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Development of novel optical materials for whispering gallery mode resonator for nonlinear optics
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Development of novel optical materials for whispering gallery mode resonator for nonlinear optics
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Content
Development of Novel Optical Materials
for Whispering Gallery Mode Resonator for Nonlinear Optics
By
Hyungwoo Choi
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
(Chemical Engineering)
December 2019
Copyright 2019 Hyungwoo Choi
ii
Acknowledgments
During my life at USC, I have had great opportunity, privilege, and honor to meet and work
with many great people, who directly and/or indirectly support and contribute to make my thesis
possible. First, I would like to say special thanks to my advisor, Professor Andrea Armani, for her
generous guidance and endless support. I can’t forget the time when I first met her to discuss about
changing advisor. At that time, I tried to find any hope in a desperate situation, and it was a great
fortune for me to meet her. She was so willing to help me get through problems and join her
research group. Everything was changed for me from hell to heaven after I started working in her
research group. She was and has been a savior to me.
Ph.D. is only 5 years, but it could affect a whole life of one person either in positive or in
negative ways. For me, it has been much better than I could imagine, and it was possible only in
Professor Armani’s research group. I have had a really enjoyable time in doing research during
my Ph.D. This was possible because I was so lucky to have chance to meet a great advisor and
mentor. She has always lavished praise on research that I did, encouraged me to enjoy my research,
and made me passionate about my research. It is a great honor to be a member of her research
group and learn about conducting research from one of the best. She is the best advisors for me
now and will be until the end.
I have been really blessed to be overlooked my Ph.D. thesis defense from great professors
in diverse research areas. I thank to all of my committee members: Professor Alan Willer,
Professor Jayakanth Ravichandran, and Professor Chongwu Zhou for their supports and guidance.
I would like to thank to all previous and current members of Armani Lab; Dr. Ashley
Maker, Dr. Ce Shi, Dr. Simin Mehrabani, Dr. Mark Harrison, Dr. Eda Gungor, Dr. Erick Moen,
iii
Dr. Michele Lee, Prof. Rigoberto C. Beltran, Dr. Soheil Soltani, Prof. Xiaoqin Shen, Dr. Alexa
Hudnut, Dr. Vinh Diep, Dr. Samantha McBirney, Dr. Victoria Sun, Andre Kovach, Dongyu Chen,
Rene Zeto, Fan Du, Jinghan He, Kylie Trettner, Yasaman Moradi, Brock Hudnut, Sangbum Kim,
Dr. Patrick Saris. You are all truly amazing people for me. It’s been a great pleasure and honor to
have opportunities to work with you all. Thank you so much for all your help, discussions, support,
teaching, coffee time on Friday morning, lunch trip to Chinese food truck, happy hours, and so on.
I’ll keep my fingers crossed for your research as well as your happy personal life.
Additionally, I would like to say thanks to all of my friends who I met at outside of the lab
at USC. Many thanks to Changrim Lee, Jungjoo Cho, Howon Choi, Yoonha Joo, Wookjin Choi,
Dongseok Kang, Daniel Kim, Haneol Lim, Sohyun Lim, Junhwan Shin, Moonchul Jung,
Seungwoo Shin, Dawoon Jung, Youngmin Joo, Hongjoo Jeon and many others.
I would like to express my deepest gratitude to all my family. My mom and sister always
truly encourage me and fully support things whatever I would do during my entire lifetime. I also
know that my dad in heaven always stands by me and support my Ph.D. During the Ph.D. program,
I was so fortunate to meet my lifetime companion, my lovely wife, Jieun Kim. My wife is my soul
mate and has shown me true love, warmness, patience, happiness. Because of her, my Ph.D. and
personal life become more fruitful. I also would like to say thank to my father-in-law, mother-in-
law, and sister-in-law for raising my wife up, supporting and encouraging my Ph.D. Additionally,
I’ll never forget uncle and aunt Park’s great favor to me during my life in LA. I hope I could pay
back their kindness to me sometime soon. All of them have been kept me and helped me to go
through any difficulties that I have had during my PhD study.
iv
This thesis could not be possible without all of your support and help. So, this dissertation
is devoted to them with my greatest respect and gratitude. Thank you so much all again, and Fight
on!
v
Table of Contents
Acknowledgments ….…………………………………………………………………………... ⅱ
List of Tables …………………………………………………...……………..…….………... ⅷ
List of Figures …………………………………………………………….....……….………… ⅸ
Abstract ....................................................................................................................................... ⅹⅴ
Chapter 1. Overview ................................................................................................................... 1
1. 1. Abstract ............................................................................................................................ 1
1. 2. Introduction ...................................................................................................................... 3
1. 2. 1. Motivation ................................................................................................................. 3
1. 2. 2. Chapter overview ...................................................................................................... 5
1. 3. References ........................................................................................................................ 8
Chapter 2. Background ............................................................................................................. 15
2. 1. Whispering Gallery Mode (WGM) Resonators ............................................................. 15
2. 1. 1. Ultra-high Q WGM Optical Resonators ................................................................. 15
2. 1. 2. General Properties of WGM resonators .................................................................. 19
2. 1. 3. Microtoroid Fabrication .......................................................................................... 26
2. 2. Experimental Testing Set-up .......................................................................................... 28
2. 2. 1. Optical Tapered Fiber Pulling ................................................................................. 28
2. 2. 2. Resonator testing set-up .......................................................................................... 31
2. 3. Nonlinear Optics in WGM Resonators .......................................................................... 34
2. 3. 1. Nonlinear Optics ..................................................................................................... 34
2. 3. 2. Stimulated Raman scattering (SRS) and stimulated anti-Stoke Raman scattering
(SARS) ……………………………………………………………………………………..37
2. 3. 3. Four-wave mixing (FWM) ...................................................................................... 41
2. 4. References ...................................................................................................................... 43
Chapter 3. Enhanced stimulated Raman scattering (SRS) and stimulated anti-Stokes Raman
scattering (SARS) in metal doped silica solgel coated silica hybrid microcavities ...................... 54
3. 1. Introduction .................................................................................................................... 54
3. 2. Background and motivation ........................................................................................... 56
3. 3. Experimental Method ..................................................................................................... 58
3. 3. 1. Fabrication of metal doped silica solgel coated toroids .......................................... 58
3. 3. 2. Ellipsometry ............................................................................................................ 61
vi
3. 4. Results: Material characterization .................................................................................. 62
3. 4. 1. Energy-Dispersive X-Ray Spectroscopy (EDS) ..................................................... 62
3. 4. 2. Raman Spectrograph ............................................................................................... 63
3. 5. Application 1: Enhanced stimulated Raman scattering with Zr-doped silica hybrid
microresonators ......................................................................................................................... 65
3. 5. 1. COMSOL Multiphysics Simulations ...................................................................... 65
3. 5. 2. Q factors of Zr-doped devices ................................................................................. 67
3. 5. 3. Raman Lasing Behavior .......................................................................................... 68
3. 5. 4. Raman Gain Coefficient and Raman Lasing Efficiency ......................................... 71
3. 5. 5. Raman Lasing Efficiency ........................................................................................ 72
3. 6. Application 2: Enhanced SARS with Zr- and Ti-doped silica solgel coated hybrid
devices ....................................................................................................................................... 75
3. 6. 1. COMSOL for SARS ............................................................................................... 75
3. 6. 2. Derivation of SARS intensity equation based on the coupled mode equation ....... 79
3. 6. 3. Q factors from Zr and Ti doped devices measured with 1550 nm tunable laser .... 81
3. 6. 4. Raman Lasing Behavior .......................................................................................... 83
3. 7. Summary ........................................................................................................................ 90
3. 8. References ...................................................................................................................... 91
Chapter 4. Raman-Kerr frequency combs in Zr-doped silica hybrid microresonators ............ 98
4. 1. Introduction .................................................................................................................... 98
4. 2. Background and motivation ......................................................................................... 100
4. 3. Experimental methods .................................................................................................. 102
4. 3. 1. Device Fabrication ................................................................................................ 102
4. 3. 2. Characterization of FWM and SRS ...................................................................... 105
4. 3. 3. COMSOL Multiphysics Simulation ..................................................................... 106
4. 3. 4. Dispersion in WGM resonator .............................................................................. 107
4. 4. Results and discussions ................................................................................................ 112
4. 4. 1. COMSOL Multiphysics Finite Element Methods Simulation .............................. 112
4. 4. 2. Quality factors of silica hybrid resonators ............................................................ 114
4. 4. 3. Frequency comb behaviors ................................................................................... 116
4. 5. Summary ...................................................................................................................... 125
4. 6. References .................................................................................................................... 126
vii
Chapter 5. Surface Raman lasing with highly aligned organic molecule monolayer on silica
hybrid microresonator ................................................................................................................. 135
5. 1. Background and motivation ......................................................................................... 135
5. 2. Experimental methods .................................................................................................. 139
5. 3. Results and Discussions ............................................................................................... 144
5. 3. 1. Characterization of the surface molecular layers .................................................. 144
5. 3. 2. Computational calculations for the microscopic hyperpolarizabilities ................. 146
5. 3. 3. Spontaneous Raman characterization for Raman gain coefficients ...................... 149
5. 3. 4. Intrinsic Q factors and Broadscan spectrum ......................................................... 151
5. 3. 5. Characterization of surface Raman lasing ............................................................ 154
5. 4. Summary ...................................................................................................................... 167
5. 5. References .................................................................................................................... 168
Chapter 6. Q-switched Raman laser with VO2 coated silica microcavity .............................. 177
6. 1. Introduction .................................................................................................................. 177
6. 2. Background and motivation ......................................................................................... 178
6. 3. Experimental Methods ................................................................................................. 179
6. 3. 1. Silica microresonator fabrication .......................................................................... 179
6. 3. 2. VO2 deposition on silica toroid ............................................................................. 180
6. 3. 3. Testing set-up with temperature stage .................................................................. 181
6. 4. Results and Discussions ............................................................................................... 182
6. 5. Summary ...................................................................................................................... 185
6. 6. References .................................................................................................................... 186
viii
List of Tables
Table 3-1. The parameters obtained experimentally or by simulations in order to calculate the
normalized Raman gain coefficient. ........................................................................................ 74
Table 3-2. Summary of all results obtained across all devices tested along with device
parameters. ............................................................................................................................... 89
Table 4-1. The parameters obtained by simulation or experimentally. ........................... 124
Table 5-1. Raman intensity ratios and Raman
vib
values determined from
computed Raman activities using RHF/6-311+G(3df,2p) method. ....................................... 148
C
ref S
I I ) / (
ix
List of Figures
Figure 2-1. (a) A picture of St. Paul Cathedral in London and (b) whispering gallery inside the
cathedral. In the circular wall of whispering gallery, the sound wave travels around the
circumference clinging to the wall, allowing the whispered communication from any part of the
gallery. ..................................................................................................................................... 16
Figure 2-2. (a) Schematic image of an optical WGM resonator where light with resonant
wavelength is confined and traveling in a resonator by total internal reflection. (b) Total internal
reflection at the boundary between glass (silica) and air with the critical angle (θc) based on the
Snell’s law. ............................................................................................................................... 16
Figure 2-3. Schematic images of WGM resonators with tapered optical fiber for the evanescent
field coupling into (a) microsphere and (b) microtoroid. A laser light with a resonant wavelength
(red) propagates through the tapered optical fiber and circulates inside the WGM resonators.17
Figure 2-4. (a) One of the representative transmission spectra showing resonant wavelengths
with calculated Q factors of each peaks. The transmission spectrum is normalized with the taper
scanned transmission. (b) The QLoaded data as a function of coupling percentage. The QInt is
corresponding to the y-intercept of the linearly fitted data. ..................................................... 21
Figure 2-5. Representative broad-scan spectrum showing the FSR of the device. The diameter
of the device is approximately 50 μm, and it is tested with 765 nm tunable laser. Experimentally
observed FSR of the device (2.63 nm or 1.32 THz) is almost the same as the FSR calculated (2.56
nm) with Equation 2.7.............................................................................................................. 25
Figure 2-6. Schematic images of the fabrication procedures for silica toroidal microcavities (a)
define silica circle pattern on top of silicon wafer by photolithograph and BOE etching, (b) XeF 2
etching to produce silica disk supported by silicon pillar, and (c) CO2 laser reflow to create
atomically smooth surface silica toroidal microresonator. (d) SEM (scanning electron microscope)
image of the finalized silica microtoroidal resonator with diameter of approximately 50 μm.
........................................................................................................................................ ……..27
Figure 2-7. A Picture of optical fiber pulling set-up with fiber spool, optical fiber stage, laser,
photodetector connected to oscilloscope, microscope, hydrogen torch, and nano-stage controller.
.................................................................................................................................................. 29
Figure 2-8. An optical microscope image of tapered optical fiber waveguide. The variation in
color in the fiber is the diffraction of light from the thin tapered optical fiber. ....................... 30
Figure 2-9. Schematic image of testing setup showing a tunable narrow linewidth laser,
oscilloscope, optical spectra analyzer (OSA), and a computer to control the tunable laser and
collect data from photodetector. .............................................................................................. 32
Figure 2-10. Schematic image of testing set-up with a laser, a tapered optical fiber, a silica
toroid, a splitter, a photodetector connected to an oscilloscope, optical spectrum analyzer, and
spectroscopy. Inset is the top-view optical microscope image showing a silica toroid with a tapered
optical fiber. ............................................................................................................................. 33
Figure 2-11. (a) Energy level diagram of red-shifted stimulated Raman scattering (SRS) and
blue-shifted stimulated anti-Stokes Raman scattering (SARS) with the vibrational state of the gain
medium. υPump, υSRS, υSARS, and υVibration are corresponding to the frequencies of pump, SRS, SARS,
and vibrational optical phonon, respectively. (b) SRS and SARS spectrum with pump wavelength
with the shift of the vibrational frequency of optical phonon of a medium. ........................... 38
x
Figure 2-12. Normalized Raman gain spectrum of silica with the respect to the frequency offset
(THz). The Raman gain of silica is high over the range of 12 ~ 15 THz. ............................... 39
Figure 2-13. (a) Energy level diagram of the FWM process. The FWM is a nonlinear optical
process where one idler (vI) and one signal photon (vS) are generated from two degenerate pump
photons (vP). (b) FWM spectrum as a function of wavelength. .............................................. 41
Figure 3-1. Schematic synthetic procedure for producing a metal-doped silica solgel,
describing (a) acid-catalyzed hydrolysis and (b) condensation reaction. ................................ 59
Figure 3-2. Metal-doped silica solgel coated hybrid toroids. Scanning electron microscope
(SEM) image of (a) metal-doped silica solgel coated hybrid toroid. (b) schematic image of a hybrid
silica toroid showing a bare silica toroid coated with Metal-doped silica solgel. Major (D) and
minor (d) diameter of the hybrid toroid are indicated. ............................................................. 60
Figure 3-3. EDS spectra from (a) Zr- and (b) Ti-doped silica hybrid devices. The silicon
(purple) has peaks at 1.740 and 3.49 keV. The oxygen (green) has a peak at 0.523 keV. The
zirconium (red) and titanium (blue) have peaks at 2.042 and 4.510 keV, respectively. Each peak is
fitted to Gaussian. .................................................................................................................... 62
Figure 3-4. Schematic images of SiO4 (a) bending and (b) stretching modes, which are
indicated by the areas of peak at 500 and 1000 cm
-1
, respectively, measured by a spectrograph
36
.
.................................................................................................................................................. 63
Figure 3-5. (a) Spectrum of Zr 10 mol% silica sol-gel coated onto the bare silicon wafer. Inset
is the schematic illustration of Zr 10 mol% silica sol-gel matrix. Similar spectra were obtained for
other mol%. (b) The degree of polarization (Ip) values, which is the ratio of the area under the
peaks at 500 cm
-1
and 1000 cm
-1
, with respect to the Zr concentrations in silica sol-gel. ....... 64
Figure 3-6. COMSOL Multiphysics finite element method simulation results. (a) Simulation
results of the optical field distribution in the coated toroidal micro-cavity with the different mol%
of Zr in the sol-gel indicated. (b) Total optical mode volume and the percentage of the mode
volume inside the coating with respect to the Zr concentrations in the silica sol-gel. ............ 66
Figure 3-7. (a) The normalized transmission spectra for Zr 10 mol% silica sol-gel coated toroid.
And (b) Loaded Q values with respect to the Zr concentrations with the coated devices. ...... 67
Figure 3-8. (a) Optical spectrograph and (b) Optical spectrum analyzer (OSA) spectra of Zr 10
mol% doped silica sol-gel coated toroid. Raman peaks are observed at 793.35 nm from the both
measurements. .......................................................................................................................... 68
Figure 3-9. (a) Optical spectrograph and (b) OSA data obtained with Zr 10 mol% sol-gel coated
toroids. The graphs have cascaded Raman peaks. Similar results are obtained for the other mol %.
.................................................................................................................................................. 69
Figure 3-10. (a) spectrograph data and (b) OSA data with three different concentrations (0, 5,
and 10 mol%), showing enhancement of lasing efficiency with Zr concentrations. ............... 70
Figure 3-11. Normalized Raman gain coefficient with respect to the Zr concentrations in silica
sol-gel. ...................................................................................................................................... 71
Figure 3-12. Raman lasing efficiency as a function of the Zr doping within the silica solgel.
The Raman lasing efficiency is enhanced substantially from 3.37% to 47.43%. Inset: The Raman
lasing efficiency with respect to the normalized Raman gain coefficient, indicating a linear
correlation with R
2
= 0.99. ....................................................................................................... 73
Figure 3-13. Cross-sectional images of the optical field distribution in the coated toroidal
microcavity obtained with a COMSOL Multiphysics simulation. Major diameter D=50μm. Miner
diameter d=6μm. Coating refractive index equals: (a) 1.44. (b) 1.52. ..................................... 76
xi
Figure 3-14. The dependence of TM fundamental mode area (Aeff) as a function of the
refractive index of coating (ncoating) and the minor diameter with the different coating thickness (a)
300, (b) 400, (c) 500, and (d) 600 nm. The dimensions used in the experimental devices are 400
nm coating and 6 μm minor diameter. The index value depends on the dopant, but all values tested
fall within the modeled range. ................................................................................................. 77
Figure 3-15. (a) Representative transmission spectrum from bare device with load Q of 3 x 10
7
with a mode splitting. (b) Intrinsic Q of all devices; bare, Zr, and Ti-doped devices. ............ 82
Figure 3-16. Emission spectra from the (a) bare, (b) Zr-, and (c) Ti-doped devices obtained via
OSA. (d) SRS and SARS shift from various devices. ............................................................. 84
Figure 3-17. Threshold graph of (a) SRS and (b) SARS. (c) The ratio of SARS versus SRS
intensities from various devices. .............................................................................................. 85
Figure 3-18. Zoomed-in spectra of (a) bare, (b) Zr-, and (c) Ti-doped devices with similar
coupled power into the devices (~ 1.5 mW) ............................................................................ 86
Figure 3-19. (a) efficiency and (b) threshold values of SRS, and (c) SARS intensity at
approximately 1.3 mW of coupled power and (d) SRS threshold, which is a minimum coupled
power to generate SARS. ......................................................................................................... 87
Figure 4-1. Schematic images of frequency comb generation with (a) pump induced four-wave
mixing and (b) pump, Raman, and anti-Stokes Raman induced four-wave mixing. ............. 101
Figure 4-2. Scanning electron microscope (SEM) image of Zr-15 mol% silica solgel coated
silica hybrid toroidal resonator. Major and minor diameters of the device are 109 and 10 μm,
respectively. ........................................................................................................................... 104
Figure 4-3. (a), (c), and (e) Geometric (red) and material (blue) dispersion of SiO2, ZrO2, and
Zr 15mol% toroidal resonator, respectively. (b), (d), and (f) Dispersion of SiO2, ZrO2, and Zr 15
mol% toroidal resonator, respectively, combining both geometric and material dispersions…..
................................................................................................................................................ 110
Figure 4-4. Cross-section images of the optical field distribution in the Zr-doped silica solgel
coated toroidal microcavity calculated with COMSOL Multiphysics finite element methods (FEM)
simulation with the different mol % of Zr in the silica solgel coating (0 to 15 mol%). ........ 112
Figure 4-5. (a) Representative transmission spectra to obtain a loaded Q factor from the Zr-15
mol% device. The resonant wavelength is 1557.45276 nm, and the Q Loaded is 1.13 x 10
7
with 25.13
% of coupling (b) The Qloaded data with respect to the coupling percentage to calculate the Qint of
the Zr-15 mol% device. The Qint is the 1.53 x 10
7
, where the y-intercept of the linearly fitted line.
(c) Intrinsic Q factors as a function of the concentration of Zr mol% in the silica solgel coating.
................................................................................................................................................ 115
Figure 4-6. Optical frequency comb generation from the Zr-00 device. A series of spectra are
shown for each device to provide evidence of the formation of the comb as a function of input
power. Inset numbers are the input powers. .......................................................................... 116
Figure 4-7. Optical frequency comb generation from the Zr-05 device. A series of spectra are
shown for each device to provide evidence of the formation of the comb as a function of input
power. Inset numbers are the input powers. .......................................................................... 118
Figure 4-8. Optical frequency comb generation from the Zr-10 device. A series of spectra are
shown for each device to provide evidence of the formation of the comb as a function of input
power. Inset numbers are the input powers. .......................................................................... 119
Figure 4-9. Optical frequency comb generation from the Zr-15 device. A series of spectra are
shown for each device to provide evidence of the formation of the comb as a function of input
power. Inset numbers are the input powers. .......................................................................... 121
xii
Figure 4-10. (a) The SRS threshold graph for the SRS efficiency (slope) and threshold (x-
intercept) and (b) the comb spans as a function of the coupled power into each device. ...... 122
Figure 5-1. (a) Scanning electron microscope (SEM) image of a microtoroidal optical resonator
on a silicon chip with false blue color indicating the location of the siloxane molecular layer on
the silica microcavity surface. (b) COMSOL Finite element method (FEM) simulation of the
optical mode profile in a microtoroidal resonator with a major diameter of 60 μm. The red arrow
represents the electric field direction of the fundamental transverse magnetic (TM) mode.
