
brittleness of the crystalline materials constrains the resonator size to the millimeter scale
or larger, limiting the applications where they can be utilized.
In contrast to crystalline resonators, silica microspheres (15) and microtoroids
(16) are easy to fabricate in large quantities and have high quality factors (Q~10
8
).
Therefore, an alternative strategy for generating low power and wide-spanning optical
frequency combs is to utilize a nanocomposite material that will combine the favorable
optical properties of a low dispersion material with the ease of fabrication of silica
microresonators. The details of the fabrication and characterization of these devices are
presented in this chapter. In order to demonstrate this method, we first investigate
growing CaF
2
nanocrystals in silica sol gel (17). Though we succeeded in fabricating
devices via this approach, the Q factor plummets, making comb generation impossible at
low input powers. An alternative method to synthesize CaF
2
nanocrystals in solution (18,
19) is developed to coat these CaF
2
nanocrystals on the surface. This method preserves
51
the high Q factor of the microresonator while giving the device some of the optical
properties of a low dispersion material. Compared to uncoated devices, the span of the
frequency comb is improved while the threshold for four wave mixing remains low.
Complementary numerical calculations confirm that this improvement is due to the
flattening of the resonator dispersion behavior, causing the FSR to change more slowly
than for a silica microresonator. This engineered dispersion allows for the resonator
modes to overlap with the FWM comb modes over a larger span and yield a wide-
spanning comb.
Details of both methods pursued are described below. The method for obtaining
freestanding CaF
2
nanocrystals proved more amenable to integration with resonators
without degrading the Q factor to the point of not being able to observe any nonlinear
effects.
3.2 Calcium Fluoride Crystals in Silica Sol Gel
3.2.1 Methods: Synthesis and Material Characterization

In order to obtain optical frequency comb generation using nanocomposite low
dispersion materials on silica microresonators, calcium fluoride (CaF
2
)

nanocrystals are
first grown in silica sol gel using a method described previously (17, 20, 21). In this
method, tetraethylorthosilicate (TEOS) is mixed with trifluoroacetic acid (TFA), acetic
acid, ethanol, calcium acetate, and deionized water. In this “one-step” process, the CaF
2
crystals precipitate within the silica matrix simultaneously as the silica condenses. TEOS
is the silica precursor, and upon hydrolyzation and condensation, forms a silica matrix.
Acetic acid serves as the catalyst. Trifluoroacetic acid serves as the fluorine source, while
calcium acetate serves as the calcium source. The molar ratio for each chemical used was
52
TEOS:Calcium acetate:TFA:H
2
0:Acetic Acid was 19:1:0.216:90:3. Details are shown in
Table 3-1.

Table 3-1. Sol gel recipe for CaF
2
nanocrystal-doped silica sol gels for approximately 5 mL
CaF
2
Sol Gel Silica
Chemicals TEOS EtOH Acetic Acid H
2
O TFA Ca(CH
3
C
OO)
2

Vendor Alfa Aesar,
99.999%
EMD Cleanroom Alfa Aesar Alfa
Aesar
MW 208.33 46.07 60.05 18.02 114.02 176.18
Purity 100% 95%* 100% 100% 99.99% 100%
Molar Ratio 19.00 Equal vol 3.00 90.00 3 1.00
Desired
Chemical
Mass
2.500 2.114 0.114 1.024 0.2160 0.111
Desired
Solution Mass
2.500 2.114 0.114 1.024 0.2161 0.111

TEOS is first removed from storage at 4°C and equilibrated to room temperature.
TFA is added to the calcium acetate in one vial and ~10 drops of water are added to the
solution to ensure the calcium acetate fully dissolves. In another vial, the TEOS, ethanol
and water are combined and stirred for 5 min. Acetic acid is then added to the TEOS
solution, and stirred for 30 min. Finally, both vials are combined and stirred for 4 hours.
The sol gels are then left to age in the vial for 1 week. After aging, the sol gels are spin-
coated on silicon or silica wafers (1 µm thermal oxide) at 7000 rpm for 30 sec. The
wafers are annealed in the tube furnace to 1000 °C (ramp rate 75°C/hr). Upon reaching
1000°C, the temperature is immediately returned to room temperature at the same rate
(ramp rate -75°C/hr).
As seen in the microscope images (Figure 3-1c), the crystal size is typically large
(>5 µm) when grown by the above procedure. This is due to the fact that the crystals in a
thin film of silica sol gel are able to nucleate heterogeneously on the surface of the silicon
53
wafer. This is significantly different than CaF
2
crystals that are generated with slower
homogeneous nucleation in thick layers of silica. The crystals reported in the literature
nucleated with slower homogeneous nucleation in millimeters-thick silica layers and are
smaller than those generated with the sol-gel method (Figure 3-1a/b) (17, 20). Bright
field optical microscope images of the crystals within the silica matrix are shown in
Figure 3-1c. In an attempt to decrease the size of the crystals, the experimental
parameters were modified incrementally. Initially, the sol-gel aging time was decreased
from one week to one day or five days. No significant decrease in crystal size was
obtained, indicating that the crystal growth primarily occurs during the annealing process.
Subsequently, the calcium acetate and trifluoroacetic acid were decreased two-fold. The
size of the crystals decreased marginally, but remained in the micrometer regime. Despite
decreasing aging time and solute concentration, the crystal sizes remained large in the
thin film silica.
The large size of the CaF
2
nanocrystals negatively impacts the quality factor of the
optical devices. As mentioned in Chapter 2, there are five primary contributing factors to
optical loss within microresonators (1) scattering loss, (2) material loss, (3) radiation loss,
(4) contamination loss, and (5) coupling loss. Because the size of the crystals is larger
than the wavelength of light used, contribute to significant scattering losses when they are
present within or on the surface of microresonators.
Furthermore, the presence of large crystals contributes to high stresses in the
silica matrix that lead to crack formation on the film (22). An example of one such crack
can be seen in Figure 3-2a. Cracks are detrimental not only for the quality factor of the
device, but also in the fabrication process. This is because cracks prevent uniform contact
54
between the sol gel surface and the photoresist, limiting the feature resolution.
Additionally, when fabricating the devices, three or more layers of sol gel are needed in
order to make fabrication of microdisks possible. The cracks prevent subsequent sol gel
layers from depositing uniformly. This creates inconsistencies within the fabrication
process and makes obtaining microdisks extremely difficult.

Figure 3-1. (a) Diagram showing mainly homogeneous nucleation of crystals within a bulk
silica sol gel matrix. (b) When the crystals are grown in a thin film of silica sol gel, the dominant
process is heterogeneous nucleation on the substrate below the film. (c) Bright field optical
microscope image showing large crystals in a thin film silica sol gel.

In order to combat the crack formation and large crystal size, a faster cooling
profile was adopted in order to encourage smaller crystallite size during the annealing
process. It is known that as the rate of cooling increases, crystal size decreases (23).
Therefore, the cooling rate was increased to 85°C/hr. At this cooling rate, we see that the
55
crystal size is smaller, approximately 500 nm (Figure 3-2b). This sol gel is coated on a
silica wafer (1 µm thermal oxide), and used to fabricate disks using the photolithographic
procedure discussed in Chapter 2. A silica wafer was used in order to eliminate the need
to coat multiple layers of the sol gel on the wafer, which would increase the likelihood of
cracks forming. The crystals in the disks are much smaller when the cooling rate
increased, indicating that scattering losses will be less severe.

Figure 3-2. (a) In most samples of the silica sol gel doped with CaF
2
crystals, extensive cracking
was observed due to the increased stress within the silica matrix. (b) Dark field image showing
decrease in CaF
2
crystal size upon increasing cooling rate during the annealing process. The
crystals seem to gather along streaks that form during the spin-coating process.

Elemental analysis was using energy dispersive X-ray spectroscopy (EDS)
performed to verify that the crystals present in the microdisks are indeed CaF
2
. A
partially broken disk was analyzed using a JEOL-7001 SEM equipped with an EDAX
unit. The electron beam is aimed at a particle within the SiO
2
-CaF
2
microdisk. The
resulting spectrum is shown in Figure 3-3, and the inset indicates the probe region where
the beam is directed. Calcium Kα and fluorine Kα lines are visible, indicating that each
element is incorporated into the particle being probed. The strong silicon Kα line is
present due to the large penetration depth of the beam. A small peak for carbon Kα is
likely due to residual reactants from the synthesis. Quantitative analysis reveals that
56
atomic percent of calcium and fluorine are 4.77 atomic % and 3.05 atomic %,
respectively.

Figure 3-3. Energy dispersive X-ray spectroscopy data for a broken microdisk fabricated from a
silica sol gel with CaF
2
nanocrystals grown in the silica matrix. The inset is the SEM image of the
microdisk, with the red cross indicating the region and nanocrystal being probed.

3.2.2 Methods: Optical Characterization

The quality factor for the microtoroidal devices made from CaF
2
crystals in silica
sol gel are on the order of 10
5
(Figure 3-4a). The low Q factor is likely due to the high
optical scattering caused by the presence of large crystals within the silica matrix. A dark
field microscope image shows visible crystals within the silica of a silica disk before
XeF
2
etching (Figure 3-4b). Large CaF
2
particles within and on the surface of the
resonator lead to a high scattering loss causing the Q factor to degrade by 2-3 orders of
magnitude. Because of the low Q factors, the CaF
2
in silica strategy was suspended. An
alternative method of fabrication was developed by synthesizing CaF
2
nanoparticles and
then coating them on the surface of the resonant cavities.
57
Figure 3-4. (a) Transmission spectrum near 980 nm used to calculate the Q factor for a
microtoroidal resonator fabricated from one layer of a CaF
2
crystal in silica sol gel deposited on a
1 µm thermal oxide wafer. (b) Dark field microscope image showing a silica pad (before XeF
2

etch) with large CaF
2
crystals in the matrix, which lead to high scattering loss when light is
coupled into a fabricated device.

3.3 Chemical Co-Precipitation Synthesis of Calcium Fluoride
3.3.1 Methods: Synthesis and Material Characterization

Most methods for synthesizing CaF
2
nanocrystals, both freestanding and within a
silica matrix, often involve the use of hydrofluoric acid. We sought to avoid use of this
highly caustic and dangerous chemical in order to make scaling up the process much
more feasible and safe. Thus, we utilized a solution-based co-precipitation approach in
order to synthesize freestanding CaF
2
nanocrystals (18, 19). This synthesis method
generates consistent CaF
2
nanocrystals that can be coated on resonators without
drastically decreasing the Q. Therefore, this is the primary process used for generating
optical frequency combs from low dispersion nanocomposite materials on
microresonators referred to in this chapter.
The CaF
2
nanocrystal particles are synthesized with a chemical co-precipitation
method based on previous literature (18, 19). First, 0.04 M calcium chloride in ethanol is
58
mixed until the solution becomes clear. It is then mixed with a slight stoichiometric
excess of ammonium fluoride, at which point the solution becomes immediately opaque.
After stirring for 12 h at 75°C, the mixture is centrifuged and washed with ethanol and
deionized water four times to remove residual calcium chloride from the supernatant. The
solution is diluted ten-fold to a concentration of 0.0868 mg/mL (determined
gravimetrically). The solution is then filtered through a syringe filter with a pore size of
0.45 µm to remove contaminants in the solution.
Microspheres with diameters of approximately 100 µm are fabricated as discussed
in Chapter 2. ~75 µm spheres are prepared using a tapered SMF-28 optical fiber (tapered
to ~2500 steps). ~125 µm spheres are prepared by taking a ~100 µm sphere and firing the
CO
2
laser near the stem to increase the diameter. These sizes are selected in order to
favor the four wave mixing process over Raman processes (24-26). Spheres are then O
2
plasma treated, and immersed in the CaF
2
solution individually for 1 min and removed
slowly. The coated microspheres and are then suspended on a glass slide and dried in a
gravity oven overnight at 75°C in order to allow all solvent to evaporate, leaving the
CaF
2
particles on the microsphere surface.
Microtoroid resonators are prepared using established fabrication methods (16).
Microtoroidal samples with major radii of ~75 µm are fabricated on silicon wafers. The
microtoroids are O
2
-plasma treated to clean the surface. Nanocrystal coatings are applied
to the microtoroids by spin-coating at 4000 rpm for 10 sec. The coated microtoroids are
also dried in a gravity oven overnight at 75°C in order to allow all solvent to evaporate,
leaving the CaF
2
particles physisorbed to the microtoroid surface.
59
Scanning electron microscopy was also performed using both a JEOL-7001 and a
Hitachi TM3000. Both CaF
2
crystals dispersed on a silicon wafer and on microresonators
are imaged. From SEM images (Figure 3-5) it is seen that there is a wide size distribution
in particle size, with the average radius of the CaF
2
crystals approximately 190 nm ± 130
nm, determined by image analysis. Having small sub-wavelength crystals is important in
order to minimize the effects of scattering losses, which can cause the Q factor to drop
precipitously when they are coated on the surface of resonant cavities (Figure 3-5).
Despite the filtration through a 450 nm pore size filter, some larger crystals were present,
likely due to aggregation of small crystals over time.

Figure 3-5. (a) SEM image of CaF
2
nanocrystals synthesized in solution, dispersed on a silicon
wafer. (b) SEM image of CaF
2
nanocrystals that have been coated on the surface of a
microtoroidal resonator.

Elemental analysis was using energy dispersive X-ray spectroscopy (EDS)
performed to verify that the crystals present are indeed CaF
2
. A piece of silicon wafer
coated with CaF
2
was analyzed using a JEOL-7001 SEM equipped with an EDAX unit.
The electron beam is aimed at a particle within the SiO
2
-CaF
2
region of the wafter. The
resulting spectrum is shown in Figure 3-6, and the inset indicates the probe region where
the beam is directed. Calcium Kα and fluorine Kα lines are visible, indicating that each
60
element is incorporated into the particle being probed. The strong silicon Kα line is
present due to the large penetration depth of the beam. A small peak for carbon Kα is
likely due to residual reactants from the synthesis. Quantitative analysis reveals that
atomic percent of calcium and fluorine are 6.15 atomic %/4.95 atomic %.

Figure 3-6. Energy dispersive X-ray spectroscopy spectrum for a CaF
2
nanocrystal on the
surface of a silicon wafer. The inset shows the spot where the electron beam is directed on the
wafer.

To further characterize the CaF
2
nanocrystals, dynamic light scattering
measurements are performed. Larger particles or aggregations are confirmed with this
method. The results show a bimodal distribution in particle size, with two peaks centered
at radii of 80 nm and 9 µm (Figure 3-7). These particle sizes are smaller than the particle
sizes determined by SEM image analysis of the nanocrystals. This difference in size is
due to the inclusion of larger aggregates when CaF
2
particles are drop-coated on silicon
61
wafers for SEM imaging. We assume that the larger peak shown in the DLS consists of
very large particle aggregates that are filtered out before coating or settle to the bottom of
the solution. Therefore, we conclude these large aggregates do not get coated on the
resonator surface. This assumption is confirmed in part due to the fact that such large
particles are not observed in the SEM images of the coated devices. Addtionally, optical
characterization of the microresonators shows high Q factors, which would be impossible
with such large particles on the surface.

Figure 3-7. Dynamic light scattering data for CaF
2
nanocrystals in ethanol showing two
prominent peaks at ~80 nm and ~9 µm.

3.3.2 FEM Modeling

In order to investigate how the optical mode of the microresonators is affected by
the presence of a CaF
2
nanocrystal on the surface of a resonant cavity, finite element
method (FEM) simulations are performed using COMSOL Multiphysics software. The
62
simulation is built to closely resemble parameters from the experiments and consists of a
small arc of a spherical resonator (R=75 µm) with an arc length approximately equal to
!
!!"
(Figure 3-8). Each edge of the arc consists of a perfect mirror, and the CaF
2
particle
(r=100 nm) is placed at the arc’s center 5 nm from the resonator surface. This distance
allows the CaF
2
particle interact with the evanescent tail. The refractive index for the
silica and CaF
2
are determined from each material’s Sellmeier equation and are
approximately 1.444 and 1.426 for 1550 nm, respectively. The model is set to restrict
maximum mesh size to λ/5 for most of the resonator, except 40 nm for the particle and 70
nm for the region where the mode is expected.

Figure 3-8. Schematic of the simulation design used in COMSOL Multiphysics.

