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Fabrication and characterization of yoroidal resonators for optical process improvement

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Fabrication and characterization of yoroidal resonators for optical process improvement

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Content 1 Fabrication and Characterization of Toroidal Resonators for Optical Process Improvement By Soheil Soltani A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL THE UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Electrical Engineering) May 2018 2 Acknowledgements Unlike preliminary stages in academic life that are defined around a single goal, Phd is a journey in life, science and philosophy. A transition from "simple way of thinking" to "facing hard to digest" problems. For the first time in PhD, I learnt that "I don't know anything" and how working with other people to find solutions for unknown problems is necessary. Fortunately, I was not alone in this journey, and I had the honor of receiving tremendous help and guidance from many people and I owe them a lot. First of all, I would like to thank the most important person in my PhD, Prof Andrea Armani, who gave me the opportunity and honor to be a member of her research group. Thank you so much for believing in me and trusting my abilities. Thank you so much for being patient with my mistakes. I appreciate all your guidance and useful discussions that we had on the projects, I learnt a lot from them. One of the greatest experiences in my life was coming to US to expand the territories of my knowledge, this transition was not easy and it was only because your support that I could successfully pass it. I know how difficult it is to lead a large research group and to guide each student to make progress in their research; it was so inspiring for me to see how you passionately directed each student and helped them solve their problems. Among the most exciting moments in these 6 years, was when we attended Photonics West, I appreciate the opportunity that you gave me to present myself in front of the most prominent scientists and gain self-confidence. I will never forget our great Lab Reunion nights in San Francisco. Perhaps the most valuable experience was the full freedom to design and build my own experiments, thank you for such high level of trust in your students. I loved our wonderful lab parties and Olympics, although I was far from my family but I felt that I have a new family here. 3 On my way towards accomplishment of my projects, I have received invaluable help and guidance from many USC professors, students and mentors. I thank all my Qualifying and Dissertation Committee members: Prof Wei Wu, Prof Han Wang, Prof Milind Tambe and Prof Alice Parker. In addition, special thanks to Prof William Steier for many hours of invaluable discussion on scientific problems. I would like to thank Prof Aluizio Prata for the creative method and wonderful story in teaching Electromagnetics. Special thanks and congratulations to Prof Armand Tanguay for such an innovative method in teaching. In addition, I would like to thank Dr. Willie W. Ng for helping me in using the Ellipsometer. I appreciate all the help and support that I received from Dr Matthew Mecklenburg and John Curulli to capture the most beautiful SEM photos in my PhD. I have no doubt, that I owe a great deal of my pleasure and great time to my lab mates. Armani Lab members created a wonderful atmosphere in our group and made each moment a unique memory. Many thanks to each member of the group specially: Vinh Diep, Hyungwoo Choi, Dongyu Chen, Kelvin Kuo, Alexa Hudnut (specially for helping me with the asymmetric project and my thesis), Rene Zeto, Andre Kovac, Victoria Sun, Mathew Reddick, Nishita Deka, Danny, Lili, Gumi, Martin, Linda, Garrison, Leah, Emma, Tara, Sam K-L, Max (specially for his help on Asymmetric device simulation), Brian, Nic, Bradley, Chai, Audrey Harker, Sahar Elyahoodian, Inae Kim, Sam Mcbirney, Dr Eda Gungor (for all her supportive role), Dr Erick Moen (for training me on cell culture project and wonderful SF nights!), Dr Xiaoqin Shen, Dr Rigoberto Castro Beltran, Dr Michelle Lee, Dr Cecilia Zurita Lopez (The Boss! Specially for training me in cell culture lab), Dr Tushar Rane, Dr Rasheeda Hawk, Dr Maria V. Chistiakova, Dr Ce Shi, Dr Simin Mehrabani (such a great cleanroom mentor bi taaarooff!), Dr Jason Gamba, Dr Ashley J Maker (The fun never ends!), Dr Mark C Harrison (a wonderful group mentor!), Dr 4 Xiaomin Zhang. In addition, I have had the honor of working with several visiting scholars and I appreciate the experience working with them, specially: Dr Yong-Won Song, Dr Abian Bentor Socorro, Dr Imran Cheema and Tobi Weinhold. I would love to thank the most influential and encouraging people all over my life, my caring parents. Without their Love, help and support, I would not have successfully made it to the end of my PhD. Thank you so much for sacrificing yourselves to give me everything I needed to become the person I am. I would love to thank my sister Roya for her support, help and encouragement during these 6 years. Besides my family in Iran, I had a second family here who were always with me in all the moments. I would love to thank you all: Shima (Khanoom Dr!), Mohsen (A fifa Pro!), Peyman, Reza, Amirsoheil (for all the Deldariii and Omiiid), Sepideh,Sadaf,Fereshteh khanoom, Nima, Marjan, Jalal, Misagh, Zohreh, Niloofar, Mohsen, Shiva, Mr Haghighat, Mrs Javanfar, Mr Taheriyn and Mrs Taheriyan, Mrs Motahari, Mr Motahari, Mahzad and Sam, Dayi Bagher, Firouzeh, Bahram, Dr Kiani , Dr Motevalli, Kasra and Milan Koochooloo. 5 Table of Contents Acknowledgements.......................................................................................................................2 Table of Contents..........................................................................................................................5 List of Figures...............................................................................................................................6 List of Tables…............................................................................................................................11 Abstract.........................................................................................................................................12 1. Chapter 1: Overview of the Thesis ...............................................................................13 1.1. Motivation ............................................................................................................................. 13 1.2. Chapter Overview ................................................................................................................. 14 1.3. Chapter 1 References ........................................................................................................... 15 2. Chapter 2: Background...................................................................................................18 2.1. Wave Nature of Light ........................................................................................................... 18 2.2. Origins of Refractive index .................................................................................................. 20 2.3. Waveguides ............................................................................................................................ 21 2.4. Resonators ............................................................................................................................. 25 2.5. Fabry-Perot Resonator ......................................................................................................... 26 2.6. Ring resonators ..................................................................................................................... 29 2.7. Circulating Power ................................................................................................................. 31 2.8. Mode Volume ........................................................................................................................ 32 2.9. Purcell Factor ........................................................................................................................ 32 2.10. Spherical Resonators ............................................................................................................ 32 2.11. Mode structure ...................................................................................................................... 34 2.12. Microtoroid Cavities ............................................................................................................. 35 2.13. Effective Refractive Index .................................................................................................... 37 2.14. I-field Percentage Weighted Refractive Index ................................................................... 37 2.15. II-Numerical Approximation of effective refractive index ............................................... 38 2.16. Device Fabrication ................................................................................................................ 38 2.17. Testing.................................................................................................................................... 39 2.18. Chapter 2 References ........................................................................................................... 41 3. Chapter 3: Optothermal Transport Behavior in Whispering Gallery Mode Optical Cavities..........................................................................................................................................43 3.1. Introduction .......................................................................................................................... 43 3.2. Theory .................................................................................................................................... 44 3.3. Simulation Details ................................................................................................................. 52 3.4. Optical Field Distribution .................................................................................................... 52 3.5. Thermal Simulations ............................................................................................................ 53 3.6. Thermal time constant of the Toroid .................................................................................. 56 3.7. Fabrication ............................................................................................................................ 58 3.8. Device Characterization ....................................................................................................... 58 3.9. Data analysis ......................................................................................................................... 59 6 3.10. Measuring the Opto-thermal constant of ITO using a Toroidal resonator ..................... 62 3.11. Quality factor calculation ..................................................................................................... 63 3.12. Thermo-optic phenomena .................................................................................................... 63 3.13. Simulation and modeling ..................................................................................................... 64 3.14. Material synthesis ................................................................................................................. 65 3.15. Experiments .......................................................................................................................... 66 3.16. Conclusion ............................................................................................................................. 68 3.17. Chapter 3 References ........................................................................................................... 68 4. Chapter 4 Opto-mechanical, regenerative oscillation in optical resonators..............71 4.1. Introduction .......................................................................................................................... 71 4.2. Theory .................................................................................................................................... 72 4.3. Finite element method modeling ......................................................................................... 78 4.4. Mechanical modes in asymmetric resonators .................................................................... 78 4.5. Dependence of Frequency on Geometry ............................................................................. 81 4.6. Fabrication ............................................................................................................................ 82 4.7. Device characterization ........................................................................................................ 84 4.8. Asymmetric Crown and Cantilever Mode.......................................................................... 84 4.9. Dependence of Frequency on Asymmetry (M) ................................................................... 86 4.10. Dependence of threshold on asymmetry ............................................................................. 87 4.11. Failure analysis ..................................................................................................................... 89 4.12. Conclusion ............................................................................................................................. 90 4.13. Chapter 4 References ........................................................................................................... 90 5. Chapter 5: Suspended Silica Splitters............................................................................93 5.1. Introduction .......................................................................................................................... 93 5.2. Theory .................................................................................................................................... 94 5.3. Fabrication ............................................................................................................................ 98 5.4. Cylindrical waveguides ........................................................................................................ 99 5.5. Simulation results ............................................................................................................... 100 5.6. Broadband operation span................................................................................................. 101 5.7. Dependence on material ..................................................................................................... 105 5.8. References ............................................................................................................................ 107 6. Chapter 6: Biological Systems......................................................................................110 6.1. Introduction ........................................................................................................................ 110 6.2. Scattering from Living cells ............................................................................................... 110 6.3. Modeling .............................................................................................................................. 111 6.4. Details of COMSOL Modeling .......................................................................................... 112 6.5. Maxwell's equations governing scattering from cells ...................................................... 117 6.6. Ultrasound Treatment of Gold Nanoparticle Infused Cells ............................................ 119 6.7. Ultrasound Generator System ........................................................................................... 120 6.8. Cell line and culture conditions ......................................................................................... 124 6.9. Conclusion ........................................................................................................................... 124 6.10. Chapter 6 References ......................................................................................................... 125 Appendix A: Nonlinear frequency comb generation and operation improvement.............127 7 A.1 Introduction ......................................................................................................................... 127 A.2. Raman Scattering ................................................................................................................. 132 A.3. Kerr nonlinearity ................................................................................................................. 133 A.4. Improvement of nonlinear response ................................................................................... 135 A.5. Theory .................................................................................................................................. 137 A.6. Characterization of off plasmonic resonance nano particle coated cavity ..................... 139 A.7. Observation of parametric frequency comb generation from coated devices ................ 140 A.8. Gold Nanoparticle Enhancement at off Plasmonic Wavelengths ................................... 142 A.10. Appendix References .......................................................................................................... 154 List of Figures FIGURE 2- 1:LIGHT CONSISTS OF TWO PERPENDICULAR TIME-VARYING ELECTRIC AND MAGNETIC FIELDS[2] .............................................................................................................................. 18 FIGURE 2- 2:A SEMI TRANSPARENT PLATE ILLUMINATED FROM A SOURCE IN POINT A ................... 20 FIGURE 2- 3: SNELL'S LAW INDICATES THAT THE TRANSMISSION ANGLES OF A BEAM OF LIGHT PASSING THROUGH THE INTERFACE BETWEEN TWO MATERIALS DEPENDS ON THE REFRACTIVE INDEX OF THE TWO SIDES. ..................................................................................................... 22 FIGURE 2- 4: A WAVEGUIDE CONSISTS OF A HIGH REFRACTIVE INDEX MATERIAL THAT IS COVERED BY A CLADDING THAT HAS A LOWER REFRACTIVE INDEX. LIGHT TRAVELS INSIDE A WAVEGUIDE BY SUCCESSIVE TOTAL INTERNAL REFLECTIONS IN TWO INTERFACES. .............. 23 FIGURE2- 5:FIRST FEW MODES SUPPORTED IN AN OPTICAL FIBER. THE PROFILES ARE GOVERNED BY BESSEL FUNCTIONS ............................................................................................................... 24 FIGURE 2- 6: FIRST FEW MODES SUPPORTED IN A SLAB WAVEGUIDE. ............................................. 24 FIGURE2- 7: DIAGRAM OF THE RESULT WHEN TWO OPTICAL WAVES MEET DEPENDING ON THE PHASE OF EACH INITIAL WAVE THE RESULTING WAVE COULD HAVE LARGER ,SMALLER OR EVEN ZERO AMPLITUDE.[10] ................................................................................................. 26 FIGURE 2- 8:FABRY-PEROT RESONATOR AND IT'S TYPICAL TRANSMISSION SPECTRUM. ................. 27 FIGURE 2- 9:QUALITY FACTOR IS DEFINED BY (A)NUMBER OF OSCILLATIONS DURING DECAY TIME CONSTANT OF A PULSE INPUT. (B) LINEWIDTH OF THE RESONANT RESPONSE IN FREQUENCY DOMAIN. ............................................................................................................................... 28 FIGURE 2- 10: OPTICAL RING RESONATOR IN RESONANCE CONDITION. WHEN THE CIRCUMFERENCE OF THE RING EQUALS TO AN INTEGER FACTOR OF THE WAVELENGTH THEN THE CIRCULATING LIGHT WILL HAVE THE SAME PHASE AS THE INPUT LIGHT AND AS A RESULT THE LIGHT BUILDS UP.[12] ................................................................................................................................. 29 FIGURE 2- 11: OPTICAL MICROSCOPE IMAGE OF A MICROSPHERE ATTACHED TO THE END OF OPTICAL FIBER .................................................................................................................................... 33 FIGURE 2- 12: THE FIRST FEW RESONANCE MODE PROFILES IN A SILICA MICRO-SPHERE WITH A RADIUS OF 75 MICRONS FOR N=1 AND (A) L=M (TE) (B)L=M (TM) (C)L=M-1 (D)L=M-2 (E)L=M-3 (F) N=2 AND L=M. ................................................................................................. 34 FIGURE 2- 13: (A) COUPLING LIGHT TO A TOROID USING A TAPERED FIBER. (B) THE FUNDAMENTAL PROPAGATING MODE INSIDE A TOROIDAL CAVITY. ................................................................ 35 FIGURE 2- 14: OPTICAL MICROSCOPE IMAGE OF A TAPERED OPTIC FIBER (TAPER). BY PULLING A TAPER ONE CAN EFFICIENTLY COUPLE LIGHT INTO A RING RESONATOR. ............................... 37 FIGURE2- 15:TOROIDAL CAVITY FABRICATION STEPS: FIRST SILICA PADS ARE CREATED ON SILICON SUBSTRATE BY PHOTOLITHOGRAPHY AND BOE ETCHING, NEXT THE SILICA DISKS ARE 8 RELEASED BY XEF2 ETCHING OF THE SAMPLES. IN THE LAST STEP THE SAMPLES ARE REFLOWED UNDER CO2 LASER TO GET A SMOOTH HIGH QUALITY SURFACE FINISH. .............. 39 FIGURE 2- 16: (A)SCHEMATIC OF THE RESONATOR TESTING SET UP. (B) TYPICAL TRANSMISSION SPECTRUM OF A PEAK IN FORWARD AND BACKWARD SWEEP. ................................................ 40 FIGURE 3- 1 (A) MODE PROFILE FOR THE FUNDAMENTAL MODE OF A TOROID WITH A RADIUS OF 35 MICRONS. (B) SEM IMAGE A REFLOWED TOROID WITH THE SAME SIZE. (C) SCHEMATIC OF A TOROID AND CONTROL PARAMETERS IN SIMULATION ENVIRONMENT. .................................. 47 FIGURE 3- 2: A)-SIMULATION OF THE RATIO OF THE THERMALLY INDUCED SHIFTS VS OXIDE THICKNESS B)-SIMULATION OF THE RATIO OF THE THERMAL SHIFT VS OVERHANGING LENGTH. IT IS IMPORTANT TO MENTION THAT THESE GRAPHS SHOW THE EFFECT OF STRUCTURAL PARAMETERS AS WELL AS MODE VOLUME SOLELY AND THE EFFECT OF THE WATER LAYER HAS NOT BEEN TAKEN INTO ACCOUNT................................................................................... 48 FIGURE 3- 3:(A) MEASURED WAVELENGTH SHIFT FOR A TOROID WITH R=26µM AT Λ= 1303.0814NM (B) THRESHOLD DIAGRAMS FOR THREE DIFFERENT WAVELENGTHS. ..................................... 51 FIGURE 3- 4:EFFECT OF VARYING THE THICKNESS IN THERMAL BROADENING OF THE SILICA MICRO TOROIDS ............................................................................................................................... 52 FIGURE 3- 5: SAME DEVICE GEOMETRY AT THREE DIFFERENT WAVELENGTHS (1550,1330 AND 765 NM) ....................................................................................................................................... 53 FIGURE 3- 6:DIFFERENT POWER REGIONS IN WHISPERING GALLERY MODE. ................................... 56 FIGURE 3- 7:(A) THERMAL PULSE APPLIED TO A TOROID (B) DETERMINING THE THERMAL TIME CONSTANT BY FITTING AN EXPONENTIAL CURVE TO THE GRAPH ........................................... 57 FIGURE 3- 8:AN EXAMPLE OF LORENTZIAN FIT TO A LOW COUPLED PEAK. .................................... 60 FIGURE 3- 9:A TYPICAL COUPLING VS SHIFT DIAGRAM CALCULATED USING THE ABOVE-MENTIONED PROCEDURE .......................................................................................................................... 61 FIGURE 3- 10: FEM MODELING RESULTS. THE OPTICAL FIELD DISTRIBUTION WITH A) AN SIO2 FILM AND B) AN ITO FILM. C) THE MODAL ENERGY DENSITY DISTRIBUTION CROSS SECTION IN THE DEVICE WITH BOTH FILMS. THE OPTICAL FIELD CLEARLY CHANGES BOTH SHAPE AND DISTRIBUTION WITH THE HIGH INDEX FILM. .......................................................................... 65 FIGURE 3- 11: A) TEMPERATURE SENSING IN REAL-TIME WITH NOISE. B) THE RESULTS FROM BOTH MEASUREMENT APPROACHES ARE PLOTTED FOR DIRECT COMPARISON. ADDITIONALLY, THE SHIFT FROM A BARE SILICA TOROID AND THE BASELINE NOISE LEVEL ARE INCLUDED. .......... 