........................................................................................................................................ ……138
Figure 5-2. One of the representative scanning electron microscope (SEM) images of the
fabricated silica toroid with major and minor diameter of 53.9 and 5.7 μm, respectively….140
Figure 5-3. Schematic image of silanization reaction between the surface hydroxyl group (-
OH) on silica and either methyl trichlorosilane (blue) or dimethyl dichlorosilane (red) based on
the chemical vapor deposition (CVD) reaction at room temperature (RT). The final product has
the grafted molecular mono-layer of either methyl siloxane (MS, blue) or dimethyl siloxane (DMS,
red) work
49,38,50,51
. .................................................................................................................. 141
Figure 5-4. (a) A rendering of the toroidal surface Raman laser. A tapered optical fiber
waveguide is used to couple pump light (v1) into the cavity and couple Raman light (v2) out of the
cavity. The microcavity is shown on resonance. The k vector indicates the propagation direction
of the circulating light inside the device, and the E vector represents the direction of the transverse
magnetic (TM) electric field. (b) Schematic of the region indicated in part (a) To simplify the
schematic, only one molecule is shown on the device surface interacting with the optical
evanescent field in air. The orientation of the molecular Raman mode is parallel to the polarization
direction of electrical field E. ................................................................................................. 142
Figure 5-5. XPS spectra of a grafted chloro-substituted monolayer on silica and an initial bare
silica. The binding energy of the primary peak of Cl (2p, ~200 eV) presences at the chloro-
substituted molecules grafted on the surface of silica. (b) Raman spectra of a grafted MS monolayer
on silica and the initial bare silica. The Raman peaks at about 2900 cm
-1
originate from the methyl
group of the MS molecules grafted on the silica surface. ...................................................... 145
Figure 5-6. RHF-based, simulated Raman spectra of three model compounds,
Si(OSiH3)2(OH)2, Si(OSiH3)2(OH)(CH3), and Si(OSiH3)2(CH3)2, plotted with a Lorentzian
broadening (FWHM=8 cm
-1
). Frequencies were calibrated by the experimental peak position of
the C-H vibration so that the peak studied for each sample was close to the experimental value of
the breathing mode at ~450 cm
−1
. .......................................................................................... 147
Figure 5-7. Spontaneous Raman spectra of silica, MS and DMS thin films taken using a
reflective micro-Raman spectrometer. Inset: The area of interest corresponding to the Si-O
vibration approximately at 460 cm
-1
. ..................................................................................... 150
Figure 5-8. (a) One of the representative transmission spectra used to obtain the loaded Q
factors from MS device. The resonant wavelengths are 766.05186 and 766.05188 nm with the
loaded Q factors of 5.23 and 4.22 x 10
7
, respectively. (b) The loaded Q factor data with respect to
the coupling percentage. The y-intercept of each linearly fitted data corresponds to the intrinsic Q
factor of either clockwise and counter-clockwise. (c) The intrinsic Q factors of a series of bulk
silica, MS, and DMS devices of two sizes of ~53 μm (solid symbol) and ~83 μm (hollow symbol).
Each point represents a unique resonant cavity device, demonstrating the reproducibility of the
fabrication and surface functionalization process. Error bars are smaller than symbols. (d) One
representative broad-scan spectrum from MS device (diameter of ~53 um) with two different
polarization states (blue and navy) from either TM or TE mode. ......................................... 152
xiii
Figure 5-9. Representative output spectra of bulk, MS and DMS devices. (a) ~ (c). Output
emission spectra captured by the OSA from bulk, MS, and DMS devices, respectively with ~53
μm diameters. All devices have similar Q factors and are pumped by the 765nm laser with ~350
μW coupled power. Both MS and DMS devices show strong Raman lasing peaks at about 795 nm,
while the bulk silica device shows a very weak emission. (d) Direct comparison of Raman lasing
emission power from the three device types. The emission peak for the bulk silica device is plotted
twice, with a shift in the y-axis only. Using the same input power, the MS and DMS devices show
an enhanced lasing power of about 50 times higher than that in the bulk silica device. (e) Schematic
of surface features of bulk silica, MS, and DMS devices with the proposed surface vibrational
Raman modes indicated. ........................................................................................................ 155
Figure 5-10. Raman shifts of the first order Raman emission peak for all devices studied. The
peak positions fall within the Raman gain band of Si-O vibrational mode. .......................... 156
Figure 5-11. Comparison of Raman spectra between the aligned Si-O mode and disordered C-
H mode in MS devices. (a) Schematic of the aligned Si-O mode (𝜈 Si − O) of the surface MS layer.
The surface Raman mode direction is parallel to the direction incident electrical field. (b)
Schematic of the disordered C-H mode (𝜈 C − H) of the surface MS layer. The mode directions,
both in-plane and out-plane (not shown in the schematic), are randomly distributed and are not
parallel to the direction electric field. (c) Output spectrum (750 nm to 810 nm) of a DMS device
(50 μm; Q = 5.4 × 10
7
) pumped at ~765 nm with coupled power of about 400 μW. The Raman
lasing peak at about 793 nm corresponding to the Si-O vibrational mode. (d) Output spectrum (950
nm to 1000 nm) of the same MS device as in part (c) also pumped at ~765 nm. .................. 157
Figure 5-12. Raman lasing performance of the devices. (a) The dependence of the output power
of the first order Raman on the coupled input power in the bulk silica, MS, and DMS devices with
a diameter of ~53 μm. Q factors are 9.1 × 10
7
, 4.7 × 10
7
and 5.4 × 10
7
for bulk silica, MS and DMS
devices, respectively. Inset is the dependence of the output power of the first order Raman
emissions on the circulating intensity of the optical field in the cavity. (b) Comparison of first order
Raman lasing efficiencies of the bulk, MS and DMS devices with diameters of either ~53 μm (solid
symbol) and ~83 μm (hollow symbol). While the efficiency does not change with diameter, the
lasing efficiency of the MS and DMS devices is significantly higher than the bulk silica device
with an approximately 10 times increase. These efficiency values are particularly notable as they
are unidirectional efficiencies. ............................................................................................... 159
Figure 5-13. Polarization dependent Raman lasing data from bulk silica device (a) Broadscan
spectrum from bulk silica indicating different fundamental modes from each polarization state. (b)
Raman threshold spectra from bulk silica indicating Raman efficiency and Raman threshold from
each polarization state. (c) Raman emission spectra from bulk silica indicating output Raman
lasing power from each polarization state. ............................................................................ 161
Figure 5-14. Polarization dependent Raman lasing data from MS device (a) Broadscan
spectrum from MS silica indicating different fundamental modes from each polarization state. (b)
Raman threshold spectra from MS silica indicating Raman efficiency and Raman threshold from
each polarization state. (c) Raman emission spectra from MS silica indicating output Raman lasing
power from each polarization state. ....................................................................................... 162
xiv
Figure 5-15. Polarization dependent Raman lasing data from DMS device (a) Broadscan
spectrum from DMS silica indicating different fundamental modes from each polarization state.
(b) Raman threshold spectra from DMS silica indicating Raman efficiency and Raman threshold
from each polarization state. (c) Raman emission spectra from DMS silica indicating output
Raman lasing power from each polarization state. ................................................................ 163
Figure 5-16. Comparison of first order Raman lasing efficiencies of the bulk silica, MS and
DMS devices with diameters of either ~53 μm (solid symbol) and ~83 μm (hollow symbol) with
different polarization states. ................................................................................................... 165
Figure 6-1. Top-view optical microscope images of (a) bare silica toroid (b) VO2 deposited
toroid with diameter of ~50 μm reflowed from 80 μm disks. ................................................ 179
Figure 6-2. (a) One of the representative transmission spectra exhibiting the loaded Q factors
from VO2 (50 nm) coated silica toroid. The resonant wavelengths are 1570.3052 and 1570.3077
nm with the loaded Q factors of 1.97 and 2.52 x 10
6
, respectively. (b) The loaded Q factors as a
function of the coupling percentage to obtain the intrinsic Q factor of VO2 coated device…….
................................................................................................................................................ 183
Figure 6-3. (a) The loaded Q factor over the range of temperature from 30 to 80
o
C with
consistent coupling percentage (approximately 10 %). (b) Resonance wavelength shift (Δλ) as a
function of the temperature change (ΔT). The slope of the linearly fitted line indicates the Δλ / ΔT
of the device (11.14 pm/
o
C). .................................................................................................. 184
xv
Abstract
Due to unique optical properties of silica, silica-based photonic devices have found many
important applications throughout science and engineering, especially in sensing,
communications, lasers, and integrated photonic devices. Recently developed on-chip silica
toroidal microresonators become one of the most promising microcavity due to their exceptional
ability to confine optical energy temporarily (high quality factor, ~10
7
) and spatially (mode
volume, ~ 1000 um
3
) while being integrated on a silicon substrate. Due to the ultra-high quality
(Q) factors, silica microresontors can generate high circulating intensity (~ 1GW/cm
2
) with small
amount of input power, that is enough to generate third-order nonlinear optical phenomena in
devices. However, nonlinear optical proceeses in silica microcavity are often limited by intrinsic
material properties of silica; third-order nonlinear susceptibility (χ
(3)
) or Raman gain coefficient
(gR). To overcome the limitation, this thesis investigates, designs, and develops chemically
modified silica materials to enhance the nonlinear optical processes in silica toroidal
microresonators. Using sol-gel process and surface chemistry combined with microfabrication
procedures, custom silica materials and silica hybrid devices are developed to benefit many
applications.
In this thesis, it is first demonstrated how chemically modified silica enables enhanced
nonlinear optical generation within ultra-high Q factor whispering gallery mode (WGM)
resonators. Metal dopants into silica sol-gel thin film or surface functionalization of silica is
utilized to generate and improve the third order nonlinear optical processes, such as stimulated
Raman scattering (SRS), stimulated anti-Stokes Raman scattering (SARS), and four-wave mixing
xvi
(FWM). The chemically modified silica properties are identified and characterized with various
analytical instruments followed by analysis of light-matter interaction of the novel materials in
silica hybrid WGM resonators. Finally, several applications are demonstrated including enhanced
generation of SRS and SARS, improved Raman-Kerr frequency combs behaviors, and surface
Raman lasing performances.
1
Chapter 1. Overview
1. 1. Abstract
Due to unique optical properties of silica, silica-based photonic devices have found many
important applications throughout science and engineering, especially in sensing,
communications, lasers, and integrated photonic devices. Recently developed on-chip silica
toroidal microresonators become one of the most promising microcavity due to their exceptional
ability to confine optical energy temporarily (high quality factor, ~10
7
) and spatially (mode
volume, ~ 1000 um
3
) while being integrated on a silicon substrate. Due to the ultra-high quality
(Q) factors, silica microresontors can generate high circulating intensity (~ 1GW/cm
2
) with small
amount of input power, that is enough to generate third-order nonlinear optical phenomena in
devices. However, nonlinear optical proceeses in silica microcavity are often limited by intrinsic
material properties of silica; third-order nonlinear susceptibility (χ
(3)
) or Raman gain coefficient
(gR). To overcome the limitation, this thesis investigates design and develop chemically modified
silica materials to enhance the nonlinear optical processes in silica toroidal microresonators. Using
sol-gel process and surface chemistry combined with microfabrication procedures, custom silica
materials and silica hybrid devices are developed to benefit many applications.
In this thesis, it is first demonstrated how chemically modified silica enables enhanced
nonlinear optical generation within ultra-high Q factor whispering gallery mode (WGM)
resonators. Metal dopants into silica sol-gel thin film or surface functionalization of silica is
utilized to generate and improve the third order nonlinear optical processes, such as stimulated
2
Raman scattering (SRS), stimulated anti-Stokes Raman scattering (SARS), and four-wave mixing
(FWM). The chemically modified silica properties are identified and characterized with various
analytical instruments followed by analysis of light-matter interaction of the novel materials in
silica hybrid WGM resonators. Finally, several applications are demonstrated including enhanced
generation of SRS and SARS, improved Raman-Kerr frequency combs behaviors, and surface
Raman lasing performances.
3
1. 2. Introduction
1. 2. 1. Motivation
The past decades have seen substantial development in generation of nonlinear optical
phenomena in whispering gallery mode (WGM) optical resonators
1
. In particular, the field has
surged since the development of ultra-high quality factor (Q) WGM microcavities, starting from
microdroplets
2–4
to various geometries of microresonators (microsphere
5–7
, microdisk
8–10
, and
microtoroid
11–13
) with diverse materials (silica
14–16
, silicon
17–19
, Si3N4
20–22
, CaF2
23–25
, Perovskite
26–
28
, and etc.
29–31
). Due to the ultra-high Q factor, or long photon lifetime, WGM microresonators
can achieve high circulating powers (~100 W) and circulating intensities (~1 GW/cm
2
), which is
enough to create nonlinear optical phenomena. As a result, generation of nonlinear optical effects
within WGM microresonators has attracted significant research interest and has promoted to novel
applications in diverse scientific research fields, such as optical communication, sensors
32–34
,
spectroscopy
35–37
, optical atomic clock
38–40
, and Lidar system
41,42
.
With its high transparency and durability, silica is one of the most promising optical
materials to confine light in WGM microresonators
1
. Due to silica’s favorable features, many
integrated devices have been developed made out of silica with various different geometries.
Because silica has very low material absorption loss over the wide range of wavelength from
visible to near-IR, the intrinsic Q factor of silica sphere reaches up to ~10
9
, only limited by material
absorption of silica
5
, and silica disks
43
and toroids
11
show the intrinsic Q factor of ~10
7
and ~10
8
,
respectively. Among them, the monolithic silica toroidal microresonators have shown great
4
promises for nonlinear optical applications, as they are fabricated directly on a silicon wafer
possible to be integrated with other photonic devices. With the inversion symmetry structure of
silica, the highest nonlinear optical phenomenon is the third order nonlinear optics, and a range of
researches have been demonstrated the generation of third order nonlinear optical effects in silica
toroidal microresonators, such as stimulated Raman scattering (SRS)
44,45
, stimulated anti-Stokes
Raman scattering (SARS)
46
, third-harmonic generation (THG)
47
, and four-wave mixing (FWM)
for frequency comb generations
48,49
.
Nevertheless, the performance of generated nonlinear optical effects in silica toroidal
microcavities are limited by silica’s intrinsic material properties, such as nonlinear refractive index
(n2 = 2.2 x 10
-20
m
2
/W)
48
or Raman gain coefficient (gR = 0.66 x 10
-13
m/W)
7
. To improve the
nonlinear optical performances, it is necessary to develop novel optical materials. In the thesis, we
demonstrate that nonlinear optical effects are significantly enhanced by modifying silica
chemically via either doping metal (Zirconium or Titanium)
45,50
into silica matrix using sol-gel
process or grafting and functionalizing surface of silica with organic monolayer by chemical vapor
deposition (CVD). Chemically modified silica properties are identified with diverse analytic
instruments, such as Raman spectroscopy, Ellipsometry, X-ray photoelectron spectroscopy (XPS),
and scanning electron microscopy (SEM) with energy-dispersive X-ray spectroscopy (EDS). The
chemically modified silica hybrid microresonators exhibits substantially enhanced nonlinear
optical process, such as SRS and SARS, Raman-Kerr frequency comb, and surface Raman lasing.
The intelligently designed silica hybrid device to improve nonlinear optical phenomena is of
significant interest in a wide range of scientific research and engineering fields, such as
telecommunications, bio-detections, optical clock, spectroscopy, and Lidar.
5
1. 2. 2. Chapter overview
This thesis is organized as follows:
In Chapter 2, a detailed background on whispering gallery mode optical resonator is
presented in general. The important properties for the optical resonators are defined, such as quality
(Q) factor, mode volume, circulating intensity, free spectra range (FSR), and etc. The detailed
fabrication procedures to fabricate silica microtoroid are introduced as well as testing procedures,
such as taper pulling, alignment, and data acquisition. Basics of nonlinear optical phenomena, such
as stimulated Raman scattering, and four-wave mixing, are explained. In subsequent chapters,
numerous completed research projects are summarized which build upon these fundamentals.
Chapter 3 contains demonstration of enhanced stimulated Raman scattering (SRS) and
stimulated anti-Stokes Raman scattering (SARS) with metal-doped silica sol-gel coated silica
hybrid microresonators. Both SRS and SARS are based on the vibration of phonon in gain medium,
and those performances in silica are limited by the silica’s intrinsic properties. By doping metal
(Titanium or Zirconium) in silica matrix, the degree of polarization of silica increases, indicating
silica phonon is more susceptible to vibrate. The metal-doped silica sol-gel layers are coated on
bare silica toroidal microcavity and tested with both visible (765 nm) and near-IR (1550 nm)
region. With the dopants, we demonstrate the enhancement of both SRS and SARS efficiencies
over 10 times
Chapter 4 presents the generation of Raman-Kerr frequency comb with metal-doped silica
hybrid microresonators. Frequency comb has been generated with microresonators although the
span of frequency comb is determined by pump induced FWM generations. With metal doped
silica layer, which has high Raman gain, we experimentally demonstrate the generation of SRS as
6
well as SARS induced FWM peaks broadening the span of frequency comb with reduced pump
power. Theoretically analysis of dispersion in metal-doped silica hybrid devices support the
enlarging of the frequency comb span. Raman-Kerr frequency comb shows metal-dopant
concentration dependent, and finally 500 nm of Raman-Kerr frequency comb span is generated
with significantly reduced pump power.
In Chapter 5, polarization dependent surface Raman lasing is demonstrated with organic
monolayer grafted silica microcavity. Organic monolayers (methylsilane or dimethylsilane) are
functionalized with chemical vapor deposition method, enabling highly aligned Si-O vibrational
Raman mode on the surface. By the asymmetricity introduced with organic molecules, the second
hyperpolarizability and Raman gain of silica increases. Moreover, the oriented surface Raman
mode is either parallel to the direction of electric field of transverse magnetic (TM) mode or
vertical to that of transverse electric (TE) mode in silica microresonators, showing polarization
dependent Raman lasing behavior. Due to the alignment between surface Raman mode and applied
electric field, the Raman lasing enhances significantly compared with bulk silica, generating
surface Raman lasing.
In Chapter 6, Q-switched Raman laser in VO2 coated silica microcavity is suggested. By
leveraging a unique property of VO2, which is meal to insulator phase transition (MIT) with
temperature, VO2 is introduced to act as a Q-switching material in silica microresonators. Basic
properties of VO2 coated silica devices are characterized, such as intrinsic Q factors, and
temperature dependent Q factors. While the devices haven’t been observed Q-switching behavior
yet, those finding are still important and useful for future demonstration of Q-switching Raman
lasing performances in VO2 coated silica microresontors.
7
As seen in those works, chemically modified silica within silica WGM microresonators
show enhancement of various nonlinear optical processes and tremendous potential to benefit
diverse applications. This work provides not only the improvement of nonlinear optical effects by
modifying silica chemically, but also the infinite possibility of modifying silica a s well as other
materials with numerous chemicals to enhance optical effects in many fields.
8
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15
Chapter 2. Background
2. 1. Whispering Gallery Mode (WGM) Resonators
2. 1. 1. Ultra-high Q WGM Optical Resonators
Whispering gallery mode (WGM) resonators are one group of optical microcavities that
can confine a certain wavelength of light inside the devices
1
. The term, whispering gallery mode,
is inspired by the Whispering Gallery at St. Paul Cathedral in London (Figure 2-1), where the sound
wave is propagating along the wall of the gallery, whereas the optical wave is traveling at the
peripheral of the optical WGM resonator by the total internal reflection (Figure 2-2). Dielectric
WGM resonators are especially important because they can support ultra-high qualify (Q) factors.
Due to the high Q factor, or long photon lifetime, high buildup power can be generated inside the
microcavities. As a result, the WGM resonators have been used to study both linear and nonlinear
optical processes for the various applications, such as sensors
2–6
, lasers
7–11
, and frequency comb
generation
12–16
.
16
Figure 2-1. (a) A picture of St. Paul Cathedral in London and (b) whispering gallery inside
the cathedral. In the circular wall of whispering gallery, the sound wave travels around
the circumference clinging to the wall, allowing the whispered communication from any
part of the gallery.
Figure 2-2. (a) Schematic image of an optical WGM resonator where light with resonant
wavelength is confined and traveling in a resonator by total internal reflection. (b) Total
internal reflection at the boundary between glass (silica) and air with the critical angle (θc)
based on the Snell’s law.
17
Among the various materials, silica is one of the most promising materials for the WGM
optical resonators due to its low absorption across a wide range of wavelengths
17
. Especially for
the silica microspherical resonators as shown as Figure 2-3 (a), it has been demonstrated that
microspheres have a quality factor as high as 10
9
, only limited by the absorption loss from silica
18
.
However, the microspheres cannot be integrated with other photonic devices due to its structure
and fabrication method. Recently, silica microtoroidal resonators have been developed onto the
silicon chip with atomically smooth surface, as shown at Figure 2-3 (b), enabling a ultra-high Q
factor (~10
8
)
19
. It is important to note that on-chip silica toroid having high quality factor has a
great potential to be integrated with other optical and electrical devices
20–24
.
Figure 2-3. Schematic images of WGM resonators with tapered optical fiber for the
evanescent field coupling into (a) microsphere and (b) microtoroid. A laser light with a
resonant wavelength (red) propagates through the tapered optical fiber and circulates
inside the WGM resonators.
As the silica toroidal microcavities have an ultra-high Q factor of 10
8
,
19
the resonators can
act as optical amplifiers, allowing low input powers to be significantly enhanced by over 10
6
times.