The solver finds the solutions for the eigenfrequency near 1550 nm, and the
fundamental modes (one TE and one TM) are the ones with a single lobe. The mode
profiles for a resonator without and with a particle on the surface are presented in Figure
3-9a. It is clear from the simulations that there is no change in the optical mode besides a
63
small perturbation at the particle-resonator interface. The close refractive index match for
the two materials ensures there is little to no change in the optical field. Cut lines
extending radially from the center of the resonator to a few microns beyond the particle
on the surface demonstrate the perturbation in the electric field amplitude (Figure 3-9b).
Based on these measurements, there is clearly no increase in the electric field that can be
used to explain any enhancement of nonlinear optical phenomena. Therefore, the
enhancement of nonlinear optical phenomena observed in these devices is due only to the
intrinsic optical properties of the low dispersion material that is coated onto the
microresonators. This lack of enhancement does not depend on distance, contrary to the
studies performed in Chapter 4. Therefore, the separation distance parameter of 5 nm is
maintained even though the particles are directly touching the surface.

Figure 3-9. (a) Finite element model of a cross section of the fundamental mode’s electric field
in a spherical microresonator (R=75 µm) without (top) and with (bottom) a CaF
2
particle on the
64
surface (r=100 nm). (b) The electric field amplitude along a radial cut line for each resonator in
part (a). The dotted line represents the boundary of the microresonator.

3.3.3 Numerical Calculations

To appreciate the significance of dispersion, it is useful to compare the chromatic
dispersion of silica and CaF
2
. The chromatic dispersion describes the change in refractive
index, which is an important consideration due to the FSR dependence on refractive
index and wavelength, as described in Chapter 2. The dispersion for each material can be
determined from the respective material Sellmeier equations. Sellmeier equations are
determined from empirical measurements across a wide range of wavelengths, and yield
Sellmeier constants B
1
, B
2
, B
3
in the generalized equation (27)
!
!
! = 1+
!
!
!
!
!
!
−!
!
+
!
!
!
!
!
!
−!
!
+
!
!
!
!
!
!
−!
!

The Sellmeier equation for silica is given by (28)
!
!
−1=
0.6961663!
!
!
!
− 0.0684043
!
+
0.04079426!
!
!
!
− 0.1162414
!
+
0.8974794!
!
!
!
− (9.896161)
!

The Sellmeier equation for CaF
2
is (29)
!
!
−1=
0.5675888!
!
!
!
− 0.050263605
!
+
0.4710914!
!
!
!
− 0.1003909
!
+
3.8484723!
!
!
!
− (34.649040)
!

The chromatic dispersion for each material is plotted in Figure 3-10. We see that
the refractive index changes more quickly for the silica compared to the CaF
2
in the
region of interest near 1550 nm. The exact values of the slopes are dn/dλ(1550 nm) = -
0.0046 µm
-1
and dn/dλ(1550 nm)= -0.0118 µm
-1
for CaF
2
and silica, respectively. Though
65
the difference between these values seem insignificant, the four-wave mixing process
responsible for comb generation becomes inefficient quickly when the comb mode and
resonator mode overlap decreases. Thus, the change in the FSR due to the refractive
index change is important when using CaF
2
to enhance frequency comb generation in
silica microresonators.

Figure 3-10. Chromatic dispersion plots for CaF
2
and silica based on each material’s respective
Sellmeier Equation. Throughout this near-IR region, the refractive index for CaF
2
changes slower
than for silica.

In order to verify that the CaF
2
nanocrystals are affecting the effective dispersion,
and consequently the free spectral range, we utilize an effective medium model to
simplify the system (30). Rather than a nanocrystal coating, we assume that there is a
uniform thin film on the surface of a microsphere resonator to decrease the computational
complexity. Such a uniform coating is much simpler to model compared to a distribution
of nanocrystals randomly distributed on a resonator surface. However, uniform coatings
66
of materials, especially CaF
2
, are difficult to experimentally obtain on curved surfaces
such as in high Q microsphere and microtoroid resonators using methods such as
sputtering (31). Therefore, the nanocrystal surface coating approach is one alternative
method to achieve a similar effect. We can understand the effect of a surface coating on
the dispersion by utilizing the characteristic equation for determining the resonance
wavelengths of a coated spherical resonator (32, 33). Because the equation utilizes
assumptions regarding symmetry, this specific characteristic equation only applies to
spherical resonators, but the trend should hold true for toroidal microresonators as well.
Whispering gallery mode resonators, including microspheres, are described by
integers l, m, and v, which are mode numbers for the angular, azimuthal, and radial
directions, respectively. If considering only fundamental mode, m=l and v = 1. If we
consider a microsphere with a radius R coated with a uniform thin film of thickness h and
surrounded by air, the resonant wavelengths !
!
can be found from the equation (34, 35)
!
!
!
!
!
(!
!
!
!"#
!
!
)
!
!
(!
!
!
!"#
!
!
)
=
!
!
!
!
!
(!
!
!
!"#!
!
!
)+!
!
!
(!
!
!
!"#!
!
!
)
!
!
!
!
(!
!
!
!"#!
!
!
)+!
!
(!
!
!
!"#!
!
!
)

where
!
!
=
!
!
!
!
!
(!
!
!
!"#!
!)!
!
(!
!
!
!"#!
!)−!
!
(!
!
!
!"#!
!)!
!
!
(!
!
!
!"#!
!)
!
!
(!
!
!
!"#!
!)!
!
!
(!
!
!
!"#!
!)−!
!
!
!
!
(!
!
!
!"#!
!)!
!
(!
!
!
!"#!
!)

In both cases, !
!
= 2! !
!
, !
!
and !
!
!
are the spherical Ricatti-Bessel function and its
derivative, !
!
and !
!
!
are the Ricatti-Neumann function and its derivative.
In each case
!
!
=
!
!"#
!
!"!
!
!" !"#$%
!
!"!
!
!
!"#
!" !"#$%

67
!
!
=
!
!"!
!
!
!"!
!
!" !"#$%
!
!"!
!
!
!"!
!
!" !"#$%

For simplicity, only TE modes are considered.
To solve this characteristic equation, we consider the identities !
!
! = !!
!
(!)
and !
!
! = !!
!
(!), where !
!
(!) and !
!
(!) are the spherical Bessel function of the first
and second kind, respectively. These functions can be further simplified to
!
!
! =
!
2!
!
!!! !
(!)
!
!
! =
!
2!
!
!!! !
(!)
where !
!
(!) and !
!
(!) are the Bessel functions. The derivatives !
!
!
(!) and !
!
!
(!) are
expressed as
!
!
!
! =
!
8!
(!!
!!! !
! + !
!!! !
! −!!
!!! !
! )
!
!
!
! =
!
8!
(!!
!!! !
(!)+!
!!! !
! −!!
!!! !
! )
Using these identities, MATLAB is used to solve for the roots of the characteristic
equation using the ‘fsolve’ function. MATLAB has the Bessel functions of the first
and second kind built in (‘bessely’ and ‘besselj’, respectively). The characteristic
equation is coupled with the Sellmeier equations for silica and CaF
2
, giving a system of
three equations and three unknown quantities (k
0
, n
CaF2
, n
SiO2
).
For a range of mode number l values, an initial guess of the resonant wavelength
is established based on the equation 2!"= !
!
!
!
. Using this initial guess region and an
established tolerance range, the solver will find the highest !
!
value, corresponding to the
68
lowest k
0
value and the fundamental mode. The FSR is then determined by the difference
between adjacent modes. Using these results, the FSR vs. wavelength is plotted.
However, we are interested in how the FSR changes, not the FSR itself. Therefore, these
results are differentiated to calculate the change in FSR, which indicates how dispersion
changes.
The plot of the differentiated FSR vs. wavelength represents the dispersion across
a range of wavelengths near 1550 nm (Figure 3-11). From this analysis, we see that the
FSR changes more rapidly without the CaF
2
coating on the surface. As the coating
thickness h increases, the effect is amplified and the FSR changes more slowly.

Figure 3-11. Numerical calculations based on the characteristic equation for resonance peaks of
a coated microsphere show the effect of CaF
2
coatings on the rate at which the FSR of a resonator
changes for a spherical microresonator with a radius of 75 µm.

In order to compare the change in FSR in coated devices to uncoated devices, we
perform numerical calculations with a different method. The positions of resonant
wavelengths, or more precisely frequency, are calculated with asymptotic equations
69
derived from Mie scattering theory for a sphere of order number q and mode number l
(36, 37).
!
!,!
=
!"
!
!+2
!! !
!
!
!
! !
−
!
!
!
−1
! !
+
3
10
2
!! !
× !
!
!
!
!! !
−
2
!! !
! !
!
−
2!
!
3
!
!
−1
! !
!
!
!
!! !
+Ο(!
!!
)
where R is the sphere radius, c is the speed of light, n is the refractive index of the sphere,
P = n for TE modes, v = l + 1/2, α
q
is the q
th
root of the Airy function Ai(-z), and Ο is the
order of growth for the asymptotic function.
The frequency dependent refractive index is determined from the Sellmeier
equation for silica. Similar to the characteristic equation for the coated spherical
resonators, we can solve for the roots of this equation using MATLAB. In this case,
‘vpasolve’ is used to find the resonance frequencies. The FSR is determined by
!"#= 2!
!
!
!!!
−
!
!
!
−
!
!
!
−
!
!
!!!

The comparison to coated spheres with varying film thicknesses are presented in Figure
3-11. We see that as the film thickness increases, the FSR changes at a lower magnitude
compared to the uncoated silica sphere, as expected. This is because the increase in film
thickness on the surface causes the dispersion to flatten out as more CaF
2
is added. In
other words, the optical behavior becomes more similar to CaF
2
than silica.
Note that when the film thickness was increased above 200 nm, the behavior of the
numerical calculations becomes erratic. This may stem from the departure from the thin
film approximation off of which the characteristic equation is designed (32). The model
70
is also designed for higher refractive index coatings. A lower refractive index coating
causes more leakage of the evanescent field into the surrounding environment, causing
the Q factor to drop and increasing the difficulty of coupling (38). However, our
experimental system consists of a distribution of nanoparticles, minimizing problems
with evanescent field leakage. Because this model utilizes a thin film approximation, our
nanoparticle system’s behavior lies somewhere in between the calculated curves for the
film and for an uncoated silica resonator.
3.3.4 Methods: Optical Characterization

Resonator characterization is performed using the testing setup discussed in
Chapter 2. Light is coupled into the device from a tunable 1550 nm laser connected to a
tapered SMF-28 optical fiber. The output of the optical signal is split with a 90/10
splitter, with the 90% branch recorded on an OSA and 10% recorded on a
photodetector/oscilloscope (Figure 3-12).

Figure 3-12. Artistic rendering of the testing setup used to characterize optical microresonators
for frequency combs. A tunable laser couples light into the resonator via a tapered optical fiber.
71
The signal is then split to an optical spectrum analyzer (OSA), a photodetector (PD) that connects
to an oscilloscope (O-scope), and an electrical spectrum analyzer (ESA).

The fundamental mode of the device is found first by performing a broad scan to
find the deepest resonance peak. This peak is then used to find the Q factor at low input
power. Next, the generation of a frequency comb is recorded on the OSA at maximum
input power, approximately 5 mW. The input power is subsequently lowered by
loosening the connection between the patch cable and the spool. Though mode-locking is
important for frequency comb measurements (39, 40), no locking is utilized in these
studies besides best efforts to achieve thermal lock (41).
For each OSA spectrum acquired, a corresponding oscilloscope spectrum is taken
to analyze the amount of coupling. In these studies, coupling was maintained at around
30% in order to favor the four wave mixing process over Raman processes (25). Finally,
when the power is low (<1 mW), the threshold for four wave mixing is determined. The
threshold can be measured at low power when only signal and idler lines are present
adjacent to the pump line. The voltage values are converted to power using the
calibration curves discussed in Chapter 2.
3.3.5 Results: Quality Factor

The transmission spectra are used to determine the Q factor of the coated
microresonators. The transmission spectra used to determine Q factor for an uncoated
microtoroid and a CaF
2
coated microtoroid are shown in Figure 3-13a/c. Representative
Q vs. coupling plots are presented in Figure 3-13b/d to show the intrinsic Q of each
device. For microsphere and microtoroidal resonators coated with freestanding CaF
2

nanocrystals, the Q factors remain relatively similar to uncoated devices. This
72
demonstrates a significant improvement over the alternative method of CaF2 grown in the
silica sol gel, where the Q factor dropped by three orders of magnitude. This
improvement is due to the fact that the size of the nanocrystals is mostly in the 80 nm
radius range. Due to the small size of the CaF2 nanocrystals, the scattering losses are
minimized, as 𝑄 𝑠𝑐𝑎𝑡 ∝
1
𝜎 2
𝐵 , where σ and B are the RMS size and correlation length of the
scattering centers on the surface (41). Therefore, the quality factor is higher than in the
case of the crystals grown in silica, where the size of the crystals reached >10 μm in
many cases.

Figure 3-13. Transmission spectra for (a) an uncoated microtoroid and (c) CaF2
nanocrystal coated microtoroid. (b) and (d) show Q factor vs. coupling plots used to
determine the intrinsic quality factor (when coupling is 0%) for uncoated and coated
microtoroids, respectively.
73
3.3.6 Results: Threshold

To determine the threshold of FWM and other nonlinear optical phenomena, the
input power is varied by changing the amount of power coupled into the device, and
numerous OSA spectra are then collected. In order to determine the amount of coupled
power into the resonant cavity, a voltage-power correlation plot is made by plotting the
voltage level recorded on the oscilloscope versus the amount of power after the taper
(before reaching the splitter input).
FWM thresholds are determined for coated and uncoated microsphere resonators
with radii of approximately 80 µm, 95 µm, and 125 µm. The threshold curves for each
device size are presented in Figure 3-14. The values for each device are 339 µW, 851
µW, and 663 µW for 80 µm, 95 µm, and 125 µm, respectively. Clearly, there is no
dependence of the absolute threshold value on the resonator radius. This is likely due to
the threshold dependence on the Q factor, nonlinear Kerr coefficient n
2
, and radius, as
expressed by the equation:(43, 44)
!
!!
=
!
!
!
!
!
8!
!
!"!
!

where V
0
is the mode volume, n is the refractive index, ω is the angular frequency of the
pump laser, n
2
is the Kerr coefficient, c is the speed of light, η is the coupling rate, and Q
is the cavity quality factor.
74

Figure 3-14. FWM threshold curves for coated and uncoated spherical resonant cavities of
varying diameter.

The Q can vary from device to device, so the threshold will not necessarily scale
monotonically. It is also important to note that the mode volume V
0
is approximately
equal to 2πλR
2
, where R is the cavity radius (45). When the threshold values of each
device are normalized to their respective Q factors, the results for both coated and
uncoated devices show a dependence on R
2
, as expected (Figure 3-15a). In order to
account for these experimental factors, the threshold is normalized by radius. When the Q
is normalized again by radius, the normalized thresholds all have similar values, as
shown in Figure 3-15b. The similarity between the thresholds of the bare and coated
devices is due to the fact that the presence of the CaF
2
does not enhance or degrade the
Kerr coefficient n
2
of the cavity. The Kerr coefficients of silica and CaF
2
are 2.6x10
-20

cm
2
/W and 1.9x10
-20
cm
2
/W, respectively (46, 47). Thus, it is unlikely that the CaF
2
75
nanocrystals can lower the effective threshold of FWM. Rather, it is the dispersion that
plays a role in enhancing the nonlinear phenomena.

Figure 3-15. (a) FWM threshold normalized by the square of the Q factor, showing the R
2
dependence. (b) Further normalization by R shows that the threshold is not significantly affected
by the presence of the CaF
2
particles.

3.3.7 Results: Comb Generation

Using the CaF
2
coated microresonators we are able to generate frequency combs.
In order to better understand the impact of fabrication on the nonlinear properties of the
devices we characterize the combs generated from several different device geometries.
First, we demonstrate that the frequency comb spacing depends on the microresonator
radius. By testing microspheres of several different radii, we see that the spacing depends
on the FSR relation λ
2
/(2πnR), where λ is the wavelength, n is the refractive index, and R
is the resonator radius. Figure 3-16 shows the comb spacing for microsphere resonators
with radii of 80 µm, 95 µm, and 125 µm at input powers of approximately 3 mW. These
results show the potential to tune the comb spacing based on device fabrication by
modifying the radius of the microresonators. Such flexibility is important in applications
76
such as comb stability testing, where the reference comb spacing must be tuned to closely
match the one being studied (48, 49).

Figure 3-16. Comb spacing for CaF
2
-coated microspheres of varying radius show the spacing
inversely proportional to the radius. The optical microscope images corresponding to each comb
are presented on the right, with the scale bar representing 100 µm.