68 FIGURE 4- 1:FIRST 14 MECHANICAL MODES OF A TOROIDAL RESONATOR. ..................................... 76 FIGURE 4- 2:(A) RENDERING OF A FIBER TAPER-COUPLED ASYMMETRIC CAVITY. (B) SCHEMATIC WHERE THE PARAMETERS OF MINIMUM MINOR RADIUS (RMIN), MAXIMUM MINOR RADIUS (RMAX), MAXIMUM MAJOR RADIUS (RMAX), MINIMUM MAJOR RADIUS (RMIN), TOTAL DIAMETER (D), VERTICAL OFFSET ( ΔZ) AND MAXIMUM PILLAR SHIFT ( ΔLMAX) ARE LABELED. (C) SEM OF A CROSS-SECTION OF THE SMALLER SIDE OF AN ASYMMETRIC DEVICE WITH LARGE VERTICAL OFFSET. ..................................................................................................... 77 FIGURE 4- 3:FEM SIMULATION RESULTS OF THE FIRST 14 MODES OF AN ASYMMETRIC CAVITY ALONG WITH THEIR CORRESPONDING FREQUENCIES. THE RED LINES INDICATE THE LOWEST THRESHOLD MODES FOR SYMMETRIC DEVICES: THE FIRST AND THIRD CANTILEVER MODES. THE BLUE LINES INDICATE THE LOWEST THRESHOLD MODES FOR THE ASYMMETRIC DEVICES: THE SECOND ASYMMETRIC CROWN MODE AND THE SECOND ASYMMETRIC CANTILEVER MODE. DEGENERATE MODES ARE REPRESENTED WITH AND AND LINKED WITH A BRACKET. .. 79 FIGURE 4- 4:THEORETICALLY CALCULATED DEPENDENCE OF SECOND ASYMMETRIC CROWN MODE (BLACK SQUARES, LEFT AXIS) AND CANTILEVER MODE (BLUE CIRCLES, RIGHT AXIS) ON THE 9 AVERAGE (A) MINOR RADIUS, (B) MAJOR RADIUS, AND (C) OVERHANG LENGTH. EACH IS FIT TO A QUADRATIC (RED LINE). ................................................................................................ 82 FIGURE 4- 5:(A) BRIGHT FIELD IMAGE OF THE ASYMMETRIC DEVICE WITH THE MAJOR AND MINOR RADII ILLUSTRATED. DASHED LINES ARE CIRCLES DRAWN AS GUIDES TO THE EYE TO AID IN VISUALIZING THE ASYMMETRY PRESENT IN THE DEVICE. ESA SPECTRA DATA FOR THE TWO LOWEST THRESHOLD MODES FROM THE ASYMMETRIC DEVICE: (B) THE ASYMMETRIC CROWN MODE AND (C) THE ASYMMETRIC CANTILEVER MODE. THRESHOLD CURVES FOR (D) THE ASYMMETRIC CROWN MODE AND (E) THE ASYMMETRIC CANTILEVER MODE. ........................ 85 FIGURE 4- 6:OVERHANG LENGTH NORMALIZED FREQUENCY DEPENDENCE OF THE (A) SECOND ASYMMETRIC CROWN MODE AND (B) SECOND ASYMMETRIC CANTILEVER MODE ON THE ECCENTRICITY PARAMETER, M. BLACK SQUARES ARE RESULTS FROM FEM SIMULATIONS, AND RED CIRCLES CORRESPOND TO EXPERIMENTAL RESULTS. THE SOLID BLACK LINE IS A FIT TO THEORETICAL DATA FOR ILLUSTRATION PURPOSES. MAXIMUM ERROR IS AROUND 5%. NOTE: THERE ARE ERROR BARS IN BOTH THE X AND Y AXES, BUT THE ERROR BARS ARE USUALLY SMALLER THAN THE SYMBOLS. THE ERROR IN THE M RATIO IS CALCULATED BY MULTIPLE MEASUREMENTS OF RMIN AND RMAX IN OPTICAL IMAGES, SIMILAR TO THE ONE SHOWN IN FIG. 4(A). THE ERROR IN THE NORMALIZED FREQUENCY IS CALCULATED BY PROJECTING THE ERRORS OCCURRED IN M TO THE VALUES OF MEASURED FREQUENCY........ 86 FIGURE 4- 7:(A) NORMALIZED THRESHOLD GRAPH FOR ASYMMETRIC CROWN MODE VS. PILLAR SHIFT. (B) NORMALIZED THRESHOLD FOR ASYMMETRIC CANTILEVER MODE VS. PILLAR SHIFT. NOTE THAT THE THRESHOLD VALUES HAVE BEEN NORMALIZED (PTH*Q3/VRM) TO DESENSITIZE THEM TO OTHER FACTORS THAT AFFECT THRESHOLD. VRM IS THE AVERAGE MODE VOLUME. ..................................................................................................................... 87 FIGURE 4- 8:CROSS SECTION OF THREE DIFFERENT TOROIDS WITH DIFFERENT DEGREES OF REFLOW ............................................................................................................................................. 88 FIGURE 4- 9:DIAGRAM OF VERTICAL OFFSET VS PERCENTAGE OF MELTED DISK. ........................... 88 FIGURE 4- 10:EXAMPLE OF DEVICES WITH NO ASYMMETRIC RESPONSE ......................................... 89 FIGURE 5- 1:THE PROTRUSION REGION FORMED BY REFLOWING PROCESS, RESULTS IN ESCAPE OF LIGHT FROM WAVEGUIDE ...................................................................................................... 94 FIGURE 5- 2:(A) SCHEMATIC OF THE SUSPENDED SPLITTER DESIGN IN LUMERICAL (B) AN SEM IMAGE OF A FINAL FABRICATED DEVICE WITH CORRESPONDING PARAMETERS. ..................... 95 FIGURE 5- 3:COMPARISON OF A SMOOTH AND ACTUAL PROTRUSION ON MULTIMODE COUPLING BETWEEN TWO SPLITTER ARMS. ............................................................................................ 97 FIGURE 5- 4:PROPAGATION OF LIGHT AT THE PROTRUSION REGION. THIS SIMULATION SHOWS HOW LIGHT GETS COUPLED TO OTHER MODES AT THE "TRAP REGION". ......................................... 98 FIGURE 5- 5:GENERAL SOLUTIONS FOR THE FIRST FEW MODES IN A CYLINDRICAL WAVEGUIDE ... 100 FIGURE 5- 6:COUPLING RATIO IN BAR AND CROSS OUTPUTS FOR A SUSPENDED SPLITTER. ........... 101 FIGURE 5- 7:(A) SIMULATION OF COUPLING RATIO VS. WAVELENGTH (B) EXPERIMENTAL COUPLING RATIO FOR A TYPICAL DEVICE. ............................................................................................ 103 FIGURE 5- 8:CALCULATED TOTAL EXCESS LOSS FOR THROUGH AND CROSS OUTPUT. ................... 104 FIGURE 5- 9:EFFECTIVE REFRACTIVE INDEX FOR TE AND TM MODES AFTER CONFORMAL MAPPING. ........................................................................................................................................... 105 FIGURE 6- 1:IMAGES OF HCT 116 COLON CANCER CELLS FROM (A) DIC AND (B) FLORESCENT IMAGES USED FOR THE BASIS OF LUMERICAL AND COMSOL MODELS OF THE CANCER CELLS. ........................................................................................................................................... 112 10 FIGURE 6- 2:SCATTERING FROM (A) ONE (B) TWO PARTICLES. (C) SCATTERING PATTERN FROM FRONT VIEW. ....................................................................................................................... 114 FIGURE 6- 3:GRAPHICAL REPRESENTATION OF THE RELATIONSHIP BETWEEN THE PERCENT POWER SCATTERED AND THE NUMBER OF BACTERIA WITHIN THE SENSING CHAMBER CALCULATED USING COMSOL. (INSET) EXAMPLE OF THE OUTPUT OF THE SCATTERED FIELD IN THE X AND Y DIRECTION IF THERE ARE TWO CELLS IN THE REGION. ...................................................... 115 FIGURE 6- 4:FIELD SCATTERING OF A SINGLE CELL USING THE NEW BACKGROUND FIELD ........... 116 FIGURE 6- 5:SCHEMATIC OF SCATTERING PROBLEM FROM A CELL ............................................... 117 FIGURE 6- 6:SIMPLIFIED SCHEMATIC OF SCATTERING FROM A CELL. ............................................ 118 FIGURE 6- 7:SCATTERING FROM A SPHERE WITH N=1.5 , R=1 MICRONS IN WATER AT 633NM ...... 118 FIGURE 6- 8:SCHEMATIC OF THE CELL TREATMENT SET UP ALONG WITH PHOTOS FROM THE TRANSDUCER. ..................................................................................................................... 121 FIGURE 6- 9:FREQUENCY RESPONSE OF CELLS IN (A) VOIGT CONSTRUCT (B) MAXWELL CONSTRUCT ........................................................................................................................................... 122 FIGURE 6- 10:FREQUENCY RESPONSE OF A SPHERICAL NANOPARTICLE INSIDE A CELL ................. 123 FIGURE 6- 11:ABSORPTION SPECTRUM OF THE GOLD NANOPARTICLES ........................................ 124 FIGURE A- 1 SIMULATION OF TM MODE AT 1550NM. (A) FIELD DISTRIBUTION NEAR THE GOLD NANO PARTICLE AT A DISTANCE OF 15 NM. (B) AND (C) FIELD PROFILE ON THE EQUATORIAL PLANE WITH AND WITHOUT GOLD NANO-PARTICLE (D) MAXIMUM FIELD ENHANCEMENT OF A GOLD NANOPARTICLE VS. DISTANCE FROM THE SURFACE OF THE RESONATOR. THE ASPECT RATIO OF PARTICLE IS 3.8 WITH A WIDTH OF ~17 NM. ......................................................... 138 FIGURE A- 2:EXPERIMENTAL SETUP. 3D SCHEMATIC OF THE EXPERIMENTAL SETUP USED FOR OPTICALLY CHARACTERIZE THE QUALITY FACTOR AND FREQUENCY COMB GENERATION. .. 140 FIGURE A- 3:(A)EXPERIMENTAL OBSERVATION OF A GENERATED FREQUENCY COMB. AS A RESULT OF CASCADED DEGENERATE AND NON-DEGENERATE OPTICAL PARAMETRIC OSCILLATION A FREQUENCY COMB IS GENERATED. (B) DEPENDENCE OF OPO ON THE TAPER-RESONATOR GAP. ........................................................................................................................................... 141 FIGURE A- 4:OPTICAL FREQUENCY COMB FORMATION IN: (A) BARE MICROSPHERE AND (B) COATED MICROSPHERE WITH GOLD NANOROD CONCENTRATIONS OF 0.125 MM. THE KERR COMB GENERATION IS ENHANCED BY THE PRESENCE OF GOLD NANORODS DECORATING THE SURFACE OF THE DEVICES. THE PERFORMANCE IS MAINLY GOVERNED BY RAMAN-ASSISTED FWM EMISSIONS. ............................................................................................................... 143 FIGURE A- 5:OPTICAL MODE PROFILE AND SCHEMATIC STRUCTURE OF THE HYBRID MICROSPHERES. A, FEM SIMULATION OF THE OPTICAL MODE OF IN THE MICROSPHERE WITH RADIUS OF 60 ΜM (LEFT). THE MODE PROFILE AT THE CROSS SECTION OF THE DEVICE (RIGHT) INDICATES ABOUT 11% OF THE OPTICAL FIELD EXTENDS OUT OF THE SILICA SURFACE, AND IS ABLE TO INTERACT WITH THE ~ 2 NM MONOMOLECULAR LAYERS. B, DIAGRAM OF FOUR WAVE MIXING IN ACTIVE THIRD ORDER NONLINEAR Χ(3) MEDIUM. C, SCHEMATIC STRUCTURE OF BARE SILICA SPHERE, HYBRID SILICA SPHERE GRAFTED WITH CHLOROOMETHYL PHENYL SILANE (CPS) MONOLAYER (BLUE COLOR), AND HYBRID SILICA SPHERE GRAFTED WITH DIETHYLAMINO-STYRYL-PYRIDIUM (DASP) MONOLAYER (RED COLOR). ........................... 148 FIGURE A- 6:COMPARISON BETWEEN DIFFERENT RESONATORS COATED WITH DIFFERENT SMALL MOLECULES. AS ILLUSTRATED IN THE FIGURE BY COATING THE RESONATOR WITH A THIN LAYER OF SMALL MOLECULES THE QUALITY FACTOR DOES NOT DROP DRASTICALLY. ........ 149 FIGURE A- 7:MEASUREMENT SCHEME. LIGHT FROM THE 1550 NM TUNABLE DIODE LASER IS COUPLED INTO THE MICROSPHERE USING AN OPTICAL FIBER TAPER. THE OPTICAL SIGNAL WAS 11 SPLIT BY A 90/10 BEAMSPLITTER (BS), WITH 90% OF OPTICAL SIGNAL IS COUPLED INTO THE OPTICAL SPECTRUM ANALYZER (OSA) TO CAPTURE THE OUTPUT EMISSION SIGNAL, AND 10% OF THE OPTICAL SIGNAL TO A PHOTODIODE (PD) TO MONITOR THE LASER TRANSMISSION SIGNAL BY OSCILLOSCOPE (O-SCOPE). ............................................................................... 150 FIGURE A- 8:OUTPUT SPECTRA FROM DIFFERENT MICROSPHERES PUMPED BY A 1550 CW DIODE LASER. ................................................................................................................................ 151 FIGURE A- 9:EXPERIMENTAL RESULTS AND ENERGY LEVEL DIAGRAM OF PARAMETRIC OSCILLATION. ..................................................................................................................... 152 List of Tables Table 2-1. Summary of the types of resonators, typical quality factor and applications.......40 Table 3-1. Thermal characteristics of a toroid at different wavelengths..............................51 Table 4-1. Summary of energy ratio and mechanical mode for the two primary symmetric and asymmetric modes calculated based on simulations. The maximum energy ratio for both the symmetric and asymmetric devices with the lowest threshold powers are presented. (*) Denotes the corresponding mode number in Fig.4-3.......................................................................80 Table 5-1. Simulation results for three different materials...............................................105 12 Abstract Due to high speed and large capacity of optical devices there is an ever increasing demand in fabrication and integration of cost effective optical devices that could be used for many applications such as sensing [1-4], data storage [5-8], medical applications [9-11], optical processing, and military applications [12-14]. Light has the capability to propagate at extremely high speeds that no other carrier can achieve (c=3×10 8 m/s). This high speed makes it the best candidate for signal transmission. However, unlike electronic devices that work with electrons as carriers and require electron controlling mechanisms such as resistance, potential, and current, optical devices must process optical signals. This necessitates the development of optical signal manipulation techniques. The most powerful factor in optical device design is refractive index manipulation. Refractive index can be controlled by the spatial shaping of a material or by doping atoms with different densities. In this thesis, I have investigated the design, fabrication, and characterization of whispering gallery mode optical resonators for applications in telecommunications. First, I have studied the wave nature of light and the equations governing propagation of light in dielectric devices. Next, I have studied how we design and fabricate Whispering gallery mode resonators, including both spheres and toroidal resonators. Finally, I have shown several interesting applications of whispering gallery mode resonators, such as thermal response, frequency combs, and cavity optomechanics. 13 Chapter 1: Overview of the Thesis 1.1. Motivation Owing to their higher speed, capacity and low power consumption, optical devices have become promising candidates to replace their electronic counterparts. Technology has passed its introductory steps and so far many all-optical devices have been designed and fabricated, such as filters [15, 16], waveguides [17, 18], couplers [19, 20], and multiplexers [21-23]. These devices have numerous applications in emerging fields, such as high accuracy drug delivery [24, 25], quantum electrodynamics (QED)[26-28], high sensitivity detection [29-31], and telemetry [32- 34]. Therefore, the accurate design and a thorough understanding of the optical processes governing these devices is crucial to transition to the "photonic era". Similar to electronic capacitors that are ubiquitous in almost every electronic circuit, one of the main components that are needed in nearly all of the optical integrated circuits is a resonator, which is able to store light, select a specific wavelength of light, introduce delay, or build up intensity. The most common type of resonator is a Fabry-Perot [35, 36]. A Fabry-Perot cavity is made of two parallel, face-to-face mirrors that resonantly confine a specific wavelength of light in between them. Another type of resonator that works by the constructive summing of light signals is called a travelling wave resonator [37-39]. In order to compare these two types of light resonators, we need to know how efficient they are in storing light. The main parameter to compare this ability is the Quality Factor (Q). For a Fabry-Perot cavity, the highest resonator quality factor achieved is in the range of 10 4 -10 5 . In contrast, traveling wave resonant cavities have demonstrated Q values in excess of 100 million. One type of traveling wave resonant cavity of particular interest is the silica microtoroid resonant cavity. Integrated on a silicon wafer, these types of resonators are formed by melting a suspended silica disk from its edge to make a torus shape [40]. As a result of its high quality 14 factor, microtoroids have enabled researchers to observe interesting features of light-matter interaction, such as, radiation pressure oscillations and thermal bistability. For my PhD research, I have studied several unique features of these toroidal resonators. I looked into the interesting behaviors that the toroids exhibit due to their high quality factor including: geometry-dependent radiation induced pressure oscillations, thermal broadening, two photon absorption, frequency comb formation, and polarization filtering. 1.2.Chapter Overview In Chapter Two, I provide a background on the wave nature of light, refractive index and propagation of light, and the mechanisms and parameters governing light propagation. Next, I introduce unique features of silica as a medium for light confinement. Then, I introduce the concept of whispering gallery mode resonators and standard formalism for resonators. I explain the differences between various device types and their quality factors. In Chapter Three, an interesting thermal response of the toroidal cavities is studied experimentally and theoretically. I have developed a 3D thermo-coupled optical model that accurately predicts the device's behavior and is used in thermal device design. This response is then harnessed to make high sensitivity thermal sensors by coating the device with thermally sensitive materials such as Indium Titanium Oxide (ITO). Finally, I have shown that this thin layer can modify the structure of the mode. In Chapter Four, I have studied optomechanical modes under the influence of radiation pressure exerted by the high circulating optical intensity. Unlike previous work, this research focused on how asymmetries in the device structure changed the mechanical oscillation frequency. These mechanical vibrations are excited as a direct result of the force induced by 15 light and is not observed in normal conditions in bulk materials due to large mass and low exerted pressure. In Chapter Five, I discuss suspended silica optical waveguides and propagating modes; specifically, suspended multimode silica splitters and the unique features of these devices for broad bandwidth splitting and on-chip sensing. I have modelled and studied the broadband response of these devices and have designed 3D FDTD models to explain the sensitivity of these devices to different environmental factors influencing the device performance. In Chapter Six, I explore the light matter interaction between optical signals and biological media. I have studied the structure of some cells and have shown how light interacts with living cells in the UV and visible wavelength range. Furthermore I have studied the effect of cell structure on scattering characteristics of any incoming light signal. In Appendix A, I have studied several nonlinear phenomena in silica microresonators. Since silica has inversion symmetry, the lowest order nonlinearity in silica is third order, which will result in many interesting nonlinear phenomena such as Raman and Brillion Scattering and Optical Parametric Oscillation (OPO). I have shown how utilizing these nonlinearities forms optical frequency combs. Furthermore, I have leveraged the nonlinear response of gold nanoparticles to improve the nonlinear behavior in optical resonators. 1.3. Chapter 1 References 1. M. Khorasaninejad, N. Clarke, M. P. Anantram, and S. S. Saini, "Optical bio-chemical sensors on SNOW ring resonators," Opt. Express 19, 17575-17584 (2011). 2. X. Zhang and A. M. Armani, "Silica microtoroid resonator sensor with monolithically integrated waveguides," Opt. Express 21, 23592-23603 (2013). 3. A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, C. Sai, D. Gill, M. Anthes-Washburn, M. S. Unlu, and B. B. Goldberg, "Optical sensing of biomolecules using microring resonators," Selected Topics in Quantum Electronics, IEEE Journal of 12, 148-155 (2006). 16 4. J.-J. Li and K.-D. Zhu, "All-optical mass sensing with coupled mechanical resonator systems," Physics Reports 525, 223-254 (2013). 5. D. Day, M. Gu, and A. 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Qu, "Optical imaging for medical diagnosis based on active stereo vision and motion tracking," Opt. Express 15, 10421-10426 (2007). 12. R. J. Pimpinella, "A fiber optic connector designed for military optical backplanes," Components, Hybrids, and Manufacturing Technology, IEEE Transactions on 15, 992-997 (1992). 13. Z. Jian-Gao, N. Yu-De, and L. Zheng, "Military avionics optical fiber data buses with active-coupler configurations," Aerospace and Electronic Systems Magazine, IEEE 14, 27-33 (1999). 14. W. G. Egan and M. J. Duggin, "Synthesis of optical polarization signatures of military aircraft," in 2002), 188-194. 15. Y. L. Lee, N. E. Yu, C. S. Kee, D. K. Ko, Y. C. Noh, B. A. Yu, W. Shin, T. J. Eom, K. Oh, and J. Lee, "All-optical wavelength tuning in solc filter based on TI:PPLN waveguide," Electronics Letters 44, 30-32 (2008). 16. J. Dong, S. Fu, X. Zhang, P. Shum, L. Zhang, J. Xu, and D. Huang, "Single SOA based all-optical adder assisted by optical bandpass filter: Theoretical analysis and performance optimization," Optics Communications 270, 238-246 (2007). 17. R. R. Hayes and D. Yap, "GaAs spiral optical waveguides for delay-line applications," Lightwave Technology, Journal of 11, 523-528 (1993). 18. R. He, Q. An, J. R. Vázquez de Aldana, Q. Lu, and F. Chen, "Femtosecond-laser micromachined optical waveguides in Bi4Ge3O12 crystals," Appl. Opt. 52, 3713-3718 (2013). 19. J. P. Donnelly, N. DeMeo, and G. Ferrante, "Three-guide optical couplers in GaAs," Lightwave Technology, Journal of 1, 417-424 (1983). 20. W.-P. Huang and B. E. Little, "Power exchange in tapered optical couplers," Quantum Electronics, IEEE Journal of 27, 1932-1938 (1991). 21. H. Huang, Y. Yue, Y. Yan, N. Ahmed, Y. Ren, M. Tur, and A. E. Willner, "Liquid- crystal-on-silicon-based optical add/drop multiplexer for orbital-angular-momentum-multiplexed optical links," Opt. Lett. 38, 5142-5145 (2013). 17 22. X. Chen, A. Li, J. Ye, A. Al Amin, and W. Shieh, "Reception of mode-division multiplexed superchannel via few-mode compatible optical add/drop multiplexer," Opt. Express 20, 14302-14307 (2012). 23. C. Xi, L. An, Y. Jia, A. Al Amin, and W. Shieh, "Demonstration of Few-Mode Compatible Optical Add/Drop Multiplexer for Mode-Division Multiplexed Superchannel," Lightwave Technology, Journal of 31, 641-647 (2013). 24. M. Zamadar, G. Ghosh, A. Mahendran, M. Minnis, B. I. Kruft, A. Ghogare, D. Aebisher, and A. Greer, "Photosensitizer Drug Delivery via an Optical Fiber," Journal of the American Chemical Society 133, 7882-7891 (2011). 25. N. Horiuchi, "Optical manipulation: Light-driven delivery," Nat Photon 10, 293-293 (2016). 26. D. Eimerl, "Quantum electrodynamics of optical activity in birefringent crystals," J. Opt. Soc. Am. B 5, 1453-1461 (1988). 27. L. C. D. Romero, D. L. Andrews, and M. Babiker, "A quantum electrodynamics framework for the nonlinear optics of twisted beams," Journal of Optics B: Quantum and Semiclassical Optics 4, S66 (2002). 28. G. Rempe, "Atoms in an optical cavity: Quantum electrodynamics in confined space," Contemporary Physics 34, 119-129 (1993). 29. B. Kuswandi, Nuriman, J. Huskens, and W. Verboom, "Optical sensing systems for microfluidic devices: A review," Analytica Chimica Acta 601, 141-155 (2007). 30. B. Troia, A. Paolicelli, F. D. Leonardis, and V. M. N. Passaro, Photonic Crystals for Optical Sensing: A Review, Advances in Photonic Crystals (2013). 31. L. Polavarapu, J. Perez-Juste, Q.-H. Xu, and L. M. Liz-Marzan, "Optical sensing of biological, chemical and ionic species through aggregation of plasmonic nanoparticles," Journal of Materials Chemistry C 2, 7460-7476 (2014). 32. B. C. Larson, "An optical telemetry system for wireless transmission of biomedical signals across the skin," (Massachusetts Institute of Technology, 1999). 33. P. Tyack, "An optical telemetry device to identify which dolphin produces a sound," The Journal of the Acoustical Society of America 78, 1892-1895 (1985). 34. J. Firth, F. Ladouceur, Z. Brodzeli, M. Wyres, and L. Silvestri, "A novel optical telemetry system applied to flowmeter networks," Flow Measurement and Instrumentation 48, 15-19 (2016). 35. N. L. Hoang, J. S. Cho, Y. H. Won, and Y. D. Jeong, "All-optical flip-flop with high on- off contrast ratio using two injection-locked single-mode Fabry-Perot laser diodes," Opt. Express 15, 5166-5171 (2007). 36. R. Quintero ‐Torres and M. Thakur, "Picosecond all ‐optical switching in a Fabry–Perot cavity containing polydiacetylene," Applied Physics Letters 66, 1310-1312 (1995). 37. W. J. Wang, S. Honkanen, S. I. Najafi, and A. Tervonen, "New integrated optical ring resonator in glass," Electronics Letters 28, 1967-1968 (1992). 38. Y. Jung, G. Brambilla, G. S. Murugan, and D. J. Richardson, "Optical racetrack ring- resonator based on two U-bent microfibers," Applied Physics Letters 98, - (2011). 39. Z. Haibin and J. Chun, "Optical Isolation Based on Nonreciprocal Micro-Ring Resonator," Lightwave Technology, Journal of 29, 1647-1651 (2011). 40. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-928 (2003). 