For example, 1 mW of input power to a resonator with Q of 10
7
is amplified to 100 W of circulating
18
power in the device. In addition to the large circulating power, due to the micro-sized, the WGM
resonators have the small volume of optical mode less than 1000 μm
3
. In other words, the high
circulating power of 100 W is confined in the small volume of 1000 μm
3
, enabling the extremely
high circulating intensity of 1 GW/cm
2
with only 1 mW of pump.
On-chip resonators of this form-factor are the state-of-art to generate nonlinear optical
phenomena
25–29
. Previously, high input power from pulsed lasers was used
30,31
. With the WGM
resonator, however, the ultra-high Q factor enables the large circulating optical intensity that is
enough to create any nonlinear optical phenomena with low input power. Therefore, many kinds
of nonlinear optical effects have been demonstrated in silica WGM resonators, such as second
harmonic generation
32–36
, third-harmonic generation
37–39
, stimulated Raman and anti-Stokes
Raman scattering
40–44
, Brillouin scattering
45–47
, and four-wave mixing
48–52
.
19
2. 1. 2. General Properties of WGM resonators
Quality factor (Q)
An ideal optical resonator could confine light with a resonant wavelength perfectly for an
infinite period of time without any optical loss. In the real world, however, the optical resonator
can only confine light for a finite period of time due to the numerous sources of optical loss which
deteriorate the photon lifetime of a device. The lifetime of photon in a resonator is described with
a term called the quality (Q) factor
1
, which accounts for the performance of the optical resonators
in a quantitative way. The Q is determined by the optical loss mechanisms with both intrinsic and
extrinsic factors based on the Equation 2-1.
18
.
1
𝑄 𝑡𝑜𝑡𝑎𝑙 =
1
𝑄 𝑅𝑎𝑑 +
1
𝑄 𝑆𝑆
+
1
𝑄 𝑀𝑎𝑡 +
1
𝑄 𝐶𝑜𝑛𝑡 +
1
𝑄 𝐶𝑜𝑢𝑝𝑙 Equation 2-1.
where QRad is the radiation loss or bending loss due to the curvature of the resonator, QSS
is the surface scattering loss because of defects or surface roughness, QMat is the material
absorption loss caused by the material from which a resonator made, QCont is the contamination
loss by contamination of a device, and QCoupl is the coupling loss due to coupling light into the
cavity.
It is also important to note that we need to distinguish between the loaded and intrinsic Q
factors of the resonator. The QTotal is the same as the loaded Q (QLoaded) in the Equation 2-2., which
is composed of the intrinsic Q (QInt) and the extrinsic Q (QExt) factor
53
.
20
1
𝑄 𝐿𝑜𝑎𝑑𝑒𝑑 =
1
𝑄 𝐼𝑛𝑡 +
1
𝑄 𝐸𝑥𝑡 Equation 2-2.
The first four variables (QRad, QSS, QMat, and QCont) in the Equation 2-1. are the intrinsic
loss (QInt) from the resonator, which is innate to the resonator itself, whereas the last term (QCoupl)
is extrinsic loss to the cavity (QExt) due to coupling light into the resonators. Even though a tapered
optical fiber is one of the best coupling methods with high coupling efficiency
54
, it still causes the
extrinsic loss while coupling light into a device. The Q Loaded can be obtained experimentally from
a transmission spectrum fitted to a Lorentzian based on the Equation 2-3.
55
Q
𝐿𝑜𝑎𝑑𝑒𝑑 =
𝜆 ∆𝜆
Equation 2-3.
, where λ is a resonant wavelength of a resonator, ∆λ is the full-width at half maximum
value of the resonant peak. Based on the Equation 2-2., the QLoaded has a linear relationship with
respect to the coupling percentage. In other words, as the coupling percentage decreases, coupling
loss decreases causing the QLoaded increases. Therefore, by plotting the QLoaded as a function of the
coupling percentage and fitting linearly, Q Int can be obtained at the y-intercept point, where the
extrinsic or coupling loss becomes zero. Figure 2-4 (a) shows one of the representative transmission
spectra fitted to Lorentzian with the QLoaded and the resonant wavelength, and Figure 2-4 (b)
contains numbers of QLoaded values calculated from the transmission spectra with respect to the
coupling percentage. The coupling percentage is obtained with the depth of the fitted peak at the
resonant wavelength. Again, the QInt is the y-intercept value of the linearly fitted line from the
QLoaded versus the coupling percentage data
56
.
21
Figure 2-4. (a) One of the representative transmission spectra showing resonant
wavelengths with calculated Q factors of each peaks. The transmission spectrum is
normalized with the taper scanned transmission. (b) The Q Loaded data as a function of
coupling percentage. The QInt is corresponding to the y-intercept of the linearly fitted data.
Material absorption loss (QMat)
Among the various intrinsic loss mechanism, the material absorption loss is especially
important in silica hybrid resonators, and the QMat can be expressed based on the Equation 2-4.
57,58
𝑄 𝑀𝑎𝑡 =
2 𝜋 𝑛 𝑒𝑓𝑓 𝛼 𝑒𝑓𝑓 𝜆 Equation 2-4.
, where neff is the effective refractive index, λ is the resonant wavelength, αeff is the effective
material absorption loss. The neff is the net refractive index experienced by the optical field inside
the resonators. The material loss is an innate property of the material from which a resonator is
made. Typically, the material loss is a key factor limiting the overall Q factor of the WGM
resonator. Based on the Equation 2-4., the QMat depends on the absorption property of materials. In
22
other words, the material loss can be minimized by fabricating resonators with low loss materials
(such as silica), whereas the material loss can increase with dopants or surface chemistry of silica
hybrid resonators.
Circulating power (PCirc)
Due to the high Q factor, or long photon lifetime, the WGM resonator enables substantially
enhanced buildup power, or circulating power, inside cavity with the Equation 2-5.
59
𝑃 𝐶𝑖𝑟𝑐 =
𝜆 𝑄 𝐼𝑛𝑡 𝜋 2
𝑛 𝑅
𝐾 ( 1 + 𝐾 )
2
𝑃 𝑖𝑛𝑝𝑢𝑡 Equation 2-5.
, where QInt is corresponded to the intrinsic Q factor, and K is defined by the ratio of
intrinsic photon lifetime to photon life time by coupling (K = Q Int/QCoupl). Based on the Equation
2-5., the buildup power is directly proportional to the QInt of the devices indicating that resonators
with the ultra-high Q factor act as an amplifier enhancing the circulating power inside the cavities
substantially. For example, in case of a resonator with the QInt of 10
7
, the circulating power can be
reached more than 100 W with only 1 mW of input power.
23
Mode volume (Vm)
While the Q factor describes the time-based photon lifetime within the optical
microcavities, the mode volume (Vm) is defined by the spatial confinement of optical filed
distribution inside the resonators
60
. Commonly, the definition of the Vm is based on the energy
density of the optical modes existing in the optical resonators and it is normally described as the
Equation 2-6.
𝑉 𝑚 =
∭ 𝜖 ( 𝑟 ) 𝐸 ( 𝑟 )
2
𝑑 3
𝑟
|𝜖 ( 𝑟 ) 𝐸 𝑀𝑎𝑥 |
2
Equation 2-6.
, where Vm is the optical mode volume, ϵ(r) = n
2
(r) is the square of the refractive index,
and E(r) represent the applied optical field. The Vm can be obtained with Equation 2-6. by running
the COMSOL Multiphysics finite element method (FEM) simulation
61
. COMSOL simulation
results will be shown at each project section according to the different experimental conditions.
Circulating intensity (ICirc)
The Vm indicates how large the optical mode is and how well-confined it is inside the
resonator. In other words, the smaller optical Vm implies that optical energy is tightly and densely
confined to physical volumes on the order of couple of hundreds cubic micrometers. The small Vm
with the high circulating power of WGM resonators results in large energy density, or high
circulating intensity (ICirc) in a resonator. The ICirc is calculated by dividing the PCirc with the Vm
based on the Equation 2-7.
24
𝐼 𝐶𝑖𝑟𝑐 =
𝑃 𝐶𝑖𝑟𝑐 𝑉 𝑚 Equation 2-7.
With the large energy density in a cavity, or ICirc, WGM resonator is a most promising
platform to create nonlinear optical phenomena, which requires high amount of input power to
generate them.
Free Spectra Range (FSR)
The free spectra range (FSR) of a resonator is the spacing of the wavelength (or frequency)
between two successive fundamental mode peaks
62
. The modes which determine the FSR are the
successive modes that have the same transverse mode, either transverse electric (TE) or transverse
magnetic (TM) mode.
∆𝜐 =
𝑐 2 𝜋 𝑛 𝑅
∆𝜆 =
𝜆 2
2 𝜋 𝑛 𝑅
Equation 2-8.
, where λ is the resonant wavelength inside the microcavity, n represents the refractive
index, and R is the radius of the resonator. The first equation is based on the frequency domain,
while the second equation is in wavelength domain. The FSR of the devices at certain operating
wavelength can be easily anticipated based on the Equation 2-8., and the calculated FSR can be
25
compare with the experimentally obtained FSR. Figure 2-5 contains one of the representative broad-
scan spectra tested with tunable 765 nm laser to observe the FSR experimentally.
Figure 2-5. Representative broad-scan spectrum showing the FSR of the device. The
diameter of the device is approximately 50 μm, and it is tested with 765 nm tunable laser.
Experimentally observed FSR of the device (2.63 nm or 1.32 THz) is almost the same as
the FSR calculated (2.56 nm).
26
2. 1. 3. Microtoroid Fabrication
Silica toroidal micro-resonators are fabricated by the same procedure as reported
previously
19
, which is composed of the three main processes; photolithography to define silica
circles pattern on silicon wafers (Figure 2-6 (a)), XeF2 etching to remove silicon isotropically in
order to obtain silica disk onto silicon pillar (Figure 2-6 (b)), and CO2 laser reflow to produce
atomically smooth silica toroids (Figure 2-6 (c)).
These three steps are elucidated more in detail at the following sections. Intrinsic silicon
wafers with a 2 μm layer of thermal grown silicon oxide (WRS Materials) are cleaned with using
acetone, methanol, and isopropanol, then dried on a hot plate at 120 °C for 2 minutes to remove
any possible residual solvent. Hexamethyldisilazane (HMDS) is applied to the wafers to improve
adhesion between the photoresist and the silica surface. The S1813 photoresist is spin-coated onto
the wafer with 500 rpm for 5 seconds and 3000 rpm for 45 seconds, followed by soft bake at 95 °C
for 2 minutes in order to harden the photoresist. UV light is exposed through the circles-patterned
mask with 80 mJ/cm
2
. The disk pattern has various disk sizes, and each project utilized the different
size for their purpose, which will be discussed in each chapter. After the pattern is transferred onto
silica, the wafer is developed with the MF-321 for 1 min, followed by the hard bake at 120 °C for
2 minutes for more hardening of the photoresist. The residual silica outside of the disk pattern is
removed by buffered oxide etchant (BOE) to define the silica disk pattern on silicon wafer. It takes
approximately 20 mins to etch the 2 μm thickness of the thermally grown silica. The
photolithography process is completed by removing the remained photoresist completely with
acetone. Once the photolithography steps are finished, the silicon underneath the silica circle
pattern is etched isotropically using XeF2 gas etcher
63–65
, producing silica micro-disks which are
27
elevated above the silicon substrate with pillars. The fabrication step is accomplished by reflowing
the as prepared silica microdisks using CO2 laser operating at 10.6 μm. Silica has high absorption
at the wavelength of CO2 laser
66
, causing silica disk to form toroid with atomically smooth surface.
Figure 2-6 (d) shows the final silica toroid taken by the scanning electron microscopy (SEM).
Figure 2-6. Schematic images of the fabrication procedures for silica toroidal
microcavities (a) define silica circle pattern on top of silicon wafer by photolithograph
and BOE etching, (b) XeF2 etching to produce silica disk supported by silicon pillar, and
(c) CO2 laser reflow to create atomically smooth surface silica toroidal microresonator.
(d) SEM (scanning electron microscope) image of the finalized silica microtoroidal
resonator with diameter of approximately 50 μm.
28
2. 2. Experimental Testing Set-up
2. 2. 1. Optical Tapered Fiber Pulling
As we discussed in the previous section regarding intrinsic and extrinsic Q factors, the
intrinsic Q factor is determined by the inherent property of a resonator itself, and the extrinsic Q
factor has a direct correlation with the coupling condition, which is affected by the properties of
the waveguide or tapered optical fiber. In other words, it is particularly important to fabricate a
single mode and low optical loss tapered optical fiber with high coupling efficiency to resonators.
The single mode tapered optical fiber is essential to excite the fundamental mode of a resonator
out of many higher order modes. Single-mode optical fibers are fabricated from different types of
optical fibers, depending on the wavelength being used (765 nm = F-SE-OPT, 1550 nm = F-SMF-
28, Newport). The single-mode and low loss tapered optical fiber indicates the optical loss by
coupling (QCoupl) is minimized, maximizing QTot, as was discussed in the previous section. The
tapered optical fiber has demonstrated the highest coupling efficiency (~99%)
67
and low loss
coupling to WGM optical resonators compared with other coupling methods, such as prism and
free-space coupling.
29
Figure 2-7. A Picture of optical fiber pulling set-up with fiber spool, optical fiber stage,
laser, photodetector connected to oscilloscope, microscope, hydrogen torch, and nano-
stage controller.
First step to pull an optical fiber waveguide is to remove approximately 1-inch length of
polymer cladding layer from a fiber with a fiber stripper, followed by placing the optical fiber on
the fiber holder. The laser is connected to the spool of the optical fiber. The end of the optical fiber
is also stripped and cleaved to make a connection with a photodetector to observe the transmission
property of the input laser via oscilloscope. The optical fiber is tapered by slowly pulling the fiber
while heating it by hydrogen torch with a flow rate of 5 mL/min. The pulling process is observed
in real time with an optical microscope placed adjacent to the fiber. While pulling a taper, the laser
30
signal at the oscilloscope shows a sinusoidal shape indicating multi-mode inside the fiber. Once
the fiber becomes a single mode, the signal at the oscilloscope becomes straight. The process is
completed by stopping both pulling and heating at the same time when the optical fiber becomes
a single mode. Figure 2-8 shows an optical microscope image of a tapered optical fiber pulled in
this manner.
Figure 2-8. An optical microscope image of tapered optical fiber waveguide. The
variation in color in the fiber is the diffraction of light from the thin tapered optical fiber.
31
2. 2. 2. Resonator testing set-up
The Q factors of the devices are characterized with a tunable narrow linewidth laser
centered at either 765 or 1550 nm (Velocity series, Newport) by coupling light into the microcavity
using a tapered optical fiber waveguide, as shown at Figure 2-9 and Figure 2-10. The tapered optical
fibers are obtained by slowly pulling a single mode optical fiber for each wavelength (765 nm =
F-SE-OPT, 1550 nm = F-SMF-28, Newport) while it is heated with a hydrogen torch as we
discussed in the previous section, followed by aligning the waveguide to the toroid with 3-axis
nano-positioning stage. The output from the optical fiber is sent to a 10:90 splitter, which is
connected to the photodetector and the optical spectrum analyzer (OSA, YOKOGAWA
AQ6370C). The photodetector is connected to the high-speed digitizer/oscilloscope. The resonant
wavelength is determined by scanning across a series of wavelengths. The resonant spectrum is fit
to a Lorentzian, and the cavity Q of the device is determined with the equation of Q = λ/Δλ, where
λ is the resonant wavelength of the device and Δλ is the full-width-half-maximum of the peak. All
data and images are recorded with a computer integrated with PCI GPIB, function generator, and
oscilloscope. A general laser communication port (PCI GPIB) and a function generator is
connected to a tunable laser, and they are used to finely tune a wavelength and find a resonant
wavelength of devices. An oscilloscope collects the transmission property data from a
photodetector in order to calculate the Q factor of a device.
32
Figure 2-9. Schematic image of testing setup showing a tunable narrow linewidth laser,
oscilloscope, optical spectra analyzer (OSA), and a computer to control the tunable laser
and collect data from photodetector.
The OSA is utilized in order to detect the emitted light from toroid that is coupled back
into the optical fiber. This instrument allows nonlinear optical processes in a resonator to be
identified. In addition to the OSA, the optical spectrograph (Andor SR-163 spectrograph) could be
located adjacent to the device in order to detect the emission in between 400 ~ 1100 nm from the
cavity. Either or both OSA and spectrograph could be utilized for the purpose of the project and
the wavelength that we want to detect.
33
Figure 2-10. Schematic image of testing set-up with a laser, a tapered optical fiber, a silica
toroid, a splitter, a photodetector connected to an oscilloscope, optical spectrum analyzer,
and spectroscopy. Inset is the top-view optical microscope image showing a silica toroid
with a tapered optical fiber.
34
2. 3. Nonlinear Optics in WGM Resonators
2. 3. 1. Nonlinear Optics
Nonlinear optics is a research area studying about the optical phenomena that happens as
a result of the modification of the optical properties of a material due to the presence of high
intensity optical fields
68
. Nonlinear optical phenomena are called “nonlinear”, because a new
optical property occurs nonlinearly with respect to the strength of an applied optical field. Optical
nonlinearity is determined by the dipole moment per unit volume, which is the polarization P(t),
and it depends on the intensity of E(t) of an applied optical field, based on the Equation 2-9.
𝑃 ( 𝑡 ) = 𝜖 0
[𝜒 ( 1)
𝐸 ( 𝑡 )+ 𝜒 ( 2)
𝐸 2
( 𝑡 )+ 𝜒 ( 3)
𝐸 3
( 𝑡 ) ] Equation 2-9.
At the above equation, ϵo is the permittivity of free space, and χ
(1)
is known as the linear
susceptibility, which enables describing all the linear optical properties. The χ
(2)
and χ
(3)
are
corresponding to the second and the third order non-linear optical susceptibility, respectively
68
.
The origin of nonlinear susceptibility is comprehensively introduced in the reference. Additionally,
the nonlinear susceptibility is dependent on the frequency of the applied electric field.
𝑃 ( 𝑡 ) = 𝑃 ( 1)
( 𝑡 )+ 𝑃 ( 2)
( 𝑡 )+ 𝑃 ( 3)
( 𝑡 )
Equation 2-10.
35
In the Equation 2-10., the P
(2)
(t) and P
(3)
(t) are known as the second and third order nonlinear
polarization, which determine each nonlinear optical property. In describing nonlinear optical
phenomena, the polarization plays a key role in the sense that time-varying polarization leads to
generate a new electromagnetic field. It is important to note that the second order nonlinear
interactions can only appear in non-centrosymmetric crystal materials
69–71
, whereas the third order
nonlinear optical properties can be observed in both centrosymmetric and non-centrosymmetric
crystal materials. For example, crystal structure of silica is an inversion symmetry so that the
highest order optical susceptibility in silica is the third order
33,35,70
. For an applied electric field,
E(t) with a certain optical frequency, the nonlinear terms could cross-link different frequency
components, causing frequency conversions. In other words, the most significant effect in
nonlinear optics is the wavelength (or frequency) conversions. Among various wavelength
conversion processes, we will focus on two nonlinear optical processes (stimulated Raman
scattering (SRS)
59,72
and four-wave mixing (FWM)
48,52
), which have been demonstrated in the
silica WGM resonators. FWM is a parametric nonlinear optical process, which contains no energy
or momentum exchange between light of applied electric fields and the material, enabling the
material to stay in the same condition as the initial state after the conversion. On the other hand,
SRS is not the parametric processes indicating that the incident photon is excited the vibrational
state through the virtual state generating of the optical phonon. Both FWM and SRS are the third
order nonlinear optical phenomena in silica WGM resonators.
Even though various nonlinear optical properties have been demonstrated with bare silica
WGM resonators with the ultra-high Q factor, the performance of nonlinear optical properties in
the resonators are typically limited by the intrinsic material properties of silica itself, such as the
Raman gain coefficient or the third order nonlinear susceptibility. Silica has relatively low Raman
36
gain coefficient (0.66 x 10
-13
m/W at 1550 nm,
72
) and nonlinear refractive index (2.2 x 10
-20
m
2
/W,
48
), which determines the third order nonlinear susceptibility, compared with other
crystalline materials.
37
2. 3. 2. Stimulated Raman scattering (SRS) and stimulated anti-
Stoke Raman scattering (SARS)
The stimulated optical scattering is one of the nonlinear optical effects where the vibration
within the material at some intrinsic eigen-frequencies interact with the incident light
73
. In general,
the scattered light contains frequencies different from those of the excitation source depending on
the materials, meaning an inelastic scattering. Those new components shifted to lower frequencies,
or higher wavelengths, are called Stokes scattering, and those shifted to higher frequencies, or
lower wavelengths are called anti-Stokes scattering. (Figure 2-11)
The energy level diagram in Figure 2-11 (a) accounts for the properties of both Stimulated
Raman (Stokes) scattering (SRS) and stimulated anti-Stokes Raman scattering (SARS). SRS
entails a transition from the ground state to the vibrational state by means of the 1
st
virtual
intermediate level, which is an excited state. SARS consists of a transition from the vibrational
state to the ground state with the 2
nd
vibrational state serving as the intermediate level. In other
words, both SRS and SARS are dependent on the vibrational frequency of a gain material and the
frequency of incident light based on the inset equations. The SARS are typically much weaker
(several orders of magnitude) than SRS because, the population of the vibration state is smaller
than the population in the ground state by the Boltzmann factor, exp(-ħwng/kT), in thermal
equilibrium
74
.
38
Figure 2-11. (a) Energy level diagram of red-shifted stimulated Raman scattering (SRS)
and blue-shifted stimulated anti-Stokes Raman scattering (SARS) with the vibrational
state of the gain medium. υPump, υSRS, υSARS, and υVibration are corresponding to the
frequencies of pump, SRS, SARS, and vibrational optical phonon, respectively. (b) SRS
and SARS spectrum with pump wavelength with the shift of the vibrational frequency of
optical phonon of a medium.