One phenomenon that has been observed in frequency combs is that as the power
increases subcombs begin to emerge (44). We observe this behavior in our CaF
2
coated
microresonators. In each comb line, above a certain threshold of power, we observe the
formation of subcombs within each comb line. These subcomb lines have a spacing of
less than 0.02 nm (Figure 3-17a). This represents a link between the optical and
microwave spectrum, as the beat signal from the subcombs corresponds to an RF signal
of 2.43 GHz, by the equation !"=−
!
!
!
!", where c is the speed of light, λ is the
wavelength, and dλ is the subcomb spacing. We confirm this by utilizing a fast
photodetector (Newport 1544-B) and feeding the signal to an electrical spectrum analyzer
77
(Agilent N9010A). The resulting beat note is seen in Figure 3-17. This represents a link
between the optical and RF domains, which is a core basis of many frequency comb
applications. The formation of subcombs has been investigated previously, so we did not
characterize the subcomb formation in detail (44).

Figure 3-17. (a) Subcombs form each comb line at high input powers, with spacing as low as
0.02 nm. (b) Beat signal observed on the electrical spectrum analyzer at 2.43 GHz.

Though the normalized threshold for FWM processes is proven to be unaffected
by the presence of CaF
2
nanocrystals, there is a clear enhancement of the frequency
combs generated by the CaF
2
coated microresonators as input power increases. The comb
generation as coupled power increases is presented in Figure 3-18 for both an uncoated
silica sphere and coated sphere resonator. At low input power, the comb lines for coated
devices reach a wider span at lower input power compared to the uncoated devices. This
is indicative of improved phase matching where the resonator modes and comb modes
(via FWM) overlap over a larger span. This overlap is imperative in order to have
efficient comb generation. Note that the flattening of the spectrum baseline at high input
78
powers is due to the use of an optical filter with the erbium doped fiber amplifier, which
reduces the spontaneous emissions from the laser and EDFA.

Figure 3-18. (a) Comb generation for an uncoated microsphere resonator as input power
increases. (b) Comb generation for a CaF
2
nanocrystal-coated microsphere resonator of similar
radius to the one in part (a).

The combs are not formed purely from FWM parametric processes. The presence
of stimulated Raman scattering is apparent for both coated and uncoated devices.
Furthermore, the photons from the Raman process can also mix in order to form
additional lines around the Raman line. In the coated devices, the improved phase
matching allows for the FWM processes around the pump line to extend across a wider
span and link up with the Raman scattering emission lines. Figure 3-19 shows the highest
spanning comb that we were able to observe. At an input power of less than 7 mW, the
span reaches over 400 nm, limited by the working range of our OSA. Notably, we also
79
see significant blue-shifted anti-Stokes Raman emissions, which is a sign that red-shifted
Stokes Raman emissions are present at even stronger levels and higher orders (50). This
is because a large population of Stokes Raman photons are necessary in order to generate
anti-Stokes photons (51). Furthermore, though the stimulated Stokes Raman scattering
processes are intrinsically phase matched, stimulated anti-Stokes Raman scattering is not
(52). This improvement in anti-Stokes Raman can be attributed to the dispersion
flattening from the CaF
2
nanocrystals.
Though the OSA window limits our ability to observe emissions past 1700 nm,
based on symmetry considerations, the comb in Figure 3-19 likely reaches a span of over
500 nm when higher order Stokes Raman emissions contribute to the comb span. This is
a ten-fold enhancement in span over the uncoated resonators at a similar input power, and
is attributed to the flattening of the dispersion that allows for the comb modes and
resonator modes to overlap over a larger wavelength range.
80

Figure 3-19. The widest spanning comb observed during testing of a CaF
2
microsphere
resonator with a radius of 95 µm. The coupled power is 6.68 mW.

During optical testing, it is difficult to isolate single modes when coupling into
microsphere resonators. Inevitably, multiple eigenmodes of the spherical cavity will be
excited simultaneously. This can lead to the formation of chaotic combs characterized by
a flat envelope (53), similar to what we observe in this study. As neither locking
mechanisms nor detuning controls are utilized during testing, this chaotic behavior is
difficult to avoid. Detuning and locking controls can help to direct which type of comb
generation will result (53-55).
Due to the difficulties with microsphere resonators, we also test the behavior in
microtoroidal resonators. Upon testing with CaF
2
nanocrystal coated toroids, we see an
improvement in the coherence of the comb compared to coated spheres and uncoated
toroids. Figure 3-20 shows a comparison of comb generation in coated and uncoated
81
microtoroid resonators. The most notable characteristic of the comb in the coated device
is the stability of the comb and the well-formed soliton envelope, indicative of lower
phase noise (55, 56). Because the microtoroid cavity has fewer azimuthal degrees of
freedom (57), the fundamental mode that we couple into is more isolated from non-
fundamental modes. Thus, combs in the stable cavity solition regime can be achieved,
even without locking and detuning controls. This enhancement from the CaF
2

nanocrystals allows for the frequency comb to span 200 nm at less than 3 mW of coupled
power, twice as wide as the comb in the uncoated toroidal resonator at similar power.

Figure 3-20. (a) Comb generation for an uncoated microtoroidal resonator (R=55 µm) as input
power increases. (b) Comb generation for a microtoroidal resonator of similar size to the one in
part (a).

This demonstrates that the CaF
2
coated silica microtoroids are an effective
strategy to obtain stable and wide-spanning frequency combs. This method is much easier
82
in terms of fabrication compared to recently reported methods, and does not involve the
use of dangerous chemicals for the nanocrystal synthesis.

3.4 Conclusions

In summary, microresonators that incorporate CaF
2
nanocrystals are fabricated
and their frequency comb generation is characterized. Compared to existing comb
generation methods, these frequency combs require less power to generate wide spans
and can be more reliably fabricated.
In order to create these devices, two methods of fabricating CaF
2
nanocrystal
coated microresonators were developed. First, CaF
2
nanocrystals were grown in silica sol
gel solutions. The average size of these crystals was 5-10 µm. When they were integrated
on the microresonators there was a decrease in the Q factor by two to three orders of
magnitude due to the increases in scattering loss. As a result, an alternative method of
synthesizing CaF
2
nanocrystals in solution and then coating these particles onto the
surface of microresonators was developed. With this approach, high Q factor was
maintained, allowing for nonlinear optical phenomena to be observed.
To further understand the implications of CaF
2
nanocrystal coated
microresonators, numerical calculations are used to show that the dispersion is flattened,
which translates to the cavity FSR changing more slowly. This allows for better matching
between the resonator cavity modes and FWM frequency comb modes, which is critical
for the formation of frequency combs. Finite element method simulations are also
performed to show that the presence of the CaF
2
nanocrystal does not affect the optical
mode of microresonators..
83
Experimentally, the CaF
2
coated microresonators are characterized for FWM
threshold and frequency comb span. Though the quality factors of the cavities decrease
with the presence of the crystals on the surface, the span of frequency combs generated
from these coated devices increases while the effective FWM threshold remains the
same. In microsphere cavities, a ten-fold enhancement in span is achieved. The widest
observed span for a frequency comb in a coated microsphere resonator is over 500 nm at
an input power of less than 7 mW. This nanomaterial-driven frequency comb
enhancement strategy represents a novel approach to improving nonlinear optical
properties via facile surface modification of silica microresonators.

84
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89
4 Gold Nanoparticle-Enhanced Frequency Comb Generation
4.1 Introduction and Background
An alternative strategy to improve the nonlinear behavior necessary to obtain
frequency combs is to enhance the optical field at the surface of the WGM resonator with
a surface plasmon-polariton (SPP). SPPs are electromagnetic waves that travel along a
metal-dielectric interface, bound to the metal surface and guided by it. Part of their
energy is stored in these surface electron oscillations. Uniquely, SPPs exist on scales that
are smaller than the wavelength of the incident photons, allowing for the oscillations to
enhance the local field intensity in a highly confined region (1). This enhancement has
allowed for SPPs to be utilized in various applications including sensing (2-4), optical
trapping (5-7), photonic data storage (8, 9), imaging (10), and nonlinear phenomena (11).
There have been inherent challenges, however, when it comes to combining SPPs with
resonators in order to get plasmonic effects within the cavity. Past efforts have resulted in
degradation in Q factors by up to six orders of magnitude (12, 13).
An alternative approach involves placing plasmonic nanomaterials external to, but
near the resonant cavity (14). One type of plasmonic nanomaterial that has been studied
extensively is gold nanorods. These structures have dimensions less than 100 nm, with
aspect ratios of approximately 3-5. Gold nanorods have been utilized in many ways in the
field of optics (15, 16), especially in applications that exploit its surface plasmon
resonance (10, 17, 18). A number of studies have explored the combination of the
plasmonic effect with whispering gallery mode resonators. These studies have shown that
the two effects together can drastically narrow the plasmonic resonance linewidth (19), as
well as improve performance in spectrometers (20) and sensors (21-23). In fact, coatings
90
of gold nanorods on WGM resonators have been previously used in our lab to create a
plasmonic upconversion laser when pumped near the plasmon resonance (~760 nm) (24).
Far fewer studies have been performed with WGM resonators to investigate surface
plasmon polaritons off-resonance.
In this chapter, a plasmonically-enhanced frequency comb based on gold
nanorods on WGM resonators is presented. We exploit a hybridization of a plasmon-
polariton with the WGM in order to increase the field intensity in the region between the
nanorod and the resonant cavity. The enhanced optical field can then interact with a small
molecule layer with a high !
!
that has been functionalized on the nanorod surface.
Experiments and modeling are performed in the near IR, far from the nanorod’s
longitudinal plasmon resonance. The results show that the hybrid mode and interaction
with the nonlinear polymer layer enhances the generation of frequency combs.

Figure 4-1. An artistic rendering of PEG-functionalized gold nanorods coated on a WGM
resonant cavity. The nanorods at the equatorial region interact with the circulating optical field to
form a hybrid surface plasmon polariton-whispering gallery mode.

91
4.2 Methods: Synthesis and Material Characterization
Spherical WGM resonant cavities are fabricated using the same method discussed
in Chapter 2. In this study, the diameters were maintained at ~130-150 µm by reflowing
stripped optical fibers that had been tapered before reflow (~3000 steps). The spheres
were then cleaned with oxygen plasma in order to remove any surface contaminants and
to create a hydrophilic surface.
Gold nanorods are synthesized using a seeded growth method described
previously (25). In this method, partially capped spherical gold seeds are added to a
growth solution, allowing for the nanorods to grow preferentially in one direction ({111}
surfaces) while the CTAB surfactant blocks growth in other directions ({110} surfaces)
(26, 27).
The initial gold seed solution is prepared with a solution of 0.25 mL of 0.01 M
HAuCl
4
·3H
2
O and 7.5 mL of 0.10 M cetyl trimethylammonium bromide (CTAB) in
water. Next, 0.6 mL of cold NaBH
4
is added and the seed mixture was kept at 30°C for 2
h. The growth solution is prepared by mixing 100 mL of 0.1 M CTAB, 5 mL of 0.01 M
HAuCl
4
·3H
2
O, 1 mL of 10 mM AgNO
3
, 2 mL of 0.5 M H
2
SO
4
, and 800 µL of 0.1 M
ascorbic acid. Nanorod formation begins when 0.24 mL of the seed solution is added to
the growth solution, and the entire mixture is kept at 30°C for 12 h. Finally, the gold
nanorods are purified and washed by centrifuging at 9,000 rpm for 1 min.
92

Figure 4-2. SEM images of (a) gold nanorods dispersed on a silicon wafer and (b) of a spherical
WGM resonator coated with gold nanorods.

The surface of the synthesized gold nanorods is then functionalized with PEG
using a previously executed method in our lab (24). First, 4 mL of a PEG-thiol solution
(0.004 mM) is added to the as-grown rods and allowed to stir for 2 h. After centrifuging
(at 9,000 RPM for 15 min) and remixing in water three times, the rods are re-dispersed in
methanol. The concentration of the solution is then diluted until it reaches three
concentrations of 0.125 M, 0.080 M, and 0.070 M. Additionally, gold nanorods without
the PEGylated surfaces are also prepared at a concentration of 0.125 M.
93
SEM images show the gold nanorods dispersed on a silicon wafer (Figure 4-2).
The approximate size of the rods is ~60 nm in length and ~15 nm in diameter, indicating
an aspect ratio of 4.5. UV/Vis absorption spectroscopy was performed in order to confirm
the rod structure and identify the location of the longitudinal surface plasmon resonance.
In this case, the longitudinal plasmon band is located at 843 nm (Figure 4-3).

Figure 4-3. UV-Vis absorption spectrum for gold nanorods dispersed in methanol. The peaks at
~515 nm and ~845 nm correspond to the transverse and longitudinal surface plasmon resonances,
respectively.

For each gold nanorod concentration, silica microspheres were dip-coated into the
solution and agitated gently for 1 min, then slowly removed. The coated devices were
then dried in a gravity oven at 75°C overnight to remove traces of residual solvent. We
noted that shorter drying times resulted in inadequate solvent removal, presenting
challenges during resonator testing. This was observed in an enhanced attraction between
the fiber taper and the sphere.
94

4.3 Methods: FEM Modeling
In order to better understand the interaction of the optical field within the WGM
resonator with nanorods, finite element modeling with COMSOL Multiphysics software
was performed. All parameters, including wavelength, resonator geometry, and nanorod
size, were designed in the software to closely match those from the experiments. The
mesh size was limited to λ/10 in the region of interest where the nanoparticle is located.
For a gold nanorod located 15 nm from the resonator surface, the circulating
optical field from the resonator is coupled into the nanorod on the surface via the
evanescent field, which extends outside of the resonator boundary (discussed in Chapter
2). This results in a hybridized photonic-plasmonic mode located between the surface of
the silica and nanorod, seen as the high intensity field region between the rod and the
silica resonator (Figure 4-4a). This occurs despite the fact that the wavelength is far from
plasmonic resonance for the gold nanorods (~845 nm, Figure 4-3). A cross sectional cut
line in the resonator’s radial direction compares the electric field amplitudes for a mode
circulating in a cavity without (Figure 4-4b, top) and with (Figure 4-4b, bottom) a gold
nanorod on the surface.
For the case of a resonator with a nanorod on the surface, there is a very
prominent spike in the field amplitude. In fact, the intensity of the optical field at this
“hot spot” reaches a value higher than in the WGM resonator itself. This is likely due to
the formation of a hybrid WGM-plasmonic mode, as previously theoretically predicted in
similar numerical FEM simulations (28). This previous model predicts the increased
intensity from the hybridized mode peaks out at an optimal particle size of ~50 nm,
95
where the plasmonic enhancement balances the degradation in Q factor due to absorption
and scattering losses. From SEM images (Figure 4-2), we see that the gold nanorods
used are near this optimal size.

Figure 4-4. a) Finite element method simulation of the circulating optical field in a spherical
resonator with a functionalized gold nanorod at the surface (15 nm separation distance) showing
the high intensity region in between the two interfaces. b) The electric field amplitude along the
cross section of the spherical resonator for a device without (top) and with (bottom) a gold
nanorod on the surface (15 nm separation). c) Enhancement of the field relative to the intensity
without a nanorod present as the separation distance is varied.

Additionally, we studied the effect that the distance between the silica surface and
the gold nanorod had on the enhancement of the electric field. The nanorod must lie in
the evanescent tail of the WGM in order to form the hybridized mode, so this distance is
an important consideration. Perpendicular to the surface, the evanescent field decays
rapidly, as described in Chapter 2. As seen in Figure 4-4c, the intensity enhancement
between the particle and the resonator surface (compared to the intensity at the same
region without a nanorod present) decreases with increasing separation distance, due to
the fast exponential decay of the evanescent tail (29). Furthermore, the SPP intensity also
decays exponentially in the z direction perpendicular from the metal surface, described
by (30):
! ! ~!
!!"

96
where ! ! is the electric potential of the SPP, k is the wavevector, and z is the distance
from the metal surface.
Thus, both considerations make the location of the plasmonic particle important.
Because the gold nanorods used in the experiments are separated from the silica surface
only by the thin PEG layer, the separation distance is below 10 nm, and the enhancement
factor is approximately fifteen times that of the field without a gold nanorod present. This
local enhancement allows for the light to interact with the nonlinear PEG layer with a
higher intensity.
4.4 Results: Optical Testing
The WGM spherical resonators are tested using the same set-up discussed in
Chapter 2 (Figure 4-5). The pump laser is a tunable laser in the 1550 nm – 1630 nm
range in consideration of silica’s favorable dispersion near 1550 nm (31). The Q factors
for each coated device is determined to be on the order of 10
7
. Q factor values for each
device tested are included in Table 4-1. The decrease in Q factor as the nanoparticle
concentration increases compared to bare spheres is likely due to the increase in
scattering loss introduced from the nanoparticles on the surface.
97

Figure 4-5. Artistic rendering of the testing setup used to characterize the comb generation of
the WGM resonators. The comb spectra are recorded on the optical spectrum analyzer, while the
photodetector is connected to an oscilloscope to analyze the transmission spectrum.