18 Chapter 2: Background 2.1.Wave Nature of Light Light primarily refers to a part of electromagnetic spectrum which has a frequency ranging from 7.5×e 14 to 1.5×e 13 , the behavior of which is governed by Maxwell’s equations. Electromagnetic waves can be thought of as two perpendicular Electric and Magnetic fields which are time-varying. Any change in the electric field will generate the magnetic field and vice versa[1]. Figure 2- 1:light consists of two perpendicular time-varying electric and magnetic fields[2] In fig.2-1, the two perpendicular waves have been shown. By Maxwell’s equations to determine the amplitude of the generated electric and magnetic field: (in non-conducting medium)[3]. H E t μ ∂ ∇× = − ∂ (2-1) E H t ε ∂ ∇× = ∂ (2-2) 19 (2-3) (2-4) The above equations also can explain the behavior of the electromagnetic waves when they are propagating inside a material. Assuming that the material is lossless and has a dielectric constant of ε, then the governing wave equation is derived to be: (2-5) where 1 c με = is the propagation speed of the wave. The general solution of the above equation is: (. ) 0 j kr t EEe ω − = (2-6) The argument of the above mentioned solution changes with time and position. Also, in the above equation, the quantity 2 22 2 kn c ω = is called propagation constant. The ability of the atoms to mimic the behavior of the field is measured by n which is called refractive index. When an electromagnetic field enters a dielectric medium, the electric field of the wave forces the atoms and electrons to vibrate at the same frequency of original wave. As a result, due to vibration of the charge carrying particles, the field is regenerated and continues to propagate inside the medium. Refractive index is a measure of how strong the particles in a medium react to the electric field of the wave. The square of refractive index is called the electric permittivity of the material. .0 .0 E H ∇= ∇= 20 2.2.Origins of Refractive index In order to understand what is the refractive index, for one moment let's assume that we have a sheet of material that is being illuminated from one side by a source. The total field at a point B far from the plate could be explained in the form of the summation on the field from the vibration of electrons inside the sheet and the original field from the source. [4] from all other charges Bsource EE E =+  (2-7) For simplicity, we will assume that there is a monochromatic source at point A which is shown by: () 0 z jt c s EEe ω − = (2-8) Figure 2- 2:A semi transparent plate illuminated from a source in point A By assuming that the origin is placed on the center of the plate one can assume that there is an electromotive force that drives the electrons to vibrate and, due to this vibration, there is a secondary electromagnetic field after the plate: () 0 0 . 2 z jt c q Total field j x e c ω η ω ε − − = (2-9) where η is the number of charges per unit area, x0 is the amplitude of vibrations from the force exerted by the electric field. By equating the field generated after the plate and the integrated B A 21 field after the field, it can be shown that the retardation due to the propagation of the field inside is associated with a refractive index of: 2 22 00 1 2( ) Ne n m εω ω =+ − (2-10) where N is the number of charge carriers per unit volume, e is the charge of electron, and ω0 is the resonant frequency of the charge carriers. As was expected, the refractive index is dependent on the density of the material as well as the strength of the interaction between the particles inside the medium. 2.3.Waveguides When a beam of electromagnetic wave meets the interface between two materials with different permittivities, a portion of the wave is reflected and a portion is transmitted. The direction of incident and transmitted light is measured in terms of the angle between the vector normal to the interface and the direction of propagation of the field. The transmitted field's angle is determined from Snell's Law:[5] 11 2 2 sin sin nn θθ = (2-11) 22 Figure 2- 3: Snell's law indicates that the transmission angles of a beam of light passing through the interface between two materials depends on the refractive index of the two sides. A special case of transmission of light between two media is when the first material has a higher refractive index than the second one. In this case, the transmission angle increases as we increase the incidence angle. The interesting case is when the incidence angle reaches to a point where the direction of the transmitted wave becomes parallel to the interface line. This angle of incidence is called critical angle: 1 2 1 sin ( ) cr n n θ − = (2-12) If we increase the angle of incidence more than the critical angle then the incident wave is not transmitted anymore, and the interface acts as a 100% reflecting mirror. This interesting phenomenon is used to trap light in a high refractive index material. By shining light into a long piece of transparent material at an angle larger than the critical angle of the interface, one can see that light is kept inside the material and comes out from the other side. This "light carrying property" is called "waveguiding" and is used to transfer optical signals for long distances. The device is called a waveguide. 23 Figure 2- 4: a waveguide consists of a high refractive index material that is covered by a cladding that has a lower refractive index. Light travels inside a waveguide by successive total internal reflections in two interfaces. Maxwell's equations are used to explain how the electromagnetic waves propagate inside a waveguide. The fundamental equations that govern the behavior of the waves are[6]: (2-13) E H t ε ∂ ∇× = ∂ (2-14) .Dq ∇= (2-15) .0 B ∇= (2-16) The first two equations describe the behavior of time varying field in a medium and the second two apply some restrictions to the value of the fields in presence of a charge source. We can show that by mixing the first two equations, we can get the equation below[3]: 2 2 2 E E t με ∂ ∇= ∂ (2-17) The last equation is called the wave equation in a sourceless and lossless medium. This equation describes how an electromagnetic wave propagates inside a waveguide. n 1 Input wave n 2 H E t μ ∂ ∇× = − ∂ 24 Figure2- 5:First few modes supported in an optical fiber. The profiles are governed by Bessel functions For optical fibers the solution of the wave equation reveals that the modes supported in a fiber are in form of Bessel functions. The first few optical modes supported in a slab dielectric waveguide have been shown in fig. 2-7. Figure 2- 6: First few modes supported in a slab waveguide. Maxwell's equations explain that the modes supported inside a slab waveguide are in pure sinusoidal form[7]. The generic solution of wave equation usually has the form of [8]: 25 ( , ,) ( , ,) tjkz E x yz A x yz e ω − =   (2-18) where A(x,y,z) is the amplitude profile of the propagating wave. Also, 2 ωπν = is the angular velocity of the wave where ν is the frequency of the propagating waveand 2 n k π λ = is the wave number of the propagating wave. Most of the time, the medium containing light is a lossy medium; therefore, it is necessary to include loss in the field calculations. Usually loss is imported as the imaginary part of the refractive index: ri nn jn =− . Since the carried power is proportional to the square of electric field intensity, it can be shown that the power loss coefficient of the medium is[9]: 0 4 i n π α λ = (2-19) Therefore, it is of crucial importance that we use a material with the lowest absorption coefficient. 2.4.Resonators One of the interesting features of light is that it can be trapped inside a structure which reflects it on itself or rotates it around one point on a circle or an ellipse. In such cases due to the ability of light to interfere with another light wave, the original light will add up with the reflected or circulated light and will produce a new complex wave. Depending on the phase difference between the two initial waves, the resulting wave could have a smaller, larger, or even zero amplitude. 26 Figure2- 7: Diagram of the result when two optical waves meet depending on the phase of each initial wave the resulting wave could have larger ,smaller or even zero amplitude.[10] If one places two mirrors in front of each other or if a circular waveguide is fabricated such that the coupled light can be trapped inside, then there are cases where the circulating light inside the structure can have constructive interference with itself. As a result, the input light will be amplified. This structure is called a resonator and since the interference of light is wavelength dependent, resonators can be used to selectively amplify one wavelength of light. There are two common types of resonators: Fabry-Perot and ring resonators. 2.5.Fabry-Perot Resonator In this type of resonator, two mirrors are placed face to face with respect to each other, and one of them has slightly less reflection and is used as an input. Light with a specific wavelength enters the resonator and is amplified by constructive interference. 27 Figure 2- 8:Fabry-Perot Resonator and it's typical transmission spectrum. The wavelengths at which constructive resonance happens are: 2 m nL m λ = (2-20) where n and L are refractive index and Length of the resonator, and m is an integer number. Also the distance between two consecutive resonant peaks is called free spectral range, and for a Fabry-Perot, this value is calculated from: (2-21) where λ0 is the resonant wavelength. One of the most important quantities that explains the ability of any resonator to store and amplify light is the Quality factor (Q). This quantity is a measure of how long the photons inside a resonator can survive without being scattered or absorbed. The quality factor is defined as: 0 0 energy stored (useful energy) 22 Energy lost per cycle f Qf f ππτ =× = = Δ (2-22) where f0 is the resonant frequency, τ is the decay time constant of the cavity, and Δf is the 3dB bandwidth of the resonator. 2 0 2 FSR nL λ = 28 (a) (b) Figure 2- 9:Quality factor is defined by (a)number of oscillations during decay time constant of a pulse input. (b) linewidth of the resonant response in frequency domain. For a Fabry-Perot resonator, it can be shown that the quality factor is primarily dependent on the reflectivity of the mirrors and can be approximated as [11]: 0 1 FSR R Q R ν π ν =× Δ− (2-23) where υ0 is the central resonant frequency, ΔυFSR is the frequency spacing between two resonant modes, and R is the reflectivity of the mirrors in the resonator. Another very important parameter in resonators is called Finesse (F). Finesse is defined as the ratio of free spectral range (FSR) to Full Width at half Maximum linewidth: = (2-24) Finesse is dependent on both internal and external (coupling) loss mechanisms. Finesse is completely independent of the resonator length, but the quality factor is dependent on the resonator length. The highest quality factor of Fabry-Perot resonators are approximately 10 5 ,and the highest finesse values are on the order of 10 5 -10 6 . The limitations are primarily due to the fact that the mirrors introduce some loss in the reflected light each time a reflection occurs. 29 2.6.Ring resonators If instead of using two face-to-face mirrors, one uses a closed loop waveguide, which interferes light with itself, then it is possible that for some wavelengths, the circulating light adds up with the in-coupled light. Similar to previous case, light will build up in the cavity, and we will see resonant peaks. Figure 2- 10: Optical ring resonator in resonance condition. When the circumference of the ring equals to an integer factor of the wavelength then the circulating light will have the same phase as the input light and as a result the light builds up.[12] In order to have a constructive resonance, the circumference of the ring resonator should be an integer factor of the wavelength such that the circulating light adds up constructively with itself. Assuming that the circulating light is propagating at the outermost radius of the ring resonator, one can write the resonant condition as: 2 eff Rm n λ π = (2-25) where R is the radius, neff is the effective refractive index of the mode, and m is an integer number. 30 In reality, due to existence of loss mechanisms in the resonator, the amount of the built up light is limited, and the quality factor is defined to describe the ratio of the stored to the lost power. This quality factor can be explained in terms of the loss mechanisms as follows[13]: Q -1 = Q -1 rad+Q -1 s.s. +Q -1 cont+Q -1 mat+Q -1 c (2-26) where Q -1 rad stands for losses due to curvature. As we know, in an optical resonator, light propagates in a zigzag path and, in each TIR, a part of light is lost. Therefore, if light is trapped in a curvature, then it starts to decay. Q -1 s.s. denotes scattering losses due to inhomogeneities in the surface of the resonator. In a resonator, due to technology limitations, there are always defects or some imperfections in the surface. The surface scattering quality factor can be calculated: 2 . 22 2 ss D Q B λ πσ = (2-27) where λ,D, σ and B are the wavelength, resonator diameter, root mean square of roughness size, and correlation length, respectively. Any process that helps improve the surface quality has direct effect on the surface scattering quality factor. Reflowing, partial melting, and polishing can improve surface characteristics of devices. Q -1 cont represents losses caused by interaction of light with surface contaminants. Q -1 mat represents losses due to propagation of light in the cavity material. Because of the interaction of light with the molecules (atoms) of each material, as the light propagates in any medium, it’s intensity decreases. Absorption is an intrinsic material property and is a fundamental limiting factor. Fused fiber grade Silica has one of the lowest optical losses with minimum absorption at 1550 nm, and therefore, it is a very important medium in communications and sensing at this wavelength. If one has the absorption coefficient of the material, then the absorption quality factor can be calculated: 31 (2-28) Here, neff and αeff are the effective refractive index of the mode and the effective absorption. The last term in the definition of the quality factor Qc is the loss occurred due to the escaping of light from the resonator into the coupler. The coupling quality factor is calculated from: 2 0 2 c c Q π λκ = (2-29) where κ0 is the coupling coefficient. 2.7.Circulating Power In almost all cases there is no internal optical source built inside the resonator. Therefore, the light is coupled into the resonator by a waveguide carrying the source wave. In time domain, there is a rate equation governing the in-out and lost intensities as follows[14]: 22 00 0 1 () 2 in da ai a dt κσ κ =− + + (2-30) where a, κ0, σ0 and ain are normalized circulating field, coupling coefficient, loss coefficient and the in-coupled field. In this analysis a is defined such that |a| 2 is the circulating Energy and |ain| 2 is the input coupled power. After coupling the light inside the resonator the internal circulating intensity reaches the steady state and the time derivative term goes to zero. It can be shown that the circulating power inside the cavity is given by: 0 22 (1 ) c eff Q K P nR K λ π = + (2-31) 2 eff mat eff n Q π αλ = 32 where K is defined as the ratio of the cavity loss due to coupling to intrinsic cavity loss and is a measure of the in-coupled light power with respect to loss in the cavity. It is important to explain that the same waveguide that couples light inside the resonator, takes some of the circulating light out of the cavity and therefore is treated a source of loss. 2.8.Mode Volume The propagating mode volume for a resonator is defined as[15]: 2 3 2 () () m rE dr V Max E ε ε =     (2-32) where ε(r) is the relative permittivity of the material. The mode volume is important in determining the interaction strength of the mode with the resonator and will be used in comparing the ability of different resonators in concentrating the optical field. 2.9.Purcell Factor The Purcell factor is a relative ratio of the quality factor to the mode volume, and it is a figure of merit to be considered for emission experiments such as lasing, nonlinear emission generation, and multi-wavelength interaction. The Purcell factor is defined as[16]: 3 2 3 () 4 p meff Q F Vn λ π = (2-33) 2.10.Spherical Resonators The most common type of circular resonator is micro-spheres. Micro-spheres have lowest spatial mode confinement and therefore have less surface interaction. Therefore, the quality factor of these resonators is mainly limited by the absorption of the material. The quality factor 33 of spherical silica resonators is typically around 10 9 [9]. This extremely high quality factor enables low threshold observation of many nonlinear optical phenomena, including quantum studies, Raman scattering[17-19], Brillouin scattering[20, 21] and lasing[22, 23]. These devices have both positives and negatives. From the positive side, using spherical microspheres is straightforward as they are easy to fabricate and have been studied comprehensively so their properties are well known. In addition, their quality factor is four orders of magnitude higher than conventional disk resonators. On the negative side, the quality factor of the micro-spheres is so high that they are thermally unstable and there can be mode interference. Also, since the spheres are not fabricated on a substrate using standard procedures in a cleanroom, they cannot be integrated with other on-chip components like waveguides. Fabrication of micro spheres is easy and is simply done by melting the end of high quality optical fiber under CO2 laser. In fig.2-11 I have shown a Silica Sphere fabricated by this method. Figure 2- 11: Optical microscope image of a microsphere attached to the end of optical fiber 34 2.11.Mode structure Because the micro-spheres are perfectly symmetric and spherical, their mode structure can be calculated by solving Helmholtz's equation in spherical coordinates[24, 25]: 2 22 22 222 11 1 () (sin ) 0 sin sin EE E rkE rR R r r θ θθ θ θ ϕ ∂∂ ∂ ∂ ∂ ++ += ∂∂ ∂ ∂ ∂ (2-34) By using separation of variables technique, this equation is separated into three separate differential equations and the solution will be in the form of: [ 0 (1) (1) 00 0 () ( ) ] for R<R (1) () [ ( ) ( ) / ( ( ) )] for R>R (1) m l TE l m l TE l l l ri Y EjnkR ll ri Y EjnkRhkR hkR ll ×∇ = + ×∇ = +     (2-35) where jl , hl (1) and Yl m are spherical Bessel functions, spherical Hankel functions, and spherical harmonics, respectively. Note that for the TM mode, the magnetic field had the same representation as the Electric field for the TE field. (a) (b) (c) (d) (e) (f) Figure 2- 12: The first few resonance mode profiles in a Silica Micro-sphere with a radius of 75 microns for n=1 and (a) l=m (TE) (b)l=m (TM) (c)l=m-1 (d)l=m-2 (e)l=m-3 (f) n=2 and l=m. 35 2.12.Microtoroid Cavities In recent years, a new type of optical ring resonator has been introduced which has similarly high quality factors to the microsphere cavities. This type of ring resonator is fabricated by etching a circular silica disk and reflowing the overhanging part by a laser. The resulting resonator has a donut shape and is called a Toroid. Experiments have shown that these toroids improve the quality factor, and in turn, the built-up light, by three orders of magnitude in comparison to the best Fabry-Perot resonators and conventional disk resonators. The typical quality factor measured for a toroid is measured to be around 3×10 8 . In order to couple light waves inside a toroid, a straight waveguide is brought into close proximity of the toroidal cavity, and the evanescent field from the waveguide excites the modes inside the toroid. (a) (b) Figure 2- 13: (a) coupling light to a toroid using a tapered fiber. (b) the fundamental propagating mode inside a toroidal cavity. One waveguide approach is based on a tapered optical fiber waveguide. In order to pull a taper, a normal fiber is pulled while being melted by a torch. Therefore, the fiber becomes 36 thinner, and the effective refractive index of the propagating modes changes, which makes it easier to phase match the mode with the whispering gallery mode inside the resonator. Also, by thinning down the fiber, the evanescent tail of the propagating mode increases and coupling is easier and more efficient. The propagating optical modes supported by a cylindrical tapered fiber are the solutions of Helmholtz equation in cylindrical coordinates:[26] (2-36) and λ is the free space wavelength. In the above equation, J ν and K ν are the Bessel function of first kind and modified Bessel functions. Also, ν is a constant used to separate variables for solving the cylindrical wave equation. By varying the thickness of pulled taper, one can match the propagation constant of fiber with that of the whispering gallery mode and get very efficient coupling. 22 2 1/2 0 221/2 0 0 (/ ) exp( ) for 0 r a () (/) E exp( ) for r>a () where u=a(n ) () 2 z z c Jur a EA j Ju Kwr a Aj Kw k wa k k ν ν ν ν νφ νφ β β π λ =≤≤ = − =− = 37 Figure 2- 14: Optical Microscope image of a tapered optic fiber (taper). By pulling a taper one can efficiently couple light into a ring resonator. 2.13.Effective Refractive Index Since there is no explicit analytical equation for the modes in a Toroidal cavity, in the experiments that we need to calculate effective refractive index of the mode, we should use some kind of approximation for effective refractive index of the mode. Here, I describe two common methods to estimate effective refractive index: 2.14.I-field Percentage Weighted Refractive Index In this method, we assume that the effective refractive index of the mode is a weighted function of the refractive indices of layers involved in carrying the mode. The weighting coefficients are the ratios of percentages of the mode intensity in each medium: eff r c m ed nn n n αβ γ =+ + (2-37) 38 Where neff,nr,nc and nmed are the effective refractive index of the mode, refractive index of the resonator material, coating and the medium respectively. Also α, β and γ are the ratio of field energy in resonator, coating and medium to the total energy of the mode. These coefficients are determined by numerically solving Helmholtz equation for mode profile. 2.15.II-Numerical Approximation of effective refractive index The second method to calculate effective refractive index relies on calculating the Numerical solution of the Helmholtz equation to find the whispering gallery mode positions. In this method, we solve for the mode structure and Eigen frequency very accurately. Therefore, it is more accurate than the first method. Once we find the resonant frequency of the mode, the effective refractive index can be calculated from: eff m mc n Rω = (2-38) where m, c, R, and ωm are the azimuthal mode number, light velocity, radius of the resonator, and resonant frequency respectively[27]. 2.16.Device Fabrication Toroidal resonators are fabricated by one lithographic step followed by Buffered Oxide Etching step to define the Silica pads on the Silicon substrate. In order to optically isolate the circular waveguide from the Silicon, the circular pads are XeF2 etched to selectively etch Silicon substrate underneath the disk. In the last step, in order to get a smooth waveguide surface finish, the circular pads are reflowed under the CO2 laser. 39 Figure2- 15:Toroidal cavity fabrication steps: first Silica pads are created on Silicon substrate by Photolithography and BOE etching, next the silica disks are released by XeF 2 etching of the samples. In the last step the samples are reflowed under CO 2 laser to get a smooth high quality surface finish. 