SRS and SARS were first generated in a microdroplet made out of CCl4, ethanol, or water
75
.
The first-order SARS intensity is ~10
4
times lower than the first-order SRS intensity. Research in
generating SRS and SARS moved toward silica fibers and are presently replaced by whispering
gallery mode (WGM) resonators
44,76
. In silica microsphere resonator having multiple modes close
to each other
72
, multiple Raman peaks were observed with the pump power higher than the
threshold due to the wide Raman gain bandwidth of silica (12~14 THz in frequency, or 400 ~ 460
cm
-1
in wavenumber as shown at Figure 2-12
73
) . In contrast, single mode Raman laser is observed
in a silica mircrotoroid
10,59
.
39
Figure 2-12. Normalized Raman gain spectrum of silica with the respect to the frequency
offset (THz). The Raman gain of silica is high over the range of 12 ~ 15 THz.
SRS process requires the conservation of energy and momentum between pump photon,
Stokes photon, and phonon. The conservation indicates that the phase-matching condition should
be satisfied to generate SRS. However, because SRS is pure gain process and the optical phonon
has a flat dispersion over the range of wavelength, the phase-matching condition is automatically
satisfied during the SRS process
76
. Therefore, the frequency shift of light is only dependent on the
vibration frequency of phonon of a gain medium. On the other hand, SARS does require phase
matching to be generated efficiently, and its amplitude depends on the interaction between the
pump and Stokes Raman signals based on the Equation 2-11.
𝐼 𝑆𝐴𝑅𝑆
∝ |𝜒 ( 3)
|
2
× 𝐼 𝑃𝑢𝑚𝑝 2
× 𝐼 𝑆𝑅𝑆 × 𝐿 2
×
sin( ∆𝑘 × 𝐿 )
2
( ∆𝑘 × 𝐿 )
2
Equation 2-11.
40
, where Ipump, ISRS, and ISARS are the intensity of pump, SRS, and SARS, respectively. χ
(3)
corresponds to the third-order nonlinear susceptibility of a medium, and L is the interaction length.
∆k (= 2 kpump - kSRS – kSARS) indicates the phase mismatch, where kpump, kSRS, and kSARS are the
propagation vectors for the pump, SRS, and SARS waves, respectively. ∆k should be zero in order
to be phase-matched for efficient generation of SARS
41
2. 3. 3. Four-wave mixing (FWM)
Four-wave mixing (FWM) is one of the third order nonlinear optical processes in which
two pump photons are converted into a red-shifted signal and a blue-shifted idler peaks with a
degenerate process, as shown at Figure 2-13
48
.
Figure 2-13. (a) Energy level diagram of the FWM process. The FWM is a nonlinear
optical process where one idler (vIdler) and one signal photon (vSignal) are generated from
two degenerate pump photons (vPump). (b) FWM spectrum as a function of wavelength.
Kerr-nonlinearity induced FWM has been reported in silica WGM resonators, and with
high pump power, cascaded FWM peaks are created, generating a frequency comb. To generate
FWM, stringent phase-matching condition is required; that is, both energy and momentum must
be conserved during the FWM process. In addition, both SRS and FWM are the third order
nonlinear optical phenomena in silica, so they are competing with each other in a silica
resonator
77,78
. SRS is the dominant nonlinear optical effect in silica over FWM because it does not
42
require the phase-matching condition as we discussed in the previous section while the FWM does.
Therefore, specific phase matching condition is essential for FMW to be prior nonlinear effect
over SRS. In a WGM resonator, momentum conservation is automatically satisfied because signal
and idler angular mode number are symmetric to the pump mode (lsiganl or idler = lpump ± N). In
contrast, energy conservation (2 𝑣 pump = 𝑣 signal + 𝑣 idler) is not satisfied due to the material and cavity
dispersion.
Δ𝑣 = 2 𝑣 𝑝𝑢𝑚𝑝 − 𝑣 𝑠𝑖𝑔𝑛𝑎𝑙 − 𝑣 𝑖𝑑𝑙𝑒𝑟 Equation 2-12.
The parametric gain is a function of the detuning frequency (Δ𝑣 ) based on the Equation
2-12., and the Δ 𝑣 should be less than the parametric gain bandwidth ( Ω ,
0 < Δ𝑣 < Ω ) (Equation 2-13.).
Ω = 4
𝑣 𝑛 2
𝑛 𝐴 𝑒𝑓𝑓 𝑃 𝐶𝑖𝑟𝑐
Equation 2-13.
, where n2 is the Kerr nonlinearity, Aeff is corresponding to the effective mode area, and
PCirc indicates the circulating power in a resonator. In the Equation 2-13., the Ω is inverse
proportional to the Aeff, that is, energy conservation for the FWM can be satisfied with minimizing
the Aeff, which gives the large Ω value. A reduction of the Aeff can be achieved the controlling
geometrical parameters of the toroidal resonator. This indicates that intelligently designing the
geometry of a toroidal resonator, we can minimize the Aeff bringing about the phase-matching
condition for the FWM generation.
43
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54
Chapter 3. Enhanced stimulated Raman scattering
(SRS) and stimulated anti-Stokes Raman
scattering (SARS) in metal doped silica solgel
coated silica hybrid microcavities
3. 1. Introduction
Spontaneous Raman scattering was first discovered by C.V. Raman in 1928
1
. To observe
Raman emission, a material is pumped by a beam of light, and the spectrum of the light scattered
by the material is observed. In general, the scattered light contains peaks at frequencies different
from those of the pump source, depending on the material being examined. New frequency peaks
in the spectra that are shifted to lower frequencies are called Stokes Raman peaks, and those shifted
to higher frequencies are called anti-Stokes Raman peaks
2–4
.
A WGM resonator is an optical cavity that can confine light inside the cavity with long
photon lifetime or high quality (Q) factor
5
. Due to the high Q factor within a small optical mode
volume, the resonator can generate the high circulating optical intensity with low input power,
which is enough to cause emission that is generated by third order nonlinear optical processes,
such as SRS and SARS
6–10
. Additionally, because of the high Q of an optical cavity, the threshold
power, which is minimum power to generate nonlinear optical phenomena, decreases substantially
to sub-mW
11–13
.
55
However, the efficiency of emission of SRS and SARS are limited by the gain material, in
this case silica. The silica has low Raman gain coefficient (gR = 0.54 x 10
-13
m/W at 800 nm, gR =
0.66 x 10
-13
m/W at 1550 nm
11
), resulting in moderate SRS and SARS efficiencies. In this project,
we introduce the dopant materials into silica solgel matrix in order to augment the intrinsic Raman
gain of silica
14,15
. The doping material makes silica become more polarized, increasing the Raman
gain. With the enhanced Raman gain, we are able to demonstrate the enhanced emission efficiency
of both SRS and SARS from the silica hybrid devices.
56
3. 2. Background and motivation
In the present work, we demonstrate that the presence of a metal dopant in a silica solgel
can enhance the Raman gain coefficient of the silica solgel, resulting in improved SRS and SARS
emission efficiencies. Either Zirconium (Zr)
15
or Titanium (Ti)
14
are selected as the doping
material into silica solgel. Metal-doped silica solgels are synthesized with an acid-catalyzed
hydrolysis and condensation reaction
16–18
. The solgels are then coated on the bare silica toroids,
making silica hybrid microresonators. Due to the dopants or impurities in the coating layer,
physical properties of the silica in this layer are modified, and the hybrid devices are compared
with both the 1) uncoated devices and 2) coated devices with undoped coatings as controls. There
are many parameters that are tuned with the metal dopants, such as the Q factor of devices, optical
mode volumes, and the SRS threshold. Before we discuss the experimental results, we will
investigate the how the dopants can have an impact on the microcavity behaviors by revisiting the
equations governing this system.
First, the Q factors of the hybrid devices can be affected by the material absorption of the
dopant
19
. The material absorption loss of a resonator describes the absorption of light due to the
material the resonator is made of. The material absorption loss is defined by Equation 2-4. as we
discussed.
Another factor that is affected by the metal-doped coating layer is the optical mode volume
(Vm). Vm can be calculated based on the Equation 2-6.
5
by conducting COMSOL Multiphysics finite
element method (FEM) simulations
20,21
. The dopant will change the index of the silica solgel to be
different from that of the silica resonator, altering the mode location and shape in silica hybrid
resonators
17,18
. Specifically, since the coating layer has a higher index than the resonator, the
57
optical mode is shifted toward the coating, and a higher fraction of the mode volume is confined
inside this outer layer, resulting in a decrease in Vm. Vm has a relationship with the SRS threshold,
which we will discuss.
Lastly, the metal-doped coating layer has an effect on the SRS threshold. The SRS
threshold (PThres) in an optical microcavity is defined by the equations below,
11
P
Thres
= β ×
n
Eff
2
V
m
λ
P
λ
R
g
R
×
1
( Q
0
)
2
Equation 3-1.
β = C( Ґ)× π
2
×
( 1 + K)
2
K
Equation 3-2.
, where β is the constant correlated with coupling parameters, and C(Ґ) is a value between
1 and 2, which describes the reduction in circulating power due to excitation of a counter-
propagating mode. K corresponds to the coupling parameters, nEff is the effective refractive index,
Vm is the optical mode volume, and λP and λR are the pump and Raman wavelength, respectively.
Q0 is the intrinsic Q factor of the device, and gR designates the Raman gain coefficient of the
material. Therefore, based on this equation, the Raman lasing threshold is proportional to nEff and
VM, and inversely proportional to both gR and Q0
2
. The metal-doped high index coating has an
effect on all the parameters above. In other words, the Raman lasing threshold can be modified by
introducing and changing the dopant.
58
3. 3. Experimental Method
3. 3. 1. Fabrication of metal doped silica solgel coated toroids
- Synthesis of metal-doped silica solgel
The metal-doped silica solgels are synthesized with the acid-catalyzed hydrolysis
condensation reaction (Figure 3-1)
18
. Either Zirconium (Zr) or Titanium (Ti) were selected as a
metal dopant, because they form tetrahedral oxygen bonds like silicon does, allowing them to make
a stable matrix with silica solgel
14,15,22–24
. Methyltriethoxysilane (MTES, Sigma-Aldrich, 98%),
which is a silica precursor, is added to ethanol (Decon Laboratories, KOPTEC 200 Proof) and
stirred for 5 min, followed by the addition of hydrochloric acid (HCl, EMD, 38.0%) for the
hydrolysis reaction. After 20 min, a variable concentration of either Zr propoxide (Sigma-Aldrich,
70 wt % solution in 1-propanol) or Ti butoxide (Sigma-Aldrich) is added to the solution, and the
reaction is allowed to progress for another 2 hours. During the hydrolysis reaction, metal alkoxide
is converted into metal hydroxide, making a sol, which is defined as a stable dispersion of colloidal
particles in a solution. After the hydrolysis is complete, the solution is aged at room temperature
for 24 hours, filtered through a syringe filter (0.45-micron), and then stored in a refrigerator (∼5 °C)
until it is used.
59
Figure 3-1. Schematic synthetic procedure for producing a metal-doped silica solgel,
describing (a) acid-catalyzed hydrolysis and (b) condensation reaction.
- Device fabrication
A silica toroid with a 53 μm major diameter is fabricated using the same procedure as
described in Chapter 2
25
. This diameter is chosen to maximize the circulating intensity, thereby,
decreasing the Raman lasing threshold.
The silica toroids are then treated with an O2 plasma to make better contact with solgel
coating and immediately coated with the metal-doped solgel, by spin-coating at 7000 rpm for 60
seconds. The samples are dried at 75 °C for 5 minutes to evaporate the residual ethanol solvent in
the solgel coating. Finally, the samples are annealed at 1000 °C for 1 hour in a tube furnace for the
condensation reaction
16
. During the condensation reaction, metal hydroxide reacts, making sol
state, which is a metal-oxygen-metal inorganic network (Figure 3-1 (b)).
60
Figure 3-2. Metal-doped silica solgel coated hybrid toroids. Scanning electron
microscope (SEM) image of (a) metal-doped silica solgel coated hybrid toroid. (b)
schematic image of a hybrid silica toroid showing a bare silica toroid coated with Metal-
doped silica solgel. Major (D) and minor (d) diameter of the hybrid toroid are indicated.
61
3. 3. 2. Ellipsometry
Ellipsometry is used to measure both the index of refraction and the thickness of the doped
solgel layers on flat silicon substrates. Silicon wafers coated with the various solgel solutions are
used as controls. The film thicknesses are constant (~400 nm) over the all samples. The refractive
index of the coating increases as the concentrations of metal dopants in the solgel increases, as
expected: the index increase is mostly due to the higher refractive index of Ti and Zr than that of
silica
14,16
. Both the thickness of the coating and the refractive index are essential parameters for
doing a COMSOL simulation, which will be discussed later.
62
3. 4. Results: Material characterization
3. 4. 1. Energy-Dispersive X-Ray Spectroscopy (EDS)
The presence of metal dopants (either Zr or Ti) is verified using SEM-EDS measurements
as shown at Figure 3-3. Notably, these measurements were performed on devices with either Zr-
doped or Ti-doped thin film coatings, not control wafers. In addition to the peaks originating from
the silicon (Si at 1.740 and 3.49 keV) and oxygen (O at 0.523 keV) intrinsic to the Si and SiO 2
26–
28
, each spectrum contains peaks corresponding to either zirconium (Zr at 2.042 keV)
29
or titanium
(Ti at 4.510 keV)
30
. The relative intensity of each signal indicates the relative concentration of the
element. Considering the intensity of the Zr or Ti signals, the concentration of each element is
fairly low compared with Si and O, as expected.
Figure 3-3. EDS spectra from (a) Zr- and (b) Ti-doped silica hybrid devices. The silicon
(purple) has peaks at 1.740 and 3.49 keV. The oxygen (green) has a peak at 0.523 keV.
The zirconium (red) and titanium (blue) have peaks at 2.042 and 4.510 keV, respectively.
Each peak is fitted to Gaussian.
63
3. 4. 2. Raman Spectrograph
In order to understand the effect of the metal dopants on the Raman gain of silica, a series
of control samples were fabricated. These samples consisted of thin films of metal-doped solgel
deposited on Si wafers. The Raman response of the different films is measured by a Reinshaw
InVia Raman microscope with attached spectrograph. The pump source for this microscope is a
532 nm laser focused through a 100× objective lens. Raman spectra are taken at room temperature
under ambient conditions. As shown at Figure 3-5 (a), silica generally exhibits two different Raman
response peaks at 500 cm
-1
and 1000 cm
-1
, indicating the SiO4 bending modes (A500, Figure 3-4
(a)) and stretching modes (A1000, Figure 3-4 (b)), respectively
31–34
. A schematic image of each
mode is described at Figure 3-4. The Raman gain of a material is related to the ratio of A500 to
A1000 (A500/A1000), which indicates the degree of polarization of silica (Ip)
35
.
Figure 3-4. Schematic images of SiO4 (a) bending and (b) stretching modes, which are
indicated by the areas of peak at 500 and 1000 cm
-1
, respectively, measured by a
spectrograph
36
.
64
Figure 3-5. (a) Spectrum of Zr 10 mol% silica sol-gel coated onto the bare silicon wafer.
Inset is the schematic illustration of Zr 10 mol% silica sol-gel matrix. Similar spectra
were obtained for other mol%. (b) The degree of polarization (Ip) values, which is the
ratio of the area under the peaks at 500 cm
-1
and 1000 cm
-1
, with respect to the Zr
concentrations in silica sol-gel.
As the dopant concentrations in the solgel increased from 0 to 10 mol% with respect to the
silica, Ip values of solgel also increased from 2.96 to 4.87 for Zr dopants
15
(Figure 3-5 (b)) and 3.55
to 5.26 for Ti dopants
14
. It is important to note that, especially in silica, stimulated Raman
scattering is due vibrations of phonon in silica. Therefore, the metal-concentration dependent
Raman gain value indicates that metal dopants could have a huge effect on the SRS and SARS
behaviors.
65
3. 5. Application 1: Enhanced stimulated Raman
scattering with Zr-doped silica hybrid microresonators
3. 5. 1. COMSOL Multiphysics Simulations
COMSOL Multiphysics finite element method (FEM) simulations are performed to
identify the effect of Zr dopant on the optical mode as described in the previous section with 765
nm pump laser
20
. As the Zr concentration in the solgel increases, the refractive indices of the
coating (ncoating) increase uniformly (Table 3-1). The changes in index of the coating have a direct
correlation with the mode behavior and the mode volume as shown in Figure 3-6, which, in turn,
influences the SRS threshold.
Figure 3-6 (a) shows the simulation results of the five different Zr concentrations used in
the present study. Each image is a cross-sectional view of the coated toroidal resonator. Figure 3-6
(b) contains both the total optical mode volume (Vm) and the percentage of Vm inside the coating
for each Zr concentration. It is clearly evident that the high refractive index of the Zr-doped coating
leads to a shift of the optical mode toward the coating, resulting in the decrease of the total optical
mode volume.
66
Figure 3-6. COMSOL Multiphysics finite element method simulation results. (a)
Simulation results of the optical field distribution in the coated toroidal micro-cavity with
the different mol% of Zr in the sol-gel indicated. (b) Total optical mode volume and the
percentage of the mode volume inside the coating with respect to the Zr concentrations
in the silica sol-gel.
67
3. 5. 2. Q factors of Zr-doped devices
The loaded Q of the cavity is determined by measuring the transmission spectrum at a
resonant wavelength and fitting it to a Lorentzian, as discussed previously
37
. Figure 3-7 (a) is the
representative transmission spectrum of the Zr 10 mol% coated toroid, and multiple spectra were
obtained for the other mol% devices measured with a tunable 765 nm laser. All data are plotted in
Figure 3-7 (b) and fit to an expression of the form y=ax
b
. As previously discussed, Q should scale
inversely with metal concentration, and therefore, b should equal -1. From the unweighted fit, b is
-0.86, which is in good agreement with the predicted value of -1. The slight difference is most
likely due to coupling losses, as the Q plotted is the loaded Q factor
19
.
Figure 3-7. (a) The normalized transmission spectra for Zr 10 mol% silica sol-gel coated
toroid. And (b) Loaded Q values with respect to the Zr concentrations with the coated
devices.
68
3. 5. 3. Raman Lasing Behavior
The first order stimulated Raman scattering from the Zr 10 mol% coated toroids are
measured at 793.35 nm via both the optical spectrograph, which collects light that radiates out of
the resonator, and the OSA (Figure 3-8 (a) and (b)), which collects light that couples back into the
taper and propagates to the end of the fiber. First order Raman emissions from other devices with
different Zr mol% were also observed at similar wavelengths
38
. Additionally, cascaded Raman
emission was observed at high input powers as shown at Figure 3-9
39–41
.
Figure 3-8. (a) Optical spectrograph and (b) Optical spectrum analyzer (OSA) spectra of
Zr 10 mol% doped silica sol-gel coated toroid. Raman peaks are observed at 793.35 nm
from the both measurements.
69
Figure 3-9. (a) Optical spectrograph and (b) OSA data obtained with Zr 10 mol% sol-gel
coated toroids. The graphs have cascaded Raman peaks. Similar results are obtained for
the other mol %.
The Raman lasing thresholds of each device are identified by measuring the emission
intensity from the spectrograph (Figure 3-9 (a)) and the output Raman emission power via OSA
(Figure 3-9 (b) as a function of the coupled power into the coated devices
11,12
. All Raman lasing
threshold values for all of the sol-gel coated devices are sub-mW (Table 2-1). The Zr-free solgel
coated device has a slightly higher Raman threshold value than the Zr containing solgel coated
devices (Figure 3-10 (a) and (b)).
70
Figure 3-10. (a) spectrograph data and (b) OSA data with three different concentrations
(0, 5, and 10 mol%), showing enhancement of lasing efficiency with Zr concentrations.
Figure 3-10 (a) and (b) highlight a unique aspect of the testing configuration. The cooled
detector on the spectrograph was significantly more responsive than the OSA. Therefore, it was
able to detect much intensities. Conversely, the spectrograph detector’s saturation level was 6.5E4
photon counts in one exposure. As a result of these two performance characteristics, the
spectrograph was unable to characterize the entire coupled power range for the highest Zr mol%.
However, as can be observed in Figure 3-10, the different spectrograph responses balanced out, and
the results measured using both methods are the same, demonstrating that the experimental
measurement technique did not affect the results. Given the variations in Q, Vm, and neff, directly
comparing the thresholds to determine the effect of the Zr concentration on lasing threshold is not
appropriate. An alternative strategy is to investigate if the increase in Raman gain measured using
the spectrograph is also observed in the OSA.
71
3. 5. 4. Raman Gain Coefficient and Raman Lasing Efficiency
The previously discussed Raman threshold power expression (Equation 3.1) can be re-
arranged and expressed in terms of Raman gain coefficient:
g
R
=
β n
eff
2
V
m
λ
P
λ
R
Q
0
2
×
1
P
Thres
Equation 3-3.
Because all of the components in the equation, except gR and β, are determined either
experimentally or from the COMSOL simulations designed to precisely match the experimental
conditions, the gR values can be normalized relative to gR of the 0 mol%. As shown in Figure 3-11,
the normalized gR values increase dramatically with respect to the concentrations of Zr in the sol-
gel, from 1.00 to 32.31, which indicate that the Zr doping alters the intrinsic material property of
silica. This trend is similar to the one observed in Figure 3-10 (b). In other words, this enhancement
suggests that Zr in the silica sol-gel increases the Raman gain of the silica.
Figure 3-11. Normalized Raman gain coefficient with respect to the Zr concentrations in
silica sol-gel.
0 5 10
0
5
10
15
20
25
30
35
Norm. Raman Gain Coeff.