Device Quality Factor (Q)
Uncoated Device 1.2 × 10
8

PEG-NR (0.070 mM) 7.7 × 10
7

PEG-NR (0.080 mM) 5.6 × 10
7

PEG-NR (0.125 mM) 6.5 × 10
7

CTAB-NR (0.125 mM) 6.3 × 10
7

Table 4-1. Quality factor for each of the uncoated and functionalized gold nanorod-coated
microsphere resonant cavities tested.

As light from the laser is coupled into the resonator, four wave mixing is observed
once a threshold power is reached. The threshold of the four wave mixing process is
determined at low input power levels when only the signal and idler lines are present. For
the functionalized gold nanorod-coated cavities, the threshold ranges from 0.148 to 1.5
mW. Because the threshold of the FWM process is inversely proportional to the Q
2
as
discussed in Chapter 2 (32), we also calculate the threshold in terms of circulating
98
intensity, which normalizes out the Q factor, in order to compare different concentrations
of devices. We use the conversion equation (33)
!
!"#!
=
!!
!
!
!
!"
!
(1+!)
!
!
!"#$%

where Q
0
is the intrinsic Q, n is the refractive index, R is the resonator radius, and
K=Q
0
/Q
coupling
, which represents the ratio of the intrinsic photon lifetime to the (lower)
photon lifetime due to coupling. Figure 4-6a shows the threshold curves for microsphere
resonators coated with each concentration studied. As the concentration of PEGylated
gold nanorods increases, the threshold decreases from 0.439 GW/cm
2
to 0.041 GW/cm
2
.
A non-PEGylated gold nanorod sample is also prepared at a concentration of 0.125 M,
the same concentration as the sample with the lowest threshold. However, the threshold
for this device is much higher, at approximately 0.260 GW/cm
2
. This suggests that it is
the combination of both the hybridized mode and the presence of the PEG layer that is
responsible for enhancing the nonlinear behavior. Because the optical field amplitude
increases dramatically due to the hybridized mode, it can interact more strongly with the
nonlinear PEG molecule to effectively lower the threshold of FWM. Furthermore, the
nonlinear Kerr coefficient n
2
of polyethylene glycol is 2 orders of magnitude higher than
that of silica (n
2,SiO2
~10
-16
cm
2
/W and n
2,PEG
~10
-14
cm
2
/W) (34). Therefore, despite the
decrease in Q factor due to higher scattering loss introduced by the gold nanorods
decorating the resonator surface, the n
2
compensates for the decrease and helps to lower
the FWM threshold.
99

Figure 4-6. a) Threshold curves for the microspheres coated with various concentrations of
functionalized and non-functionalized gold nanorods. b) Threshold values in terms of circulating
intensity and power for each device tested in this study show a decrease as gold nanorods
functionalized with PEG are introduced. CTAB-functionalized nanorods on the resonators did not
decrease the thresholds as effectively.

Upon further increase in the circulating intensity, non-degenerate four wave
mixing processes begin to occur, beginning the formation of a frequency comb. As input
power increases, it is apparent that frequency comb generation is greatly enhanced by the
presence of the gold nanorods on the surface. We see combs that reach a span of up to
100
300 nm at input circulating intensity values much lower than that in bare silica devices
(Figure 4-7). As the concentration of PEGylated gold nanorods on the surface increases,
the frequency comb generation process becomes more efficient, resulting in wider spans
at lower input powers. Consider the circulating intensity of 1.2 GW/cm
2
in a bare silica
sphere, where only Raman emission is present (Figure 4-7a). In the coated spheres, at
similar input intensities, both strong Raman and FWM processes are already observed
(Figure 4-7d). Furthermore, as the concentration of nanorods on the surface increases,
the number of lines generated by FWM near the pump line increases. In the 0.125 mM
coated device, a continuous comb is already present at 1.46 GW/cm
2
.

101

Figure 4-7. Comb spectra for (a) bare silica spheres, and PEGylated gold nanorod-coated
spheres at a concentration of (b) 0.070 M, (c) 0.080 M, and (d) 0.125 M with increasing input
power.

We see that the gold nanorod coating decreases the FWM threshold such that
FWM appears before Raman emission, the opposite of the trend seen in bare spheres due
to the higher Raman gain coefficient (g
R
~ 10
-14
m/W) compared to Kerr coefficient (n
2
~
102
10
-20
m
2
/W). Because there are both strong Raman and strong FWM processes occurring
simultaneously in gold nanorod-coated devices, the comb generation is believed to be
enhanced by a Raman-assisted FWM process, where photons from the stimulated Raman
scattering mix with photons from degenerate and non-degenerate FWM mixing
processes. In the bare silica device where FWM is weak, there is less interaction between
the Raman emission photons and FWM emission photons, resulting in a weaker and
narrower comb span.
Furthermore, we see the presence of the PEG on the surface also plays a pivotal
role in comb generation, as discussed above. Though PEG functionalization is an optional
step in the synthesis of gold nanorods that helps to prevent the nanorods from
agglomerating (35), CTAB is an integral part of the synthesis to allow for directional
growth of the gold seed (27). The comb generation spectra for CTAB-functionalized gold
nanorods at a colloidal concentration of 0.125 mM are shown in Figure 4-8. Though
FWM begins at a lower circulating intensity than in uncoated devices, the Raman
processes dominate. A comb spanning ~300 nm is obtained at 3.6 GW/cm
2
, though the
lines are not continuous as in the PEG-functionalized nanorod case. This indicates that
the FWM process is not as well phase-matched, resulting in lower comb generation
efficiency. As we see in Figure 4-6, the threshold is also higher in the CTAB-
functionalized gold nanorod-coated devices. Note that regardless of functionalization,
above a concentration of 0.125 mM gold nanorods, we observe that the Q factor drops
significantly, resulting in far less efficient FWM processes.
103

Figure 4-8. Comb generation spectra for a spherical microresonator coated with CTAB-
functionalized gold nanorods at a concentration of 0.125 mM.

4.5 Conclusions
To summarize, we have shown that we can increase the amplitude of the optical
field by decorating the surface with functionalized gold nanorods. With finite element
method modeling, we see that the presence of gold nanorods on the surface results in a
hybridized plasmon polariton-whispering gallery mode. Despite the fact that the nanorods
104
are not excited at their surface plasmon resonance, the resulting hybrid mode results in
amplitudes higher than those within the cavity. Experimentally, we show that with this
hybrid device, frequency comb generation is enhanced due to the higher field interacting
with a PEG coating with high Kerr coefficient n
2
. This allows for a decrease in FWM
threshold and increase in comb span, despite a decrease in Q factor caused by increased
surface scattering from the surface particles.
This plasmonic approach to improving frequency comb performance will have a
significant impact on the quest for low power on-chip comb generators. The simplicity of
applying a nanomaterial surface coating will allow for this process to be compatible with
nearly any current fabrication protocol. This eliminates the need for new fabrication tools
to be developed, as was the case for past advancements in frequency comb technology.

105
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109
5 Zinc Oxide Nanotetrapod-Based Flexible Fluorescent Material
5.1 Introduction and Background
Zinc oxide (ZnO) is a II-VI compound semiconductor with a wide band gap of 3.3
eV. ZnO has been used in a multitude of products including sunscreens (1), sensors (2-
4), and photovoltaics (5, 6). ZnO is found in two polymorphs – hexagonal wurtzite and
cubic zinc blende (Figure 5-1). Of the two crystal structures, hexagonal wurtzite is the
more thermodynamically stable form and, thus, more commonly encountered. Neither
form possesses inversion symmetry, allowing for ZnO to have unique piezoelectric and
optical properties. As discussed in Chapter 2, the non-centrosymmetric nature of
materials gives rise to a material’s second-order susceptibility coefficient !
(!)
, which
allows for second order processes such as second harmonic generation and sum
frequency generation to occur (7-9). ZnO is also biocompatible, expanding its potential
applications into biological systems.

Figure 5-1. Zinc oxide is found in two polymorphs, with hexagonal wurtzite being the more
thermodynamically stable form.

110
In this chapter, we explore some of the diverse optical properties of ZnO
nanomaterials. Though ZnO exhibits both second-order and third-order nonlinear optical
properties, here, we focus on an alternative application of developing a flexible ZnO
nanocomposite material. Further discussion of ZnO’s nonlinear optical properties is in
Appendix 3. The integration of flexible materials in a wide variety of consumer
applications including optical displays (10, 11), sensors (12, 13), and wearable
technologies (14-16) has triggered a significant rise in research on fluorescent materials.
In recent years, utilizing nanomaterials has become a common strategy to obtain these
functional flexible materials (17-21). The main advantage of nanomaterials is that they
fluoresce more efficiently and do not photobleach due to favorable quantum confinement
effects. Furthermore, they are often capable of being synthesized via more
environmentally friendly methods (22-24).
Zinc oxide nanomaterials have become a very widely researched material due to
their many favorable optical properties. Though most research has focused on ZnO
nanowires (NW) and thin films (25-28), other morphologies of ZnO also hold promise in
various applications. One of these is the zinc oxide nanotetrapod (ZnO NTP) (29-31),
pictured in Figure 5-2. These ZnO NTPs can be synthesized in large quantities with a
facile and environmentally friendly bottom-up chemical vapor transport (CVT) method,
which affords a high degree of flexibility in tuning various characteristics of the
nanostructure (32, 33).
Under UV excitation, the ZnO NTPs emit UV and green light. One important
advantage of this morphology of ZnO over one-dimensional morphologies like NWs is
that the material properties are spatially invariant in three dimensions. Thus, aligned

111
growth of the NTPs is often unnecessary, in contrast with many applications where ZnO
NWs are used (34-36).
However, one of the principal concerns with this material is that it is fragile and
difficult to handle. Thus, an approach to improve its mechanical properties and
processability is to embed the nanomaterial in a transparent and flexible substrate to
provide a supporting matrix while preserving its optical properties. Such a system will
allow for expansion to applications such as long-life light-activated sensors (37, 38).

Figure 5-2. Scanning electron microscope image of a single ZnO NTP on silicon substrate,
showing the characteristic four legs at 109.5° from adjacent legs.

In this study, we synthesize ZnO NTPs with a chemical vapor transport method
and use an inverse soft lithography method to embed them in an elastomeric matrix. We
then characterize this composite material’s emission after mechanical bending.
Complementary finite element method modeling is also performed in order to quantify
the stresses within the nanocomposite material during flexural bending.

112
5.2 Methods: Synthesis and Material Characterization
ZnO NTPs are synthesized using a catalyst-free chemical vapor transport method
in a tube furnace (Lindberg Blue M model) (Figure 5-3a-b), similar to one described
previously (32, 39). The tube furnace was modified with flanges for gas inlet and exhaust
ports. Gas flow rate is monitored for each gas mixture using a Correlated Flowmeter
(Cole-Parmer EW-03217-12). Approximately 1.5 g of zinc powder (Sigma-Aldrich,
purum grade) is first placed in a 2.5 mL quartz vial (Koehler K41000), which is placed at
one end of an alumina combustion boat (VWR 89037-982). Clean silicon handler wafers
are then placed downstream from the zinc powder vial at a distance of 5-12 cm. Argon is
first introduced into the tube furnace at a flow rate of 370 mL/min for 1 h. The
temperature in the furnace is then ramped up to 750°C at a rate of 24°C/min, and the flow
rate is decreased to 200 mL/min. After maintaining the temperature at 750°C for 20 min,
a 0.5% oxygen in argon flow is introduced at 50 mL/min for 10-20 min. Finally, pure
argon is flowed through the tube while the temperature decreases at 6°C/min. The final
product is deposited as a white colored fragile and fluffy layer on the surface of the
silicon handler substrate (Figure 5-3c).

113

Figure 5-3. (a) Schematic rendering showing the chemical vapor transport (CVT) method for
synthesizing ZnO NTPs. (b) Photograph of the modified tube furnace used for the CVT growth.
The inset shows the gas line splitter before the inlet port. (c) Photograph showing final product of
ZnO NTPs on the surface of silicon wafers.

Initial growths resulted in ZnO structures that were non-tetrapod in morphology.
The shape and size of ZnO nanostructures are very sensitive to oxygen and zinc vapor
concentration gradients, often resulting in structures that vary greatly within a single
synthesis (32). Therefore, troubleshooting was necessary in order to find the root cause of
large structures growing in favor of nanostructures. First, a good seal on the tube furnace
connections must be ensured. The process is very sensitive to oxygen concentration as
expected, so excess oxygen causes the shape and size to fluctuate uncontrollably, yielding
undesirable products, as seen in Figure 5-4a. This unusual shape is likely due to the

114
unstable oxygen concentration from leaks in the seal causing the nanowires to grow at
different rates in the [0001] direction. Leaks in the system were confirmed by running
control growths without O
2
flow and seeing ZnO structures still form on the wafers.
Additionally, the time where oxygen flow (0.5% O
2
in 99.5% Ar) is present was also
found to have the biggest effect on decreasing the size of the deposited ZnO structures.
Initial studies began with 20 min, but 7 min proved to be more favorable in obtaining
NTP structures with the correct shape (Figure 5-4b/c).

Figure 5-4. (a) Non-uniform ZnO structure that resulted from a poor seal on the CVT tube
furnace. (b) When the oxygen mixture is left for 20 min at 50 mL/min, the tetrapod structure is
lost in many regions of the growth substrate. (c) With 7 min of O
2
flow at the same rate, the
resulting structures are more tetrapod-like.

The ZnO NTPs grow by the initial nucleation of an octahedral zinc blende core of
approximately 200 nm (Figure 5-5a) (40). The facets of the octahedron consist of
alternating +c [0001] or –c [0001] faces. The [0001] faces are zinc terminated, and
growth of a nanowire is favored on this face (41). Thus, a tetrapod is formed, as seen in
Figure 5-5b-c, where each leg is 109.5° from each of the other three. The hexagonal basal
plane on the end of the NTP leg can also be observed (Figure 5-5b). SEM images show
that the size of the ZnO NTP legs grown under these conditions range from 0.5 µm - 3.5
µm in length and 120 nm - 350 nm in diameter. Previously published studies have shown
that the size and density of ZnO nanostructures can be tuned by varying the growth

115
parameters including oxygen concentration, flow rates, temperature gradients, and many
others (42, 43). Scanning electron microscopy and energy dispersive X-ray spectroscopy
analysis were also performed with a JEOL JSM-7001F to confirm the elemental
composition of the structures (Figure 5-5d). Results show the presence of only zinc and
oxygen, with silicon also appearing due to the penetration of the electron beam to the
silicon substrate below the NTP. Additionally, the quantitative results show that zinc and
oxygen are present in an approximately equal atomic percent ratio of 10.48 atomic % to
8.88 atomic %, respectively.

Figure 5-5. (a) A zinc blende core is the initial nucleation site with alternating +c/-c facets.
Growth is favored in the +c facets over the –c facets. (b) SEM image showing the tetrapod
morphology and hexagonal basal plane. (c) SEM of ZnO NTPs as-grown on the surface of a
silicon wafer. (d) EDX spectrum and quantitative results for a single ZnO NTP on a silicon wafer.
The inset shows the spot where the electron beam is aimed during the collection, marked with a
yellow cross.

116

TEM images show the lattice spacing of the ZnO NTP legs is 2.6 Å, which is
consistent with previous studies on ZnO nanostructures (Figure 5-6a). This spacing is
indicative of the preferential growth in the [0001] direction (44). Additionally, X-ray
diffraction studies were also done with a Rigaku Ultima IV diffractometer to confirm the
crystal structure of the synthesized NTPs (Figure 5-6b). The pattern confirms the
wurtzitic crystal structure of the ZnO NTP legs.

Figure 5-6. (a) TEM images of a ZnO NTP leg showing lattice fringe spacing of 2.6 Å,
consistent with growth in the [0001] direction. (b) XRD pattern of ZnO NTPs removed from the
silicon substrate, confirming wurtzitic structure.

117

To fabricate the flexible fluorescent composite, an inverse soft lithography
method is used (Figure 5-7). After the ZnO NTPs have been grown, the handler wafer
with the NTPs on the surface is placed in a petri dish. Next, a polydimethylsiloxane
elastomer (PDMS, Sylgard 184) is mixed with its curing agent at a ratio of 10:1. After
degassing the mixture under vacuum for 15 min, it is poured into the petri dish until the
PDMS thickness reaches ~2 mm. The PDMS is allowed to cure for 2 h at 75°C and then
cut into 1.5 cm x 3 cm slices. After curing, the PDMS is peeled off the silicon wafer,
leaving all of the ZnO NTPs on the interface of one side of the elastomer. This allows for
the handler substrate to potentially be reused, reducing costs and waste in manufacturing
processes.