2.17.Testing To test our devices, the linewidth of the resonant peaks is measured. In this method, the resonator is placed on a xyz nano stage and is brought in close proximity to a pulled fiber taper. Light from a tunable laser is coupled into fiber and if the taper has appropriate thickness, light can be coupled into the resonator. In order measure the linewidth, the wavelength of laser is swept using a sawtooth waveform over the resonant peak, and the transmission signal is recorded. Next, the resonant linewidth is calculated by fitting a Lorentzian fit to the transmission signal. This way, the quality factor of the resonant wavelength can be accurately calculated. This method is limited by the linewidth of laser. If the linewidth of the resonant peak is narrower than the linewidth of the laser then sweeping laser wavelength will not be able to resolve the Lorentzian lineshape. 40 (a) (b) Figure 2- 16: (a)Schematic of the resonator testing set up. (b) Typical transmission spectrum of a peak in forward and backward sweep. Finally, there are a variety of whispering gallery mode resonators in addition to microspheres and microtoroids. Therefore, thre are a wide range of quality factors for the different resonators. These are summarized in Table 2-1. Table 2-1. Summary of the types of resonators, typical quality factor and applications Resonators Typical Quality Factor Applications 41 Rings Laser Sensors Optical memory Toroids High sensitivity sensors Lasers Bio-sensors Spheres Force sensor Low threshold non-linear phenomena High Q crystalline Disks Ring-down spectroscopy Wide span Frequency Combs 2.18.Chapter 2 References 1. B. Thidé, "Electromagnetic Field Theory," (Upsilon Books, Uppsala, Sweden, 2007). 2. https://www.wonderwhizkids.com/conceptmaps/EM-Radiation.html. 3. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989). 4. E. Hecht, Optics (Pearson, 2012). 5. S. O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice Hall, 2001). 6. D. K. Cheng, "Field and wave electromagnetics," (1983). 7. S. O. Kasap, "Optoelectronics and Photonics : Principles and Practices / S.O. Kasap" (Upper Saddle River, EUA : Prentice-Hall), retrieved http://quijote.biblio.iteso.mx/dc/ver.aspx?ns=000120254. 8. P. Tenenbaum, "Fields in waveguides-a guide for pedestrians," A) ≡ ∇( ∇· A) 2, 2. 5 110 × 8 210 × 9 310 × 11 110 ≈× 42 9. X. Zhang, H. S. Choi, and A. M. Armani, "Ultimate quality factor of silica microtoroid resonant cavities," Applied Physics Letters 96, 153304 (2010). 10. http://www.physicsclassroom.com/class/light/Lesson-3/The-Path-Difference. 11. M. Malak, N. Pavy, F. Marty, Y. A. Peter, A. Q. Liu, and T. Bourouina, "Stable, high-Q fabry-perot resonators with long cavity based on curved, all-silicon, high reflectance mirrors," in 2011 IEEE 24th International Conference on Micro Electro Mechanical Systems, 2011), 720- 723. 12. http://www.softmatter.si/wgms.html. 13. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996). 14. H. A. Haus, "Waves and Fields in Optoelectronics," Prentice-Hall-Englewood Cliffs (1984). 15. M. Oxborrow, "How to simulate the whispering-gallery modes of dielectric microresonators in FEMLAB/COMSOL," in Lasers and Applications in Science and Engineering, (International Society for Optics and Photonics, 2007), 64520J-64520J-64512. 16. T. Kippenberg, S. Spillane, and K. Vahala, "Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip," Applied Physics Letters 85, 6113-6115 (2004). 17. M. V. Chistiakova and A. M. Armani, "Cascaded Raman microlaser in air and buffer," Optics Letters 37, 4068-4070 (2012). 18. N. Deka, A. J. Maker, and A. M. Armani, "Titanium-enhanced Raman microcavity laser," Opt. Lett. 39, 1354-1357 (2014). 19. B.-B. Li, Y.-F. Xiao, M.-Y. Yan, W. R. Clements, and Q. Gong, "Low-threshold Raman laser from an on-chip, high-Q, polymer-coated microcavity," Opt. Lett. 38, 1802-1804 (2013). 20. C. D. Cantrell, "Theory of nonlinear optics in dielectric spheres. III. Partial-wave-index dependence of the gain for stimulated Brillouin scattering," JOSA B 8, 2181-2189 (1991). 21. H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, "Brillouin observation of bulk and confined acoustic waves in silica microspheres," Applied Physics Letters 84, 4182-4184 (2004). 22. L. He, Ş. K. Özdemir, and L. Yang, "Whispering gallery microcavity lasers," Laser & Photonics Reviews 7, 60-82 (2013). 23. A. Pal, S. Y. Chen, R. Sen, T. Sun, and K. Grattan, "A high-Q low threshold thulium- doped silica microsphere laser in the 2 μm wavelength region designed for gas sensing applications," Laser Physics Letters 10, 085101 (2013). 24. R. K. Chang and A. J. Campillo, "FRONT MATTER," in Optical Processes in Microcavities (WORLD SCIENTIFIC, 2011), pp. i-x. 25. G. Righini, Y. Dumeige, P. Féron, M. Ferrari, D. Ristic, and S. Soria, "Whispering gallery mode microresonators: fundamentals and applications," Rivista del Nuovo Cimento 34, 435-488 (2011). 26. C. Yeh, "Guided-wave modes in cylindrical optical fibers," IEEE Transactions on Education, 43-51 (1987). 27. V. S. Ilchenko, X. S. Yao, and L. Maleki, "Pigtailing the high-Q microsphere cavity:? a simple fiber coupler for optical whispering-gallery modes," Opt. Lett. 24, 723-725 (1999). 43 Chapter 3:Optothermal Transport Behavior in Whispering Gallery Mode Optical Cavities 3.1.Introduction One of the main requirements in all the photonic devices is a component, which can store light similar to capacitors and flip-flops in electronic and digital circuits. This light reservoir should be able to store light with minimum possible loss or for the longest possible time. A Fabry-Perot is one of the most well-known light resonators which has been used to store light in lasers and filters [1-7]. A Fabry-Perot is made of two parallel, face to face mirrors which confine a defined wavelength of light between them. There is another family of optical resonators which operates based on returning a light signal back on itself and adding it constructively. This type of resonator is called a traveling wave resonator. In order to compare light resonators, we need to know how effective they are in storing light. The main parameter which is usually used is called quality factor or Q. For a Fabry-Perot resonator, the quality factor is in the range of 10 4 -10 5 [8-10]. Recently, a new type of traveling wave resonator has been introduced which has very high quality factors, up to 3×10 8 [11-13]. Melting a silica disk from its edge to make a toroid shape tube forms the resonator. As a result of the high quality factors, toroids have enabled researchers to observe unique features of light, such as high sensitivity detection[14, 15], strong interaction with material[15, 16] and radiation pressure oscillation[17, 18]. One of the interesting features of toroids is that they are anchored to the substrate by a round silicon pillar which could be used as a heat sink to change the temperature of the waveguide structure. Unlike other types of resonators, which are usually filled with air, toroids carry light in a silica medium connected to the above mentioned silicon pillar. Therefore, it is possible to control the temperature of the resonator via the silicon pillar. 44 In this research, we analyze the effect of wavelength and toroid dimensions on the coupling induced thermal shift. 3.2.Theory To develop a generalizable theoretical construct for opto-thermal behavior in whispering gallery mode cavities, we start with the fundamental equation describing the resonant condition. Specifically, because the resonant condition is satisfied only when light undergoes constructive interference, the circumference of the cavity must be an integral multiple (m) of the wavelength, according to: 2 , mR meff n eff λ π = (3-1) where λ, neff and Rmeff are resonant wavelength, effective refractive index of the propagating mode and the effective radius of the mode, respectively. From equation (1), the dependence of the resonant wavelength on the refractive index is clear. All materials experience temperature- dependent refractive index and expansion changes which are quantitatively described by the thermo-optic coefficient (dn/dT) and the expansion coefficient ( ε) of the material. Therefore, the thermally induced resonant wavelength change ( Δλ) can be described by:[19] ()( )( ) dn TT ndt λ λλε Δ= Δ + Δ (3-2) From the above expression, it is clear that the index and the device radius ( εΔT~ ΔR) can be changed thermally, inducing a resonant wavelength change. However, in most resonant cavities fabricated using standard CMOS methods, the dn/dT is substantially larger than ε, resulting in the first term dominating the opto-thermal effect. As such, all subsequent analysis will assume that λε ΔT=0. 45 While any source of heat can change the effective refractive index of the mode, one particularly interesting case is when the optical mode behaves as the heat source. This unique scenario occurs in devices with particularly long photon lifetimes or high quality factors (Q) where the optical loss of the material can be converted to heat. In order to predict the opto-thermal shift, it is first necessary to calculate the circulating power (Pcirc) as well as the dissipated power (Pd). Subsequently, we need to simulate the amount of temperature change induced. The first two calculations only assume a high Q whispering gallery mode cavity and are therefore generalizable. However, the optical field distribution and thermal simulations are specific to the cavity geometry, material system and wavelength. The rate equation for light circulating in the toroid is:[20] 22 00 0 1 () 2 in da ai a dt κσ κ =− + + (3-3) Where a, κ0, σ0 and ain are normalized circulating field, coupling coefficient, loss coefficient and the in-coupled field. In this analysis, a is defined such that |a| 2 is the circulating Energy, and |ain| 2 is the coupled power. Assuming that we are in steady state, then the circulating power inside the resonator is calculated to be: 0 22 (1 ) c eff meff Q K P nR K λ π = + (3-4) In the above equation, Qo= ωτo is the intrinsic quality factor due to intrinsic loss mechanisms such as absorption, scattering, and radiation. Also, K is defined as the ratio of the cavity loss due to coupling to intrinsic cavity loss and is a measure of the in-coupled light power with respect to loss in the cavity. Therefore by measuring the total transmission (T), we can calculate K from T=[(1-K)/(1+K)] 2 and use K to calculate circulating power. 46 The dissipated or lost power (Pd) in the cavity is described by the loss coefficient ( σo), the circulating energy (|a| 2 ), and the single circulation time in the cavity (tr). Specifically: 22 2 00 || dcr P aPt σσ == (3-5) The loss coefficient ( σo) is not specific to an individual loss mechanism, but captures all of the loss mechanisms present in the system, such as material loss, surface scattering and radiation loss. However, only the material loss behaves as a heat source. Therefore, to isolate this loss mechanism, we can re-write the previous generalized loss equation in terms of the absorptive loss time constant ( τabs), creating an expression for the power lost to material absorption (Pabs): 2 abs abs a P τ = . (3-6) However, not all of the absorbed power is converted to heat. Therefore, an effective power (Peff) is defined as Peff= γPd, where γ is an experimentally determined constant. Once we calculate the lost power, we import it into Comsol and calculate the thermal shift. By comparing the simulated thermal shift and experimental shift, we can get the effective power. It is the effective power that acts on the mode containing mass and changes the temperature of the device. Therefore, for each point we need to calculate Peff from Pd and import Peff in Comsol. Once we find the temperature change from the simulation, we use equation 2 to calculate the wavelength shift for any coupling. This method is very effective in characterizing any toroid for the purpose of getting any controlled amount of shift or detuning. In addition, it is worth mentioning that the threshold coupling at which the thermal shift starts is dependent on the resonant wavelength as well as the structural parameters of the device 47 such as the heat capacity of the effective mode volume, quality factor, opto thermal coefficient, thermal time constant of the structure, and the ratio of the absorbed to lost power.[21] To verify these theoretical equations, the temperature change induced by circulating power is simulated for the specific case of the toroidal resonant cavity (fig.3.1a). This device is a replica of the mask and provides us with a deep understanding of thermal behavior for design purposes. While it is clear that the circulating optical field generates the temperature increase, this increase is not a constant value or even a step function. Additionally, because the optical mode profile depends on the operating wavelength and the device geometry, the thermal profile should mirror this dependence. Therefore, in the present work, to accurately capture this opto-thermal behavior, the optical mode profiles are simulated for a series of device geometries and subsequently imported as the heat source profiles for the heat transport modeling. The transient nature of the heating is incorporated into the model by applying the heat source as a single pulse of a finite amplitude and length. This duration mimics the thermal lifetime within the cavity, and the intensity is the input power. As such, the model is able to accurately capture of the relevant physical parameters of the opto-thermal coupling. (a) (b) (c) Figure 3- 1 (a) Mode profile for the fundamental mode of a toroid with a radius of 35 microns. (b) SEM image a reflowed toroid with the same size. (c) Schematic of a toroid and control parameters in simulation environment. Mode Overhanging length 48 Using this model, we are able to explore several different variables, which appear in Equation (3-5), as well as the thermal time constant of the structure. To be close to experimental values, we vary the oxide thickness from 1.0 to 2.0 μm and the overhang length from 5.0 to 12.0 μm. In both sets of simulations, the device major and minor diameters are held constant at 60 μm and 7 μm, and the wavelength was selected from [1550, 1330 and 765nm]. Fig.3-2 shows the results from these simulations. As we can see from the modeling results, by increasing the overhanging length or decreasing the oxide thickness, the thermally induced shift increases. This increase is directly related to the increase in the thermal time constant of the overall structure. Figure 3- 2: a)-Simulation of the ratio of the thermally induced shifts vs oxide thickness b)-Simulation of the ratio of the thermal shift vs overhanging length. It is important to mention that these graphs show the effect of structural parameters as well as mode volume solely and the effect of the water layer has not been taken into account. To more thoroughly analyze the thermal time constant or the thermal response of the system, the thermal decay from a single heat pulse to the toroid is modeled. Based on this simulation, a thermal time constant of 2.5e -4 seconds is determined for a device with a minor/major diameter of 30 μm and 7 μm. Assuming that the dominant heat transfer mechanism 49 is conduction through the silica pillar, we can estimate that if the whole device was made out of silicon, this device can work 108 times faster. (The thermal conductivity of silica is 1.38 W/(m.K) and for Sillicon that value is 149 W/(m.K))[22]. Unfortunately, the experimental validation of this time constant is not possible. However, the thermal time constant of the structure should be larger than the calculated value due to additional loss mechanisms (absorption and conduction of heat from single water layer). Therefore, this value sets the lower bound. To experimentally explore the opto-thermal shift dependence on the oxide thickness, a series of silica toroidal cavity devices are fabricated using the classic combination of photolithography, oxide and silicon etching, and carbon dioxide laser reflow. One method for quantifying the opto-thermal behavior is to measure the threshold for the on-set of the opto-thermal response. This characterization experiment is performed by coupling light from a tunable, narrow-linewidth laser into the cavity using a tapered optical fiber waveguide and measuring the resonant wavelength. At the onset of the optothermal response, the resonant wavelength will shift. Tapered fiber waveguides are ideal for this measurement as they allow control over the amount of optical power which is coupled into the device. The waveguides are aligned using side and top-view machine vision systems, and the output power from the fiber is monitored and recorded on a NI LabView-controlled high speed digitizer/oscilloscope PCI card. Resonance spectra are recorded over a range of coupling conditions, and the effect of the thermal build-up on the resonant wavelength is determined. The opto-thermal threshold is calculated by using of the power coupled into the cavity, which can be obtained from transmission spectrum. Specifically, the optothermal effect threshold is the % coupled power = Ton-resonance/Toff-resonance where Ton-resonance is the on-resonance 50 signal level and Toff-resonance is the off-resonance signal level. From this value, the threshold coupling ratio is determined. The value is the point at which the device first exhibits opto- thermal behavior or the onset of this nonlinearity. In addition, the ratio of the net “heating power” to the lost power has been introduced as the absorbed power ratio. This ratio takes care of the non-absorbed power as well as the conduction in the structure and the fact that the temperature distribution has been approximated by one effective temperature at the hottest part of the mode. Initially, the dependence of the opto-thermal effect threshold on the wavelength is obtained by measuring the opo-thermal shifts at 765nm, 1330nm and 1550nm. Fig.3-3(a) is a sample spectrum at 1330 nm showing thermal broadening. Fig.3-3(b) contains the threshold data for all three wavelengths, and the results are also summarized in Table 3-1. The linear part of the threshold data is fit to the theoretical predictions based on the FEM modeling. From these results, we can draw several important conclusions. Obviously the threshold is wavelength dependent. By increasing the wavelength, the threshold increases sharply. Since there is a monolayer of water on the surface of the resonator and because the optical absorption coefficient of water increases from 765nm to 1550nm, the overall absorption coefficient of the structure is increased, and the threshold optical power needed is reduced. Also, from these results, we can estimate the total conducted heat as well as the effective power absorbing mass (meff). 51 Figure 3- 3:(a) Measured wavelength shift for a toroid with R=26µm at λ= 1303.0814nm (b) Threshold diagrams for three different wavelengths. Table 3-1. Thermal characteristics of a toroid at different wavelengths Wavelength (nm) R Threshold total coupling ratio Q0 Effective absorbed power ratio range Threshold coupling ratio Slope Efficiency x1E-3 772.15 (exp) 22 24% 1×e 8 0.45-0.65 0.0685 1.09 772.15 (FEM) 22 23% 0.0652 1.15 1302.51 30 19% 3×e 7 0.5-0.7 0.0526 1.45 1302.51 30 18.9% 0.0523 1.50 1562.51 28 2.28% 4×e 7 0.5-0.7 5.766e-3 0.488 1562.51 28 2.85% 7.22e-3 0.478 To get a deeper insight into the opto-thermal behavior we have studied the effect of oxide layer thickness on the threshold of the device. To accurately compare the thresholds of the five different devices, which each had unique Q’s, mode volumes and overhanging lengths, these parameters are normalized out of the opto-thermal threshold coupling ratio, creating the 52 Normalized Threshold which is independent of other parameters and only dependent on oxide thickness. Fig. 3-4 summarizes the experimental results. Figure 3- 4:Effect of varying the thickness in thermal broadening of the Silica micro Toroids From the results in fig.3-4 we can see that the threshold coupling has a linear dependence on oxide thickness, which is in agreement with what we have observed in fig.3-4(a). Note that the threshold coupling is inversely proportional to temperature shifts and therefore fig.3-4 and fig.3-2(a) are opposite trends. 3.3.Simulation Details For our simulations, we have used the RF module to study the optical mode and the Chemical Engineering module to study thermal dynamics. 3.4.Optical Field Distribution COMSOL Multiphysics 3.5. is used to study the optical mode distribution in the device. We measured the major and minor diameter of the device to be 60 μm and 7 μm respectively. We have run simulations for all three wavelengths. For each wavelength, the mesh size in the 53 simulations is less than λ/10 to get acceptable accuracy. We have assumed the refractive indices for Silica to be 1.445 (1550nm) and 1.45 (1330nm) and 1.46 (765nm) respectively. Next, the optical field distributions of the resonators have been determined by varying the azimuthal mode number for each wavelength. Finally, we have calculated the physical quantities needed for each device. Optical field distributions at different wavelengths are shown in fig.3-5. The dependence of the mode area on the wavelength is clearly observed for each simulation. (1550 nm) (1330 nm) (765 nm) Figure 3- 5: Same device geometry at three different wavelengths (1550,1330 and 765 nm) 3.5.Thermal Simulations The governing equation for the thermal dynamics in our devices is: 2 2 (). ( ) (, ) ((,)) abs wt f r dT rt ckTrt dt ρ τ Δ =∇ Δ + (3-7) In the above equation, ρ is the density of material, c is the specific heat capacity, k is thermal conductance, abs τ is the absorption time constant, 2 w is the circulating energy in the cavity, and f(r) is the field distribution of the mode in a cross section of the cavity perpendicular to the mode. 54 Long (compared to optical time constant of the laser) after coupling the laser in the cavity, the temperature distribution of structure reaches steady state, and we can ignore the time dependent derivative. Here, we use an assumption: instead of taking into account the effect of field distribution in different points, we can assume that there is an effective temperature change at the hottest part of the optical field, which determines the resonant wavelength change. As a result of this approximation, there could be an effective temperature change which determines the temperature at the hottest part of the cavity. This temperature change is proportional to the absorbed power which itself is proportional to the circulating energy. Therefore: 2 abs w T τ Δ∝ (3-8) In our simulations, we have assumed that there is an effective absorbed power, which is proportional to the lost power through a constant. This assumption makes analysis easier. eff lost PP γ = (3-9) The reason for choosing this assumption rather than the former one is because we can compare the simulation results with experimental results to determine γ easily. Thermal simulations are performed using the heat transfer Module of COMSOL Multiphysics 4.4. In order to match the thermal and optical structures, we use the same dimensions as in the optical simulations (major radius 30 microns and minor radius 3.5 microns). We used the experimental parameters as a reference for the duration of the heat pulse. Specifically, when performing experiments, we continuously scan the laser across the resonant wavelength using a function generator at a frequency of 100 Hz. Therefore, the optical mode behaves as a pulsed heating source with a repetition rate of 100Hz. In order to simulate these 55 test conditions, we chose the same rate for our thermal signal. Similarly, the shape of the thermal pulse is triangle function. This shape is the closest to the heating pattern that we observe experimentally. Finally, the duty cycle of the thermal ramp is selected based on the coupling time of the optical signal and varies with coupling. The simulation time step is set to be smaller than (step=0.000025 seconds) the time constant of the structure to improve the accuracy. Therefore, before we can run the thermal simulations, we need to both complete the optical simulations and experimentally measure the lost power. To determine the lost power, we experimentally measure the quality factor and the coupling. Based on these two parameters, we can calculate circulating power based on: 0 22 (1 ) c eff meff Q K P nR K λ π = + (3-10) where λ is wavelength, neff is the effective refractive index, Qo is the intrinsic cavity Q, K is coupling, and Rmeff is the effective radius of the mode. From this value, the total lost power (Pd) can be calculated from: 22 2 00 || dcr Pa Pt σσ == (3-11) where σo is the loss coefficient, |a| 2 is the circulating energy and tr is the single circulation time in the cavity. This power is the input power in the thermal simulations. However, the optical field intensity is not uniformly distributed over the device surface or even throughout the silica. As can be seen in fig.3-5, the optical field has an asymmetric Gaussian profile. As such, the thermal profile which is generated by this optical field will be similarly asymmetric. In order to accurately capture this profile, it is necessary to import the optical mode profile and convert the optical intensities to thermal intensities. To accomplish this task, we have divided the optical mode into several smaller elliptical regions. The value of the 56 optical intensity in these regions is approximated as constant and is determined. Using this constant value, the optical power is converted to a thermal intensity. Figure 3- 6:Different power regions in whispering gallery mode. 3.6.Thermal time constant of the Toroid The thermal time constant represents the thermal decay time of the structure or how long the structure takes to return to the initial room temperature value. As such, assuming that light is applied as a pulse train, the thermal time constant sets the upper limit on how fast the pulses can be applied before the device reaches thermal runaway. However, it is important to note that in this simulation, we haven’t taken the effect of the single layer water into account and as a result, the thermal time constant we measured here is a lower limit and will give us the lowest time constant possible. This limit will be useful for switching and sensing applications where we want to know the highest possible frequency that we can apply to the device. 