Zr in Silica Solgel (mol%)
72
3. 5. 5. Raman Lasing Efficiency
While threshold is a commonly measured metric, lasing efficiency or slope efficiency is
also of critical importance. Previously, in Figure 3-10 (a), (b), the threshold curves for 0 mol %, 5
mol% and 10 mol% are plotted. There is a clear improvement in lasing efficiency or slope
efficiency as the Zr concentration increases. This enhancement is quantified by plotting the slope
efficiencies for all concentrations (Figure 3-12). The efficiencies enhance dramatically from 3.37%
to 47.43% as the Zr concentrations in silica solgel increase. It is important to note that these are
the unidirectional, not bidirectional, efficiencies. This improvement is directly related to the
Raman gain, which scales with the Zr concentration.
The output lasing power (Po) above the lasing threshold is related to the input power (or
pumping rate (∆N0)) and the Raman gain factor (g0) according to the Equation 3-4.
42
( 𝑃 𝑜 )
𝐴𝑏𝑜𝑣𝑒 𝑡 ℎ𝑟𝑒𝑠 ℎ𝑜𝑙𝑑 =
ℎ𝑣 𝑉 𝑚 τ
(
𝑔 0
𝐿 𝑖 + 𝑇 − 1)∆𝑁 0
Equation 3-4.
, where τ corresponds to the cavity photon lifetime, Li is the internal loss factor, and T is
the coupling factor. From this expression, the relationship between the output lasing power, input
power, and gain is evident. That is, the lasing efficiency, or slope efficiency (dPo/d ∆N0), is linearly
related to the gain of the material.
This relationship is readily apparent when the efficiency is plotted as a function of
normalized Raman gain coefficient (Figure 3-12, inset). The enhancement of Raman lasing
73
efficiency is attributed to the fact that the silica bond is highly polarized due to the Zr doping,
increasing number of phonons activated in silica, and the Raman gain coefficient.
Figure 3-12. Raman lasing efficiency as a function of the Zr doping within the silica
solgel. The Raman lasing efficiency is enhanced substantially from 3.37% to 47.43%.
Inset: The Raman lasing efficiency with respect to the normalized Raman gain coefficient,
indicating a linear correlation with R
2
= 0.99.
The device performance slightly degrades over time if it is stored in an ambient
environment due to the adsorption of water on the hydrophillic silica solgel. However, the
performance can be recovered by performing a dehydration process on a hot plate at 120 °C for 30
minutes. With the dehydration step, the device showed only a moderate performance change of 1 %
after 1 week. This variation is within the measurement error.
74
Table 3-1. The parameters obtained experimentally or by simulations in order to calculate
the normalized Raman gain coefficient.
Zr-00 Zr-02 Zr-05 Zr-08 Zr-10
ncoating
[neff]
1.4699
[1.4562]
1.4801
[1.4603]
1.4877
[1.4639]
1.5038
[1.4731]
1.5217
[1.4854]
Vm (um
3
)
[% in coating]
205.98
[33.72]
192.54
[37.92]
183.82
[41.09]
165.63
[47.69]
149.29
[54.46]
Quality factor
(10
7
)
12.8 6.94 4.17 3.06 2.27
λP
(nm)
766.16 765.27 765.11 765.38 765.19
λR
(nm)
790.27 789.58 790.15 787.13 793.35
PThreshold
(uW)
183.36 131.94 156.15 140.17 136.42
75
3. 6. Application 2: Enhanced SARS with Zr- and Ti-
doped silica solgel coated hybrid devices
SARS relies on SRS as a seed source
2,43–46
. Therefore, by reducing the SRS threshold, it is
reasonable to assume that the threshold for SARS would be similarly reduced. In a follow-up
project to the previous one, we investigated if metal-doped hybrid cavities had improved SARS
efficiency.
3. 6. 1. COMSOL for SARS
COMSOL Multiphysics finite element method (FEM) simulations are used to identify the
effect of the metal dopant in the silica sol-gel coating on the optical mode distribution in the
toroidal microcavity
15,20
. Figure 3-13 (a) contains the cross-sectional images of toroids with the
fundamental transverse magnetic (TM) modes of both undoped (left) and metal-doped (right) silica
hybrid resonators. The undoped devices have a 400 nm layer with the same index as silica (1.454),
whereas the metal-doped devices have a coating layer with a high index (1.520). These values are
based on the experimental devices tested. Due to the high index of the metal-doped coating layer,
the optical mode shifts towards the edge of the toroid and is more tightly confined in the coating
layer, causing a decrease in the Aeff.
76
Figure 3-13. Cross-sectional images of the optical field distribution in the coated toroidal
microcavity obtained with a COMSOL Multiphysics simulation. Major diameter
D=50μm. Miner diameter d=6μm. Coating refractive index equals: (a) 1.44. (b) 1.52.
The experimental parameters and geometry of plain silica toroids are used to design the
COMSOL Multiphysics models. For example, the wavelength, the major and minor diameters,
film thickness, and refractive index of silica are used. Then, a series of models are created with
variations on these values. Specifically, the minor diameter is varied from 3 to 7 μm, and the
coating layer index (ncoating) and thickness are varied from 1.44 to 1.60 and 300-600 nm,
respectively. Then, the optical mode area (Aeff) within each layer (silica, coating, and surrounding)
are calculated based on the Equation 3-5
5
. The results are plotted in Figure 3-14.
A
𝑒𝑓𝑓 =
∬ 𝜀 ( 𝑟 ) |𝐸 ( 𝑟 ) |
2
𝑑 2
𝑟 𝑀𝑎𝑥 [𝜀 ( 𝑟 ) |𝐸 ( 𝑟 ) |
2
]
Equation 3-5.
77
Figure 3-14. The dependence of TM fundamental mode area (Aeff) as a function of the
refractive index of coating (ncoating) and the minor diameter with the different coating
thickness (a) 300, (b) 400, (c) 500, and (d) 600 nm. The dimensions used in the
experimental devices are 400 nm coating and 6 μm minor diameter. The index value
depends on the dopant, but all values tested fall within the modeled range.
Figure 3-14 clearly indicates that the changes of ncoating have a significant impact on the Aeff
due to the mode confinement effect by the high index coating layer. As discussed in Figure 3-13,
the optical mode shifts towards the coating layer and is more tightly confined inside the coating
78
due to the high-index of the layer
6,7
. In Figure 3-14, it is clear that the Aeff decreases with the increase
in ncoating.
In addition, the minor diameter has a linear relationship with the Aeff behavior. In other
words, the Aeff decreases as the minor diameter decreases. This is attributed to the fact that the
smaller radius of curvature in small minor diameter contributes to the concentration of the optical
mode.
Over the range of values studied here, increasing the ncoating always decreases the mode
area. However, the magnitude of the change depends on the film thickness. Comparing all graphs
in Figure 3-14, the mode confinement effect is less significant as the coating thickness decreases.
In other words, the change in Aeff is limited by coating thickness. As the coating thickness increases
to 600 nm (Figure 3-14 (d)), the mode confinement effect becomes substantial with the increase in
ncoating. In addition to the coating thickness, the minor diameter has a linear relationship with the
Aeff behavior. That is, the Aeff decreases as the minor diameter decreases. This is attributed to the
fact that the smaller radius of curvature in small minor diameter devices contributes to the
concentration (or focusing) of the optical mode.
79
3. 6. 2. Derivation of SARS intensity equation based on the
coupled mode equation
The anti-stokes wave is generated through a four-wave mixing process involving the pump
mode and the Raman mode
10,45
. As the amplitude of the Raman mode is several orders of
magnitude higher than the anti-stokes mode, the coupled mode equations for the amplitude of the
anti-Stokes mode (AA) can be written as:
𝜕 𝐴 𝐴 𝜕 𝑡 = 2 i γ 𝐴 𝑃 𝐴 𝑃 𝐴 𝑅 ∗
𝑒 𝑖 ∆𝜔 𝑡
Equation 3-6.
, where 𝛾 =
𝜔 𝑃 𝑐 𝑛 2
𝐴 𝑒𝑓𝑓 , ωP is the pump frequency, 𝑛 2
≈ 2.2 × 10
−20
𝑚 2
𝑊 ⁄ is the Kerr
nonlinearity for silica
47
, c is the speed of light in vacuum, and Aeff is the effective mode area. AP
and AR are the amplitude of the pump and the stimulated Raman mode, respectively. Δ𝜔 = 2𝜔 𝑃 −
𝜔 𝑅 − 𝜔 𝐴 is the frequency detuning, where ωR and ωA are the frequency of the Raman and the anti-
Stokes modes, respectively. t is the interaction time between the pump and the Raman modes. By
solving the Equation 3-6 with an initial condition (t = 0, AA = 0), the AA can be described as shown
in Equation 3-7.
𝐴 𝐴 =
2 𝛾 ∆𝜔 𝐴 𝑃 𝐴 𝑃 𝐴 𝑅 ∗
( 𝑒 𝑖 ∆𝜔𝑡
− 1)
Equation 3-7.
80
The intensity of electric field (I) is related to the amplitude of the field (A) according to:
I =
𝜀 2
𝐴 2
, where ε is the permittivity of the medium. Using this expression, the intensity of the
anti-Stokes (IA) can be determined:
𝐼 𝐴 =
16
𝜀 2
𝜔 𝑃 2
𝑐 2
𝑛 2
2
𝐴 𝑒𝑓𝑓 2
𝐼 𝑃 2
𝐼 𝑅 (
sin( ∆𝜔 𝑡 2 ⁄ )
( ∆𝜔 𝑡 2 ⁄ )
)
2
𝑡 2
Equation 3-8.
Here IP and IR are the intensity of the pump and the Raman modes, respectively. Above the
Raman threshold, a clamped pump field is observed. As the pump mode is a clamped mode, IP can
be taken as a constant and is independent of the coupled power
5
. This assumption modifies the
typical relationship between the coupled power into the resonator and the launched fiber power,
which gives a square root dependence of the pump-to-Raman conversion.
In our analysis, we plotted the Raman power as a function of the coupled power, which
rules out the “pumping inefficiency”. As a result, IR is linearly dependent on the coupled power,
as expected. From the Equation 3-8, because IA is also linearly proportional to IR, the intensity of
the anti-stokes wave is linearly dependent on the coupled power. It is also interesting to notice that
IA is inversely dependent on the Aeff
2
.
81
3. 6. 3. Q factors from Zr and Ti doped devices measured with
1550 nm tunable laser
Figure 3-15 (a) is one of the representative normalized transmission spectra, which is
recorded from an oscilloscope connected to the photodetector. From the transmission spectra, the
loaded cavity Q is determined by Q = λ / Δλ, where λ is the resonant wavelength of the resonator
and Δλ is the full-width at half maximum (FWHM) of the resonant peak fitted with a
Lorentzian
37,48,49
. Due to the ultra-high Q of the device, the mode-splitting shown in the
transmission spectra occurs in most measurements
50
.
Figure 3-15 (b) contains intrinsic Q values from various devices. Intrinsic Q values of the
metal-doped devices are slightly lower than that of bare silica due to the material absorption loss
from the metal dopants as we discussed previously
14,15,19
. Even though the intrinsic Q values of
the metal-doped devices are lower than that of the bare devices, the intrinsic Q values are still high
enough (> 10
7
) to observe the nonlinear optical phenomena, SRS and SARS.
82
Figure 3-15. (a) Representative transmission spectrum from bare device with load Q of 3
x 10
7
with a mode splitting. (b) Intrinsic Q of all devices; bare, Zr, and Ti-doped devices.
83
3. 6. 4. Raman Lasing Behavior
Figure 3-16 (a) – (c) shows the first order SRS and SARS emissions from the bare, Zr-, and
Ti-doped devices measured via the OSA. The spectra contain both the red-shift SRS peaks and the
blue-shifted SARS peaks as well as the pump laser, which is on a resonance of the device, located
at the center of the spectra. The bare silica device requires the erbium-doped fiber amplifier (EDFA)
to amplify the input pump power in order to generate SARS. This is due to the high threshold
values of SARS in bare devices. On the other hand, SARS is easily observed in the metal-doped
devices without using the EDFA, which indicate that the threshold of SARS in metal-doped
devices are much lower than that in bare devices. The frequency shifts of SRS and SARS within a
device are the same because the shifts of both scatterings are dependent only on the vibrational
spectrum of the gain medium, in this case silica. However, the frequency shift is different in each
device due to a continuous Raman gain band in silica
38
over the range of 12~14 THz, or 400 ~ 460
cm
-1
. As a result, the shift of SARS and SRS is always the same within a device but alters
depending on devices. As shown at Figure 3-16 (d), the frequency shift in all devices are within the
range of the shift of silica value.
84
Figure 3-16. Emission spectra from the (a) bare, (b) Zr-, and (c) Ti-doped devices
obtained via OSA. (d) SRS and SARS shift from various devices.
Figure 3-17 (a) contains the efficiency and threshold measurements of the SRS signal. The
SRS signal is linearly dependent on the coupled input power as predicted by Equation 3-8, and
from these graphs, it is clear that the Zr- and Ti-doped devices show approximately a 10 times
improvement in efficiency. All data for all devices tested is contained in Table 3-1.
Figure 3-17 (b) presents the SARS measurement results. In agreement with Equation 1, the
SARS intensity depends linearly on the coupled power (Equation 3-8). Additionally, the slope of
the SARS emission also exhibits significant improvement in the metal-doped devices as compared
to the undoped device. This is due to the fact that the enhancement of SRS efficiency in metal-
85
doped devices increases the population of the vibrational state (Figure 2-12), allowing more pump
photons to be excited from the vibrational state to the 2
nd
virtual state, resulting in a higher SARS
efficiency. The linear relationship between SRS and SARS shown in Figure 3-17 (c) support the
predicted dependence from Equation 3-8. In the case of the undoped device, the plotted values are
confined in a small range because of the low efficiency, or challenges faced in achieving high SRS
intensities, compared with metal doped devices.
Figure 3-17. Threshold graph of (a) SRS and (b) SARS. (c) The ratio of SARS versus
SRS intensities from various devices.
The unit of power obtained from the OSA is the dBm, which is in the log-scale. The
enhancement of SARS in metal-doped device becomes evident when the output power is converted
into the unit of Watt. In Figure 3-18, all the graphs are acquired with similar coupled power of
approximately 1.5 mW. The bottom graphs are the magnification of the wavelength range that
contains the SARS peaks with the unit of nW. As shown in Figure 3-18 (a), there is a tiny SARS
peak (1.32 nW) at around 1463.16 nm generated from the bare device. In contrast, the SARS
intensities from metal-doped devices become discernable and substantial (12.83 and 12.40 nW for
Zr- and Ti-doped device, respectively) compared with that from the bare device (Figure 3-18). This
86
improvement suggests that the metal dopants have a significant effect on the enhancement of
SARS in silica hybrid devices.
Figure 3-18. Zoomed-in spectra of (a) bare, (b) Zr-, and (c) Ti-doped devices with similar
coupled power into the devices (~ 1.5 mW)
Figure 3-19contains the properties of SRS and SARS behaviors from various devices. Figure
3-19 (a) and (b) show the efficiencies and the thresholds of SRS, respectively. In case of the SRS
efficiency, the average SRS efficiencies are 3.38, 36.22, and 33.22 % for bare, Zr-, and Ti-doped
devices, respectively. In other words, metal-doped devices show more than 10 times improvement
in efficiency than bare silica devices, similar to the values that we discussed at the previous chapter.
Doping metal has an impact on not only the efficiency but also the threshold of SRS. Figure 3-19
(b) clearly reveals that the metal dopants cause the SRS threshold to decrease by half compared
87
with bare devices. The decrease in threshold is ascribed to the confined optical mode volume in
high-index of metal-doped coating, as discussed in the COMSOL simulation result (Figure 3-6).
Figure 3-19. (a) efficiency and (b) threshold values of SRS, and (c) SARS intensity at
approximately 1.3 mW of coupled power and (d) SRS threshold, which is a minimum
coupled power to generate SARS.
Figure 3-19 (c) and (d) contain the SARS intensities with similar coupled power (~ 1.3 mW)
and minimum coupled power that the SARS is observed, or SARS threshold. As shown in Figure
3-19 (c), the generated SARS power shows a substantial improvement from both Zr- and Ti-doped
devices, approximately 12 nW, compared with that of the bare devices (~1 nW). This is again due
to the fact that metal dopants make the silica matrix more polarized, allowing more vibration of
88
phonon in silica. (Figure 2-11). Additionally, the minimum required power to generate SARS also
has a significant enhancement with metal doping as shown at Figure 3-19 (d). Bare silica devices
need at least 1.3 mW of coupled power into the resonator to create SARS, whereas Zr- and Ti-
doped devices only requires approximately 700 uW to generate SARS. The decrease in SARS
threshold is ascribed to the fact that the high-index of metal-dopants causes the optical mode
volume shifting to coating layer, decreasing the optical mode volume, as discussed at Figure 3-13.
Consequently, the metal dopants enable a significantly reduced SARS threshold, compared with
bare silica devices.
89
Table 3-2. Summary of all results obtained across all devices tested along with device
parameters.
Bare Bare Bare Zr Zr Zr Ti Ti Ti
Diameter
(μm)
53.42 55.20 55.73 53.53 53.80 51.60 52.67 52.07 53.80
Intrinsic Q
(x 10
7
)
5.43
±
0.80
8.52
±
0.88
4.03
±
0.17
3.94
±
0.06
4.96
±
0.24
2.84
±
0.08
2.43
±
0.05
5.09
±
0.17
4.18
±
0.16
Raman
Shift
cm
-1
429.63 486.67 422.29 441.97 429.63 454.98 491.00 412.29 453.65
THz 12.88 14.59 12.66 13.25 12.88 13.64 14.72 12.36 13.60
SARS
Threshold
(μW)
1166.12
±
20.23
1095.62
±
16.29
982.72
±
53.48
568.78
±
15.51
681.47
±
15.43
562.87
±
10.14
620.19
±
49.48
572.29
±
49.26
616.89
±
25.21
Efficiency
(x 10
-4
%)
1.29
±
0.13
0.84
±
0.04
0.69
±
0.02
15.09
±
0.21
14.56
±
0.31
14.32
±
0.14
11.41
±
0.19
15.52
±
0.50
15.68
±
0.41
SRS
Threshold
(μW)
514.69
±
57.83
605.51
±
30.64
661.61
±
30.50
339.20
±
30.59
301.86
±
8.72
348.97
±
18.53
379.43
±
25.09
276.79
±
17.41
372.20
±
9.14
Efficiency
(x 10
-4
%)
3.51
± 0.07
3.44
± 0.13
3.18
± 0.10
37.38
± 1.13
37.86
± 0.23
33.42
± 0.25
28.90
± 1.21
38.25
± 0.70
32.50
± 0.35
SARS/ SRS emission
ratio
(x 10
-6
)
3.81
±
0.04
3.66
±
0.08
3.41
±
0.03
3.71
±
0.15
3.86
±
0.12
3.92
±
0.08
3.95
±
0.09
3.79
±
0.27
3.64
±
0.09
90
3. 7. Summary
In this work, we demonstrated that both SRS and SARS can enhance substantially by
doping metal (either Zr or Ti) into silica sol-gel coatings by more than 10x. The improvement
arises from an increase in the Raman gain coefficient by polarizing the silica solgel with the Zr
dopants. Additionally, despite the decrease in optical Q factor with Zr concentrations, μW
thresholds were obtained for all concentrations. In the meanwhile, the SRS and SARS threshold
decrease by half with doping metal in silica hybrid devices. The smart design approach of using a
hybrid silica resonator demonstrated here is broadly generalizable to other geometries of resonant
cavities as well, resulting in greatly expanding the impact of the present findings beyond the
specific cavity architecture studied.
91
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98
Chapter 4. Raman-Kerr frequency combs in Zr-
doped silica hybrid microresonators
4. 1. Introduction
Optical frequency combs have found applications in a wide range of fields, such as optical
communication
1–5
, spectroscopy
6–10
, optical clock
11–15
, and LIDAR (light detection and
ranging)
16,17
. One approach for generating frequency combs is based on optical resonant cavities
with high quality (Q) factors
18–20
. These devices generate optical frequency combs based on four-
wave mixing (FWM), a nonlinear optical process that requires a high intensity optical field
interacting with a nonlinear medium. By definition, the long photon lifetime within an ultra-high
Q factor (UHQ) resonator generates high intensity circulating optical fields within the cavity
21
.
Based on this concept, researchers have focused on increasing either the Q
22–24
or the
nonlinear coefficient of the material
25–27
to improve the comb. Silica devices are a particularly
interesting case as the lowest-order optical nonlinearity is the third-order susceptibility due to the
material’s inversion symmetry. Using UHQ silica microcavities, several different nonlinear
behaviors have been previously demonstrated including stimulated Raman scattering (SRS) from
the Raman gain
28–32
and optical parametric oscillation (OPO) from the Kerr nonlinearity
33–37
. To
generate frequency combs, a combination of degenerate and non-degenerate FWM resulting from
OPO is commonly used. The OPO is governed by the Kerr coefficient. Therefore, the efficiency
of this process is ultimately limited by the third order nonlinear coefficients of silica (χ
(3)
). To
99
enhance the fundamental material behavior, researchers have investigated leveraging plasmonics
25
and creating hybrid organic-inorganic structures
26,27
.
100
4. 2. Background and motivation
Recently, variations on Kerr frequency combs have been demonstrated
38–42
. In this
research, it was shown that the SRS emission can be used as a seed to generate the FWM process
which gives rise to the frequency comb formation. These combs are called Raman-Kerr combs
27
.
It was shown that, by improving the SRS, the comb formation could be enhanced. A few different
strategies have been demonstrated including seeding the SRS process with a secondary laser.
However, by leveraging both the Stokes and anti-Stokes emissions, a greater effect could be
achieved. This behavior has been predicted theoretically, and it was studied as part of the present
thesis.