118

Figure 5-7. Schematic rendering demonstrating the inverse soft lithography method for
embedding the ZnO NTPs in the flexible PDMS substrate. The bottom right image shows the
composite material emitting green light under a UV lamp (λ=365 nm).

Another approach that was briefly explored was the mixing the ZnO NTPs into
the PDMS matrix by first sonicating the fluffy white layer that remains after the CVT
growth in order to obtain a homogeneous distribution of the nanomaterial in the
elastomer. This film consists of a network of ZnO NTPs that are interlocking (Figure 5-
8a). In order to separate the NTPs, the film is placed directly in the curing agent and
sonicated for 30 s. The mixture is then poured into a petri dish and cured in a gravity

119
oven at 75°C overnight. An image of the material under a UV lamp is shown in Figure 5-
8b (λ=365 nm).

Figure 5-8. a) SEM image of the fluffy white layer that results after the CVT growth. It consists
of an interconnected network of ZnO NTPs. b) After the film is sonicated in the PDMS curing
agent, the ZnO NTPs are homogenously distributed in the elastomer, shown here under a 325 nm
UV lamp.

5.3 Results: Optical Properties
A spectrofluorometer (Horiba FluoroMax-4) is utilized to investigate the emission
properties of the ZnO NTPs and the composite material. The excitation and emission slits
are set to 2 nm. Under UV excitation (wavelength of 325 nm) at room temperature, ZnO
NTPs display two prominent fluorescence peaks at ~380 nm and ~490 nm (Figure 5-9).
This is in agreement with many other studies on ZnO nanomaterials (45-48). The UV
peak is attributed to exciton recombination, while the green peak is due to recombination
at defect sites including oxygen vacancies (49). Figure 5-9a and Figure 5-9c show the
fluorescence spectra for ZnO NTPs before and after being embedded in PDMS by the
inverse soft lithography technique, respectively. From this data, it is notable that there is
no shift or increase in fluorescence intensity for either peak, suggesting that the NTPs are

120
not being chemically altered or damaged after embedding. Such changes in the
luminescence may indicate a change in the concentration of defects (50).

Figure 5-9. Spectrofluorometer spectra (λ
excitation
=325 nm) of ZnO NTPs (a) as-grown and (c)
embedded in PDMS with corresponding dark-field microscope images in (b) and (d).

The area under the UV peak and its intensity are not altered by mechanical
damage to the sample due to the band gap recombination mechanism behind the UV
emission. The green peak, on the other hand, depends on the concentration of defects
within the material (51). This phenomenon has been exploited in previous studies where
ZnO-elastomer composites were utilized as strain sensors (50). Because the UV peak
remains constant, we can use it to self-normalize our optical measurements. To study the
stability of the fluorescence, we flexurally bend the samples (for 100+ cycles) to two
different bending radii of 6.4 mm and 13.9 mm. The fluorometry results are shown in
Figure 5-10. The data shows that the ratio of the area under the UV peak to the area under
the green peak remains the same throughout the flexural bending cycles. An additional

121
metric of taking the ratio of the intensity of the UV peak to the intensity of the green peak
was also used. With this intensity metric, the ratio values also stayed the same throughout
the bending studies. These trends suggest that the NTPs are protected by the PDMS
matrix and are in a thin enough layer such that they do not interact with each other. This
is in stark contrast to previously published studies where entangled networks of ZnO
NTPs in PDMS were damaged in bending tests (50).

Figure 5-10. Fluorometry spectra for ZnO NTPs embedded in PDMS when flexurally bent to
radii of (a) 13.85 mm and (b) 6.42 mm, and (c-d) corresponding changes in ratio of the area under
the UV peak to the area under the green peak.

122
To study if the ZnO NTP density within the elastomer has an effect on the stable
fluorescence after flexural bending, we repeated the bending tests on composite samples
with a range of NTP concentrations (Figure 5-11). The slope of the ratio change is
tracked, but we never observe a negative slope, which would indicate the formation of
defects in the material. This shows that, for the range of concentrations obtainable in our
CVT growth approach, the NTPs are still not becoming entangled to the point of
transferring mechanical energy when the concentration is increased, as seen in the
previously published studies (50, 52). The most likely explanation for this is that the
density of the CVT-grown NTPs used in this study is much lower. Furthermore, the size
of the nanotetrapods in this study is much smaller than the micron-scale ZnO tetrapods
obtained by other methods.

123

Figure 5-11. When the growth density of ZnO NTPs was varied, a negative slope for the ratio of
the area under the UV peak to the area under the green peak was never achieved, as seen in other
studies. A negative slope would be indicative of an increase in the concentration of defects within
the ZnO NTPs.

The samples with ZnO NTPs homogeneously distributed in the elastomer were
also studied briefly. The fluorometry spectrum for a sample under 325 nm excitation is
shown in Figure 5-12a. The peaks are located at similar locations compared to the
samples with ZnO NTPs only on the surface, with a UV peak at 380 nm and a broad
green peak at 493 nm. The bending tests were also performed over 100 cycles to a
bending radius of 6.42 mm, and the results for intensity ratio are presented in Figure 5-
12b. Similar to the previous samples, there is no change in the ratio of the UV peak to the
green peak. No further tests were performed for these homogeneous samples.

124

Figure 5-12. a) Fluorometry spectrum for a PDMS sample with ZnO NTPs homogeneously
distributed in the elastomer, with a UV peak at 380 nm and a green peak at 493 nm. b) The ratio
of the intensity of the UV peak to the intensity of the green peak during 100 bending cycles to a
bend radius of 6.42 mm.

5.4 Results: Modeling
Finite element method modeling using COMSOL Multiphysics software was also
performed to visualize the areas of the PDMS that are subject to the largest stresses
during flexural bending. A PDMS slab (10 mm x 40 mm x 2.5 mm) is flexurally bent
across a hollow steel cylinder with a diameter of 5 mm, smaller than the diameter of the
rod used in the experiments. The rod was fixed in place, and the mesh size for all
domains were restricted to larger than 200 µm. Stresses of 0.1 N/m
2
were applied to two
regions on the top of the PDMS block. The results of the model are shown in Figure 5-13.
As expected, we see that the upper region displays a positive strain because it is subject
to tensile stress. This is the region where ZnO NTPs are located in the experiments, and
the calculated maximum strain is 1.29x10
-5
. At the lower region, subject to compressive
stress, there is a negative strain that reaches a maximum value of -3.4x10
-5
. In between
the two surfaces, there is a region with zero strain, called the neutral plane (53). In the

125
fabrication in this study, no attempt was made to shift the ZnO NTPs into this neutral
plane. However, the strain at the top surface where they are located is much lower than
the fracture strain of 7.7% for ZnO nanowires with a diameter close to the diameter of the
NTP legs (54). Thus, it is expected that this degree of flexural bending is not enough to
introduce fractures and defects into the NTPs.

Figure 5-13. Finite element method model of the strain imparted on a PDMS slab when bent to
a radius of 5 mm and (b) corresponding cross section of the slab. In the experiments, the ZnO
NTPs are located at the top surface, where they are subjected to tensile stress.

5.5 Conclusions
In conclusion, a new approach for fabricating a flexible fluorescent material has
been developed, overcoming the challenge of integrating nanomaterials into flexible
materials for stable long-term optical performance. This technique represents a low-cost,
non-toxic, and environmentally friendly strategy for fabricating a UV-responsive
nanocomposite material. First, a chemical vapor transport method is used to synthesize
zinc oxide nanotetrapods, which are subsequently incorporated into an elastomeric matrix
via inverse soft lithography. The inverse soft lithography approach presents a
nondestructive strategy for embedding a nanomaterial in an elastomeric matrix without
degrading optical performance. Furthermore, the elastomeric matrix affords a degree of

126
protection to the nanostructures within. Through 100+ cycles of flexural bending, no
degradation of the optical signal is observed. Finite element method simulations also
confirm that the strains within the elastomer are not sufficient to fracture the ZnO
nanomaterials, allowing for the preservation of the optical response.
This work represents findings that will help in the development of stable light-
emitting materials in flexible substrates, an important topic with the proliferation of
flexible technologies in many areas. One direct application is in counterfeit detection in
polymer currency. Polymer currency has many advantages over paper currency including
higher robustness, lower absorption of dirt and oils, and difficulty in counterfeiting (55).
ZnO NTPs can provide a security measure in spotting fake money with its strong
fluorescence under UV light. The tetrapod morphology is also visible under low
magnifications, providing an additional layer of security in ensuring that the fluorescence
is indeed coming from ZnO NTPs rather than a dye.

127
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133
6 Future Work
6.1 Enhanced Stimulated Brillouin Scattering

Although the nonlinearity in silica is not high, the small mode area of the resonant
cavity allows for nonlinear effects to become apparent. This makes multiple nonlinear
optical phenomena possible, including Brillouin scattering. The frequency shift of
Brillouin scattering is much lower than Raman scattering, on the order of 10 GHz (1). At
a pump wavelength of 1550 nm, this corresponds to a shift of less than 1 nm. Thus, the
Brillouin emissions appear very close to the pump line.
Previously, Stimulated Brillouin scattering (SBS) has been observed in
whispering gallery mode resonators (2). However, due to a number of barriers that
prevent Brillouin gain, it is often very challenging to observe. First, in addition to the
optical resonance, the acoustic frequency must also be resonant with a mechanical mode
of the resonator in order to constructively interfere with itself (2). Further, for SBS to
occur in WGMRs, phase matching conditions must also be fulfilled (3). During our
testing, we observed very strong Stokes-shifted stimulated Brillouin scattering in samples
coated with CaF
2
nanocrystals, as described in Chapter 3.

6.1.1 Methods

Thus far, the observed Brillouin scattering has been with CaF
2
nanocrystal-coated
silica microspheres. These have been prepared and optically characterized in the same
way as described in Chapter 3.

134
6.1.2 Preliminary Results

When pumped near 1550 nm, we observe strong red-shifted peaks less than 1 nm
from the pump line (Figure 6-1). Each peak near the pump line is spaced at ~0.08 nm
from adjacent lines, in good agreement with the expected Brillouin shift of ~10 GHz.

Figure 6-1. Optical spectrum when a) on resonance and b) off-resonance, showing strong SBS
near the pump line.

Further away from the pump line, we also observe strong four wave mixing
(FWM) lines similar to that detailed in Chapter 3 (Figure 6-2). There is the possibility
that the FWM is enhanced by the presence of SBS, a phenomenon that has been studied
135
previously (1, 4). Further studies with an electrical spectrum analyzer to monitor the beat
signal will be necessary to more thoroughly characterize this phenomenon.

Figure 6-2. Optical spectrum near the pump line shows simultaneous FWM and SBS.

6.2 Frequency Comb Enhancement via Simultaneous Dispersion and
Kerr Coefficient Engineering

This thesis has introduced the concept of utilizing both dispersion compensation
and an enhanced Kerr coefficient to obtain wide-spanning or low-threshold frequency
combs. These efforts have, thus far, been investigated independently. One possibility to
improve comb span and lower threshold simultaneously is to utilize a multi-material
system. For example, dispersion can be flattened out via CaF
2
nanocrystals while FWM
threshold can be lowered via functionalized gold nanorods. If nanomaterial coatings such
as CaF
2
nanocrystals and gold nanorods are to be used in this approach, the concentration
136
of each component will have to be carefully optimized in order to improve the behavior
but not destroy the cavity Q factor.
There is also the possibility of combining fluoride nanomaterials with high n
2

materials in frequency comb systems, such as diamond photonic devices, silicon nitride
resonators, and organically modified silica resonators (5-7). Because the low dispersion
nanomaterial approach only involves surface coatings, it is compatible across a wide
range of material systems and cavity geometries, including some that have been
developed in the Armani lab (8, 9).
6.3 Nonlinear Optical Phenomena in Carbon Nanotubes

Carbon nanomaterials have been widely researched due to their widely diverse
optical and electrical properties. In particular, in its one-dimensional form, carbon
nanotubes (CNTs) have garnered a lot of interest since their discovery in the early 1990s
(10). In the Armani Lab, carbon nanotube clusters have been utilized in conjunction with
WGMRs to detect carbon monoxide and carbon dioxide absorption (11). Besides acting
as an active material with properties favorable for interacting with gases, CNTs also have
unique optical properties that can be exploited for nonlinear upconversion lasing.
Past studies have shown that multiphoton absorption of near-IR photons can result
in visible photoluminescence via transitions between Van Hove singularity states. This
three-photon process has been shown at 1064 nm (12) resulting in emission near 780 nm,
and also at 720 nm (13) resulting in emission near 480 nm. Pump lasers of 1064 nm and
765 nm are available in the Armani lab, allowing for future study of this system to
explore if stimulated emission is possible.
137
Another interesting one-photon process has also been studied recently, in which
pump light near 1100 nm is upconverted to 950-1000 nm (14). This anomalous nonlinear
process relies on a one-phonon assisted upconversion process. The significance of the
one-photon process is that efficiency is much higher, eliminating the need for the ultrafast
high-power lasers used in multiphoton processes. The emission wavelengths obtained
(~1000 nm) are particularly important in biological imaging, as this lies within a
biological transparency window where autofluorescence is minimized (15). Thus, the use
of CNTs for upconversion emission studies on WGMRs is of particular interest for future
studies, and presents exciting potential applications.
138
Chapter 6 References

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139
12. M. E. Brennan, J. N. Coleman, A. Drury, B. Lahr, T. Kobayashi, W. J. Blau,
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15. K. Welsher, Z. Liu, S. P. Sherlock, J. T. Robinson, Z. Chen, D. Daranciang, H. J.
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140
Appendix 1: Enhanced Stimulated Anti-Stokes Raman Scattering with
Functionalized Gold Nanorods

During the studies outlined in Chapter 4, enhanced Kerr frequency combs were
observed. Unexpectedly, increased intensity of anti-Stokes Raman emission lines was
also observed. Stimulated anti-Stokes Raman scattering (SARS) plays an important role
in applications such as microscopy and spectroscopy (1-3). SARS is one of the nonlinear
optical effects associated with (the imaginary part of) the third-order susceptibility !
!"
(!)

(4, 5). Though nonlinear optical phenomena are weak, anti-Stokes Raman scattering is
even weaker due to the reliance on photons at the Stokes Raman shift, as discussed in
Chapter 2. Furthermore, Stimulated Stokes Raman Scattering is intrinsically phase
matched, while SARS is not. Enhancing SARS emission has been pursued using a range
of strategies including using high Raman gain materials (6-8), quasi-phase matching (9-
11), and external seeding at the Raman wavelength (12, 13). These methods are often
very complex and cost-prohibitive; therefore, a simpler strategy for enhancing SARS is
needed. This project was undertaken as part of a collaboration with Dr. Soheil Soltani.

A1.1: Methods: Gold Nanorod Synthesis and Microresonator
Fabrication

Gold nanorods are synthesized utilizing a process similar to the aforementioned
seeded growth method, as explained in Chapter 4 (14). In this method, partially capped
spherical gold seeds are added to a growth solution, allowing for the nanorods to grow
preferentially in one direction (at {111} surfaces) while the CTAB surfactant blocks
growth in other directions (at {110} surfaces) (15, 16).
141
The initial gold seed solution is prepared with a solution of 0.25 mL of 0.01 M
HAuCl
4
·3H
2
O and 7.5 mL of 0.10 M cetyl trimethylammonium bromide (CTAB) in
water. Next, 0.6 mL of cold NaBH
4
is added and the seed mixture is kept at 30°C for 2 h.
The growth solution is prepared by mixing 100 mL of 0.1 M CTAB, 5 mL of 0.01 M
HAuCl
4
·3H
2
O, 1 mL of 10 mM AgNO
3
, 2 mL of 0.5 M H
2
SO
4
, and 800 µL of 0.1 M
ascorbic acid. Nanorod formation begins after 0.24 mL of the seed solution is added to
the growth solution, and the entire mixture is kept at 30°C for 12 h. Finally, the gold
nanorods are purified and washed twice by centrifuging at 9,000 rpm for 1 min.
The surface of the synthesized gold nanorods is then functionalized with PEG
using a previously executed method (17). First, 6 mL of a PEG-thiol solution (0.005
mM) is added to the as-grown rods and allowed to stir for 2 h. After centrifuging (at
9,500 RPM for 15 min) and remixing in water three times, the rods are re-dispersed in
methanol. The concentration of the solution is then diluted until it reaches three
concentrations of 0.125 M. This nanorod solution is used to dip-coat oxygen plasma-
treated silica microsphere resonators with ~200 µm diameters.