1 2 3 4 57 In order to determine the thermal time constant of the toroidal cavity structure, we have applied a single thermal pulse with the same profile as the optical mode. The only difference is that we have changed the input signal function from a triangle to a rectangle function in order to be able to accurately estimate the thermal time constant. This pulse results in an initial temperature increase and a gradual (exponential) decrease. The thermal time constant is measured by fitting the decay portion of the results to an exponential function or exp(-t/ τ), where t is the thermal time constant. To study the dependence of τ on the cavity geometry, we modeled cavities with oxide thicknesses ranging from 1 to 2 μm operating at 1550nm. While the membrane thickness does not change the mode volume, it does change the thermal transport, thus affecting the time constant. Here the simulated time constant is 2.5e -4 seconds. (a) (b) Figure 3- 7:(a) Thermal pulse applied to a toroid (b) determining the thermal time constant by fitting an exponential curve to the graph 58 3.7.Fabrication For all of the devices fabricated during the course of this project, we start with two microns of thermal oxide grown on a silicon wafer. Two micron-thick membrane devices The standard toroidal cavity fabrication process begins with photolithographic patterning of the oxide using Shipley 1813 photoresist and developer. The circular pattern is subsequently transferred to the oxide using Transene buffered oxide etchant (BOE). Then, the silica is under- cut using xenon difluoride. Finally, the cavity reflowed using a carbon dioxide laser. The diameter of the final toroidal cavity depends on the diameter of the initial circular oxide pad. Reduced membrane devices To control the membrane thickness, the wafers are initially immersed in BOE for different periods of time ranging from 0-10 minutes. This process uniformly removes thin layers of the oxide. Subsequently, the microdisks are patterned and etched in BOE as described previously. Using a profilometer, the oxide thickness is measured. Then, the microcavity fabrication process proceeds as described previously. 3.8.Device Characterization The opto-thermal behavior of the toroidal cavities are characterized using three different Newport/New Focus narrow linewidth CW tunable lasers with center wavelengths at 1550, 765 and 1330 nm. The light is coupled from the lasers into the cavities using tapered optical fibers. The tapers are fabricated in the lab immediately prior to performing these experiments and are optimized for the specific wavelength. As such, they are low loss and high efficiency. 59 The cavity is mounted on a pair of three axis stages. One is a manual three axis stage, with micron resolution; the second is a nano-resolution, motorized stage. The alignment of the cavity with the taper and the coupling of light into the cavity are monitored two ways: 1) using top and side view cameras and 2) monitoring the transmitted power through the taper. The transmitted power is detected on a LabView-controlled PCI high speed digitizer/oscilloscope which is integrated in a computer. Data can be automatically downloaded and saved from this card. To identify the resonant wavelength of the cavity, the laser wavelength is modulated using a triangle wave sent from a function generator. During the course of these experiments, several different measurements are taken for each device at each wavelength. First, a series of transmission spectra showing the evolution of the device’s resonance linewidth over a series of coupling conditions, starting in the highly under-coupled regime, is captured. Then, the input and output power from the laser to the cavity is measured. Finally, after testing is completed, the device geometry (major and minor diameter) are measured under an optical microscope. 3.9.Data analysis In order to calculate the input values that we need we should measure the intrinsic quality factor of the device. In order to do that, we should find a fundamental mode coupling peak at the output spectrum of the tapered fiber. Next, by keeping coupling at lowest possible value and fitting a Lorentzian peak to the spectrum, we can get an estimation of the Q0 (intrinsic quality factor). Below we have shown an example of this fitting curve. 60 Figure 3- 8:An example of Lorentzian fit to a low coupled peak. The next step, as we have explained in thermal simulation section, is to enter the value of coupling and quality factor in the equation of circulating power: 0 22 (1 ) c eff meff Q K P nR K λ π = + (3-12) Next, we need to find the lost power using circulating power and quality factor: 22 2 00 || dcr P aPt σσ == (3-13) It is worth to mention that, in a toroid the thermal dynamics are governed by: 2 2 (). ( ) (, ) ((,)) abs wt f r dT rt ckTrt dt ρ τ Δ =∇ Δ + (3-14) 61 In the above equation, ρ is the density of material, c is the specific heat capacity, k is thermal conductance, abs τ is the absorption time constant, 2 w is the circulating energy in the cavity, and f(r) is the field distribution of the mode in a cross section of the cavity perpendicular to the mode. Therefore after getting the lost power and finding the right γ, we multiply Plost by γ for each coupling point and define that as an input for each simulation. Next, we read the temperature at the hottest part from the simulation results and calculate wavelength shift for each coupling point from: ()( )( ) dn TT ndt λ λλε Δ= Δ + Δ (3-15) Then, we can plot the graph of shift vs coupling for each wavelength, and fit a linear curve to nonzero points to get the threshold coupling. In fig.3-9, we have shown one example. Figure 3- 9:A typical coupling vs shift diagram calculated using the above-mentioned procedure 62 3.10.Measuring the Opto-thermal constant of ITO using a Toroidal resonator Scientists have been working on engineering new types of optical sensors. Depending on the type of sensor and the responsible mechanism used for sensing, these sensors can have various working frequencies as well as response times. One of the methods that is used to sense the surrounding environment is a temperature sensor. So far a variety of temperature sensors have been fabricated. The main building block in any thermal sensor is a material that changes its properties as a result of a change in the temperature. This change could be in length, transparency, refractive index or even conductivity. The higher the change in the property of the material is, the better the sensitivity of the sensor will be. Among the above mentioned properties, refractive index is one of the most sensitive ones which could be used to change the optical properties of a waveguide which controls the monitored signal. One of the best candidates that could be used for thermal controlling of the refractive index are the toroidal micro resonators. These resonators have shown high sensitivities to any changes in the surrounding environment including temperature. One important feature that distinguishes these resonators from other types of resonators is that, owing to extremely high quality factors, these cavities have a very narrow line width which in turn sets a high detection resolution for sensing. In addition, functionalizing the device by doping a sensitive molecule inside the waveguide or coating the waveguide by a layer of temperature sensitive material could increase the responsivity. In this section we have shown that ITO is an excellent candidate for thermal sensing and switching purposes. We have shown that by coating Toroidal resonators with a thin coating of ITO the thermal response of the resonator increases by a factor of 10-18 times. We have also developed a 2 D simulation to study the mode distribution inside the coating layer as well as the resonator. 63 3.11.Quality factor calculation In an externally coupled optical cavity, the quality factor is dependent on extrinsic and intrinsic losses [27]. The extrinsic losses are primarily determined by the coupling method used, but the intrinsic losses are inherent property of the cavity. Previous work has shown that in a hybrid cavity or coated device the quality factor is limited by the material loss of the system [28, 29]. The described loss is calculated by: Qmat=2πneff/λαeff, where neff is the effective refractive index, λ is the resonant wavelength and αeff is the effective material loss. The expressions for neff and αeff are: neff=β ∙ncavity+γ ∙nfilm+δ·nair and αeff=β ∙αcavity+γ ∙αfilm+δ·αair, respectively, where β, γ, and δ are the portion of the optical field located in the cavity, film and air. In the case of toroidal cavities, these values are determined using Comsol simulations and β+γ+δ=1. 3.12.Thermo-optic phenomena The temperature-dependent refractive index change of a material is called the thermo- optic effect. In dielectric materials, the thermo-optic coefficient (dn/dT) is typically positive, resulting in an increase in refractive index as the temperature increases. In hybrid cavities, dneff/dT=β ∙dncavity/dT+γ ∙dnfilm/dT+δ·dnair/dT [29]. Where the coefficients β, γ, and δ are the portion of the optical field located in the cavity, film and air and are determined using finite element method modeling. Given that dn/dT of silica and air are known, from the experimental data and the FEM model, it is possible to determine the dn/dT of the film. Refractive index based detection relies on the dependence of the resonant wavelength on the cavity’s refractive index and geometrical parameters [30, 31]. Previous work has demonstrated cavity-based sensing using a variety of mechanisms; however, by far, resonant wavelength change is the most commonly used [23, 32-36]. 64 In the case of thermal sensing, the thermo-optic effect is particularly important. The resonant wavelength is directly related to the refractive index of the cavity according the relationship: Δλ/ΔT=(dneff/dT)(λ/neff), where Δλ is the change in resonant wavelength and ΔT is the change in temperature [26]. Therefore, by increasing the thermo-optic coefficient, the sensor will generate a larger signal; therefore, increasing the sensitivity of the sensor. 3.13.Simulation and modeling To solve for the optical field distribution in the different regions of the hybrid device, finite element method (FEM) simulations are performed using COMSOL Multiphysics [28]. The modeling parameters are determined from microscopic measurements to allow direct comparison between the results. The major and minor diameters are 60 microns and 7 microns, and the wavelength is 780 nm. The refractive index and film thickness of the ITO is measured using ellipsometry. Other constants used in the simulations are taken from the COMSOL library. In order to improve the simulation efficiency, the mesh size was varied between 60nm in the regions near the maximum optical field to 120nm in the regions far from the field intensity. By controlling the azimuthal mode order (M) in the cavity, we can determine the optical field distribution, which corresponds to the values for β, γ, and δ. A pair of simulations is shown in fig.3-10(a) and (b). In the first simulation, the film has the same properties as the silica toroid; as a result, the film simply increases the diameter of the device and the optical field is not perturbed or changed by the presence of the film. In contrast, in the second simulation, an ITO film is used. By comparing these two simulations, it becomes evident that the presence of the coating changes the optical field profile. Due to the large refractive index contrast between the coating and the resonator, the mode is split when the ITO film is included. While the majority of the optical mode is pushed back 65 into the resonator, a small optical lobe appears inside the coating. This effect is apparent in fig. 10 (c). This small, secondary field increases the field inside the coating. As a result, the field and material interaction is improved. (a) (b) (c) Figure 3- 10: FEM modeling results. The optical field distribution with a) an SiO 2 film and b) an ITO film. c) The modal energy density distribution cross section in the device with both films. The optical field clearly changes both shape and distribution with the high index film. 3.14.Material synthesis To make the ITO coating, first, an ITO sol-gel solution is made. The stock solution is synthesized by combining 30 ml ethanol (CH2OH), 35 mg tin chloride (SnCl4) and 200 mg indium chloride (InCl3), and stirring them for 3 hours. Then, 1 ml of Tween 80 ® is added, obtaining the sol-gel solution after 2 additional hours of stirring. Throughout the process, the solution is kept at 25ºC, and it is vortexed several times, to minimize the formation of aggregates. The ITO is deposited twice on the wafer twice using spin-coating to form a uniform thin film. The first ITO layer is deposited by dropping the solution on the samples and spin-coating at 7000 rpm for 30 seconds. The samples are annealed at 500ºC for 20 minutes in an ambient environment. The samples are immediately removed from the furnace at 20 minutes. A second ITO layer is deposited using the same conditions. However, the annealing process is changed. 66 This time, after the 20 min anneal, the samples remain in the furnace as the temperature is gradually decreased from 500 o C to room temperature at a rate of 1 o C/min. This gradual decrease allowed very smooth, defect-free films to be produced. The average thickness of the ITO thin- film is measured using ellipsometry and is 260 nm. 3.15.Experiments To measure the thermal behavior of the device, a temperature control stage with a thermo-couple controlled feedback loop is integrated into the previously described set-up [37]. Using this stage, the device can be heated in 0.5 o C steps with minimal overshoot. Two different, complementary approaches are used to measure the temperature response of the ITO-SiO2 hybrid cavity. Additionally, for comparison, the response of a plain SiO2 cavity was also measured. In the first method, the minimum position (wavelength) and the transmission (coupled power) are continuously tracked and recorded at a frequency of 691 pts/min. This approach has several advantages. Because the transmission point is recorded, we can detect changes in coupling, also known as “taper jitter”. This jitter is widely acknowledged to be a source of noise in high Q cavity measurements. Therefore, using this method, we are now able to isolate and remove these points with automated filters without comprising the volume of results (e.g. reject all data with transmission variation >5%). Additionally, we can perform statistically significant error analysis on the wavelength change. However, the high speed acquisition is only possible because the whole spectra is not recorded; thus, we lose information about the cavity Q. In the second method, resonance spectra are recorded at the distinct temperature points. Specifically, after changing the temperature, the resonance is allowed to stabilize, and then the spectra is saved. Based on a Lorentzian fit, the resonant wavelength and the Q are determined. However, because of the amount of time it takes to save an entire spectrum, it is not possible to 67 use this approach to perform real-time detection; for similar reasons, acquiring a sufficiently large amount of data to perform statistics upon is unrealistic. As can be observed in Fig.3-11(a), the resonant wavelength increases in direct response to each 0.5 o C temperature increase. The background noise shown in the inset is determined by evaluating the final 240 seconds of the signal (N > 1600 pts). As such, it includes all sources of noise in the system, including taper jitter. The three sigma (3σ) value is similar to the mean loaded cavity linewidth (4.65 pm 3σ value vs 6.2 pm for the mean cavity linewidth). However, after a bandpass filter has been applied to remove the points with more than a 5% intensity variation, the 3σ noise level is reduced to 0.7pm. This improvement is readily apparent in the pair of noise histograms in Fig.3-4(a), inset. Throughout these measurements, the loaded cavity Q was fairly constant (Fig.3-4(b)). The overall decreasing trend could be attributed to a decrease in coupling efficiency. This decrease results in an increase in the extrinsic loss (Qcoupling), which will decrease the loaded Q. The sensor response can be more explicitly evaluated if the wavelength shift versus temperature increment is plotted. Fig.3-4(c) shows the results from both measurement methods: 1) wavelength tracking in real-time (ITO-SiO2, RT) and 2) measuring the spectra at discrete time points (ITO-SiO2, Q). Most importantly, the results are clearly self-consistent. For comparison, we have also plotted the baseline noise level and the theoretically predicted shift from a pure SiO2 device. The change in resonant wavelength in the ITO-SiO2 hybrid cavity is significantly larger than the SiO2 device. This improvement in device performance is directly related to the increase in thermo-optic coefficient of the cavity from 1.2x10 -5 o C to 1.722x10 -5 o C due to the presence of the ITO thin-film. 68 (a) (b) Figure 3- 11: a) Temperature sensing in real-time with noise. b) The results from both measurement approaches are plotted for direct comparison. Additionally, the shift from a bare silica toroid and the baseline noise level are included. 3.16.Conclusion In conclusion, we have developed a method to systematically characterize thermal behavior of the whispering gallery mode resonators. We have designed 3D coupled model that can predict the device's behavior with high accuracy. Also we have shown that this technique can be applied to design a temperature sensor that has the capability of characterizing new materials as well as temperature monitoring. In addition we have demonstrated a new complex thermal system including a thin layer of ITO as thermal sensitizer. We have shown that by using this approach the thermal response of the complex system is improved by a factor of 3. The thermal sensor has many applications in thermal monitoring and thermal switching. 3.17.Chapter 3 References 1. A. J. Vickers, R. Tesser, R. Dudley, and M. A. 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Armani, "Characterization of thermo-optic coefficient and material loss of high refractive index silica sol-gel films in the visible and near- IR," Optical Materials Express 2, 671-681 (2012). 30. H. K. Hunt and A. M. Armani, "Label-Free Biological and Chemical Sensors," Nanoscale 2, 1544-1559 (2010). 31. M. S. Luchansky and R. C. Bailey, "High-Q Optical Sensors for Chemical and Biological Analysis," Analytical Chemistry 84, 793-821 (2012). 32. M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, and A. G. Kirk, "Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy," Optics Express 20, 9090-9098 (2012). 33. S. Mehrabani, P. Kwong, M. Gupta, and A. M. Armani, "Hybrid microcavity humidity sensor," Applied Physics Letters 102(2013). 34. S. Mehrabani, A. J. Maker, and A. M. Armani, "Hybrid Integrated Label-Free Chemical and Biological Sensors," Sensors 14, 5890-5928 (2014). 35. Y. Lin, V. Ilchenko, J. Nadeau, and L. Maleki, "Biochemical detection with optical whispering-gallery resonators," in Laser Resonators and Beam Control IX, (SPIE, 2007), U4520- U4520. 36. J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, "Back-scatter based whispering gallery mode sensing," Scientific Reports 3, 2974 (2013). 37. H.-S. Choi and A. M. Armani, "Thermal non-linear effects in hybrid optical microresonators," Appl. Phys. Lett. 97, 223306 (2010). 71 Chapter 4 Opto-mechanical, regenerative oscillation in optical resonators 4.1.Introduction Photonic devices have shown many advantages over their electronic counterparts, such as speed, power handling, loss, and capacity. As such there has been extensive research to develop optical devices which could be used in detection, communication and procedure control. One of the main hurdles in using photonic devices is that since they are mostly integrated in optoelectronic circuits, at some points in the circuit, light signals need to be converted to electronic signals and vice versa. This conversion might limit efficiency and the speed of the circuit and adds to the overall complexity of the system. One idea to overcome this problem is to design all optical devices in which all of the processes are done without photonic to electronic conversion in the middle stages. As such, recently there have been many efforts to design and fabricate all optical devices such as transistors[1, 2], switches[3, 4], all optical logic gates[5, 6], sensors[7, 8] and demultiplexers[9, 10]. In recent years, improvements in device fabrication have enabled us to reach ultra low losses in photonic devices. One of the optical devices that plays an important role in light storage, monitoring, filtering and laser operation is an optical resonator. There are two types of resonators: traveling wave resonators and Fabry-Perot type resonators. One of the interesting types of traveling wave resonators is whispering gallery micro cavities, specifically, toroidal micro cavities. Due to low loss and smooth surface, these resonators show extremely high Quality factors, and as a result, they can store very high optical powers. The quality factors for these resonators are in the order of 10 7 to 10 8 . Due to these high quality factors, the device exhibits some unique features such as extremely high sensitivity of the resonant wavelength to environmental changes[11], thermal broadening [12]and observation of radiation force induced, regenerative mechanical vibrations[13]. The direct result of these mechanical vibrations is the 72 amplitude modulations, which show up at the frequency spectrum of the output light. Since these high-quality mechanical vibrations are generated without using any electronic interface, and they could play an important role in all optical devices. In this chapter, the effect of the pillar offset on the mechanical modes of toroids and the consequent frequency shifts of the mechanical vibrations have been studied. 