Our strategy to broaden the span of the frequency combs with reduced pump power is
utilizing the Stokes as another seed to the generate the FWM. Previously the optical frequency
combs were only generated with input pump induced FWM peaks, which limits the frequency
combs span as shown at Figure 4-1 (a)
18
. In this project we focus on generating not only the input
pump induced FWM peaks, but also Stokes and anti-Stokes induced FWM peaks
43–47
. As shown
at Figure 4-1 (b), Raman emission and its induced FWM peaks broaden the span of FCs in the
longer wavelength region, and likewise, anti-Stokes and their cascaded FWM peaks enlarge the
FC span at shorter wavelengths.
101
Figure 4-1. Schematic images of frequency comb generation with (a) pump induced four-
wave mixing and (b) pump, Raman, and anti-Stokes Raman induced four-wave mixing.
Based on the theoretical analysis, the number of the generated comb lines, the comb shape,
and the comb span depend on the Raman gain (gR) of the cavity material
44
. In other words, by
increasing the Raman gain, the performance of the comb will improve.
Here, we demonstrate a Raman-Kerr frequency comb using a Zr-doped silica hybrid
toroidal microcavity. The Zr-doped silica hybrid resonators have a significant improvement in
Raman efficiency as compared to conventional silica devices. As a result, we are expecting to
generate the Raman-seeded FWM, increasing the spans of the frequency combs.
102
4. 3. Experimental methods
4. 3. 1. Device Fabrication
- Synthesize Zr doped silica solgel solutions
The different concentrations of Zirconium (Zr) doped silica solgel solutions are synthesized
via the acid-catalyzed hydrolysis and condensation reaction with the same method described in the
previous chapter
27,32,48
, except the different concentrations of Zr mol% to Si. For this project,
different concentrations of Zr propoxide (0, 5, 10, and 15 mol% of Zr to Si) is synthesized with
the MTES solution. Other than the Zr concentrations, all procedures are the same as explained
previously.
- Fabrication of silica toroidal microresonators
Silica toroids are fabricated with the same procedure as described previously, which is
composed of the three main steps; photolithography to define silica circle patterns (150 um) on
silicon wafers, XeF2 etching to remove silicon isotropically in order to obtain silica disks on silicon
pillar, and CO2 laser reflow to produce atomically smooth silica toroids
49
.
In order to generate the FWM for frequency comb in silica toroidal microcavities, the
detuning frequency (Δv = 2 vp – vs – vi, where vp, vs, and vi, are the frequency of pump, signal and
idler, respectively) is an especially important parameter
33
. This is because there is a competition
103
of the nonlinear optical processes between FWM and SRS in silica
45,47
. Generating SRS does not
require phase-matching due to the flat dispersion of phonon of silica in all wavelength range.
Consequently, SRS has a priority over FWM with wide range of the detuning frequencies. In a
specific condition, however, FWM becomes a dominant nonlinear optical process over SRS. The
parametric gain bandwidth (Ω) is a function of the effective mode area (Aeff) based on the Equation
2.13, and the Ω is inversely proportional to the Aeff. Therefore, by decreasing the Aeff by controlling
the device configuration, the FWM preferred condition can be achieved. Smaller Aeff can be
obtained from a toroid with large major diameter and small minor diameter. As a result, the large
silica disk with diameter of 150 um is selected for the present study. Additionally, the reflowing
processes are carefully controlled in order to obtain a toroid with small Aeff, which is the phase-
matched condition for FWM.
- Coating Zr doped silica solgel onto toroids
The different concentrations of Zr-doped silica solgel solutions are spin-coated onto the
as prepared silica toroids with 7000 rpm for 60 seconds. The solgel solutions are applied directly
onto silica toroids after the O2 plasma cleaning steps in order to obtain better contact between
silica and solgel solutions. After spin coating, the samples are dried at 75 °C for 5 minutes to
evaporate the residual ethanol solvent. The final Zr-doped silica hybrid resonators are obtained
by annealing at 1000 °C for 1 hour in a tube furnace. The final silica hybrid toroidal resonator is
shown at the Figure 4-2
27
.
104
Figure 4-2. Scanning electron microscope (SEM) image of Zr-15 mol% silica solgel
coated silica hybrid toroidal resonator. Major and minor diameters of the device are 109
and 10 μm, respectively.
105
4. 3. 2. Characterization of FWM and SRS
Emitted signals generated from the device by nonlinear optical processes such as FWM or
SRS are detected via the optical spectrum analyzer (OSA). For the characterization of FWM or
SRS, either the signal (and idler) or SRS emission intensity measured with the OSA is plotted as
a function of the amount of power coupled into the device. The coupled power into the device is a
product of the power traveling through the tapered optical fiber and the percentage of power
coupled into the device, which is determined from the transmission spectra. The threshold of either
FWM or SRS is corresponding to the x-intercept of the linearly fitted line from the plotted graph,
while the efficiency of either FWM or SRS is determined from the slope of the linearly fitted line.
In case of the FWM, each signal and idler peak has the same output power as the FWM is the
degenerate process, so the idler threshold graph is exactly the same as the signal threshold graph
33
.
All the threshold and the efficiency values are in the Table 4-1.
106
4. 3. 3. COMSOL Multiphysics Simulation
As we discussed, the optical effective mode area (Aeff) is the one of the most important
parameters to make FWM favored phase-matching condition. In order to verify the effect of Zr
dopants in silica solgel coating layer on generating frequency comb, Aeff behaviors are calculated
with the COMSOL Multiphysics finite elements method (FEM) simulations with the same method
described at the previous chapter
50,51
. The geometries of the devices (major and minor diameters)
for the simulations are obtained from the SEM image of the silica hybrid toroid. In the simulation,
the Zr-doped silica coating layer (~ 400 nm) is created on top of the bare silica toroid with different
refractive indices determined via ellipsometer.
107
4. 3. 4. Dispersion in WGM resonator
The definition of dispersion in optics is the phenomenon in which the phase velocity of a
wave depends on its frequency. Dispersion is one of the most important factors determining the
frequency comb property in the WGM resonators. In the resonator, energy conservation should be
satisfied to generate FWM based on the equation ( 2 ℎ 𝜐 𝑃 = ℎ 𝜐 𝑆 + ℎ 𝜐 𝐼 ). The frequency
difference between adjacent modes is the FSR (𝜐 𝐹𝑆𝑅 = |𝜐 𝑆 − 𝜐 𝐼 |), which can vary owing to the
dispersion. For modes close to the pump frequency, the variation in the FSR can be small.
However, the modes far from the pump frequency are affected significantly by the dispersion. If a
cavity has low dispersion, the successive FWM to higher orders would intrinsically lead to the
generation of phase-coherent sidebands with equal spacing, while satisfying the energy
conservation.
Dispersion in the WGM microresonator is characterized by the variation in the free spectra
range (FSR, Δ𝜐 𝐹𝑆𝑅 = ( 𝜐 𝑚 +1
− 𝜐 𝑚 )− ( 𝜐 𝑚 − 𝜐 𝑚 −1
) ), which can vary owing to both geometric
and material dispersions in the WGM resonators
18
.
First, in case of the geometric dispersion, WGM microcavities exhibit an intrinsic variation
of the FSR due to the geometry of a resonator. The resonance frequency of the fundamental mode
is approximately given by Equation 4-1.
𝜐 𝐹𝑆𝑅 =
𝑐 2 𝜋 𝑛 𝑅
(𝑚 +
1
2
+ 𝜂 1
(
𝑚 + 1 2 ⁄
2
)
1 3 ⁄
+ ⋯ ) Equation 4-1.
108
, where c is light speed in vacuum, n corresponds to the refractive index, R designates the
cavity radius, and η1 represents the first zero of the Airy function (η1 ≈ 2.34). Hence, the variation
of the free spectral range by the cavity geometry is described by the Equation 4-2.
∆υ
𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 ≈
𝜕 2
𝜐 𝑚 𝜕𝑚
2
= −
𝑐 2 𝜋 𝑛 𝑅
×
𝜂 1
18
× (
𝑚 + 1 2 ⁄
2
)
−5 3 ⁄
Equation 4-2.
The second contribution is due to the resonator material, which is silica (SiO2), zirconia
(ZrO2), and Zr-doped silica (Zr-15). The effect can be estimated by considering that the refractive
index of a material is a function of frequency (or wavelength) based on the Sellmeier equations
below. Equation 4-3. and 4.4 represent the Sellmeier equation of silica and zirconia, respectively.
𝑛 𝑆𝑖𝑙𝑖𝑐𝑎 2
− 1 =
0.6961663 𝜆 2
𝜆 2
− 0.684043
2
+
0.4079426 𝜆 2
𝜆 2
− 0.1162414
2
+
0.8974794 𝜆 2
𝜆 2
− 9.896161
2
Equation 4-3.
𝑛 𝑍𝑖𝑟𝑐𝑜𝑛𝑖𝑎 2
− 1 =
1.347091 𝜆 2
𝜆 2
− 0.062543
2
+
2.117788 𝜆 2
𝜆 2
− 0.166739
2
+
9.452943 𝜆 2
𝜆 2
− 24.30570
2
Equation 4-4.
In addition, the refractive index of the optical mode is a function of the mode number (m),
where m = 2 π n R / λ. As a result, the FSR of the material dispersion is demonstrated based on the
Equation 2-8.
109
Δυ
𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ≈
𝜕 2
𝜕 𝑚 2
(
𝑐 2 𝜋 𝑛 ( 𝑚 ) 𝑅 × 𝑚 )
≈
𝑐 2
𝜆 2
4 𝜋 2
𝑛 3
𝑅 2
× (−
𝜆 𝑐 𝜕 2
𝑛 𝜕 𝜆 2
)
Equation 4-5.
Based on the Equation 4-2. and the Equation 4-5., both geometric and material dispersions
of various resonators in the near-IR region are displayed in the Figure 4-3.
110
Figure 4-3. (a), (c), and (e) Geometric (red) and material (blue) dispersion of SiO2, ZrO2,
and Zr 15mol% toroidal resonator, respectively. (b), (d), and (f) Dispersion of SiO2, ZrO2,
and Zr 15 mol% toroidal resonator, respectively, combining both geometric and material
dispersions.
111
As shown at Figure 4-3 (a), the material dispersion of silica has a zero-dispersion point at
approximately 1300 nm, while the geometric dispersion of silica resonator is always negative in
the near-IR range. Because the material dispersion of silica is positive for wavelength greater than
1300 nm (anomalous dispersion), it can compensate the intrinsic resonator dispersion
18
. Figure 4-3
(b) represents a graph combining both geometric and material dispersions of a silica resonator.
Considering both dispersions, the zero-dispersion point is shifted to approximately 1500 nm,
which is the operating wavelength of the frequency comb, and the resonator has the anomalous
dispersion region at above 1500 nm.
Figure 4-3 contains both the geometric and material dispersions in the resonator made out
of the zirconia
32,52,53
. Though the zero dispersion point of the zirconia material dispersion is located
at ~1900 nm, the total dispersion of the zirconia resonator has a normal dispersion over the near-
IR range due to the negative value of the geometric dispersion of the zirconia. The overall
dispersion of zirconia in the near-IR region, however, is flatter than that of silica. Comparing the
dispersion of SiO2 and ZrO2 devices, the ZrO2 device has a flatter dispersion than the SiO2 device
in the near-IR region. In other words, doping ZrO2 into the SiO2 matrix enables the Zr-15 mol%
device to have a lower dispersion than the bare SiO2 device due to the low dispersion of ZrO2.
Additionally, both SiO2 and Zr-15 mol% devices show the zero dispersion point close to the
frequency comb operating wavelength, which is 1550 nm. As a result, we could expect broadening
of the frequency comb span from the Zr doped silica hybrid device owing to the improved
dispersion.
112
4. 4. Results and discussions
4. 4. 1. COMSOL Multiphysics Finite Element Methods
Simulation
Figure 4-4. Cross-section images of the optical field distribution in the Zr-doped silica
solgel coated toroidal microcavity calculated with COMSOL Multiphysics finite element
methods (FEM) simulation with the different mol % of Zr in the silica solgel coating (0
to 15 mol%).
The Zr dopants have an effect on the optical field distribution in the devices, which are
obtained with COMSOL Multiphysics finite element method simulations (Figure 4-4). For the
simulation parameters, the geometry of toroid (major and minor diameters) is obtained from the
SEM image. The refractive index and the thickness of the coating are determined via ellipsometer.
As the concentration of Zr dopants in the silica solgel increases, the refractive indices of the coating
increase linearly from 1.445 to 1.545 (Table 4-1). The coating thickness is constant (~400 nm) for
113
all devices. Due to the high index of the coating as compared to silica, the optical field moves into
the film, improving the confinement of the optical field in the coating layer and decreasing the
effective optical mode area (Aeff)
54–56
. All the parameters discussed in here are in the Table 4-1.
114
4. 4. 2. Quality factors of silica hybrid resonators
As we discussed in the previous chapter, the loaded Q factor (Qloaded) can be obtained
experimentally from a transmission spectrum fitted to a Lorentzian based on the equation (Qloaded
= λ / Δλ)
22
. Figure 4-5 (a) is one example of the Qloaded from the Zr-15 mol% device. The Qloaded has
a linear relationship with respect to the coupling percentage. Therefore, the intrinsic Q factor (Qint)
can be obtained by plotting the Qloaded as a function of the coupling percentage and by fitting
linearly based on a coupled cavity model. As shown at Figure 4-5 (b), the Qint corresponds to the
y-intercept of the linear fitted line, where the extrinsic or coupling loss becomes zero. The presence
of Zr causes the Qint of the coated devices to decrease from 1.34 × 10
8
for the Zr-free coatings to
1.52 × 10
7
for the Zr 15 mol.% coatings as shown at Figure 4-5 (c). When fit to a function of the
form y=a x
b
, the value for b is -0.83, which indicates that the Qint scales inversely with the
concentration of Zr and is limited by the material absorption loss
54
. These results agree with
previous studies, which show that the Q decreases in metal-doped silica devices due to the
increased material absorption losses by the dopants. However, it is important to note that the Qint
values are still in excess of 10 million for all concentrations, which are high enough to generate
the frequency combs.
115
Figure 4-5. (a) Representative transmission spectra to obtain a loaded Q factor from the
Zr-15 mol% device. The resonant wavelength is 1557.45276 nm, and the Q Loaded is 1.13
x 10
7
with 25.13 % of coupling (b) The Qloaded data with respect to the coupling percentage
to calculate the Qint of the Zr-15 mol% device. The Qint is the 1.53 x 10
7
, where the y-
intercept of the linearly fitted line. (c) Intrinsic Q factors as a function of the concentration
of Zr mol% in the silica solgel coating.
116
4. 4. 3. Frequency comb behaviors
Figure 4-6. Optical frequency comb generation from the Zr-00 device. A series of spectra
are shown for each device to provide evidence of the formation of the comb as a function
of input power. Inset numbers are the input powers.
117
Figure 4-6 ~ Figure 4-9 are the OSA spectra that show the optical frequency combs generated
by the coated devices with respect to the different Zr concentrations in the coating with the
different input powers into the devices. As shown at Figure 4-6, the frequency comb in the Zr-00
device is generated by FWM-based optical parametric oscillation (OPO) process centered around
the pump wavelength at low pump power
18,33
. Each signal and idler photon has the same output
power due to the degenerate FWM process. As the input coupled power increases, the signal and
idler photons generate additional cascaded FWM peaks based on both degenerate and non-
degenerate processes, increasing the spans adjacent to the pump wavelength. The span of
frequency comb generated in Zr-00 device is mainly due to the input pump induced FWM and
their cascaded peaks.
118
Figure 4-7. Optical frequency comb generation from the Zr-05 device. A series of spectra
are shown for each device to provide evidence of the formation of the comb as a function
of input power. Inset numbers are the input powers.
Figure 4-7 contains the OSA spectra obtained from the Zr-05 device. Comparing Figure 4-6
(c) with Figure 4-7 (c), which are taken with similar input power, the Zr-05 device starts showing
the SRS and its induced FWM peaks at around 1700 nm, where there is only pump induced FWM
119
in the Zr-00 device. Consequently, the Zr-05 has the larger frequency comb span than the Zr-00
device at the longer wavelength region due to the SRS induced FWM peaks.
Figure 4-8. Optical frequency comb generation from the Zr-10 device. A series of spectra
are shown for each device to provide evidence of the formation of the comb as a function
of input power. Inset numbers are the input powers.
120
The frequency comb behaviors in Zr-10 device are also investigated as shown in Figure 4-8.
Unlike the Zr-05 device, the Zr-10 device generates anti-Stokes Raman at low input power (Figure
4-8 (c))
31,57,58
. In addition, the generated anti-Stokes Raman acts as another seed to the FWM,
causing the anti-Stokes Raman induced FWM. As a result, with similar input power (Figure 4-7 (e)
vs. Figure 4-8 (e)), the Zr-10 device shows a larger frequency comb at the shorter wavelength region
owing to the anti-Stokes Raman induced FMM generation compared with the Zr-05 device.
121
Figure 4-9. Optical frequency comb generation from the Zr-15 device. A series of spectra
are shown for each device to provide evidence of the formation of the comb as a function
of input power. Inset numbers are the input powers.
The contribution of anti-Stokes Raman and their induced FWM on frequency comb
generation becomes particularly apparent in the Zr-15 device (Figure 4-9), where the higher order
anti-Stoke’s Raman scattering as well as the first order SRS have a significant effect on the increase
122
of the span. In other words, both the Stoke’s and the anti-Stoke’s Raman play a major role in
improving the span of the frequency comb in the Zr doped devices. Given the SRS enhancement
and high signal strength, it is likely that the combs span beyond the OSA detection range of
1700nm.
To verify that the improvement in SRS is the dominant contributor to the comb span, the
Raman thresholds and efficiencies are measured and compared to the comb spans. The SRS
behaviors in the coated devices are analyzed by measuring the output Raman emission intensity
from the toroids via the optical spectrum analyzer (OSA) with respect to the amount of power
coupled into the optical cavity. The Raman threshold graph is obtained by plotting the output
Raman intensity as a function of the coupled power into the coated toroids. The SRS threshold is
acquired by the x-intercept of the linearly fitted line from the threshold graph while the Raman
efficiency is determined from the slope of the line.
Figure 4-10. (a) The SRS threshold graph for the SRS efficiency (slope) and threshold
(x-intercept) and (b) the comb spans as a function of the coupled power into each device.
123
The SRS efficiency, or slope efficiency, shows a clear enhancement as Zr concentration
increases (Figure 4-10 (a)). The SRS efficiencies improve substantially from 0.027 to 0.414 % as
the Zr concentrations in silica sol−gel increase from 0 to 15 mol%, respectively, which is 15 fold
improvement with Zr dopants. Due to the enhancement of the Raman efficiency, the SRS peak
with high power becomes the other seed to generate the cascaded FWM peaks with high coupled
power based on degenerate and non-degenerate processes. In parallel, the threshold of the SRS
decreases significantly from 4.19 mW to 0.82 mW, or 5x, as Zr concentration increases, which
enables the frequency comb span to increase with lower input coupled power.
Figure 4-10 (b) shows the span of the frequency comb as a function of the coupled power
from the different Zr devices. The comb span exhibits a saturation behavior with respect to the
input coupled power. This behavior is an artifact of the experimental set-up. The OSA is limited
to 1700 nm. Considering that the peaks at 1700 nm have high intensities with 5 mW of pump
power, it is highly probable that the comb extends well beyond 1700 nm.
In the Zr-free device, the comb span is approximately 150 nm with ~5 mW of input coupled
power. On the other hand, as the concentration of Zr in silica solgel coating increases, the span of
the frequency comb also increases. Notably, when 15 mol% of Zr is doped into the coating, the
frequency comb spans more than 300 nm, which is almost two-fold enhancement compared with
Zr-00 device. This broadening of the frequency comb span is due to the combination of
improvement of the Stoke’s and anti-Stoke’s Raman scattering, causing cascaded FWM peaks
from the both Raman emission peaks, as well as the improvement in dispersion matching.
124
Table 4-1. The parameters obtained by simulation or experimentally.
Zr-00 Zr-05 Zr-10 Zr-15
Diameter
(μm)
108 107 108 109
Refractive
Index
1.445 1.478 1.512 1.545
A Eff
(μm
2
)
2.63 2.52 2.42 2.36
Intrinsic Q
(x 10
7
)
13.4 ± 1.8 2.78 ± 1.09 1.62 ± 0.93 1.52 ± 0.81
Idler
Efficiency (%)
0.178 0.186 0.208 0.245
Idler
Threshold (μW)
273 284 411 367
Raman
Efficiency (%)
0.027 0.063 0.125 0.414
Raman
Threshold (mW)
4.19 1.26 0.79 0.82
Span of Comb
with 5 mW (nm)
164
(1496 ~ 1660)
215
(1485 ~ 1700)
253
(1447 ~ 1700)
322
(1378 ~ 1700)
125
4. 5. Summary
In conclusion, we demonstrate a Raman–Kerr frequency comb using a Zr-doped silica
hybrid toroidal microcavity. The Zr-doped layer has a significant effect on both flattening the
dispersion and improving the stimulated Raman scattering efficiency. This enhancement enables
the generation of FWM around both the Stokes and anti-Stokes Raman scattering emissions. As a
result, the Raman–Kerr frequency comb spans more than 300 nm in the near-IR region with less
than 5.2 mW of input power.
126
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135
Chapter 5. Surface Raman lasing with highly aligned
organic molecule monolayer on silica hybrid
microresonator
5. 1. Background and motivation
Recent advances in surface feature nanostructuring revealed that the electronic properties
at the end and surface deviate greatly from the material bulk behavior
1–7
. By leveraging these
surface or edge effects, exceptional optical behavior including surface or edge second harmonic
generation
8–11
, and 2-D topological edge lasing
12,13
, have been demonstrated. In contrast, surface
or edge vibrational nonlinear optical behaviors, such as stimulated Raman scattering (SRS) on
surface has been rarely reported due to difficulties with achieving the requisite excitation
conditions
14,15
. As a result, current Raman lasers are unable to take advantage of a potentially
transformational enhancement strategy.