A1.2: Results: FEM Modeling
In order to understand the interaction between functionalized gold nanorods on
the surface and the whispering gallery mode, COMSOL Multiphysics finite element
method (FEM) software is used. The parameters are designed to match the experiments
as closely as possible. A representative FEM model is shown in Figure A1-1. As in
Chapter 4, we see the hybridized whispering gallery-plasmonic mode despite the
142
wavelength not being near the surface plasmon resonance wavelength of the gold
nanorods.

Figure A1-1. FEM model shows the hybrid whispering gallery-plasmonic mode located
between the gold nanorod and the silica WGMR when 1550 nm light is circulating in the cavity.

A1.3: Results: Numerical Calculations
As phase matching and dispersion are vital considerations in SARS, numerical
calculations are required in order to study how the resonator radius affects dispersion.
The metric used quantify the dispersion is the frequency difference between adjacent
modes Δ!= !
!!!
−!
!
− !
!
−!
!!!
. We calculate this based on Mie scattering
theory (18)
-1/3 2 2
-1/3 1/3 -2/3 2 -1/3 -2/3 -1
q,l q q q 21/2 2 3/2
cK3 2K(n(ω)-2K /3)
ω=[υ+2 αυ-+(2)αυ - αυ +O(υ )]
n( )a (n(ω)-1) 10 (n(ω)-1) ω

where ω
q,l
, c, n(ω), and a are the resonant frequency, speed of light, frequency dependent
refractive index, and radius of the resonator, respectively. υ=l+1/2, where l is the
143
azimuthal mode number. In addition, α
q
is the qth root of the Airy function, and K=n(ω)
for the TE and K=1/n(ω) for the TM mode.
This equation is solved using MATLAB (code presented in Appendix A5). The
results for two spheres of 75 and 97 µm in radii are presented in Figure A1-2a. This plot
shows that silica spherical microresonators are able to operate in anomalous, normal, or
zero dispersion regimes. Furthermore, the dispersion flattens out for larger spheres,
allowing for more efficient phase matching. Note the different scales for each vertical
axis. The zero dispersion wavelength, where the spacing of the resonator modes is
constant for cavities of varying radius, is also calculated (Figure A1-2b). Thus, we
proceed with studies using spheres approximately 200 µm in diameter.

Figure A1-2. a) Dispersion for microsphere resonators of different radii. b) Zero dispersion
wavelength versus cavity radius for silica spheres.

A1.4: Results: Optical Testing
Optical testing is performed, as described in Chapter 2. Quality factors are
determined by the linewidth method to vary from 8×10
6
to 2×10
7
. At various input
power, the output Stokes and Anti-Stokes peak power is measured on the optical
spectrum analyzer. Using spherical cavities with similar Q factor and radius, SARS
144
emission is observed at 14 mW input power in the coated devices. In an uncoated cavity
at 20 mW of input power, SARS emission is not observed. This is in agreement with
previous work with spherical silica microresonators, which required 80 mW input power
for SARS emission (19). SARS generation in a device coated with functionalized gold
nanorods on is illustrated in Figure A1-3. Here we see that SARS is generated at 15 mW
and 30 mW in coated resonators, much lower than the 80 mW required in uncoated
devices observed previously.

Figure A1-3. Optical spectra for a microsphere coated with functionalized gold nanorods at a)
15 mW and b) 30 mW of input power.

The power of the SARS emission is expected to be linearly dependent on the
Stokes emission power due to the mechanism of SARS generation, as described in
Chapter 2. Experimental data demonstrates the ratio between the Stokes and Anti-Stokes
Raman powers is linear, and the slope approximately 10
-5
(Figure A1-4), as expected by
theoretical predictions for a resonator with a diameter of 195 µm (20).
145

Figure A1-4. Anti-Stokes emission power versus Stokes emission power for a coated
microsphere resonator.

The improvement in SARS emission demonstrates the pivotal role played by the
functionalized gold nanorods. Because the interaction between the nonlinear PEG
molecules and the optical field is increased by the hybrid plasmonic-whispering gallery
mode (21), Raman emission is increased, allowing for SARS emission to increase as
well. Fortunately, the presence of the gold nanorods does not drastically decrease the Q
factor or interfere with the optical mode within the resonator.

A1.5: Conclusion
As discussed above, a new method for enhancing anti-Stokes Raman scattering in
silica WGM microresonators was developed. First, silica microspheres of a certain size
were selected to ensure efficient phase matching and dispersion. Then, the surface of gold
nanorods were functionalized with a nonlinear molecule, PEG. This results in a hybrid
plasmonic-whispering gallery mode, allowing for the interaction between the optical field
and the nonlinear molecule to increase. This interaction allows for enhanced SARS
146
interaction. PEG has a high third order nonlinear coefficient, which facilitates strong
Stokes and Anti-Stokes emissions. At less than 20 mW of input power, strong SARS
emission was observed, which is much lower input power than the 80 mW, as observed
in prior studies.

147
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149
Appendix 2: Magnesium Fluoride Nanocrystal Coated Whispering
Gallery Mode Resonator

In Chapter 3, the use of fluoride nanocrystals for dispersion compensation was
discussed. Though we observed frequency comb span enhancement, further improvement
is possible if the four wave mixing process, which is the primary comb generation
process, is preferred over the stimulated Raman scattering processes. This is because the
parametric oscillation from the four wave mixing process must compete with the Raman
processes for photons. Previous studies have shown that ultra high Q monolithic
monocrystalline magnesium fluoride (MgF
2
) resonators are capable of generating
Raman-free frequency combs in the near-IR (1, 2). MgF
2
is a particularly promising
material due to its mechanical stability, hardness, and wide transparency window (3).
In past studies that use MgF
2
monolithic resonators, Kerr combs based on FWM
are observed at lower threshold powers than stimulated Raman scattering. Monolithic
MgF
2
resonators have even shown capability of generating frequency combs near 765
nm, where group velocity dispersion is in the normal regime (4). As with the monolithic
CaF
2
resonators mentioned in Chapter 3, however, these resonators require mechanical
polishing, resulting in resonators that are about 5 mm in diameter. Thus, we seek to
utilize a similar strategy in obtaining MgF
2
nanocrystals for dispersion-compensating
coatings. The work described here was done in collaboration with Teresa Estrella, an
undergraduate student in the Armani lab.

A2.1 Methods: Nanocrystal Synthesis

Magnesium fluoride nanocrystals were synthesized with a solution-based co-
precipitation method similar to the one described in Chapter 3. First, an aqueous solution
150
of 2 M magnesium chloride (MgCl
2
) and 2 mM ammonium fluoride (NH
4
F)

were mixed
in a three-neck flask in an oil bath at 75°C for 1 h, modified from a previously published
paper (5). The reaction was performed in a nitrogenous environment, but later studies
show that the nitrogen does not have a significant impact on the synthesis. Therefore,
synthesis proceeded without nitrogen. A purification step is required due to the highly
hygroscopic nature of the MgCl
2
. Any remaining MgCl
2
on the surface of a resonator will
result in high water absorption, which will deplete cavity Q factor. This effect is
particularly apparent in MgF
2
resonators (6). The excess of salt is very apparent when the
solution is drop-coated on a silicon wafer and imaged (Figure A2-1).

Figure A2-1. Scanning electron microscope image of MgF
2
nanocrystals in dried up salts
dispersed on a silicon wafer.

Due to high solubility in water, the MgF
2
nanocrystals and solutes could not be
concentrated and washed via centrifugation. When centrifuged, no pellet of particles
formed as in synthesis of CaF
2
nanoparticles. Therefore, to remove as much unreacted
151
solute as possible, we place the synthesis solution in dialysis bags for 1 week. The DI
water was changed twice daily. The final aqueous growth solution was then filtered with
a 0.45 µm syringe filter before coating onto devices.

A2.2 Methods: Microresonator Fabrication and Coating

The methods used for fabricating silica microsphere and microtoroidal resonators
are the same as those described in Chapters 2 and 3. Silica microresonators are oxygen
plasma treated and then dip-coated (spheres) or spin-coated (microtoroids) with the MgF
2

particle solution. The microresonators are then dried in a gravity oven overnight at 75°C
in order to evaporate as much water as possible from the resonator surface and
nanoparticles.

A2.3 Preliminary Results
MgF
2
nanocrystals were dispersed on a silicon wafer for imaging and elemental
analysis. SEM images indicate that particle size ranges from approximately 50 nm to 500
nm (Figure A2-2a). As in the studies with CaF
2
nanocrystals, we assume that the larger
particles are filtered out or settle to the bottom of the solution before they are coated onto
microresonators. Therefore, the Q factor is not significantly affected by the higher
scattering loss.
Elemental analysis by EDX shows that the particles consist of magnesium and
fluorine, as expected (Figure A2-2b).
152

Figure A2-2. a) Scanning electron microscope image of purified MgF
2
nanocrystals dispersed
on the surface of a silicon wafer. b) EDX spectrum of a single MgF
2
nanoparticle. The presence
of silicon and oxygen lines is due to the penetration depth and large size of the electron beam
reaching the silicon substrate below the nanoparticle.

We optically characterized a MgF
2
nanocrystal-coated silica microsphere
resonator with a diameter of ~200 µm (Figure A2-3). Preliminary data indicates that
FWM is preferred over stimulated Raman scattering. At 1.27 mW of input power, a comb
of ~100 nm has been achieved, with no Raman emissions present. As input power
increases, FWM remains the stronger phenomenon to a higher extent than in CaF
2

nanocrystal coated resonators. We see a maximum span of ~150 nm, not including Stokes
and anti-Stokes Raman emissions. This corresponds to ~18.6 THz, which is higher than
153
the 2.4 THz spanning combs obtained in previously studied monolithic MgF
2
resonators
(2).
Interestingly, we also see that anti-Stokes shifted lines are also more apparent
over Stokes shifted lines. The reason for this remains unclear, and further experiments are
ongoing.

Figure A2-3. Frequency comb generation in a silica microsphere resonator coated with MgF
2

nanocrystals as coupled input power increases.

154
Chapter A2 References

1. W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki,
Generation of Kerr Combs in MgF(2) and CaF(2) Microresonators. P Ieee Int
Freq Cont, 1006-1011 (2011).
2. W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki,
Generation of near-infrared frequency combs from a MgF2 whispering gallery
mode resonator. Opt Lett 36, 2290-2292 (2011); published online EpubJun 15
(Doi 10.1364/Ol.36.002290).
3. J. Lucas, F. Smektala, J. L. Adam, Fluorine in optics. J Fluorine Chem 114, 113-
118 (2002); published online EpubApr 28 (Pii S0022-1139(02)00016-7Doi
10.1016/S0022-1139(02)00016-7).

4. W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B.
Matsko, L. Maleki, Generation of a coherent near-infrared Kerr frequency comb
in a monolithic microresonator with normal GVD. Opt Lett 39, 2920-2923 (2014);
published online EpubMay 15 (10.1364/OL.39.002920).
5. P. Li, H. Y. Wang, W. E. Wu, L. Shuai, Process parameters optimization of Direct
synthesis nano magnesium fluoride powders. Frontiers of Mechanical
Engineering and Materials Engineering, Pts 1 and 2 184-185, 1146-+
(2012)10.4028/http://www.scientific.net/AMM.184-185.1146).
6. I. S. Grudinin, K. Mansour, N. Yu, Properties of fluoride microresonators for
mid-IR applications. Opt Lett 41, 2378-2381 (2016); published online EpubMay
15 (10.1364/OL.41.002378).

149
Appendix 2: Magnesium Fluoride Nanocrystal Coated Whispering
Gallery Mode Resonator

In Chapter 3, the use of fluoride nanocrystals for dispersion compensation was
discussed. Though we observed frequency comb span enhancement, further improvement
is possible if the four wave mixing process, which is the primary comb generation
process, is preferred over the stimulated Raman scattering processes. This is because the
parametric oscillation from the four wave mixing process must compete with the Raman
processes for photons. Previous studies have shown that ultra high Q monolithic
monocrystalline magnesium fluoride (MgF
2
) resonators are capable of generating
Raman-free frequency combs in the near-IR (1, 2). MgF
2
is a particularly promising
material due to its mechanical stability, hardness, and wide transparency window (3).
In past studies that use MgF
2
monolithic resonators, Kerr combs based on FWM
are observed at lower threshold powers than stimulated Raman scattering. Monolithic
MgF
2
resonators have even shown capability of generating frequency combs near 765
nm, where group velocity dispersion is in the normal regime (4). As with the monolithic
CaF
2
resonators mentioned in Chapter 3, however, these resonators require mechanical
polishing, resulting in resonators that are about 5 mm in diameter. Thus, we seek to
utilize a similar strategy in obtaining MgF
2
nanocrystals for dispersion-compensating
coatings. The work described here was done in collaboration with Teresa Estrella, an
undergraduate student in the Armani lab.

A2.1 Methods: Nanocrystal Synthesis

Magnesium fluoride nanocrystals were synthesized with a solution-based co-
precipitation method similar to the one described in Chapter 3. First, an aqueous solution
150
of 2 M magnesium chloride (MgCl
2
) and 2 mM ammonium fluoride (NH
4
F)

were mixed
in a three-neck flask in an oil bath at 75°C for 1 h, modified from a previously published
paper (5). The reaction was performed in a nitrogenous environment, but later studies
show that the nitrogen does not have a significant impact on the synthesis. Therefore,
synthesis proceeded without nitrogen. A purification step is required due to the highly
hygroscopic nature of the MgCl
2
. Any remaining MgCl
2
on the surface of a resonator will
result in high water absorption, which will deplete cavity Q factor. This effect is
particularly apparent in MgF
2
resonators (6). The excess of salt is very apparent when the
solution is drop-coated on a silicon wafer and imaged (Figure A2-1).

Figure A2-1. Scanning electron microscope image of MgF
2
nanocrystals in dried up salts
dispersed on a silicon wafer.

Due to high solubility in water, the MgF
2
nanocrystals and solutes could not be
concentrated and washed via centrifugation. When centrifuged, no pellet of particles
formed as in synthesis of CaF
2
nanoparticles. Therefore, to remove as much unreacted
151
solute as possible, we place the synthesis solution in dialysis bags for 1 week. The DI
water was changed twice daily. The final aqueous growth solution was then filtered with
a 0.45 µm syringe filter before coating onto devices.

A2.2 Methods: Microresonator Fabrication and Coating

The methods used for fabricating silica microsphere and microtoroidal resonators
are the same as those described in Chapters 2 and 3. Silica microresonators are oxygen
plasma treated and then dip-coated (spheres) or spin-coated (microtoroids) with the MgF
2

particle solution. The microresonators are then dried in a gravity oven overnight at 75°C
in order to evaporate as much water as possible from the resonator surface and
nanoparticles.

A2.3 Preliminary Results
MgF
2
nanocrystals were dispersed on a silicon wafer for imaging and elemental
analysis. SEM images indicate that particle size ranges from approximately 50 nm to 500
nm (Figure A2-2a). As in the studies with CaF
2
nanocrystals, we assume that the larger
particles are filtered out or settle to the bottom of the solution before they are coated onto
microresonators. Therefore, the Q factor is not significantly affected by the higher
scattering loss.
Elemental analysis by EDX shows that the particles consist of magnesium and
fluorine, as expected (Figure A2-2b).
152

Figure A2-2. a) Scanning electron microscope image of purified MgF
2
nanocrystals dispersed
on the surface of a silicon wafer. b) EDX spectrum of a single MgF
2
nanoparticle. The presence
of silicon and oxygen lines is due to the penetration depth and large size of the electron beam
reaching the silicon substrate below the nanoparticle.

We optically characterized a MgF
2
nanocrystal-coated silica microsphere
resonator with a diameter of ~200 µm (Figure A2-3). Preliminary data indicates that
FWM is preferred over stimulated Raman scattering. At 1.27 mW of input power, a comb
of ~100 nm has been achieved, with no Raman emissions present. As input power
increases, FWM remains the stronger phenomenon to a higher extent than in CaF
2

nanocrystal coated resonators. We see a maximum span of ~150 nm, not including Stokes
and anti-Stokes Raman emissions. This corresponds to ~18.6 THz, which is higher than
153
the 2.4 THz spanning combs obtained in previously studied monolithic MgF
2
resonators
(2).
Interestingly, we also see that anti-Stokes shifted lines are also more apparent
over Stokes shifted lines. The reason for this remains unclear, and further experiments are
ongoing.

Figure A2-3. Frequency comb generation in a silica microsphere resonator coated with MgF
2

nanocrystals as coupled input power increases.