4.2.Theory The concept of optically-induced mechanical behavior was initially studied by Braginsky[14] in a Fabry-Perot interferometer. In this system, if the power circulating in the main mode of the resonator exceeds a certain amount then the optical force from the light induces a deformation in one of the mirrors of the resonator. As a result, the resonant wavelength inside the interferometer and the total power in that specific wavelength drops, causing the mirror to revert back to the original state. This process can continue regeneratively. The net result of this effect is a mechanical vibration induced in one of the mirrors of the Fabry-Perot by the optical force. This phenomenon is called “dynamical back action” and is a direct result of the force induced by light. In 2005, this same behavior was observed in toroidal optical micro cavities[15]. Specifically, by pumping the toroidal cavity at a blue detuned wavelength, then under some circumstances, the energy of optical photons is transferred to natural mechanical modes of the structure. The governing equations for the circulating optical mode and mechanical mode are: 2 0 () ( ) () () 2 L eff eff F ft xt xt xt mm γ ++Ω = +   (4-1) which is the well-known damped harmonic oscillator equation. In this equation, , , and f(t) eff m γ Ω are the intrinsic damping coefficient of the structure, mechanical frequency, 73 effective vibrating mass of the cavity and the optical force, respectively. The optical force for the case of a toroidal cavity is 2 2 r na cT π where n, |a| 2 , c and Tr are effective refractive index of the mode, energy amplitude inside the cavity, speed of light and cavity round trip time. Also, it is worth to mention that it is assumed that 2 m Q γ Ω = where Qm denotes mechanical quality factor. To satisfy Fluctuation Dissipation Theorem, FL is included to account for the Langevin Force. For macroscopic particles over long time scales, the Langevin force has no correlation with itself at any other time, and hence, its correlation function takes the form of a Delta function: 0 (), ( ') ( ') LL B eff F tF t kTm t t γδ =− (4-2) where kB and T are Boltzman's constant and resonator temperature, respectively [16]. On the other hand, due to the deformation induced by the optical force, the radius of the cavity undergoes changes which modify the resonant wavelength. The governing equation for the circulating light in the resonator is the “rate equation”: 0 11 1 1 () ( ) 2 ex ex da ixa i s dt ττ τ =Δ − + + (4-3) In the above equation, |a| 2 ,τ0,τex and |s| 2 represent stored energy, intrinsic cavity life time (corresponding to intrinsic loss mechanisms), extrinsic cavity life time (represents the light being coupled to the outside waveguide as a result of evanescent coupling), and the launched input power. These equations are coupled through the dependence of the resonant frequency on variations of x: 00 () () om x xgx ωω Δ= − =Δ− (4-4) 74 where, Δ0 is the initial detuning of the laser frequency with respect to the resonant wavelength and gom is the optomechanical coupling coefficient. When the above equations are applied to a circular whispering gallery mode cavity, the major radius of the cavity (R) is constant over the periphery of the resonator and represents x [16]. Keeping the above mentioned assumptions in mind and owing to the fact that for physical devices the quantity m= is always small, it is possible to find a perturbative solution for the power circulating inside the cavity. 0 n n n aml ∞ = =  (4-5) By using the above perturbative method and if we keep the expansion terms up to first order, it is possible to show that the mechanical cooling or gain coefficient is: 2 0 222 22 22 8 11 () 14 14( ) 14( ) ext meff m m n Gf P fm c f f τ ωτ ττ τ =− × × − +Δ + Δ− + Δ+ (4-6) Where 2 tr f T τ π = is called cavity finesse. Also, fm and P are the mechanical frequency of the structure and input power. By setting the above gain coefficient, one might find the threshold power needed for the onset of cavity oscillations to be: 23 0 4 (1 ) , (1 ) c th mech th loaded mech Q f P PC f P QQ γγ + ==− (4-7) where Pth is the threshold and γ is the damping factor. Qc, Qloaded, and Qmech are the coupling quality factor, loaded quality factor, and mechanical quality factor. The constant 22 0 /64 mech eff CR m ω =Ω is a measure of the strength of the coupling between the optical and 75 mechanical modes. Additionally, 0 0 2 loaded fQ ωω ω − = is the detuning factor of the laser wavelength for the resonant frequency ( ω0) [17]. Although equations 4-1 to 4-5 are generally valid for any type of optomechanical system, these equations are significantly simplified for the case of a radially symmetric device. Specifically, the changes in the major diameter of the device induced by the mechanical vibrations that give rise to the optical bistability behavior are directly related to the mechanical degrees of freedom of the system. Therefore, the optomechanical coupling coefficient is simply gom=- ωc/R[17, 18]. On the other hand, for an asymmetric device, the major diameter varies with azimuthal angle ( ϕ); therefore, gom is a function of R and ϕ. This dependence limits the appropriateness of using symmetric weighting functions to perform the mapping of the 3D mechanical displacement field to a 1D harmonic oscillator, as done in previous work[19, 20]. In addition, the orthogonal Eigen modes of the structures are calculated using the spatial equation of Hooke's law [21, 22]: 22 ().(.()) () () nn nn rr r λμ μ ρω +∇∇Φ + ∇Φ =− Φ       (4-8) where ρ is the density of the material and (1 )( 1 2 ) E σ λ σσ = +− and 2(1 ) E μ σ = + are Lame´s constants with σ and E being Poisson's ratio and Young's modulus. Also ωn is the eigen frequency of nth mode and Φn(r) is the position dependent mode profile function. However, due to complexity of the structures, it is not possible to solve for modes analytically and we have used COMSOL, a Finite Element Method (FEM) software, to numerically calculate the Eigen frequencies of our structures. Details on the FEM modeling are in the next section. In fig.4-1, we have simulated the first 14 vibrational modes in a symmetric toroid. 76 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Figure 4- 1:First 14 mechanical modes of a toroidal resonator. Among the modes shown in fig.4-1, in symmetric devices modes No 2 and 14 are self excited due to higher optomechanical interaction with the resonant mode. For comparison, we have shown the first 14 modes of an asymmetric device along with their corresponding frequencies, in fig.4-2. (AR of 0.68, pillar offset of 2.1 μm and a major diameter of 45.7 μm) 77 As a result of this optomechanical coupling and since the exerted force is in radial direction, mainly the radial modes are regeneratively excited. However, among the mechanical modes of the structure, some have higher mechanical quality factor. Therefore, it is of utmost importance to find techniques that enable us to excite modes with higher mechanical quality factor. One method that has been suggested in literature is using optoelectromechanical techniques[23, 24]. However, this method adds another level of complexity to the system. In the following discussion, I have shown how the introduction of asymmetry enables the regenerative excitation of crown modes of a toroidal cavity. To perform this work, it was necessary to develop a repeatable and precise approach for fabricating asymmetric, high optical Q devices integrated on silicon. A schematic highlighting the general principles of this device and key points of asymmetry is presented in fig.4-2. By introducing asymmetry mechanical modes are regeneratively excited at sub-mW threshold powers. 3D Finite Element Modeling (FEM) simulations show that there is strong agreement between the measured and simulated frequencies. Figure 4- 2:(a) Rendering of a fiber taper-coupled asymmetric cavity. (b) Schematic where the parameters of minimum minor radius (rmin), maximum minor radius (rmax), maximum major radius (Rmax), minimum major radius (Rmin), total diameter (D), vertical offset ( Δz) and maximum pillar shift ( ΔLmax) are labeled. (c) SEM of a cross-section of the smaller side of an asymmetric device with large vertical offset. 78 4.3.Finite element method modeling Due to the complexity of the asymmetric structures, it is not possible to solve for the mechanical modes analytically. To overcome this limitation, COMSOL Multiphysics, Finite Element Method (FEM) software, is used to numerically calculate the Eigen Frequencies of the asymmetric structures. By extracting the exact dimensions of each device from optical microscope images, accurate models of each asymmetric device are drawn in SolidWorks and imported into COMSOL to solve for the mechanical Eigen Frequencies. The mesh size for mechanical simulations is set to 0.7 µm. In addition, a second set of simulations were performed to better understand how the asymmetry changes the optical to mechanical energy conversion. In these models, a known radially symmetric force simulates the radiation pressure excitation from the whispering gallery mode, and the mechanical oscillation is determined. 4.4. Mechanical modes in asymmetric resonators The first fourteen modes and optomechanical frequencies from a single asymmetric device with an aspect ratio of 0.68 and a pillar offset of 2.1 μm are shown in fig.4-3. A cursory analysis of the modes reveals that the behavior of the asymmetric device is completely unique. While many of the conventional cantilever and crown modes are present in the simulation spectrum of this device, several previously unobserved mechanical modes appear, because the optical force is not uniformly distributed along the device periphery. This effect results in the mechanical modes becoming degenerate and aligning along the maximum and minimum axis of asymmetry. 79 Figure 4- 3:FEM simulation results of the first 14 modes of an asymmetric cavity along with their corresponding frequencies. The red lines indicate the lowest threshold modes for symmetric devices: the first and third cantilever modes. The blue lines indicate the lowest threshold modes for the asymmetric devices: the second asymmetric crown mode and the second asymmetric cantilever mode. Degenerate modes are represented with α and β and linked with a bracket. To understand the force transduction, the potential energy stored in the structure from a radial force is calculated by running a second set of FEM simulations. To simulate a whispering gallery mode optical field, a 10mN circulating force is applied perpendicular to the sidewalls. This force mimics the pressure that the circulating optical whispering gallery mode field applies to the device. Both an asymmetric and a symmetric device are modeled. The frequency of the applied force is varied over each mechanical resonance, and the maximum potential energy is calculated for each mechanical mode. In order to clearly understand the efficiency of the process, the first cantilever mode is used as the reference potential energy for each device geometry. Therefore, a value greater than 1 indicates that the higher order mode is a more efficient mechanical oscillator than the first cantilever mode. Given the number of mechanical modes present in the device (fig.4-3), the following discussion is focused on the two highest energy modes for both device geometries. These modes are underlined in fig. 4-3, and the relative potential energy values are shown in Table 4-1. 80 Table 4-1. Summary of energy ratio and mechanical mode for the two primary symmetric and asymmetric modes calculated based on simulations. The maximum energy ratio for both the symmetric and asymmetric devices with the lowest threshold powers are presented. (*) Denotes the corresponding mode number in Fig. 4-3 In symmetric devices, the radial breathing mode has the highest energy ratio, indicating it is able to efficiently convert optical to mechanical energy. This finding agrees with previous experimental findings that demonstrated that the radial breathing mode had the lowest threshold [25]. In contrast, in asymmetric devices, the threshold power for the radial breathing mode was only slightly different from the first cantilever mode. However, notably, it was still greater than 1, indicating that these modes can still be excited. This change in behavior can be directly tied to the presence of the asymmetry. For the case of the cantilever mode, it is particularly straightforward. As mentioned previously, an rmin and rmax can be defined. For the cantilever mode, these points act as pivot points. However, unlike in the case of a symmetric or balanced device, in an asymmetric device, it takes more energy to move the rmax side than the rmin side. Moreover, given the dependence of the overhang length on r, the rmin side experiences a larger torque, further increasing the disparity between rmin and rmax. As a result of this imbalance, this mode takes more power to excite. Mechanical mode (symmetric) Maximum Energy Ratio (symmetric) Mechanical mode (asymmetric) Maximum Energy Ratio (asymmetric) First Cantilever mode 1 First Cantilever mode (2*) 1 Second Crown mode 0.00297 Second Crown mode (4- α*) 30.075 Second Cantilever mode 0.17376 Second Cantilever mode (8*) 8.75 Radial Breathing mode 47.1629 Radial Breathing mode (14*) 1.12 81 In the asymmetric devices, the second crown mode (mode 4 α) had the highest energy ratio, followed by the second cantilever mode (mode 8). Interestingly, the second crown mode is a degenerate mode. Neither of these modes has been observed in symmetric devices. A simple analysis of the energy ratios in Table 4-1 provides key insight. While the radial breathing mode experiences a greater than 47x increase in energy ratio, the energy ratio for the second crown mode decreases by nearly three orders of magnitude, and for the case of the second cantilever mode, the energy ratio decreases by almost an order of magnitude. As a result, both modes are very energetically unfavorable. 4.5.Dependence of Frequency on Geometry To develop a more quantitative analysis for the asymmetric modes observed, we compare the frequencies of the second asymmetric crown mode (fcrn) and the second asymmetric cantilever mode (fcntl) of a device with varying average parameters. These modes are selected because their threshold power drops drastically in devices where the major and minor radii vary as previously described. A series of simulations demonstrate the effect of major and minor radii as well as the overhanging length on the frequency of the crown and cantilever modes, fig.4-4. In each simulation only one variable is swept. Finally, we fit curves to the resulting frequencies to estimate the trend of variations. The analysis reveals that the dependence on the different values of the geometrical parameters is: () 2 1 2 23 4 () () *( ) crn r f LR α αα α − ∝ −− + (4-9) () () ()( ) 22 2 56 7 8 1 ** cntl f rL R αα α α ∝ −− − − (4-10) 82 where r, R, and L are the average minor radius, major radius and overhanging length, respectively. All αn terms are offset constants. The results are plotted in fig.4-4. To have a clear comparison only one parameter is changed in each graph. From fig.4-4, it is apparent that the frequency of the cantilever mode decreases for all parameter variations. In contrast, for the crown mode, the frequency decreases for the major radius and the overhanging length, but it exhibits a significantly different trend for the minor radius. The asymmetric crown mode has a shifted parabolic dependence on the minor radius. Therefore, for smaller minor radii, increasing r results in a frequency decrease due to a larger torus mass. However, for larger values of r (with respect to α1), the frequency increases as a result of an increase in mechanical stiffness. It is possible to define a threshold overhanging length, above which the impact to the frequency is negligible, which could enable the design of optimized device architectures. Figure 4- 4:Theoretically calculated dependence of second asymmetric crown mode (black squares, left axis) and cantilever mode (blue circles, right axis) on the average (a) minor radius, (b) major radius, and (c) overhang length. Each is fit to a quadratic (red line). 4.6.Fabrication To fabricate asymmetric high-Q devices, a combination of photolithography, buffered oxide etching, and XeF2 etching are used to create an array of silica microdisk cavities integrated on silicon. To induce asymmetry in a controlled and systematic manner, the microdisk is reflowed using an intentionally misaligned CO2 laser. Specifically, the laser beam and the silicon 83 pillar are slightly offset, creating a non-uniform thermal gradient around the periphery of the device during reflow. In the final asymmetric device, the minor and major radii vary as a function of azimuthal angle as shown in fig.4-2(b). Asymmetry is defined in terms of the location of the pillar relative to the device center. To quantify the role of major and minor diameter, we introduce the parameter M as: max min max RR M R − = (4-11) where Rmax and Rmin along with other relevant structural parameters are defined in fig. 4-2(b). A key aspect of this device is the non-uniformity of both the overhang length and the cavity radius. Both values change gradually as one progresses radially around the circumference of the microcavity, with the overhang length increasing as the cavity minor radius (r) decreases. As such, both the overhang length and the device radius are dependent on angle ( ϕ). For the values of Rmax ≈Rmin, the device is almost symmetric and behaves similar to symmetric toroidal microcavities. As M increases, the asymmetry in the structure increases. To achieve the range of asymmetries studied in the present work, offsets ranging from 60-80 µm are introduced between the center of the CO2 laser beam and the silica microdisk to control the degree of asymmetry. The CO2 laser intensity is increased at a constant rate of 5 W/s to 25 W. Specifically, devices with major diameters of 44-48 μm, AR (AR=rmin/rmax) of 0.67-0.9 and pillar offsets ( Δz) of 1-3.5 μm, are studied. Symmetric devices are fabricated using the conventional method and serve as a control measurement with zero degrees of asymmetry [26, 27]. 84 4.7.Device characterization Using a tapered optical fiber waveguide, light from a 1550 nm tunable laser (Newport Velocity series) is coupled into the optical cavities. While continuously scanning the laser wavelength across the resonance frequency, the transmission spectrum is recorded and fit to a Lorentzian to calculate the optical quality factor. It is important to note that the Q is measured in the under-coupled regime with minimal power to reduce artifacts that arise from thermal broadening [27]. The quality factors for the asymmetric devices range from 3 ×10 6 to 3 ×10 7 . Therefore, the measured quality factors prove that by using the described method, it is possible to fabricate an asymmetric device while maintaining the requisite high quality factor to achieve optomechanical behavior. The primary optical loss mechanism is radiation loss due to the varying optical mode profile [28-30]. An Electrical Signal Analyzer (ESA) is used to measure the mechanical frequency spectrum of the transmitted light [31]. The threshold power for the onset of mechanical oscillations is determined by varying the input power of the laser from sub-threshold power to the saturation region, while monitoring the change of the output measured by the ESA. 4.8.Asymmetric Crown and Cantilever Mode To characterize the mechanical behavior of our device, the thresholds and frequency spectrum for mechanical oscillations are determined. Fig.4-5 shows the spectra of the two lowest threshold mechanical modes of an asymmetric device. The mode at 15.96 MHz has a 38 μW threshold, and the mode at 47.3 MHz has a 148 μW threshold. When these values are compared to the previously discussed FEM results, they correspond to the second asymmetric crown and the second asymmetric cantilever modes, as predicted. 85 Additionally, the first and third cantilever modes are excited at 9.58 MHz and 72.8 MHZ; however, the power thresholds are greater than 1.4 mW which is an order of magnitude larger than the asymmetric modes. In a symmetric device, these modes would be excited with threshold powers on the order of 20-40 µW [25]. Figure 4- 5:(a) Bright field image of the asymmetric device with the major and minor radii illustrated. Dashed lines are circles drawn as guides to the eye to aid in visualizing the asymmetry present in the device. ESA spectra data for the two lowest threshold modes from the asymmetric device: (b) the asymmetric crown mode and (c) the asymmetric cantilever mode. Threshold curves for (d) the asymmetric crown mode and (e) the asymmetric cantilever mode. While the mechanical modes with the lowest threshold in the asymmetric device are different from those in the symmetric device, the absolute threshold values for the two lowest threshold modes are of the same order of magnitude [17, 25]. This similarity indicates that the energy conversion process in symmetric and in asymmetric devices is equally efficient for the different mode types as predicted by the FEM simulations and the results in Table 4-1. Therefore, the introduction of the asymmetry provides access to previously unobserved modes at 86 low threshold powers without completely suppressing previously characterized mechanical modes. 4.9.Dependence of Frequency on Asymmetry (M) In order to fully understand the dependence of oscillation frequency on device asymmetry, a suite of devices with varying degrees of asymmetry are characterized. The experimentally determined frequencies of crown and second cantilever modes are plotted versus M in fig. 4-6. Complementary FEM modeling is performed at specific M values and is included for comparison. The simulated frequency is in agreement with the measured frequency for all the modes discussed here with a maximum error of 5%. The error is calculated by subtracting the simulated values from the real value, dividing by the real value, and then multiplying by 100%. Figure 4- 6:Overhang length normalized frequency dependence of the (a) second asymmetric crown mode and (b) second asymmetric cantilever mode on the eccentricity parameter, M. Black squares are results from FEM simulations, and red circles correspond to experimental results. The solid black line is a fit to theoretical data for illustration purposes. Maximum Error is around 5%. Note: There are error bars in both the x and y axes, but the error bars are usually smaller than the symbols. The error in the M ratio is calculated by multiple measurements of R min and R max in optical images, similar to the one shown in Fig. 4(a). The error in the normalized frequency is calculated by projecting the errors occurred in M to the values of measured frequency. For the asymmetric crown mode and the second cantilever mode, the mechanical frequency initially increases and then plateaus as M increases. This behavior originates from dependence of the device stiffness (spring constant) on the membrane overhang length and the 87 AR. Specifically, as M increases, the torus minor diameter increases and the overhanging length decreases. Therefore, for small values of M, the mechanical frequency scales with M. But as M increases beyond 0.06, the impact of structural changes on the spring constant diminishes and the mechanical frequency reaches an upper limit. 