In an SRS process in a nonlinear medium, an initial pump light spontaneously generates
and amplifies a longer wavelength emission signal. This signal is Stokes-shifted from the initial
pump wavelength by a frequency difference equal to the atomic or molecular vibration frequency
of the material. Therefore, leveraging SRS for laser development is a popular strategy due to the
versatility and tunability of the emission wavelength. While originally limited to large footprint
systems, with recent advances in integrated photonic devices, new designs for Raman lasers have
emerged in a wide range of platforms including optical waveguides
16–20
, on-chip
136
microresonators
21–25
, and random nanocrystalline particles
26
. However, these devices all rely on
the bulk material for generation of the SRS which overlooks the directionality of the vibrational
mode.
Previous work has investigated surface SRS signals generated by molecular monolayers
deposited randomly on the surface; however, only extremely weak SRS was observed in these
non-integrated systems
15
. The challenge for surface SRS was ascribed to the lack of efficiently
excitation of the Raman modes on surface, due to the lack of alignment of the Raman gain with
the incident field and the exceptionally small gain of a single-molecular layer
14,27,28
. If a surface
Raman process is used, the Raman scattering intensity is dominated by the vibrational mode
orientation with respect to the incident wave and the electric polarization geometry
29–33
. Using a
range of deposition and grafting techniques, molecules can be attached to and oriented on surfaces
and edges in highly controlled manners
34–38
. To effectively excite the surface Raman vibrational
modes in a single molecular mono-layer, the excitation source must also be structured and
propagating along the surface.
On-chip waveguides and traveling wave resonant cavities form evanescent fields that
create the requisite surface propagating excitation source
39
. Among the possible device types,
whispering gallery mode optical cavities are particularly unique
40
. These devices confine light in
circular orbits at the device-air interface with 1-5% of the optical field located at the cavity surface
depending on the precise device geometry and index
41
. They create a uniform and oriented
evanescent field which will enable the excitation of molecules attached to the device surface.
In addition, whispering gallery mode (WGM) resonators can have quality factor (Q) in
excess of 10 million; thus, they can act as optical amplifiers
40
. Due to their high Q factors that
result in large circulating optical intensities and long light-mater interaction time (up to
137
nanoseconds), optical resonators have enabled numerous investigations into nonlinear optical
effects. Previously, low threshold power (Pthres) Raman lasing has been demonstrated using bulk
silica microcavities, and the Raman lasing threshold was shown to scale as Veff/Q
2
where Veff is
the effective optical mode volume
42,43
. In previous work, the ultra-high Q factors have been
leveraged to achieve sub-uW lasing thresholds. Unfortunately, because the bulk or isotropic silica
has a low Raman gain coefficient, the lasing efficiency is poor, particularly in the visible range
44
.
Here, we leverage the highly oriented surface vibrational Raman mode by grafting single-
molecular layer on the surface of WGM resonators to generate surface Raman lasing. Silica
toroidal resonators integrated on silicon are used as the testbed platform study the surface Raman
lasing process as shown at Figure 5-1 (a). Organic siloxane single-molecular layers are chemical
grafted on the surface of the microresonator, resulting a highly oriented Si-O vibrational mode on
surface interacting with the circulating optical field. As a result of aligning the vibrational surface
Raman mode with the polarization direction of incident electric field, the devices show
dramatically enhanced surface Raman lasing performance, with efficiency increases from ~5 % to
over ~40 % compared to bulk silica devices.
138
Figure 5-1. (a) Scanning electron microscope (SEM) image of a microtoroidal optical
resonator on a silicon chip with false blue color indicating the location of the siloxane
molecular layer on the silica microcavity surface. (b) COMSOL Finite element method
(FEM) simulation of the optical mode profile in a microtoroidal resonator with a major
diameter of 60 μm. The red arrow represents the electric field direction of the fundamental
transverse magnetic (TM) mode.
139
5. 2. Experimental methods
- Optical mode behaviors with COMSOL simulation
We use COMSOL Multiphysics finite element method (FEM) to model the optical modes
of the cavity
45,46
. As shown at Figure 5-1 (b), the optical resonator is simplified with a 2-
dimensional cross section of the resonator, and the Maxwell's equations are solved by assuming
an axially symmetric mode. The device geometries (major and minor diameters) and material
properties are defined by the devices used in the experiments. We chose the mesh size to be λ/8 to
achieve an acceptable accuracy. The cross section of the fundamental transverse magnetic (TM)
mode along with the field amplitude profile on the equatorial plane is shown in Figure 5-1 (b). The
red arrow indicates the electric field direction of the fundamental TM mode, whereas the direction
of electric field of the fundamental transverse electric (TE) mode is vertical to that of TM mode.
- Fabrication of silica toroidal microresonators
Silica toroidal microcavities are fabricated with the same procedure as described
previously, which is composed of the three main steps; photolithography to define silica circle
patterns (either 80 or 150 um) on silicon wafers, XeF2 etching to remove silicon isotropically in
order to obtain silica disks elaborated on silicon pillar, and CO2 laser reflow to produce atomically
smooth silica toroids
47
. A series of silica microtoroidal devices integrated on silicon wafer are
fabricated with major diameters of 52.7 ± 8.8 μm and 83.3 ± 2.1 μm, and minor diameters of 6.7
± 0.6 μm and 11.6 ± 0.7 μm from the 80 and 150 um disks, respectively. Figure 5-2 shows one of
140
the representative scanning electron microscope (SEM) images of the fabricated silica toroid from
80 μm disk.
Figure 5-2. One of the representative scanning electron microscope (SEM) images of the
fabricated silica toroid with major and minor diameter of 53.9 and 5.7 μm, respectively.
- Surface functionalization of the silica devices
The native hydroxyl (-OH) layer on the silica device surface is replaced with an organic
methylsiloxane (MS) or dimethylsiolxane (DMS) molecular monolayer using a chemical vapor
deposition (CVD) process with the silanization reaction as shown at Figure 5-3
48
.
141
Figure 5-3. Schematic image of silanization reaction between the surface hydroxyl group
(-OH) on silica and either methyl trichlorosilane (blue) or dimethyl dichlorosilane (red)
based on the chemical vapor deposition (CVD) reaction at room temperature (RT). The
final product has the grafted molecular mono-layer of either methyl siloxane (MS, blue)
or dimethyl siloxane (DMS, red) work
49,38,50,51
.
The prepared silica toroidal microcavities were treated by O2 plasma using an SCE 104
plasma system (Anatech USA) to generate hydroxyl groups (-OH) on the surface as shown the
initial step at Figure 5-3. Organic chlorosilane agents (either methyl trichlorosilane (blue) or
dimethyl dichlorosilane (red)) are deposited on the surface of the silica resonators using chemical
vapor deposition at room temperature for 7 minutes under Argon condition. During the CVD
process, free chlorosilane molecules in a vacuum chamber diffuse and contact with the hydroxyl
group at the surface of the silica resonators. These highly reactive chlorosilane molecules react
with the surface hydroxyl groups based on the silanization reaction, yielding new Si-O-Si bonds
on the boundary and releasing hydrochloride (HCl) molecules. Because only the reactive Si-Cl
sites in the asymmetric chlorosilane molecules can react with the hydroxyl groups on the silica
142
surface, the silanization reaction spontaneously forms an oriented surface molecular mono-layer
until the surface hydroxyl groups are all consumed. In other words, it is worth to note that this
reaction is intrinsically self-limiting, allowing only a single molecular mono-layer to form. This
process generates uniformly grafted MS (blue) or DMS (red) oriented molecular mono-layers on
the surface of the resonant cavities as shown at Figure 5-4 (b). This oriented and ordered monolayer
forms the foundation of the observed surface Raman behavior.
Figure 5-4. (a) A rendering of the toroidal surface Raman laser. A tapered optical fiber
waveguide is used to couple pump light (v1) into the cavity and couple Raman light (v2)
out of the cavity. The microcavity is shown on resonance. The k vector indicates the
propagation direction of the circulating light inside the device, and the E vector represents
the direction of the transverse magnetic (TM) electric field. (b) Schematic of the region
indicated in part (a) To simplify the schematic, only one molecule is shown on the device
surface interacting with the optical evanescent field in air. The orientation of the
molecular Raman mode is parallel to the polarization direction of electrical field E.
143
- Characterization of surface Raman in the silica hybrid resonators
Raman lasing emissions generated from the devices are detected via the optical spectrum
analyzer (OSA). For the characterization of Raman lasing performances, the Raman lasing
emission intensity measured with the OSA is plotted as a function of the amount of power coupled
into the device. The coupled power into the device is a product of the power traveling through the
tapered optical fiber and the percentage of power coupled into the device, which is determined
from the transmission spectra. The threshold of the surface Raman corresponds to the x-intercept
of the linearly fitted line from the plotted graph while the unidirectional efficiency of Raman lasing
is determined from the slope of the linearly fitted line.
144
5. 3. Results and Discussions
5. 3. 1. Characterization of the surface molecular layers
The formation of the mono-molecular single layers is characterized by both indirect and
direct methods. The former indirect method leverages a Cl-substitution with XPS (X-ray
Photoelectron spectroscopy) measurements (Figure 5-5 (a)), and the latter direct method utilizes
the Raman spectroscopy (Figure 5-5 (b)).
Because the surface MS and DMS molecules on silica only consist of carbon (C) and
hydrogen (H) atoms as well as the intrinsic silicon (Si) and oxygen (O), XPS cannot effectively
characterize the molecules due to the high background carbon signal during the XPS
measurements. To address this limitation, the methyl silane (Si(CH3)4) is replaced by a chloro-
substituted methyl silane. This substitution allows the same chemical vapor deposition method to
be used to form a chloro-substituted methyl molecular layer on the surface. The Cl acts as a label
for the methyl group, enabling the molecular mono-layers to be easily distinguished from the initial
bare silica sample by simply tracking the peak of binding energy of chloride in the XPS spectra.
As shown in Figure 5-5 (a), the XPS spectrum of the chloro-substituted methyl silane molecular
layers on silica shows a characteristic peak of binding energy of Cl (2p) at approximately 200 eV,
suggesting the formation of a grafted molecular layer on the surface of silica.
145
Figure 5-5. XPS spectra of a grafted chloro-substituted monolayer on silica and an initial
bare silica. The binding energy of the primary peak of Cl (2p, ~200 eV) presences at the
chloro-substituted molecules grafted on the surface of silica. (b) Raman spectra of a
grafted MS monolayer on silica and the initial bare silica. The Raman peaks at about 2900
cm
-1
originate from the methyl group of the MS molecules grafted on the silica surface.
To directly characterize the grafted molecules, Raman spectroscopy is utilized. Compared
to the initial bare silica surface, the spectra of the MS or DMS coated surfaces clearly show Raman
peaks at 2900 cm
-1
(Figure 5-5 (b)), even though the intensity from the molecular monolayer is
typical low. These peaks are the characteristic Raman peaks of C-H in methyl groups, directly
confirming the formation of MS and DMS molecular layers on the surface silica. These data
confirm the formation of the grafted organic molecular on the surface of silica resonators using the
silanization reaction with CVD method.
146
5. 3. 2. Computational calculations for the microscopic
hyperpolarizabilities
The performance of the molecular surface Raman laser is governed by the vibrational
second hyperpolarizability (γ
vib
) of molecules comprising the surface monolayer as well as their
orientation with respect to the optical field. The surface chemistry process results in a single
molecular mono-layer of perpendicularly oriented Si-O-Si chemical bonds in the molecular layer
that form a surface-specific vibrational mode as shown at Figure 5-4 (b). The γ
vib
can be
approximated using density functional theory (DFT) of related model molecules
52
. As shown at
Figure 5-6, the γ
vib
corresponding to the Si-O mode are calculated to be 1.2 and 1.7 x 10
-36
cm
6
/erg
for the MS and DMS model molecules, respectively. These values are about two times larger than
the silicon dioxide model molecule (0.78 x 10
-36
cm
6
/erg) due to the asymmetry that is introduced
by the organic methyl group in the siloxane structure.
147
Figure 5-6. RHF-based, simulated Raman spectra of three model compounds,
Si(OSiH3)2(OH)2, Si(OSiH3)2(OH)(CH3), and Si(OSiH3)2(CH3)2, plotted with a
Lorentzian broadening (FWHM=8 cm
-1
). Frequencies were calibrated by the
experimental peak position of the C-H vibration so that the peak studied for each sample
was close to the experimental value of the breathing mode at ~450 cm
−1
.
The theoretical vibrational γ
vib
of three model molecules Si(OSiH3)2(OH)2,
Si(OSiH3)2(OH)(CH3), and Si(OSiH3)2(CH3)2 were computed using Gaussian 2003 software
package with RHF and DFT calculations as described in previous literatures
52
. The levels and basis
sets used here were RHF/6-311+G(3df,2p). The calculations focused on the breathing mode of the
compounds around 500 cm
-1
. The ring breathing mode of benzene at 992 cm
-1
( 2 in Herzberg
notation) served as an internal standard to compare across molecules. Here, we used its Raman
of 1.5 10
-35
esu, reported by Levenson and Bloembergen
53
, for the γ
vib
calculations. The
simulated spectra were plotted with a Lorentzian broadening using 8 cm
-1
for the full width at half
magnitude (FWHM). Data are shown in Table 5-1.
400 450 500
0.0
0.2
0.4
0.6
0.8
1.0
Si(OSiH
3
)
2
(OH)
2
Si(OSiH
3
)
2
(OH)(CH
3
)
Si(OSiH
3
)
2
(CH
3
)
2
Intensity (a.u.)
Wavenumber (cm
-1
)
ref
148
Table 5-1. Raman intensity ratios (I
S
/ I
ref
)C and Raman
vib
values determined from
computed Raman activities using RHF/6-311+G(3df,2p) method.
. Molecular Models Exp freq
(cm
-1
)
vib
(cm
6
/erg) 10
-
37
C6H6 992 1.00
150
Si(OSiH3)2(OH)2 462 0.0595
7.8
Si(OSiH3)2(OH)(CH3) 468 0.0871 12
Si(OSiH3)2(CH3)2 429 0.131 17
Note that the simulated spectra are for the three simplified model molecules that are not
anchored to a substrate. Therefore, the results are expected to be slightly different from the
experimental data of the three deposited films in Figure 5-4 (b), which is more similar to the
experiments. However, the simulated results should be informative to show the impact of the
asymmetric structure on the microscopic molecular nonlinear properties due to the fact that the
Raman lasing is dependent on the γ
vib
values of molecules. Frequencies were calibrated by the
experimental peak position of the C-H vibration so that the peak studied for each sample was close
to the experimental value of the breathing mode of silica at ~450 cm
−1
.
C
ref S
I I ) / (
149
5. 3. 3. Spontaneous Raman characterization for Raman gain
coefficients
The spontaneous Raman spectra measurements are exhibited utilizing a Reinsaw InVia
Raman spectrometer with a 100x objective lens. The Raman spectroscopy was performed on three
samples to mimic the chemical structures. The first sample was a silica thin film (a glass slide).
The second and third samples were MS and DMS thin film, prepared by drop-casting
methyltrichlorosilane and dimethyldichlorosilane on silicon wafers followed by exposure to water
vapor for 30 min and then vacuum drying.
This approach results in a disordered thin film which is expected to have reduced gain as
compared to an oriented layer. However, the comparison between samples should prove
informative. The results are presented in Figure 5-7. For both MS and DMS thin films, the C-H
vibration of the methyl groups shows intensive characteristic Raman peaks at ~ 2980 cm
-1
, and the
Si-O vibration shows Raman peaks at about 460 cm
-1
. Because the Raman peaks of interest in this
study are from Si-O vibration, the Raman spectra in the range of ~350 cm
-1
to 550 cm
-1
from the
MS, DMS and silica thin films are directly compared. Comparative Raman gain coefficient at
about 460 cm
-1
of MS and DMS thin film are calculated using the silica thin film as a reference.
150
Figure 5-7. Spontaneous Raman spectra of silica, MS and DMS thin films taken using a
reflective micro-Raman spectrometer. Inset: The area of interest corresponding to the Si-
O vibration approximately at 460 cm
-1
.
The gain values for the MS and DMS layers are ~13.5 × 10
-13
m/W and ~12.9 × 10
-13
m/W
while the silica layer has a negligible signal (0.53 × 10
-13
m/W). The gain coefficient values for
the C-H Raman modes are also calculated to be ~ 1.62 × 10
-11
m/W and 2.97 × 10
-11
m/W for MS
and DMS layers, respectively. These values are ~12 times and ~23 times higher than the values
for the Si-O Raman modes of the MS and DMS layers, respectively. However, in the MS and DMS
microresonators, these C-H Raman modes are randomly distributed and disordered, in contrast to
the Si-O Raman modes which are anchored on the surface and aligned in parallel to the direction
of the electrical field.
500 1000 1500 2000 2500 3000
0
20000
40000
60000
400 450 500 550
0
1000
2000
3000
Intensity (a.u.)
Raman Shift (cm
-1
)
Silica thin film
MS thin film
DMS thin film
151
5. 3. 4. Intrinsic Q factors and Broadscan spectrum
The Q factors are characterized with the tunable laser operated at 765 nm. The resonant
wavelength is determined by scanning across a series of wavelengths. The resonant spectrum is fit
to a Lorentzian, and the loaded Q factor of the device is determined with the equation: Q = λ/Δλ,
where λ is the resonant wavelength of the device and Δλ is the full-width-half-maximum of the
peak, as shown in Figure 5-8 (a). All data and images are recorded with a computer integrated with
PCI GPIB, function generator, and oscilloscope. A general laser communication port (PCI GPIB)
and a function generator are connected to a tunable laser, and they are used to finely tune the laser
wavelength and locate the resonant wavelength of the device. During these measurements, the scan
rate and range of the laser is optimized to ensure the linewidth is not distorted due to thermal or
other effects.
152
Figure 5-8. (a) One of the representative transmission spectra used to obtain the loaded Q
factors from MS device. The resonant wavelengths are 766.05186 and 766.05188 nm
with the loaded Q factors of 5.23 and 4.22 x 10
7
, respectively. (b) The loaded Q factor
data with respect to the coupling percentage. The y-intercept of each linearly fitted data
corresponds to the intrinsic Q factor of either clockwise and counter-clockwise. (c) The
intrinsic Q factors of a series of bulk silica, MS, and DMS devices of two sizes of ~53
μm (solid symbol) and ~83 μm (hollow symbol). Each point represents a unique resonant
cavity device, demonstrating the reproducibility of the fabrication and surface
functionalization process. Error bars are smaller than symbols. (d) One representative
broad-scan spectrum from MS device (diameter of ~53 um) with two different
polarization states (blue and navy) from either TM or TE mode.
153
Figure 5-8 (b) contains the loaded Q factors as a function of the coupling percentage to
calculate the intrinsic Q factor (QInt) of a device. The QInt is determined by attaining the loaded Q
from the transmission spectra over a range of coupling percentage and by removing the extrinsic
losses, or in this case the coupling losses, using a coupled-cavity model
54
. All devices exhibit ultra-
high Q between 1×10
7
to 1×10
8
, as shown at Figure 5-8 (c). The presence of grafted MS and DMS
molecules causes the QInt of the devices to decrease. However, it is important to note that the Q Int
are still in excess of 10 million for all devices, which are high enough to generate Raman lasing.
Figure 5-8 (d) is one of the representative broad-scan spectra from MS device containing
two different polarization states, either TM or TE. Polarization state is finely controlled with
polarization controller before coupling to the devices. Each broadscan spectrum has fundamental
TM or TE mode with a distance of one FSR, which is approximately 2.33 nm for 765 nm with a
55 μm diameter device.
154
5. 3. 5. Characterization of surface Raman lasing
Figure 5-9 (a) ~ (c) contains representative emission spectra from the three device types
with ~ 350 μW of coupled power, pumped at ~765 nm. In the bulk silica devices (Figure 5-9 (a)),
the Raman emission is solely from the SRS of bulk silica, where the Si-O vibrational Raman mode
is randomly aligned, and the intensity of the Raman emission is exceptionally weak
55
. In contrast,
in the devices functionalized with MS and DMS, Raman lasing can be generated more efficiently
than the bulk silica devices as shown at Figure 5-9 (b) ~ (d). This is due to the fact that the highly
oriented Si-O vibrational Raman modes on surface by single molecules are parallel to the direction
of incident electric field circulating in the resonators. The shifts of the emission from both MS and
DMS devices are around 450 cm
-1
, which is corresponding to the Raman shift of the Si-O
vibrational mode
56
.
155
Figure 5-9. Representative output spectra of bulk, MS and DMS devices. (a) ~ (c). Output
emission spectra captured by the OSA from bulk, MS, and DMS devices, respectively
with ~53 μm diameters. All devices have similar Q factors and are pumped by the 765nm
laser with ~350 μW coupled power. Both MS and DMS devices show strong Raman
lasing peaks at about 795 nm, while the bulk silica device shows a very weak emission.
(d) Direct comparison of Raman lasing emission power from the three device types. The
emission peak for the bulk silica device is plotted twice, with a shift in the y-axis only.
Using the same input power, the MS and DMS devices show an enhanced lasing power
of about 50 times higher than that in the bulk silica device. (e) Schematic of surface
features of bulk silica, MS, and DMS devices with the proposed surface vibrational
Raman modes indicated.
156
The Raman shift of the first order Raman peaks for all devices tested as part of this work
are plotted in Figure 5-10. The peak position in the devices varies slightly from ~420 to ~500 cm
-
1
. All frequency shifts measured for all devices fall within the broad, continuous Raman gain
spectrum of silica
57,58
.
Figure 5-10. Raman shifts of the first order Raman emission peak for all devices studied.
The peak positions fall within the Raman gain band of Si-O vibrational mode.