154
Chapter A2 References

1. W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki,
Generation of Kerr Combs in MgF(2) and CaF(2) Microresonators. P Ieee Int
Freq Cont, 1006-1011 (2011).
2. W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki,
Generation of near-infrared frequency combs from a MgF2 whispering gallery
mode resonator. Opt Lett 36, 2290-2292 (2011); published online EpubJun 15
(Doi 10.1364/Ol.36.002290).
3. J. Lucas, F. Smektala, J. L. Adam, Fluorine in optics. J Fluorine Chem 114, 113-
118 (2002); published online EpubApr 28 (Pii S0022-1139(02)00016-7Doi
10.1016/S0022-1139(02)00016-7).

4. W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B.
Matsko, L. Maleki, Generation of a coherent near-infrared Kerr frequency comb
in a monolithic microresonator with normal GVD. Opt Lett 39, 2920-2923 (2014);
published online EpubMay 15 (10.1364/OL.39.002920).
5. P. Li, H. Y. Wang, W. E. Wu, L. Shuai, Process parameters optimization of Direct
synthesis nano magnesium fluoride powders. Frontiers of Mechanical
Engineering and Materials Engineering, Pts 1 and 2 184-185, 1146-+
(2012)10.4028/http://www.scientific.net/AMM.184-185.1146).
6. I. S. Grudinin, K. Mansour, N. Yu, Properties of fluoride microresonators for
mid-IR applications. Opt Lett 41, 2378-2381 (2016); published online EpubMay
15 (10.1364/OL.41.002378).

155
Appendix 3: UV Lasing in Zinc Oxide Nanowire Coated Whispering
Gallery Mode Resonators

As briefly discussed in Chapter 5, zinc oxide (ZnO) possesses numerous nonlinear
optical properties.(1-3) Though the third-order susceptibility !
(!)
is typically much lower
than the !
(!)
, at high pump intensities, third-order nonlinear optical phenomena can be
observed. For ZnO, the Kerr coefficient n
2
has been calculated to be as high as 1.0 x 10
-13

cm
2
/W(4, 5), higher than that of silica (6). ZnO has been shown to exhibit nonlinear
optical behavior including third harmonic generation (2, 7) and upconversion lasing
based on two-photon absorption (8-10). Additionally, ZnO has a high exciton binding
energy of 60 meV (11, 12). An exciton binding energy much greater than the thermal
energy at room temperature (26 meV) ensures that excitonic recombinations do not occur
spontaneously. These properties, in conjunction with ZnO’s wide band gap, make it an
attractive material for the development of upconversion UV lasers at room temperature.
Significant progress has already been made on UV lasers based on multiphoton
absorption in ZnO nanomaterials (8, 9, 13-15). However, the threshold for lasing is on the
order of TW/cm
2
. Thus, we explore the feasibility of integrating ZnO nanomaterials with
WGM resonators to obtain optically-pumped UV lasing via nonlinear two-photon
absorption at lower input powers. This Appendix describes the use of ZnO crystal pre-
seeding in efforts to obtain aligned growth of ZnO nanowires, a condition necessary for
the upconversion process. Additionally, the synthesis of ZnO nanomaterials via solution-
based hydrothermal growth is investigated. These studies were performed in
collaboration with PhD student Rene Zeto and undergraduate student Omar Garcia.
Besides the ZnO nanostructures on the surface of the WGM resonator, a high
index coating can be useful in order to allow the optical field to interact more with the
156
ZnO. Previous studies have shown that the presence of a coating with a higher refractive
index than silica helps to shift the field into the coating. This will help the light interact
more with the nonlinear material by “pushing” the mode onto the nanomaterial/coating
layer, rather than having just the resonator’s evanescent tail interacting with the material.
Therefore, we also want to investigate if a polymer coating on the surface will increase
the interaction between the optical field and the nonlinear optical nanomaterial.
The aim was to optimize the synthesis of the nanowires on whispering gallery
mode resonator surfaces such that quality factor remains high enough to allow for
testing and investigating potential UV lasing. Furthermore, initial efforts were made to
coat the resonators with polymer coatings.
A3.1 Methods: ZnO Nanocrystals Pre-Seeding

In order to achieve lasing, the ZnO nanowires (ZnO NWs) must be
perpendicularly aligned to the growth substrate. This requirement stems from the
nanowire acting like a cavity, where each hexagonal basal plane of the nanowire acts as a
mirror for light to resonate within (16). Therefore, an established method based on
decomposition of zinc salts for obtaining aligned growth of ZnO NWs was utilized (17).
In this approach, we first wet the surface of a clean silicon wafer with an ethanolic
solution of 5 mM zinc acetate dihydrate. The solution is left on the surface for 10 sec and
then rinsed off with ethanol. The coating and rinsing is repeated 3-5 times, resulting in
zinc acetate crystallites on the wafer surface. The wafer is then heated to 350 °C in a tube
furnace for 20 min. This process results in a wafer coated in ZnO seeds with the (0001)
planes parallel to the surface (Figure A3-1). The SEM image shows the comparison of a
157
region on a silicon wafer with and without ZnO seeds present. The seeded side is textured
with aligned crystallites, allowing for directional growth to occur.

Figure A3-1. SEM image of a silicon wafer that has been partially seeded with ZnO crystallites
from decomposed zinc acetate.

A3.2 Methods: Hydrothermal Synthesis

Hydrothermal synthesis of zinc oxide nanowires (18-20) is sometimes favorable
compared to the chemical vapor transport method for numerous reasons. In particular, the
process is much less complex, requiring only mixing chemicals in an aqueous solution,
and occurs at low temperatures (~70°C), allowing for growth on temperature sensitive
substrates. We proceeded with this process in an attempt to grow ZnO NWs on seeded
and unseeded microtoroidal resonators.
First, an aqueous solution is prepared with 0.25 mM zinc nitrate hydrate and 25
mM hexamethylenetetramine in a beaker. This growth solution is heated to 90°C and
158
growth wafers with microtoroids are suspended upside down in the beaker. The solution
is stirred with a magnetic stir bar for 2-5 hours. The wafers are then rinsed with DI water.
Initial attempts with 0.25 mM reactants yielded ZnO structures on the surface that
were far too dense and large to support high Q factors in microresonators (Figure A3-2a).
Additional growths with 5 mM and 10 mM reactants and shorter growth times (0.5-1
hour) were performed in attempts to reduce the size and amount of ZnO NWs on the
surface (Figure A3-2b). However, for the parameters tested, the ZnO remained dense and
some ZnO tetrapods and octapods were also seen on the surface.
159

Figure A3-2. SEM images of silica toroids with ZnO nanostructures hydrothermally grown with
solute concentrations of a) 25 mM and b) 10 mM.

A3.3 Methods: Polymer Coating

Polymethlmethacrylate was prepared based on a previously established protocol
(21). A 0.5 wt% solution of PMMA (Sigma, 35k MW) is prepared in toluene. The
solution is sonicated for 30 min to 1 hour until the PMMA powder is dissolved. A drop of
the solution is then placed on a chip with reflowed silica microtoroids and spin-coated at
160
4000 RPM for 1 min. Samples are then placed in the gravity oven set to 130 °C for 2
hours.
The biggest challenge in this approach is maintaining a high Q factor after the
growth of a uniform ZnO nanostructure layer and deposition of the high index coating
layer. With multiple layers, there is more opportunity for inhomogeneities to be
introduced on the surface, causing an increase in scattering loss and degradation of the Q.
Preliminary studies with a toroidal WGM resonator coated with ZnO NTPs and
polymethylmetacrylate (n
0
~1.48) have shown that the Q is very low due to the uneven
coating on the surface (Figure A3-3). However, the ZnO structures remain on the surface
during the spin-coating process, an encouraging step towards optimizing the fabrication
procedure.

Figure A3-3. A toroidal WGM resonator with ZnO nanostructures on its surface is coated with
PMMA. Though the Q is very low, the intact ZnO after spin-coating the polymer onto the device
is a positive step.

161
A3.4 Results: Optical Testing
Because the band gap of ZnO is 3.37 eV, we must use a laser with approximately
half the band gap energy to obtain two-photon absorption and upconversion emission.
Thus, our 633 nm tunable laser (Newport Velocity) will likely be required when UV
lasing is obtainable. However, we first test with the tunable 765 nm laser (Newport
Velocity) in order to test for quality factor and other nonlinear effects because the power
output of the 765 nm laser is higher (~10 mW). The standard testing procedure is
followed as described in Chapter 1.
As expected due to the high degree of scattering from the thick layers of ZnO on
the resonator surface, the Q factor is too low for nonlinear effects to occur (~10
5
) (Figure
A3-4a). As a result, no emissions are observed. Visible scattering from the coated
microtoroid is seen in the Figure A3-4b, indicating a large amount of scattering loss that
diminishes Q factor and makes nonlinear optical phenomena impossible.

Figure A3-4. a) Q spectra for a silica microtoroidal cavity coated in ZnO nanostructures
and a thin coating of PMMA polymer. b) Top-view microscope image of a coated toroid
during testing shows a high degree of scattering loss when light is coupled into the cavity.

162
A3.5 Conclusion
Attempts to obtain UV lasing from hydrothermally grown ZnO NWs on
whispering gallery mode resonators were unsuccessful. This is mainly due to
unsuccessful optimization of the ZnO NW growth in such a way that limits the NW size
and density on the surface of the resonators. The NWs tended to grow in large clusters
that drastically increase scattering losses. Attempts were made to encapsulate the ZnO
nanomaterials in PMMA polymer in order to (1) increase interaction between the optical
field and ZnO and (2) smooth out the surface of the resonators with ZnO grown on them.
Though the ZnO nanomaterials remained on the surface after PMMA coating, the Q
factor was far too low to obtain nonlinear effects. However, with further optimization of
the growth parameters, it may still be possible for UV lasing to be obtained with this or a
similar approach.

163
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4. V. Narayanan, R. K. Thareja, Harmonic generation in ZnO nanocrystalline laser
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166
Appendix 4: Organic-Silica Hybrid Whispering Gallery Mode
Resonators for Selective Four Wave Mixing and Raman Emission

In whispering gallery mode resonators, stimulated Raman and four wave mixing
(FWM) processes often occur simultaneously, especially when input power is high. Due
to their concurrence, these two non-linear processes compete for pump photons, limiting
the efficiency of any one process (1). We are interested in developing methods where
each nonlinear phenomenon can be decoupled and selected based on the application. It is
difficult to limit Raman processes even when cavity size and geometry are optimized (2,
3). Alternatively, recent advances have demonstrated that stimulated Raman can also be
limited by controlling the transition from Raman to FWM by precisely adjusting the
detuning frequency or coupling (4, 5). However, these changes are inefficient and do not
significantly improve results.
Typically in silica microcavities, stimulated Raman scattering is more dominant
compared to FWM, the primary process responsible for comb generation. This is because
the Raman gain coefficient is often much higher than the Kerr coefficient. Therefore, the
threshold for Raman emission is low for a nonlinear process. Several methods have been
developed in an attempt to limit the Raman processes such as increasing the Q (6, 7),
decreasing effective dispersion (Chapter 2), or employing high n
2
materials (Chapter 3).
In our studies, strong stimulated Raman scattering and FWM processes coexist, both of
which contribute to the formation of a broadband frequency comb (8). However, it would
be advantageous to selectively favor FWM over Raman scattering without stringent
coupling or detuning restrictions.
In an attempt to design more flexible WGM resonator based frequency combs, we
develop a materials based approach for controlling which nonlinear behaviors are
167
favored. We utilize organic small molecules functionalized to the microcavity surface to
suppress one of the nonlinear processes. The use of organic molecules in photonic
devices is a relatively new concept, but one that holds much promise due to potentially
high n
2
and fast optical response properties of the molecules. Therefore, they have been
used in silicon-organic optical devices, but not for frequency comb generation (9-11). .
In this project, we functionalize the surface of the WGMR with a monolayer of
chloromethyl phenyl silane (CPS) organic molecules to quench FWM (Figure A4-1) .
We then functionalize the surface of the WGMR with a monolayer of 4-
[4[diethylamino(styry)]pyrindinium (DASP) organic molecules, which quenches
stimulated Raman scattering (Figure A4-1). With these organic coatings on the surface of
our WGMRs, we show that FWM or Raman can be excited while completely excluding
the other.

A4.1 Methods: Synthesis

Silica WGM resonators are fabricated using the same method described in
previous chapters. The preferred device diameter is 120 µm, so tapered optical fibers are
used in the reflow step to generate spheres of the correct diameter. The surface of the
CPS-silica spheres is functionalized by first treating the bare spheres in oxygen plasma to
create a hydrophilic surface with hydroxyl groups (Figure A4-1). Subsequently, a
chloromethylphenyltrichlorosilane coupling agent is deposited onto the spheres via a
chemical vapor deposition process at room temperature for 8 min.
DASP-silica spheres are functionalized by drop-coating a solution of 4-[4-
diethylamino(styryl)]pyridine in chloroform on the CPS-silica spheres described above.
168
These are then heated to 110°C in a vacuum oven for 20 min. Once cooled, the spheres
are rinsed with chloroform and again dried in a vacuum oven at 100°C for 2 min.

Figure A4-1. Schematic showing the surface functionalization of the spheres tested. Insets of
each device show the unique surface chemistry of each sphere: bare sphere (gray), CPS coated
sphere (blue), and DASP coated sphere (red).
A4.2 Methods: Modeling
Complementary finite element method (FEM) modeling is performed to simulate
the mode profile of the optical field circulating in the spherical WGM resonator. The
sphere is set to have a 120 µm diameter to match the experimental parameters. The
presence of a thin 2 nm monolayer of organic molecules on the surface is shown to not
distort the optical field (Figure A4-2). These results are contrary to previous studies that
demonstrate modes shifting into thicker coatings with refractive index higher than that of
silica (12, 13). The optical mode of our WGM resonators does not shift due to the
negligible thickness of the coating and similar refractive index with silica. Additionally,
we see in Figure A4-1 that approximately 11% of the optical field is located outside the
resonator boundary (in the evanescent field). Consequently, we expect the optical field to
readily interact with the 2 nm organic monolayer at the surface.
169

Figure A4-2. Finite element method simulation of the optical mode circulating inside a
spherical WGM resonator with an organic monolayer coating. The optical mode and evanescent
tail are not distorted by the presence of the ~2 nm thick layer.

A4.3 Results: Optical Testing
The same testing setup from Chapters 2 and 3 is used to characterize the hybrid
WGM resonators. The 1550 nm tunable continuous-wave laser is used to pump the
cavities. The Q factor, is determined by the linewidth method, and is found to be ~1x10
8

for the CPS-silica spheres and bare silica spheres, and ~8x10
7
for the DASP-silica
spheres.
Output spectra from the optical spectrum analyzer are shown in Figure A4-3 for
bare, CPS-silica, and DASP-silica spheres. For bare silica spheres, Raman emission near
1650 nm appears first followed by non-equidistant FWM near the pump as input power
increases (Figure A4-3a). For CPS-silica spheres (Figure A4-3b), Raman emission is
dominant, with no FWM present at even the highest studied input power. This is
ascribed to the enhanced Raman gain coefficient stemming from the increased
170
hyperpolarizabilty from the modified silica surface (14). The Kerr coefficient n
2
of the
phenylene molecules in these spheres is on the order of 10
-16
cm
2
/W, approximately the
same as that of silica. Therefore, the effective Kerr coefficient of the device is not
enhanced by the presence of the CPS coating. For DASP-silica spheres (Figure A4-3c),
the FWM is dominant, with no Raman emission present at even the highest studied input
power. This phenomenon can be explained by the Kerr coefficient n
2, DASP
~3x10
-11

cm
2
/W, five orders of magnitude larger than that of silica (15). It is notable that all of
these studies are conducted at low input powers without amplification of the pump laser,
so this strategy for selection of Raman and FWM processes is compatible with low power
applications.

Figure A4-3. Comb spectra for (a) bare sphere, (b) CPS-silica sphere, and (c) DASP-silica
sphere.
The threshold for FWM is measured by plotting the output power of the idler lines
from the degenerate FWM process vs. the input power. We see that the FWM threshold is
approximately 900 µW, compared to ~1 mW for a bare sphere (Figure A4-4).
171

Figure A4-4. Threshold plots for the FWM process in a DASP-silica sphere and bare sphere.
The plot on the right is a zoomed view of the bare sphere data points on the left.