4.10.Dependence of threshold on asymmetry To show the effect of eccentricity on the threshold for the onset of mechanical vibrations, the threshold powers of different devices with different asymmetries are measured and plotted in fig.4-7 as a function of the normalized threshold (Pth*Q 3 /Vrm), where Vrm is the average mode volume. There is a clear dependence of the threshold power on asymmetry. Specifically, the threshold power drops drastically in both modes, which is in agreement with the previous predictions based on energy transfer. Figure 4- 7:(a) Normalized threshold graph for asymmetric crown mode vs. pillar shift. (b) Normalized threshold for asymmetric cantilever mode vs. pillar shift. Note that the threshold values have been normalized (P th *Q 3 /V rm ) to desensitize them to other factors that affect threshold. V rm is the average mode volume. In order to investigate how introduction of an offset influences mode excitation a Focused Ion Beam (FIB) was used to cut a series of six symmetrical toroids after CO2 laser reflow to observe their cross-section.the results have been shown in fig.4-8. 88 (a) (b) (c) Figure 4- 8:cross section of three different toroids with different degrees of reflow By measuring the vertical offset of different reflowed toroids and plotting it vs percentage of melted material from the initial disk, we can get interesting results. Figure 4- 9:Diagram of vertical offset vs percentage of melted disk. From fig. 4-9, it is clear that the vertical offset of the torus varies with the percentage of the melted silica. For the case of symmetric device, the vertical offset has an equal value for all the corresponding points, which translates equal force in all directions. This leads to effective excitation of radially symmetric modes. However, for the case of asymmetric toroids, vertical offset is a function of azimuthal angle. This dependency creates uneven distribution of vertical component of the force, which results in varying deformation of the structure. This behavior warrants further study in the future. 89 4.11.Failure analysis The main problem in fabrication and characterization of asymmetric devices is repeatability and design control. Initially, when we reflow the devices, the asymmetry introduced in the structure deteriorates the optical quality factor. Varying the cross section in the torus part of the device results in the mode mismatch loss, especially in the thick to thin transition regions. By reflowing the devices at a certain rate, we could obtain devices that had improved mismatch loss, and we could successfully fabricate devices that had a quality factor around 10 6 . The second important problem was the percentage of reflowed material. It is important not to make both sides of the device thick. In other words, fabrication of samples that have both sides thick will not show stable results. This is in part due to elevated stiffness and small difference in two sides of asymmetric device. We noticed that by reflowing the device at a rate of 5 W/s and melting 50- 60% of the initial disk volume will result in optimum mode excitation. In fig.4-10, several devices with no asymmetric mode excitation are shown. The transition could be an interesting area of future investigation. (a) (b) Figure 4- 10:Example of devices with no asymmetric response 90 4.12.Conclusion In conclusion, we have shown that by modifying the fabrication process of microtoroid resonators to introduce asymmetry, it is possible to control the frequency and threshold power of optomechanical vibrations. It is possible to suppress the previously observed first and third order radially symmetric modes while simultaneously lowering the onset threshold for other previously unobserved modes. These mechanical vibrations have many applications within the field of quantum optics. The introduction of repeatable asymmetry while keeping the quality factor relatively high not only aids in engineering the mechanical behavior of these devices but it also facilitates new schemes for high efficiency directional excitation of optical modes which has many applications in quantum chaos studies [32-35] 4.13.Chapter 4 References 1. D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, "All-optical polariton transistor," in CLEO: QELS_Fundamental Science, (Optical Society of America, 2013), QM1D. 4. 2. M. F. Yanik, S. Fan, M. Solja či ć, and J. D. 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Kim, "Chaos-assisted nonresonant optical pumping of quadrupole-deformed microlasers," Applied Physics Letters 90, 041106 (2007). 93 Chapter 5: Suspended Silica Splitters 5.1.Introduction The continual need for higher capacity in components in optical communications has resulted in an ever-increasing interest in design of optical devices for monitoring and sensing purposes[1-6]. On one hand, highly computerized systems require the high speed of light for communication and calculation, and, on the other hand, medical devices need sensitivity of light for detection. One of the main components in most of the integrated optical circuits is power splitters which are necessary to monitor the operation of the device[7-12]. In sensing applications, splitters are used to detect any surface binding, which results in a change in the effective refractive index of the guiding mode and ,as a result, the coupling ratio. Splitters used for this purpose need a relatively long evanescent tail to increase the sensitivity and a wide sensing area for molecule binding. There are a variety of mechanisms used for splitting including:[13-19] 1-Evanescent coupler: In this type of coupler two waveguides are brought into close proximity and the evanescent tail of the mode in one waveguide excites the mode in the neighboring waveguide and thus splitting the power. 2-Y-branch splitter: In this type of splitter power is divided by spatially dividing the waveguide into two waveguides at a small angle. Depending on the refractive index of each side and the symmetry of the structure, the input light can excite modes in each waveguide symmetrically or with a weighted ratio. This type of splitter suffers from excessive loss due to an abrupt change in refractive index. The angle of the waveguide at 94 the branch region could be minimized by using a cosine curvature for the branches or by using a MMI region before the Y –branch region. In this chapter, we have introduced a new type of power splitter by introducing a transition curvature in the waveguide branches and using a wide multimode diaphragm to trap the transition loss. The main figure of merit for this device is its potential to be used in optical integrated circuits along with toroidal cavities. Figure 5- 1:The Protrusion region formed by reflowing process, results in escape of light from waveguide 5.2.Theory In order to understand how this device operates, we have designed a piece by piece accurate model by taking several microscopic and SEM images from the device and replicating the structure in Lumerical (FDTD). In fig.5-2 we have shown the details of the model that have been extracted from our mask design and also SEM pictures of the final structure. Light is coupled into the 5 μm reflowed waveguide using a lensed fiber (focal point=12 μm ). Next, light passes through a curved region with a radius of curvature of approximately 200 μm which is supported by a 2 micron thick diaphragm. The bumped waveguide has been connected to an angled waveguide using another 95 curved waveguide with R 120 μm ≈ . After propagating the length ' (transition length) cos( ) L α ≈ , light enters the rectangular diaphragm with two circular waveguides on two sides and finally, is split by a Y-branch. For this simulation we assumed that the refractive index of silicon oxide is 1.445 at 1550 nm [20]. In this simulation, we will calculate coupling ratios and field distribution for silicon oxide, silicon nitride (n=2) and 10 % wt titanium oxide doped silica (n=1.493) [21-23] numerically. In addition, in order to understand how the coupling ratio changes with α , we will calculate the coupling ratios for several angles ranging from 5 to 15 degrees. All of our simulations have been run in air (n=1) and also the maximum mesh size has been set to 90 nm to make sure that we are below 10 λ and have an acceptable accuracy. Figure 5- 2:(a) Schematic of the suspended splitter design in Lumerical (b) An SEM image of a final fabricated device with corresponding parameters. 96 To calculate the power splitting ratio, we placed monitors at the positions indicated in fig.5-2. It is important to note that we extended the monitors out of the boundaries of the waveguides to include the evanescent field, associated with the propagating mode inside the waveguides. As a result, a negligible amount of power is coupled into the monitor directly from the source from outside the waveguide. However, since the extension of the monitor out of the waveguide is 400nm, we have neglected the direct coupled power in our calculations. Using the values from the monitors, the loss is calculated using the following expression: Loss=Lic+Lrad+LTr+LY, where Lic, Lrad, LTr, and LY are input coupling loss, radiation loss, mode transition loss, and Y-branch loss respectively. Clearly, the actual value of input loss is higher than the calculated value and is affected by other factors such as the input waveguide end-cut, input fiber misalignment, and lensed fiber quality. In this simulation, our purpose was to find the total effect of radiation, transition and Y-branch loss. Therefore, we have not included propagation loss in our calculations, as this loss source is simply a constant offset.[24, 25] In order to explain the coupling mechanism, first we simulate the case where all the transitions are smooth (R>300 μm ) and we do not have any “bumps”. As the results show in fig.5-3, since the transition and radiation loss are minimum, all of the power is coupled into and maintained in the reflowed waveguide, and a negligible amount of power is coupled into the diaphragm ( less than 3%). It is worth mentioning that, although the thickness of the diaphragms is larger than the wavelength inside the medium (2 μm ), due to orthogonality of the modes inside the structure, the field remains inside the reflowed waveguide [26]. In fig.5-3, we can see that the coupled modes inside the reflowed waveguide are phasing in and out. However, when a protrusion is present, a controlled amount of the field leaks into the membrane where it excites propagating modes, which subsequently couple either into the cross or through port. 97 Figure 5- 3:Comparison of a smooth and actual protrusion on multimode coupling between two splitter arms. At the bent waveguide, two types of loss mechanism are responsible: [27] 1-Waveguide transition loss: Since the propagating light inside the straight waveguide could not be fully expanded in terms of the modes of the curved waveguide, a part of light can not propagate in the “bump” region and leaks out. 2-From the ray optics perspective, at a bend, the incident angle of rays is greater than the critical angle of the waveguide. Therefore, one may expect that in a bent waveguide, the leaky modes are supported and are continuously losing power. Due to these loss mechanisms, a controlled amount of the field inside the straight input waveguide leaks out into the thick diaphragm region where it excites propagating modes inside the wide floating region which is followed by a Y-branch splitter. By controlling the input waveguide angle and also the reflow process, we can achieve the desired coupling ratio. 98 Also, it is worth mentioning that since two waveguide channels are reflowed, they have very smooth surfaces and the effect of propagation loss in the reflowed waveguides can be ignored. One of the challenges in the fabrication of this device is that special care should be taken when reflowing the sample. The power used for melting silicon should be consistent with the speed at which the sample moves under the laser. If melting speed is higher than the motion speed, we will have a wavy waveguide, and as a result, the coupling ratio will change drastically. In fig.5-4, I have shown how the coupling to multimode region at the protrusion area happens. Figure 5- 4:Propagation of light at the protrusion region. This simulation shows how light gets coupled to other modes at the "trap region". 5.3.Fabrication The general splitter structure is fabricated using a simple process which combines two photolithography steps, buffered oxide etching, XeF2 etching and a CO2 laser reflow. The details of the fabrication are published elsewhere[28]. However, as a result of the pair of photolithographic masks used in the multi-step lithography, the device has several clearly identifiable regions. One of the key features of the structure is the slight protrusion at the input waveguide. This change in curvature is the result of combining the CO2 laser reflow method with a multi-step lithography process, in which the silica thickness varies. However, it is 99 extremely reproducible, and it appears in all high quality devices. Therefore, it was included in the modeling. 5.4.Cylindrical waveguides These devices are made of two components: One is the cylindrical waveguides resulting from reflow process. Two: the multimode splitting region. In addition to the splitting region, the input cylindrical waveguides play an important role in multimode coupling at the entrance of the "trap region". The propagating optical modes supported by a cylindrical silica waveguides are the solutions of the Helmholtz equation in cylindrical coordinates:[29] (5-1) and λ is free space wavelength. In the above equation J ν and K ν are the Bessel function of first kind and modified Bessel functions. Also, ν is a constant used to separate variables for solving the cylindrical wave equation. In fig.5-5, I have shown the first few modes in a cylindrical waveguide with a diameter of 10 μm. 22 2 1/2 0 221/2 0 0 (/ ) exp( ) for 0 r a () (/) E exp( ) for r>a () where u=a(n ) () 2 z z c Jur a EA j Ju Kwr a Aj Kw k wa k k ν ν ν ν νφ νφ β β π λ =≤≤ = − =− = 100 Figure 5- 5:General solutions for the first few modes in a cylindrical waveguide 5.5.Simulation results In addition to the operation principle, we have repeated the simulations with different angles for the input waveguide to determine the effect of the angle ϕ on the coupling ratio of the silica structures. In fig.5-6 we have shown the effect of the input waveguide angle on coupling ratio. From this graph, we can conclude that the coupling ratio is almost 50/50 at 13° and does not have sharp changes from 5 to 15 degrees. However, it should be noted that although the coupling ratio is independent of coupling angle, the mode mismatch loss will increase due to sharp changes in the direction of propagation. 101 Figure 5- 6:Coupling ratio in bar and cross outputs for a suspended splitter. 5.6.Broadband operation span One of the unique features of this device is its unique transmission spectrum. Typically, the splitting ratio is dependent on the wavelength and polarization of the input light. The suspended splitter is capable of maintaining its coupling ratio over a large wavelength range. This feature makes our splitters a promising candidate for broadband applications. Fig. 5-7 shows the experimental results and the complementary simulation results for both TE and TM input polarizations. In both, the coupling ratio remains nearly constant. In addition, the maximum polarization dependent difference in coupling ratio is around 10% for 1550nm range, which shows the operation of this device is slightly polarization dependent. While there is very good qualitative agreement between the experimental and modeling results, some discrepancies are observed which are believed to be due to the following reasons: 102 1-Fabrication defects: In the process of fabrication we have used (100) silicon wafers with a 2 µm thermal silica on top. The end faces are cut by scratching the wafer on two sides and cutting the device on atomic planes. Although for most of the cases the device is cut on perpendicular planes, in some cases the end faces are cut at an angle, resulting in slanted input ends. Also, after fabricating the devices in order to get a suspended coupling region, the waveguides are reflowed by a CO2 laser. During this process, sometimes some micro size waviness is introduced in the reflowed parts which affects device characteristics. 2-Alignment: Although the lensed fiber is mounted on a XYZ high precision stage and is aligned accurately, in some cases the lensed fiber and the input waveguide are positioned at an angle with respect to each other which results in exciting higher order modes. Depending on the degree of the misalignment, the characteristics could be different from the results that are given by the simulations in which all the end faces are perpendicular and have no defects. In addition it should be noted that since the lensed fiber that was used is not AR-coated, a parasitic Fabry-Perot might be generated between the input interface and the fiber or the defects in the input waveguide and the input face itself which results in observation of periodic fluctuations in experimental transmission graphs. In fig.5-7, I have summarized the simulation results and have compared them with experimental results. 103 (a) (b) Figure 5- 7:(a) Simulation of coupling ratio vs. wavelength (b) Experimental coupling ratio for a typical device. In order to explain the slight difference in the coupling ratios for two output ports, the total loss for two outputs for each polarization is calculated by simply taking the logarithm of the total normalized output power. The result from these calculations is shown in fig.5-8. As can be observed from fig.5-8, the total loss for TM polarization is slightly less than that of TE polarization across all wavelengths. This slight difference in the total loss is primarily the result of the difference in mode mismatch and radiation loss at the bent waveguides for TE and TM polarizations. 104 Figure 5- 8:Calculated total excess loss for through and cross output. In order to explain the difference in the coupling coefficient of the two outputs for different polarizations, we have calculated the total excess loss for two output waveguides for two polarizations. As could be seen from the figure, the total loss for the TM modes is less than that of TE modes. It is believed that the difference in coupling ratio originates from the difference in loss at the bends for the two polarizations which is not equally distributed on two outputs. In fig.5-9, we have schematically explained the reason for different values of loss for TE and TM polarizations using conformal mapping. In this model, light is proportional to exp(-I) where I is: I= , 22 , 2 ( x caus eff eq x core cladd nndx π λ − −  (5-2) 105 where λ is wavelength, neff if effective refractive index of the mode and neq is equivalent mapped refractive index. Also , core cladd x is core-cladding boundary and xcaus is TE or TM caustic position.[30, 31] In fig.5-9, we have shown the refractive index distribution after conformal mapping. Figure 5- 9:Effective refractive index for TE and TM modes after conformal mapping. The equivalent index of the TM modes is lower than the equivalent index of TE modes; therefore, the TM mode has to overcome a larger tunneling barrier to penetrate into oscillation region. As a result, the TM modes have lower curvature loss. 5.7.Dependence on material In the last series of simulations, we explored the dependence of the splitting ratio on the waveguide material by replacing the silica with silicon nitride or 10%wt TiO2 doped silica. All other parameters were held constant. The results are summarized in Table 5-1. TABLE 5-1: Simulation results for three different materials. Refractive index Coupling ratio (%) Loss (dB) Silica 1.445 62.637.4 -2.72 10% wt TiO2 doped silica 1.493 60.9/39.1 -2.58 106 Silicon Nitride 2.000 58/42 -3.51 As it can be seen from the results, the splitting ratio gradually approaches 50/50 as the refractive index of the material increases. Additionally the cross coupled ratio is always less than the bar channel output. This result is believed be due to the fact that not all of the in-coupled light leaks in the diaphragm region, and there is always some uncoupled light in the reflowed waveguide which adds to the back-coupled light from the Y-branch. The main component of loss is the input coupling loss, which was calculated to be in the range of 1-1.37 dB. It is worth mentioning that we focused on the analysis of the case where the splitting ratio was 50/50 or very close to this value. However, it is possible to have other splitting ratios by changing various factors including: 1-Protrusion length: By increasing the curved region length and therefore increasing the radius of curvature, radiation loss decreases, and as a result, splitting ratio changes. Protrusion length could be modified by changing the angle of the input waveguides or the waveguides connecting the input waveguides to the coupling region. 2-Material: By using a different material and in general by changing the refractive index of the waveguide, both radiation loss and transition loss are altered. This would result in a modification of the splitting ratio. 3-Mask misalignment: Introducing a misalignment in the second pattern transfer would result in having a wider diaphragm region in one side and a narrower one on the other 107 side. As a result, the Y-branch would split the input light with different weights and the splitting ratio is modified. In conclusion, we have developed a 3D FDTD model, which accurately predicts the splitting behavior of a novel suspended silica device which contains a lithographically patterned protrusion. This device uses transition loss trapping to split the incoming light. The precise splitting ratio is governed by the insertion angle, bend angle and radius of curvature of the protrusion. Additionally, we have shown that the coupling ratio is wavelength independent and has a slight polarization dependence. Due to its large surface area, this device can have a variety of applications in the biodetection community. 5.8.References 1. P. J. Winzer and R.-J. Essiambre, "Advanced modulation formats for high-capacity optical transport networks," Journal of Lightwave Technology 24, 4711-4728 (2006). 2. R.-J. Essiambre, R. Ryf, N. Fontaine, and S. 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Armani, "Low-loss silica-on-silicon waveguides," Optics letters 36, 3729-3731 (2011). 25. X. Zhang, M. Harrison, A. Harker, and A. M. Armani, "Serpentine low loss trapezoidal silica waveguides on silicon," Optics express 20, 22298-22307 (2012). 26. R. Sammut and A. W. Snyder, "Leaky modes on a dielectric waveguide: orthogonality and excitation," Applied Optics 15, 1040-1044 (1976). 27. I. Papakonstantinou, K. Wang, D. R. Selviah, and F. A. Fernández, "Transition, radiation and propagation loss in polymer multimode waveguide bends," Optics Express 15, 669-679 (2007). 109 28. X. Zhang and A. M. Armani, "Suspended bridge-like silica 2× 2 beam splitter on silicon," Optics letters 36, 3012-3014 (2011). 29. C. Yeh, "Guided-wave modes in cylindrical optical fibers," IEEE Transactions on Education, 43-51 (1987). 30. M. Krause, H. Renner, and E. Brinkmeyer, "Polarization-dependent curvature loss in silicon rib waveguides," IEEE Journal of selected topics in quantum electronics 12, 1359 (2006). 31. R. T. Schermer and J. H. Cole, "Improved bend loss formula verified for optical fiber by simulation and experiment," IEEE Journal of Quantum Electronics 43, 899-909 (2007). 