It is worth noting that emission peaks around 980 nm (Raman shift in the range of ~2850
cm
-1
to ~2980 cm
-1
) from the C-H stretching modes of the methyl groups on the functionalized
devices are not observed, even under high input power (Figure 5-11). In contrast to the highly-
aligned Si-O vibrational mode that is anchored directly on the surface and oriented with the
circulating field, the orientation of the C-H stretching modes of the methyl groups in the surface
molecules are randomly distributed (in-plane and out-plane) and are not parallel to the polarization
direction of the electrical field. The absence of emission peaks at ~980 nm agrees with the
300
400
500
DMS Device MS Device Bulk Silica
~ 52 m ~ 83 m
Bulk Silica
MS Device
DMS Device
Raman Shift (cm
-1
)
157
hypothesis that the orientation of the sub-molecular vibrational mode is critical to the enhancement
observed.
Figure 5-11. Comparison of Raman spectra between the aligned Si-O mode and
disordered C-H mode in MS devices. (a) Schematic of the aligned Si-O mode (𝝂 𝐒𝐢 −𝐎 ) of
the surface MS layer. The surface Raman mode direction is parallel to the direction
incident electrical field. (b) Schematic of the disordered C-H mode (𝝂 𝐂 −𝐇 ) of the surface
MS layer. The mode directions, both in-plane and out-plane (not shown in the schematic),
are randomly distributed and are not parallel to the direction electric field. (c) Output
spectrum (750 nm to 810 nm) of a DMS device (50 μm; Q = 5.4 × 10
7
) pumped at ~765
nm with coupled power of about 400 μW. The Raman lasing peak at about 793 nm
corresponding to the Si-O vibrational mode. (d) Output spectrum (950 nm to 1000 nm)
of the same MS device as in part (c) also pumped at ~765 nm.
158
To further investigate the impact of the surface single-molecular layer on the device
performance, the lasing threshold and the efficiency for first order Raman of a series of devices
was analyzed. The MS and DMS devices (~53 μm) have similar threshold power values of ~ 200
μW), compatible to those of the bulk silica devices (Figure 5-12 (a)). The circulating intensity is a
particularly useful metric as it includes Q and size in the calculation, allowing a more direct
comparison across devices. The circulating intensity in the cavity is presented as Pcirc/Am, where
Pcirc is the circulating power derivates from coupled power and Am is the optical mode area (Figure
5-12 (a), Inset). For both device diameters, the circulating intensity thresholds for the MS and
DMS devices are about one third smaller than those for the bulk silica devices.
159
Figure 5-12. Raman lasing performance of the devices. (a) The dependence of the output
power of the first order Raman on the coupled input power in the bulk silica, MS, and
DMS devices with a diameter of ~53 μm. Q factors are 9.1 × 10
7
, 4.7 × 10
7
and 5.4 × 10
7
for bulk silica, MS and DMS devices, respectively. Inset is the dependence of the output
power of the first order Raman emissions on the circulating intensity of the optical field
in the cavity. (b) Comparison of first order Raman lasing efficiencies of the bulk, MS and
DMS devices with diameters of either ~53 μm (solid symbol) and ~83 μm (hollow
symbol). While the efficiency does not change with diameter, the lasing efficiency of the
MS and DMS devices is significantly higher than the bulk silica device with an
approximately 10 times increase. These efficiency values are particularly notable as they
are unidirectional efficiencies.
The slope efficiencies (output Raman lasing power vs coupled pump power) of the bulk,
MS and DMS devices with two set of sizes are plotted in Figure 5-12 (b). Distinguished from the
bulk silica devices (slot efficiencies: 3-6%), all of the MS and DMS devices have exceptionally
high unidirectional Raman efficiencies of about 40% or about ten-fold higher than bulk silica
devices.
160
For an oriented Raman mode, the Raman scattering intensity (S) is dominated by the mode
orientation (Raman tensor) and polarization geometry. The relation can be expressed as 𝑆 ∝
|𝑒 𝑠 ⋅ 𝛼 𝑅 ⋅ 𝑒 𝑖 |
2
, where 𝑒 𝑠 and 𝑒 𝑖 are the polarization vector of the scattered and incident light
respectively, and 𝛼 𝑅 is the Raman tensor of a specific vibrational mode
17,59
. In WGM
microresonators, the electric field direction of the fundamental TM mode is on the radial direction,
while that of the fundamental TE mode is perpendicular to the radial direction. Because of the
isotropic nature of the Raman gain in the bulk silica device, the Raman lasing behavior lacks a
polarization dependency as shown at Figure 5-13. However, in the MS and DMS devices, the
Raman behaviors show a dependence on the polarization (Figure 5-14 and Figure 5-15,
respectively). The sloped lasing efficiency under one polarization is about two times higher than
the other polarization, for both MS and DMS devices. These results, as well as the enhanced
Raman efficiencies, suggest that a new and high efficiency single-molecular-layer Raman laser
can be developed based on microresonator-enhanced surface vibrational nonlinear process.
161
Figure 5-13. Polarization dependent Raman lasing data from bulk silica device (a)
Broadscan spectrum from bulk silica indicating different fundamental modes from each
polarization state. (b) Raman threshold spectra from bulk silica indicating Raman
efficiency and Raman threshold from each polarization state. (c) Raman emission spectra
from bulk silica indicating output Raman lasing power from each polarization state.
As shown at Figure 5-13 (a), two different fundamental modes (black and grey) from
different polarization states (TM and TE) are utilized as pump to generate Raman lasing in the
bulk silica device. With the similar input pump power (~400 μW), the output Raman power is
almost the same from two different polarization states (Figure 5-13 (c)). As plotting the output
Raman intensity with respect to the coupled power into the device as shown at Figure 5-13 (b), the
Raman lasing efficiencies, or slope of the linearly fitted lines, are almost the same from two
different polarization states in the bulk silica device. This result indicates that the Raman lasing
162
performances in bulk silica is independent on the polarization states of the incident electric field
due to the randomly distributed Si-O vibrational mode over the bulk silica.
Figure 5-14. Polarization dependent Raman lasing data from MS device (a) Broadscan
spectrum from MS silica indicating different fundamental modes from each polarization
state. (b) Raman threshold spectra from MS silica indicating Raman efficiency and
Raman threshold from each polarization state. (c) Raman emission spectra from MS silica
indicating output Raman lasing power from each polarization state.
Figure 5-14 (a) contains representative broadscan spectrum from MS device indicating that
two different fundamental modes (blue and navy) from different polarization states (TM and TE)
are utilized as pump to generate surface Raman lasing in the MS device. With the similar input
pump power (~400 μW), the output Raman power is significantly different from one polarization
163
state to the other (Figure 5-13 (c)). This discrepancy supports the polarization dependent surface
Raman lasing performances in the MS device owing to the highly aligned surface Si-O vibrational
Raman mode by single molecular layer. As plotting the output Raman power with the coupled
power into the device as shown at Figure 5-13 (b), the Raman lasing efficiencies, or slope of the
linearly fitted lines, from one polarization state (~ 40 %) is substantially higher than that of the
other polarization state (~ 12 %). This result demonstrates the polarization dependent surface
Raman lasing performances in the MS device compare with the bulk silica device (Figure 5-13).
Figure 5-15. Polarization dependent Raman lasing data from DMS device (a) Broadscan
spectrum from DMS silica indicating different fundamental modes from each polarization
state. (b) Raman threshold spectra from DMS silica indicating Raman efficiency and
Raman threshold from each polarization state. (c) Raman emission spectra from DMS
silica indicating output Raman lasing power from each polarization state.
164
Figure 5-15 (a) is corresponding to the representative broadscan spectrum from DMS
device exhibiting two different fundamental modes (red and wine) from different polarization
states (TM and TE). As two different fundamental modes are used to generate surface Raman
lasing in the DMS device (Figure 5-15 (c)), the output Raman power shows significantly difference
from one polarization state to the other like the MS device (Figure 5-14). This similar result with
MS device explains the polarization dependent surface Raman lasing behaviors in the DMS device
as well. The polarization dependent Raman performance is attributed to the fact that highly
oriented surface Si-O vibrational Raman mode by DMS molecules has substantially enhanced
interaction with the applied electric field, which is parallel to each other. As plotting the output
Raman power with the coupled power into the device as shown at Figure 5-15 (b), the Raman
lasing efficiencies, or slope of the linearly fitted lines, from one polarization state (~ 40 %) is
substantially higher than that of the other polarization state (~ 12%). This result demonstrates the
polarization dependent surface Raman lasing performances in the DMS device compare with the
bulk silica device (Figure 5-13).
165
Figure 5-16. Comparison of first order Raman lasing efficiencies of the bulk silica, MS
and DMS devices with diameters of either ~53 μm (solid symbol) and ~83 μm (hollow
symbol) with different polarization states.
Figure 5-16 contains all the Raman lasing efficiency data from bulk silica, MS, and DMS
devices with two different sizes (solid symbol: ~53 μm or hollow symbol: ~83 μm) from two
different polarization states (TM or TE mode). As we discussed in Figure 5-13 to Figure 5-15, the
bulk silica devices show Raman lasing efficiency of approximately ~5% with no polarization
dependent
60
. On the other hands, MS and DMS devices exhibit substantially enhanced Raman
lasing efficiency with a strong polarization dependence compared with bulk silica devices
22
. For
one polarization state with efficiency of around ~12 %, the enhancement of Raman lasing
efficiency is due to the asymmetric structure induced by organic molecules causing more vibration
of the surface Raman mode as we discussed at Figure 5-6 and Figure 5-7. In the meantime, for the
other polarization state with efficiency of around ~40%, Raman lasing efficiency improvement is
owing to the alignment between surface vibrational Raman mode and the direction of electric field
of circulating optical field
22,31,32
. Both the enhancement of Raman lasing efficiency and the
0
10
20
30
40
50
Efficiency (%)
Bulk Silica DMS Device MS Device
166
polarization dependent performances indicates that the surface Raman lasing is generated by
grafting organic molecules on the surface of silica microresonators.
167
5. 4. Summary
In conclusion, surface Raman lasing is demonstrated by combining an highly oriented
organic monolayer with an ultra-high-Q optical microcavity. Due to the improved alignment of
the surface Raman modes by the siloxane molecule with the incident optical field, the efficiency
and lasing thresholds are significant improved. The ordered asymmetric monolayers of MS and
DMS are formed on the surface of the toroidal microresonators using CVD, allowing Q > 10
7
to
be maintained. Using a 765 nm excitation source, low threshold Raman emissions located at ~465
cm
-1
are observed in both the MS and DMS devices with Raman lasing efficiencies above 40%.
These efficiencies represent over 10 times improvement as compared to bulk silica devices, and
the enhancement is attributed to the alignment of the oriented surface Si-O-Si vibrational Raman
mode to the direction of the applied electric field of the optical whispering gallery mode. This
work represents a new strategy for dramatically increasing the nonlinear optical performance of
integrated photonic devices using organic molecules.
168
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Chapter 6. Q-switched Raman laser with VO
2
coated
silica microcavity
6. 1. Introduction
The temperature dependent metal to insulator transition (MIT) of vanadium dioxide (VO
2
)
has been an area of intense scientific research in the last decade due to the fact that it is
accompanied by dramatic electrical and optical properties changes with temperature
1–5
. A balance
of cooperative interactions of crystal structure and electronic degrees of freedom drives the
material into a critical regime in which it undergoes a first-order transition from a low-temperature
insulator phase to high-temperature metallic phase at a critical temperature of 340 K. As the crystal
symmetry changes from monoclinic to rutile in single crystal VO2, the resistivity change can reach
a factor of 10
5
over a temperature range of 0.1 K
6
. The MIT in VO2 has been studied by ultrafast
spectroscopy
7
, spectroscopic ellipsometry
8
and X-Ray spectroscopy
9
, Photo-assisted electrical
gating
10
, plasmonic switches
11
, hybrid VO2/Si photonic microring switches
12
, and thermal
homeostatic surfaces
13
as well as various other electronic, photonic and electro-optic devices based
on the MIT of VO2 have been proposed and demonstrated
14–18
.
178
6. 2. Background and motivation
To the best of our knowledge, there have been no research exploring the use of this unique
phase transition material with high quality factor whispering gallery mode optical resonators to
generate Q-switched Raman laser. WGM resonators have found applications as on-chip lasers
19–
23
, optical frequency combs
24–28
, chemical and biological sensors
29–33
since these devices can
support ultra-high quality factor (Q) resonances near the device surface
34
.
The WGM microresonator is well suited platform to investigate the effects of a phase
transition material coating on device operation since the optical modes are confined near the
boundary
35
. We hypothesize that coating a critical thickness of VO2 on the surface of a high-quality
factor silica microtoroid will induce a regenerative bi-stability in the resonator, or Q-switched
behavior, with temperature dependent. In other words, the high-quality factor would be preserved
in the dielectric state generating stimulated Raman scattering (SRS) but drops an order of
magnitude when the material switches to the metallic phase (at local temperatures > 70
o
C) limiting
the generation of SRS, resulting a Q-switching Raman laser
36–40
.
179
6. 3. Experimental Methods
6. 3. 1. Silica microresonator fabrication
Silica toroidal microcavities are fabricated with the same procedure as described
previously, which is composed of the three main steps; photolithography to define silica circle
patterns (80 μm of diameter) on silicon wafers, XeF2 etching to remove silicon isotropically in
order to obtain silica disks elaborated on silicon pillar, and CO2 laser reflow to produce atomically
smooth silica toroids
41
. Figure 6-1 (a) shows one of the representative top-view optical microscope
images of the fabricated silica toroid with diamter around 55 μm.
Figure 6-1. Top-view optical microscope images of (a) bare silica toroid (b) VO2
deposited toroid with diameter of ~50 μm reflowed from 80 μm disks.
180
6. 3. 2. VO2 deposition on silica toroid
A 248 nm KrF excimer laser with an energy density of 1.5 J/cm
2
is used for the VO2
growth. The deposition chamber is evacuated to a background pressure of ∼10
−7
Torr before the
deposition followed by filling to an optimal oxygen partial pressure of 10 mTorr
42
. The chamber
heats up the growth temperature of 800 °C. High chamber temperature is required to obtain
polycrystalline VO2 rather than amorphous VO2 growth at low temperature
43
. The chamber
temperature is measured by a thermocouple attached to the substrate heater. A dense
polycrystalline V2O5 is utilized as a target, which is pre-ablated to maintain a fresh surface during
each growth. After the deposition, the devices are cooled down with rate of 5 °C/min to room
temperature under an oxygen partial pressure of 10 mTorr.
181
6. 3. 3. Testing set-up with temperature stage
To investigate the unique property of VO2, which is the temperature dependent MIT, a
temperature stage is accompanied with the previous testing set-up. The quality (Q) factor of the
devices are characterized with a tunable narrow linewidth laser (Velocity series, Newport),
operated at 1550 nm, which is the wavelength that shows significant MIT of VO2 compared with
the visible wavelength region. The laser light propagates through a tapered optical fiber, which is
obtained by slowly pulling a single-mode optical fiber (F-SMF-28, Newport) while it is heated
with a hydrogen torch. A single mode fiber is obtained by monitoring a transmission property
through the fiber via oscilloscope while pulling the optical fiber
44
. The device is aligned parallelly
with the tapered optical fiber, and the coupling between the device with the fiber is controlled with
a 3-axis nano-positioning controller stage. The light from the taper is coupled into the device by
the evanescent field coupling and coupled back to the tapered optical fiber again.
The output from the optical fiber is sent to a 90:10 splitter for 1550 nm, which is connected
to the photodetector with oscilloscope and the optical spectra analyzer (OSA, YOKOGAWA
AQ6370C). The photodetector is connected to the high-speed digitizer/oscilloscope. The resonant
wavelength is determined by scanning across a series of wavelengths. The resonant spectrum is fit
to a Lorentzian, and the loaded Q factor of the device is obtained using the expression: Q = λ/Δλ,
where λ is the resonant wavelength and Δλ is the full-width-half-maximum
45–48
. The OSA detects
the emitted light from toroid that is coupled back to the optical fiber. The intrinsic Q factor is
determined by attaining the loaded Q from the transmission spectra over a range of coupling
percentage and by removing the extrinsic losses, or in this case the coupling losses, using a
coupled-cavity model
49,50
.
182
6. 4. Results and Discussions
The Q factors of the devices are compared before and after the VO2 coating on silica toroid
devices. In case of bare silica devices, the intrinsic Q factors are in the range of 10
7
~ 10
8
,
41,47
whereas the intrinsic Q factor is expected to drop after VO2 coating due to the material absorption
loss caused by the VO2 layer
51–53
. Figure 6-2 (a) contains one of the representative transmission
spectra to obtain the loaded Q factors from 50 nm VO2 coated device, and the intrinsic Q factor of
the device is shown at Figure 6-2 (b)
54
. Due to the high Q factors of over 10
6
, the mode splitting is
observed from the device
55–57
. Even with the 50 nm thickness, however, VO2 has intrinsic
absorption at the testing wavelength of 1550 nm, decreasing intrinsic Q factors from 10
8
to 10
6
. In
order to generate the third order nonlinear optical processes, such as stimulated Raman
scattering
58,59
, the resonator requires high Q factor, which indicates that the thickness of VO2 layer
is optimized minimizing the material absorption loss while maintaining MIT property of VO 2
layer.
183
Figure 6-2. (a) One of the representative transmission spectra exhibiting the loaded Q
factors from VO2 (50 nm) coated silica toroid. The resonant wavelengths are 1570.3052
and 1570.3077 nm with the loaded Q factors of 1.97 and 2.52 x 10
6
, respectively. (b) The
loaded Q factors as a function of the coupling percentage to obtain the intrinsic Q factor
of VO2 coated device.
The temperature dependent MIT of VO2 on silica device is investigated by increasing the
temperature of device as shown at Figure 6-3 (a). The coupling percentage is set to be similar over
the range of temperature to properly compare the loaded Q factors as a function of temperature.
The MIT temperature is approximately 65 ~ 75
o
C, where the insulator state of VO2 is transitioning
to the metal state
60
. In other words, at high temperature, the absorption of VO2 around 1550 nm
dramatically increase due to the transitioning from the insulator to the metal state
61
. With the
sudden change, we are expecting to observe Q-switching property of VO2 coated device caused
by the material absorption loss of the VO2 metal state
35
. As shown at Figure 6-3 (a), however, there
is no Q switching behavior observed with increasing the temperature up to 80
o
C, which is higher
than the VO2 MIT temperature.
184
Figure 6-3. (a) The loaded Q factor over the range of temperature from 30 to 80
o
C with
consistent coupling percentage (approximately 10 %). (b) Resonance wavelength shift
(Δλ) as a function of the temperature change (ΔT).
As the device temperature increases, the resonance shift is also observed as shown at Figure
6-3 (b). The resonance wavelength shift is due to the thermal coefficient of the material
62,52,63
. The
thermal shift of bare silica and VO2 are ~10 pm/
o
C and ~0.1 μm/
o
C, respectively, based on the
thermal coefficient of the materials. The measured thermal shift of the VO2 coated devices is 11.14
pm/
o
C, which is similar to silica than VO2. The thermal shift result represents that most of the
optical mode in the silica layer instead of VO2 layer despite the fact that the refractive index of
VO2 (~3.21 at insulator and ~2.15 at metallic state at 1550 nm
35
) is much higher than that of silica
(1.444 at 1550 nm). This behavior could be due to phase matching between the tapered silica
optical fiber and the VO2 coated devices, where deviation of effective refractive index between
them is huge
44
. In other words, even if the index of VO2 is higher than that of silica, the coupling
efficiency between the tapered optical fiber to the VO2 layer becomes low owing to the phase
mismatch causing hard to excite an optical mode in VO2 layer
64
.
185
6. 5. Summary
VO2 has the unique property of MIT with temperature. By leveraging this property, VO2
could be act as a Q-switching material when it is integrated with silica microresonators. The
intrinsic Q factors of VO2 (50 nm) coated silica toroids are investigated showing over 10
6
, which
is high enough to observe the SRS, or Raman lasing. The temperature dependent Q factor behavior
in VO2 coated toroid is measurement with increasing device temperature. However, there is no Q-
switching behavior with VO2 layer. This could be due to the fact that the optical mode is mostly
in the silica layer instead of VO2 layer, confirmed by thermal shift of a resonance wavelength.
More rigorous study, such as simulating to optimize the geometry of VO2 coated device and testing
with various VO2 conditions, should be conducted to demonstrate the Q-switched Raman laser
with VO2 coated silica microresonators.
186
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Abstract (if available)
Abstract
Due to unique optical properties of silica, silica-based photonic devices have found many important applications throughout science and engineering, especially in sensing, communications, lasers, and integrated photonic devices. Recently developed on-chip silica toroidal microresonators become one of the most promising microcavity due to their exceptional ability to confine optical energy temporarily (high quality factor, ~10⁷) and spatially (mode volume, ~ 1000 um³) while being integrated on a silicon substrate. Due to the ultra-high quality (Q) factors, silica microresontors can generate high circulating intensity (~ 1GW/cm²) with small amount of input power, that is enough to generate third-order nonlinear optical phenomena in devices. However, nonlinear optical proceeses in silica microcavity are often limited by intrinsic material properties of silica
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Creator
Choi, Hyungwoo
(author)
Core Title
Development of novel optical materials for whispering gallery mode resonator for nonlinear optics
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Chemical Engineering
Publication Date
12/11/2019
Defense Date
08/30/2019
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OAI-PMH Harvest,whispering gallery mode, nonlinear optics, stimulated Raman scattering, laser
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Armani, Andrea M. (
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), Ravichandran, Jayakanth (
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), Willner, Alan E. (
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), Zhou, Chongwu (
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)
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chyungwo@usc.edu,hwchoi0109@gmail.com
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whispering gallery mode, nonlinear optics, stimulated Raman scattering, laser