A4.4 Conclusions and Future Work
We have demonstrated the capability of selecting a single nonlinear behavior by
coating spherical WGM resonators with monolayers of organic molecules. This is an
important advancement in the development of frequency combs based on four-wave
mixing processes without the competing Raman processes. These results will enable
efficient frequency comb generation by eliminating competing nonlinear optical
phenomena. The use of organic coatings is a particularly promising approach for
functional photonic devices, as there are a multitude of organic molecules with unique
optical properties.
In this project, the selectivity of Raman or FWM processes over the other process
is accomplished with different surface functionalization schemes. In future work, we
hope to develop a single system that can select for multiple nonlinear behaviors in
response to external stimuli. One method of achieving this is to integrate an organic
172
switch onto the device. Molecular switches are organic molecules that can revert between
two states (17, 18). A promising approach to these molecular switches is isomeric
photochromic systems, which are classified into P-type (non-reversible isomerization)
and T-type (reversible isomerization) (19). One T-type system that we propose utilizing
is an azobenzene derivative to functionalize the surface of WGM resonators. Azobenzene
isomerizes from its trans to cis state when radiated by one wavelength of light (~365
nm). When radiated with another wavelength (~420 nm), a cis to trans isomerization
takes place (Figure A4- 5) (20, 21). This isomerization occurs extremely quickly, on the
scale of picoseconds, allowing for ultrafast switching between the two states (22).
Alternatively, the reversal from cis to trans also occurs when the molecule is left in the
dark, though the time scale is much slower (~minutes). With this surface
functionalization, we hope to develop a system that will allow for in-situ switching on a
WGM resonator. Future work conducted by the Armani Research Group will focus on
leveraging these advances in reversible organic molecules to developing a device that can
reversibly switch between non-linear optical behaviors in situ.

Figure A4- 5. Schematic showing the T-type isomerization of azobenzene (adapted from
Garcia-Amoros)
173
Chapter A4 References

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Lipson, M. Loncar, A. L. Gaeta, Competition between Raman and Kerr effects in
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using a spherical dielectric microcavity. Nature 415, 621-623 (2002); published
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04383710.1103/Physreva.76.043837).

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Opt. Soc. Am. B 35, 100-106 (2018); published online Epub2018/01/01
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6. I. S. Grudinin, N. Yu, L. Maleki, Generation of optical frequency combs with a
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(10.1038/nphoton.2014.72).
8. R. Castro-Beltran, V. M. Diep, S. Soltani, E. Gungor, A. M. Armani,
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(2017); published online EpubNov (10.1021/acsphotonics.7000808).
9. M. Hochberg, T. Baehr-Jones, G. X. Wang, M. Shearn, K. Harvard, J. D. Luo, B.
Q. Chen, Z. W. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, A. Scherer,
Terahertz all-optical modulation in a silicon-polymer hybrid system. Nat Mater 5,
703-709 (2006); published online EpubSep (10.1038/nmat1719).
10. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B.
Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, All-
optical high-speed signal processing with silicon-organic hybrid slot
waveguidesx. Nat Photonics 3, 216-219 (2009); published online EpubApr
(10.1038/NPHOTON.2009.25).
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11. D. Korn, M. Lauermann, S. Koeber, P. Appel, L. Alloatti, R. Palmer, P. Dumon,
W. Freude, J. Leuthold, C. Koos, Lasing in silicon-organic hybrid waveguides.
Nat Commun 7, (2016); published online EpubMar (Artn
1086410.1038/Ncomms10864).

12. A. J. Maker, B. A. Rose, A. M. Armani, Tailoring the behavior of optical
microcavities with high refractive index sol-gel coatings. Opt Lett 37, 2844-2846
(2012); published online EpubJul 15 (
13. H. Choi, A. M. Armani, High Efficiency Raman Lasers Based on Zr-Doped Silica
Hybrid Microcavities. ACS Photonics 3, 2383-2388 (2016); published online
Epub2016/12/21 (10.1021/acsphotonics.6b00608).
14. R. Jose, Y. Ohishi, Higher nonlinear indices, Raman gain coefficients, and
bandwidths in the TeO2-ZnO-Nb2O5-MoO3 quaternary glass system. Appl Phys
Lett 90, (2007); published online EpubMay 21 (Artn 21110410.1063/1.2741412).

15. U. Meier, M. Bosche, C. Bosshard, F. Pan, P. Gunter, Parametric interactions in
the organic salt 4-N, N-dimethylamino-4 '-N '-methyl-stilbazolium tosylate at
telecommunication wavelengths. J Appl Phys 83, 3486-3489 (1998); published
online EpubApr 1 (Doi 10.1063/1.366560).
16. M. E. Lee, E. Gungor, A. M. Armani, Photocleavage of Poly(methyl acrylate)
with Centrally Located o-Nitrobenzyl Moiety: Influence of Environment on
Kinetics. Macromolecules 48, 8746-8751 (2015); published online EpubDec 22
(10.1021/acs.macromol.5b01496).
17. A. Nakano, T. Yamazaki, Y. Nishimura, I. Yamazaki, A. Osuka, Three-
dimensionally arranged windmill and grid porphyrin arrays by Ag-I-promoted
meso-meso block oligomerization. Chem-Eur J 6, 3254-3271 (2000); published
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Chem3254>3.0.Co;2-6).
18. J. Garcia-Amoros, A. Bucinskas, M. Reig, S. Nonell, D. Velasco, Fastest
molecular photochromic switches based on nanosecond isomerizing
benzothiazolium azophenolic salts. J Mater Chem C 2, 474-480
(2014)10.1039/c3tc31803f).
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20. C. R. Crecca, A. Roitberg, Theoretical study of the isomerization mechanism of
azobenzene and symmetrically disubstituted azobenzene Derivatives. Abstr Pap
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21. T. T. Yin, Z. X. Zhao, H. X. Zhang, Theoretical study of the cis-trans
isomerization mechanism of a pendant metal-bound azobenzene. Rsc Adv 6,
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22. H. M. D. Bandara, S. C. Burdette, Photoisomerization in different classes of
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176
Appendix 5: MATLAB Code for Resonance Peak Solver

This code was utilized to solve the characteristic equations for resonance peaks of
a microsphere resonator with a coating (presented in Chapter 3). MATLAB R2017a was
mainly used, but earlier versions are still compatible.

% Constants from user
r=75; % Microsphere radius, in um
h=0.025; % The thickness of the coating, in um
a=r+h; % Sum of sphere and thickness
n3=1; % Refractive index of the medium (air usually)
resolution=7; % Higher gives more robust solving but takes longer

% Initial guesses from the user. w needs to be guessed automatically in
the for loop
nc_nominal=1.42; % Approximate RI of CaF2
ns_nominal=1.44; % Approximate RI of SiO2

% Variables for output and saving the data
currentfolder=pwd;
save_filepath=strcat(currentfolder,'\','output.txt');

format long
format compact
figNum = 1;

if nargin ~=0
l_all = varargin(1);
else
l_all = (300:1:800)'; % Azimuthal mode number, specify range to
check here
end

% Preallocate final output vectors
final_lambda_resonance = zeros(length(l_all),1);
final_nc = zeros(length(l_all),1);
final_ns = zeros(length(l_all),1);

for i = 1:length(l_all)

fprintf('Mode %d of %d',i,length(l_all))

l=l_all(i); % Make variable l to pass to the nested function below

w_guess = (2.*pi.*a.*mean([nc_nominal,ns_nominal]))./l_all(i); %
Nominal guess value w (lambda) governed by 2*pi*r = (l*w)/n
w_range=linspace(0.8.*w_guess,1.2.*w_guess,resolution)'; % Get a
range of -10% to +10% of nominal guess value w with "resolution" total
values

% Preallocate for the temporary solutions of the range of
177
wavelengths
% to test
lambda_solutions = zeros(length(w_range),1);
nc_solutions = zeros(length(w_range),1);
ns_solutions = zeros(length(w_range),1);

for ii = 1:length(w_range) % Step through the "appropriate range of
wavelengths", w_range
% Solve the system of equations for lambda, nc, and ns
[solution_temp,~,exitFlag] =
fsolve(@find_resonance,[w_range(ii),nc_nominal,ns_nominal],optimoptions
...

('fsolve','MaxFunEvals',1000,'MaxIter',1000,'Display','off'));
if exitFlag == 1 || 2 || 3 || 4 % If a solution was found, pass
it upwards
lambda_solutions(ii)=solution_temp(1);
nc_solutions(ii)=solution_temp(2);
ns_solutions(ii)=solution_temp(3);
else
% If the solver failed, make the solutions NaN
lambda_solutions(ii)=NaN;
nc_solutions(ii)=NaN;
ns_solutions(ii)=NaN;
end
end
% Get rid of the NaNs
lambda_solutions_nanfree =
lambda_solutions(~isnan(lambda_solutions));
nc_solutions_nanfree = nc_solutions(~isnan(lambda_solutions));
ns_solutions_nanfree = ns_solutions(~isnan(lambda_solutions));

% If there's a real solution, find the max lambda, which equates to
% smallest k0
% Use the index of the max to pass lambda, nc, and ns upwards into
the
% final vectors
if ~isempty(lambda_solutions_nanfree)
[temp_max,index] = max(lambda_solutions_nanfree);
final_lambda_resonance(i) = temp_max;
final_nc(i) = nc_solutions_nanfree(index);
final_ns(i) = ns_solutions_nanfree(index);
else
% If there's no solution let's just call it NaN for now
final_lambda_resonance(i) = NaN;
final_nc(i) = NaN;
final_ns(i) = NaN;
end
clc;
end

% fsr is the differences between adjacent elements of
% final_lambda_resonance. Since diff produces a vector of
length(l_all)-1,
% zero-pad fsr so it has the same length as final_lambda_resonance
fsr=[0;diff(final_lambda_resonance)];

178
% % Plot lambda, nc, and ns vs. l
% figure(figNum);figNum=figNum+1;
% h1 = subplot(3,1,1);
% plot(l_all,final_lambda_resonance,'b.')
% grid on; grid minor
% xlabel('l (Azimuthal Mode Number')
% ylabel('Resonance Wavelength (um)')
%
% h2 = subplot(3,1,2);
% plot(l_all,final_nc,'b.');
% grid on; grid minor
% xlabel('l (Azimuthal Mode Number')
% ylabel('CaF_2 Refractive Index')
%
% h3 = subplot(3,1,3);
% plot(l_all,final_ns,'b.');
% grid on; grid minor
% xlabel('l (Azimuthal Mode Number)')
% ylabel('SiO_2 Refractive Index')

% Plot fsr vs. lambda
figure(figNum);figNum=figNum+1;
plot(final_lambda_resonance,fsr,'b.')
grid on; grid minor
xlabel('Lambda_resonance (um)')
ylabel('FSR')

% Write data to .txt file
header1='Lambda';
header2='FSR';
fid=fopen(save_filepath,'wt');
fprintf(fid, [ header1 ' ' header2 '\n']);
fprintf(fid, '%f %f \n', [final_lambda_resonance,fsr]');
fclose(fid);

output=[final_lambda_resonance,fsr];

% linkaxes([h1 h2 h3],'x');
function F=find_resonance(x)
% This function creates a system of equations
% for the resonant lambda of a coated spherical WGMR
% Lamda is w

w=x(1); % First input needs to be the approximate wavelength of
incident light
nc=x(2); % Second input, approximate refractive index of CaF2
ns=x(3); % Third input, approximate refractive index of SiO2

k0=(2.*pi)./w; % Covert wavelength into k0 for input into
Bessel functions

% The bessel function F takes inputs z = k0*n*a, for each
refractive index n of a material
zs_a=k0.*ns.*a; % z's for the function F which use a1 = r + h
zc_a=k0.*nc.*a;
z3_a=k0.*n3.*a;
179
% z's for the constant B which use a0 = r
zs_r=k0.*ns.*r;
zc_r=k0.*nc.*r;
z3_r=k0.*n3.*r;

% Calculate the function F
H=(sqrt(pi./(8.*zs_r))).*((zs_r.*besselj(l-
0.5,zs_r))+(besselj(l+0.5,zs_r))-(zs_r.*(besselj(l+0.5,zs_r)))); %
psi_prime, n1, r
I=zc_r.*(sqrt(pi./(2.*zc_r)).*bessely(l+0.5,zc_r)); % chi, n2,
r
J=zs_r.*(sqrt(pi./(2.*zs_r)).*besselj(l+0.5,zs_r)); % psi, n1,
r
K=(sqrt(pi./(8.*zc_r))).*((zc_r.*bessely(l-
0.5,zc_r))+(bessely(l+0.5,zc_r))-(zc_r.*(bessely(l+0.5,zc_r)))); %
chi_prime, n2, r
L=(sqrt(pi./(8.*zc_r))).*((zc_r.*besselj(l-
0.5,zc_r))+(besselj(l+0.5,zc_r))-(zc_r.*(besselj(l+0.5,zc_r)))); %
psi_prime, n2, r
M=zc_r.*(sqrt(pi./(2.*zc_r)).*besselj(l+0.5,zc_r)); % psi, n2,
r
N=(sqrt(pi./(8.*zc_a))).*((zc_a.*besselj(l-
0.5,zc_a))+(besselj(l+0.5,zc_a))-(zc_a.*(besselj(l+0.5,zc_a)))); %
psi_prime, n2, a
O=(sqrt(pi./(8.*zc_a))).*((zc_a.*bessely(l-
0.5,zc_a))+(bessely(l+0.5,zc_a))-(zc_a.*(bessely(l+0.5,zc_a)))); %
chi_prime, n2, a
P=(sqrt(pi./(8.*z3_a))).*((z3_a.*bessely(l-
0.5,z3_a))+(bessely(l+0.5,z3_a))-(z3_a.*(bessely(l+0.5,z3_a)))); %
chi_prime, n3, a
Q=z3_a.*(sqrt(pi./(2.*z3_a)).*bessely(l+0.5,z3_a)); % chi, n3,
a
R=zc_a.*(sqrt(pi./(2.*zc_a)).*besselj(l+0.5,zc_a)); % psi, n2,
a
S=zc_a.*(sqrt(pi./(2.*zc_a)).*bessely(l+0.5,zc_a)); % chi, n2,
a

% Constant B
B=((ns./nc).*H.*I-J.*K)/((J.*L)-((ns./nc).*H.*M));

% The solution to the function F is output as the 1st element
of the
% 3-element array F
F(1)=((n3/nc).*(P./Q))-((B.*N+O)./(B.*R+S));

% Sellmeier equation for CaF2
F(2)=(sqrt(((0.5675888.*w.^2)./(w.^2-
0.050263605.^2))+((0.47109914.*w.^2)./(w.^2-
0.1003909.^2))+((3.8484723.*w.^2)./(w.^2-34.649040.^2))+1))-nc;
% Sellmeier equation for SiO2
F(3)=(sqrt(((0.6961663.*w.^2)./(w.^2-
0.0684043.^2))+((0.4079426.*w.^2)./(w.^2-
0.1162414.^2))+((0.89747.*w.^2)./(w.^2-9.896161.^2))+1))-ns;
end
end

Abstract (if available)

Abstract A frequency comb consists of a broad span of highly resolved and precisely spaced spectral lines. These lines are a tool that has been utilized in a wide range of applications requiring high-precision measurements, including atomic clocks, astronomic spectrographs, and spectroscopy. The phenomena responsible for frequency comb generation are based on nonlinear optical effects. However, these phenomena have required the comb generators to be extremely bulky, complex, and power-intensive. Micron-scale whispering gallery mode resonant cavities are an ideal candidate to overcome these limitations, as they are capable of achieving large power buildups within a small footprint. One strategy to further improve frequency comb generation in these resonators is to utilize nanomaterials coatings to enhance nonlinear optical phenomena. ❧ In this dissertation, various nanomaterial-based strategies are investigated for enhancing different nonlinear optical effects with the aim of improving frequency combs. First, fluoride nanoparticles coated on the surface of silica resonators are shown to improve the span of frequency combs by favorably altering material dispersion. Next, a plasmonic enhancement strategy based on gold nanorods and nonlinear optical polymers is demonstrated, yielding lower thresholds for frequency comb generation. Finally, a flexible fluorescent nanocomposite material is developed using zinc oxide nanomaterials. This work lays the foundation for future work that will utilize other nanomaterials and strategies for generating frequency combs in integrated photonic devices.

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Asset Metadata

Creator Diep, Vinh Mien (author)

Core Title Nonlinear optical nanomaterials in integrated photonic devices

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Publication Date 08/09/2018

Defense Date 03/29/2018

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

Tag frequency combs,Materials Science,nanocrystals,nanomaterials,nonlinear optics,OAI-PMH Harvest,optical resonators,photonics,plasmonics

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Armani, Andrea (committee chair), Branicio, Paulo (committee member), Ravichandran, Jayakanth (committee member), Wu, Wei (committee member)

Creator Email vdiep@usc.edu,vinh.m.diep@gmail.com

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