110 Chapter 6: Biological Systems 6.1.Introduction With new diseases emerging, the need to study the properties and variations in cells becomes more crucial. Therefore, there has been considerable interest in studying cell imaging and identifying the optical properties of the cells. Methods such as confocal and optical coherence tomography are among the successful methods that enable us to image tissues for diagnostic applications. The success of these methods depends on how accurate we can relate changes in the light wave as it travels inside the cells to changes in the optical signal. To reach that goal, we need to have a deep insight in light matter interaction. In addition, in recent years, gold nano particles have shown promising results in study, characterization imaging, and treatment of living cultures. Being a biocompatible and easy to make platform, gold nano particle based systems have opened up a new area for biological systems studies. In this section, we study the theoretical fundamentals behind biological systems that are suitable to be integrated in optical systems. 6.2.Scattering from Living cells Scattering based optical detection methods have made a significant impact in a wide range of fields from pathogen detection to water monitoring [1-3]. However, size, weight, and power requirements are still a challenge. Over the past few decades, rapid advances have been made in the development of novel molecular screening platforms and protein diagnostic assays. Using these methods, we are able to routinely detect <fM quantities of proteins and DNA in high-throughput [4-6]. However, the gold standard for monitoring of batch processing is based on imaging and counting the cells using methods like hemocytometry. This method still relies on cell plating [7]. 111 An alternative strategy for cell analysis is based on flow cytometry. In this method, cells are fluorescently labeled and are streamed past a detector that analyzes and counts them [8-10]. Additionally, physical properties, such as cell size, can be determined by analyzing the cell diffusivity. Unfortunately, both of these processes are time-consuming and require extensive sample preparation, making them unsuitable for real time applications like biomanufacturing and diagnostics. Our alternative is optical scattering spectroscopy, where instead of counting the cells one tries to estimate the number of cells by studying optical scattering patterns in the cells. Based on optical scattering spectroscopy, the system acts as a flow cytometer. To have a thorough understanding of dynamics of this system, it is necessary to build a comprehensive theoretical model that can explain the details of cell behavior when interacting with electromagnetic waves. 6.3.Modeling Using FEM and FDTD software we created a number of models to better understand the scattering within our system to predict and analyze the interaction between the cells and the laser source. To understand the expected profile of our cells and their scattering patterns, we modeled different numbers of cells and different refractive indices of their unique membrane alignment and spacing. We primarily focused on two types of cells (1) cancer cells and (2) MRSA bacterial cells. These two systems are different in their scale and the number of membranes. Cancer cells are 20 μm and MRSA cells are 650 nm. Cancer cells have a single membrane and MRSA cells have four membranes [14]. Models like this can help optimize the design of the system to maximize the operating range. To assist in the modeling efforts and to cross-confirm the device detection readings, we used imaging measurements, including differential interference contrast 112 (DIC) imaging and fluorescence imaging of the cells that we test with our device to determine the relative concentrations and behavior (fig.6-1). Figure 6- 1:Images of HCT 116 colon cancer cells from (a) DIC and (b) florescent images used for the basis of Lumerical and COMSOL models of the cancer cells. 6.4.Details of COMSOL Modeling Sometimes when we want to predict an optical device's behavior or light matter interaction, analytical equations will not be able to provide us with accurate results. In such cases we use simulation software that will calculate the behavior of the device to acceptable accuracy. There are two types of commonly used modeling software: FEM and FDTD. In the first category, FEM (Finite element method), we divide the optical structure into very small regions (mesh) and assume that the field in each region is uniform and constant. Next we solve Maxwell's equations in steady state in each meshed area. In this method we ignore all the transient states in light propagation and only calculate the final steady state of the structure. This method is memory efficient and uses less memory compared to the second category. However, it doesn't give us any information about the transient behavior of wave. In the second category, FDTD (Finite Difference Time Domain), the software captures all the information from the starting of the power launch to the end of the simulation time. In this method, the software 113 allocates much more memory than the FEM method. However, it is very useful in understanding transient behavior of the light-matter interaction. Similar to the other method, FDTD divides the space into very tiny meshes and solves for Maxwell's equations in each mesh but with the difference that time also is taken into consideration and results from one time step are saved and used as inputs for next step. In order to model the scattering behavior of living bacteria, we use Lumerical FDTD software. We define a large plane wave source that illuminates a bacteria cell right in front of it. Next we use "Power Monitors" after the cell to capture the power transmitted through the cell and to calculate the scattered light. We approximately estimate the scattered light based on the angle and amplitude of the refracted light. In our simulations, we used 1064 nm as the operating wavelength and chose the mesh size to be 100 nm, approximately 1/10th of the wavelength. Furthermore, we assume that the wave is propagating in air and the cells are spheres with a diameter of 685 nm and a refractive index of 1.4. In fig.6-2 we have shown the results of calculating the scattering from one cell. (a) 114 (b) (c) Figure 6- 2:Scattering from (a) one (b) two particles. (c) Scattering pattern from front view. Although the Lumerical FDTD can accurately calculate and predict the behavior of the scattered light, it is very difficult to separate the incoming and the scattered signals from each other in Lumerical FDTD environment. Also, it is almost impossible to define a completely uniform wave front in FDTD Lumerical environment. We began by trying to model the system in Lumerical because of the ease of modifying the refractive index and adding additional membranes. While we were able to model the propagation and cross section, we were not able to easily translate these models into useful information for comparison with our experimental results. We transitioned to performing the studies in COMSOL because the outputs were more relevant to our applications. 115 Figure 6- 3:Graphical representation of the relationship between the percent power scattered and the number of bacteria within the sensing chamber calculated using COMSOL. (Inset) Example of the output of the scattered field in the x and y direction if there are two cells in the region. Using COMSOL we were able to better visualize both the field scattering and the power scattering for an individual particle (fig.6-3). For example, in the model below, we studied how particle conformation (e.g. particle clumping), not just particle number, affected the amount of the light that is scattered. As the number of particles increases, the percent of light scattered increases. 116 (a) (b) (c) (d) Figure 6- 4:Field scattering of a single cell using the new background field In addition, using COMSOL it is possible to get the scattering profile for one or multiple cells and one can calculate how much power is scattered at a certain angle range. In fig. 6-4, I have shown an example of scattered power profile. 117 6.5.Maxwell's equations governing scattering from cells If we assume that the incident light on a cell is a plane wave, then we can describe the incident light as: 0 (, ) exp(( . )) i Ert E ikr t ω =− (6-1) E i ,H i Figure 6- 5:Schematic of scattering problem from a cell The equation governing incident and scattered fields is the Helmholtz equation: 22 [()]()0 kr E r ∇+ = (6-2) For convenience, we assume that the incident field has two components, one parallel and another one perpendicular to scattering field. By assuming that the cell has a spherical profile, we can convert all of the vector components to spherical coordinates. cos 0 ˆ (sin cos cos cos sin ) ˆ ˆ ikr i EEe r θ θ φ θ φθ φϕ =+ − (6-3) 22 2 22 2 2 2 11 1 sin 0 sin sin rk rr r r θ θθ θ θ φ  ∂∂∂ ∂ ++ +Ψ=  ∂∂∂ ∂  (6-4) (, , ) ( ) ( ) ( ) rRr θ φ θ φ Ψ= ΘΦ (6-5) () ( ) ,, (, , ) cos( ) jjn emn n m rzP m θφϕ Ψ= (6-6) () ( ) ,, (, , ) sin( ) jjn om n n m rzP m θφϕ Ψ= (6-7) 118 x Figure 6- 6:Simplified schematic of scattering from a cell. The scattered field is in the form of spherical waves emanating from the cell with radially decreasing intensity: ikr s e E A ikr −  (6-8) By applying the boundary conditions and assuming that the scattered field is a combination of all the possible solutions of the Helmholtz equation, one can get two series of equations for the Electric field and Magnetic field. In fig.6-7 we have plotted one example solution for the scattered light from a cell. Figure 6- 7:Scattering from a sphere with n=1.5 , r=1 microns in water at 633nm z Incident light ϕ Scattering plane 119 6.6.Ultrasound Treatment of Gold Nanoparticle Infused Cells The most effective way in cancer cell treatment is non-invasive methods where only certain cells are targeted and the tissue is not affected. One method is to direct a high power laser source on the cancer cells to kill them, however this method might affect the healthy tissue. Also one common treatment strategy is chemotherapy that eliminates the cells by chemical methods, again the healthy tissue is damaged. One promising method is Gold nanoparticles with ultrasound irradiation for a therapeutic in biomedical applications including targeted cancer cell death. It is possible to kill the cancer cells by directly exposing them to high intensity ultrasound waves. However, high intensity ultrasound might have unwanted side effects such as burns. In addition, the use of ultrasound alone does not completely remove cancerous cells [15]. The combination of gold nanoparticles with ultrasound irradiation is a noninvasive treatment strategy in which the medium frequency low power ultrasound waves pass through the tissue and only treat the targeted cells with gold nano particles in them. A recent study by Sazgarnia et al[16], who targeted cancerous tumors in mice, showed that intense pulsed light and gold nanoparticles with ultrasound irradiation decreased the tumor volume and produced overall longevity of mice with colon carcinoma tumors[16, 17]. In another study, coated gold nanoparticles were used as a contrast-intensified ultrasound imaging agent in addition to cell death induction[18]. These studies exhibit the potential ability of gold nano particles in infected or mutated cell treatment, but they don't explain the underlying reason for why gold nano particles has such ability. There are three underlying mechanisms that explain the cell death exposed to ultrasound radiation: acoustic cavitations, acoustic radiation forces, and heat generation[18-20]. In some interesting cases, scientists have used photothermal effect to improve cell imaging. Some use gold nanoparticles that are functionalized to improve contrast for imaging[21, 22]. Other groups 120 have focused on the effects of acoustic cavitation for therapeutic means[16, 17]. Overall, the functionalization of gold nanoparticles to target specific cells is well established[20, 23]. When living cells absorb nanosized metal particles and are exposed to medium intensity ultrasound waves, a percentage of the cells die. We hypothesize that the heat generated by the gold nanoparticles upon ultrasound irradiation is what ultimately causes cell death. To shed light on what happens when cells are exposed to ultrasound waves, it is necessary to mention that when the sound waves propagate inside the medium, the acoustic force from the waves causes vibrations throughout all the intracellular elements. However, since different elements have different densities and hence different inertia, a differential oscillatory motion is generated between the elements inside the cell, thus affecting the structure of the cell. The heat generated due to the differential oscillatory response is responsible for irreversible cell death. 6.7.Ultrasound Generator System In order to test the cells, we place the ultrasound transducer in the container and apply an amplified electric signal at resonant frequency of the transducer. 121 Figure 6- 8:Schematic of the cell treatment set up along with photos from the transducer. By Using Hooke’s Law and taking the effect of virtual friction and added mass into account, we can calculate the frequency response of the nanoparticle inside the cell in two 122 configurations: Maxwell and Voigt configurations[24]. In fig.6-9, we have shown the frequency response of each construction. (A) (B) Figure 6- 9:Frequency response of cells in (a) Voigt construct (b) Maxwell construct 123 In addition, we have simulated the behavior of the nano particles inside a living cell using COMSOL by measuring the differential displacement between a rigid nano sphere and the free oscillating environment. Again, we see similar behavior to Maxwell construct. Figure 6- 10:Frequency response of a spherical nanoparticle inside a cell Additionally, the UV-VIS absorption spectrum of the gold nano particles show that there is only one absorption peak at 520nm which indicates that the nanoparticles are uniform. 124 Figure 6- 11:Absorption Spectrum of the gold nanoparticles 6.8.Cell line and culture conditions Preliminary experiments have been performed using human acute monocytic leukemia suspension cell line known as THP-1. They were obtained from ATCC (Cat # TIB-202). The cells are cultured in RPMI 1640 medium (Cat # A1049-01; Life Technologies) supplemented with 10% (vol/vol) fetal bovine serum (Cat# 10082-139; Life Technologies) and 1% (vol/vol) penicillin-streptomycin (Cat# 15140122; Life Technologies) at 37 ˚C in a 5% carbon dioxide humidified incubator. The cells are grown to 100% confluence after 3-4 days. The cell survival rate and their numbers are determined by a hemocytometer using trypan blue. 6.9.Conclusion In conclusion, we have theoretically studied two biological systems. In the first case we have studied the scattering characteristics from a cell culture line. We have shown that it is possible to predict the angular dependence of cell scattering on solution and cell structure. In the second case, we have studied the possibility of ultrasound treatment of gold nanoparticle diffused living cells. We have shown that it is possible to model cells in COMSOL as well as build an 125 analytical rigid body model for it. Analysis of cells has many applications in disease treatment, imaging, tomography and genetics. 6.10.Chapter 6 References 1. P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. 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Mou, Z. Chen, and N. He, "Influence of nanoparticle shape, size, and surface functionalization on cellular uptake," Journal of nanoscience and nanotechnology 13, 6485-6498 (2013). 21. K. Bhattacharyya, M. Njoroge, B. S. Goldschmidt, B. Gaffigan, K. Rood, and J. A. Viator, "Detection, isolation, and capture of circulating breast cancer cells with photoacoustic flow cytometry," in SPIE BiOS, (International Society for Optics and Photonics, 2013), 85700A- 85700A-85712. 22. J. R. Cook, W. Frey, and S. Emelianov, "Quantitative photoacoustic imaging of nanoparticles in cells and tissues," ACS nano 7, 1272-1280 (2013). 23. M. J. Santos-Martinez, K. Rahme, J. J. Corbalan, C. Faulkner, J. D. Holmes, L. Tajber, C. Medina, and M. W. Radomski, "Pegylation increases platelet biocompatibility of gold nanoparticles," Journal of biomedical nanotechnology 10, 1004-1015 (2014). 24. M. Or and E. Kimmel, "Modeling Linear Vibration of Cell Nucleus in Low Intensity Ultrasound Field," Ultrasound in Medicine and Biology 35, 1015-1025. 127 Appendix A:Nonlinear frequency comb generation and operation improvement A.1 Introduction The unique optomechanical properties of silica glass have allowed it to be a mainstay material in photonic applications over the years. Because of the material symmetry, in silica the lowest order optical nonlinearity is third order. Third harmonic generation, parametric gain, Raman gain and third order sum of frequencies are the most common phenomena encountered when this material is optically pumped with high peak powers. All these optical nonlinearities are crucial in information transfer, processing onto multiple wavelength channels, and next generation laser sources and spectroscopy tools. Although there are many studies concerning the third order nonlinearity of bulk materials, over the past decade there has been a high interest in developing multifunctional photonic devices capable of performing all optical signal processing at incident threshold powers of around a few μW in a very compact device. Microcavities are good candidates to achieve this goal. In optical microcavities, surface-tension-induced microcavities are superior to other geometries. This is due to the capability of developing a multitude of dielectric microresonant structures with very low surface roughness, such as silica microspheres and silica microtoroids, which have the ability to trap light for long periods of time in circulating orbits within a small volume. This allows silica microdevices to have ultra high quality (Q) factor (as high as 10 8 -10 9 ). All of these important features make silica microcavites well-suited for investigating optical nonlinearities. 128 Below those Q factors, it is difficult to access Kerr nonlinearities in microcavities, unless they are pumped with high energy excitation sources which dramatically effects the performance of the cavity. Despite this, new trends in applied photonic technologies demand ultralow- threshold powers to attain the optical nonlinearities under discussion. It has been experimentally demonstrated that optically pumped silica microcavities with Q above 10 8 and threshold power ranging from 20 µW to 500 µW can attain optical third order nonlinearities[1]. However, for optically pumped microcavities with Q factors below 10 8 , it is hard to achieve those phenomena with sub-mW input powers. Normally, microresonators based on silica with Q factors of 10 6 -10 7 require incident powers > 1mW, which linked with the small volume occupied by the whispering gallery modes (WGM) supported in the microcavity and the poor thermal conductivity of silica, ensure strong thermal effects. This thermal behavior impacts the stability of the cavity by shifting the resonance wavelengths. An important aspect in nonlinear optical effects is that these are both governed by the photonic interactions in materials and are superlinearly dependent on the electromagnetic fields. Therefore, novel routes of material interactions to enhance these desired nonlinear effects can be developed. One approach is to use plasmonic structures such as metallic nanoparticles (NPs) as coatings on the surface of waveguiding photonic devices. Moreover, the presence of particles in microcavities broaden the range of potential applications due to the intrinsic capability of metallic NPs to both improve optical responses, particularly those that are inherently weak (such as the optical nonlinearity from pure silica devices), and for use as a laser gain medium when these are optically excited in their corresponding surface plasmon resonances[2]. A significant improvement in nonlinearity can be achieved by leveraging plasmonic effects. It is well demonstrated that metal nanoparticles can improve the nonlinear optical effects 129 near the metal-dielectric interface, mostly because these interactions allow for strong local electromagnetic fields which enhance the nonlinear optical responses of the metal and/or the material adjacent to it[3, 4]. The excitation of the metal nanoparticles is carried out by exploiting the evanescent field extending outside the microsphere. Thus, it is possible to constantly excite the intrinsic response of the silica microsphere by following these photon-plasmon interactions. Localized surface plasmons (LSP) are electromagnetic resonances from which the optical responses of the particles arise. At wavelengths far away from those LSP resonances, the intrinsic nonlinearity of the metallic particles is dependent on the real part of the permittivity. Nevertheless, the optical nonlinearity of gold nanoparticles is mainly governed by changes in the corresponding imaginary part, and when operating off resonance, the gold nanoparticles decorating the microdevice surface enhance the nonlinearities of the dielectric via metal- dielectric interaction. The metal-dielectric interface turns the performance of the cavity to a hybrid plasmonic system where the interactions of the gallery modes and the surface plasmon mode hybridize, which brings new capabilities to easily achieve Kerr nonlinearities. The hybrid mode causes the circulating energy to be confined in volumes below the wavelength dimensions which results in the enhancement of the optical signals from the cavity. As a result, the microsphere supports hybrid plasmonic modes providing a highly localized field distribution to enable nonlinearities at very low threshold input powers. One of the most interesting and highly studied optical nonlinearities in microcavities is derived from the Kerr effect: optical parametric oscillation (OPO). The nonlinear property of the microsphere to obtain bistability makes it very attractive for molecular IR spectroscopy and for secure transfer information applications[5-7]. 130 For generating frequency combs a typical method is to enhance an optical parametric process based on four wave mixing (FWM). In the optical parametric process, two photons ( ω1 and ω2) are converted to a pair of photons that are of different frequencies. The most common type of optical parametric process that aids in frequency comb generation is degenerate parametric oscillation ( ω1= ω2) that results in the generation of symmetric signals (called signal ( ωs) and idler ( ωi)) around a pump frequency. In this process, energy and photon momentum are both conserved according to their respective conservation laws: ( 2ω = ω +ω ) and ( 2β(ω )= β(ω )+β(ω )). To achieve a sufficient concentration of photons for the FWM process to occur, the conventional lasers and combs rely on highly nonlinear crystals. During the last decade, as a result of advances in device fabrication methods, on-chip photonic structures, such as microresonators and waveguides, have demonstrated parametric amplification and oscillation. Recently, frequency combs based on optical parametric oscillation (OPO) were realized in ultra-high quality factor (Q) optical microcavities[33-36]. In recent years, enhancements in clean fabrication methods have resulted in improvements in quality factors of the resonators that have many applications in generating a wide range of nonlinear optical processes[37]. The ultra-high Q and strictly confined optical mode ensures high circulating light intensities within the resonator, reducing the threshold power needed. These devices have been fabricated from a wide range of dielectric and semiconductor materials, and nearly all have demonstrated OPO and frequency combs, to varying degrees of efficiency. However, while a high cavity Q can facilitate OPO, it is not a sufficient condition. In contrast to non-parametric processes, parametric processes require strict phase matching. While in the whispering gallery mode resonators the momentum is intrinsically satisfied [34], due to cavity and material dispersion, the energy conservation condition (2ω = ω +ω ) is not 131 universally satisfied. Typically, for high Q microresonators with normal dispersion, the frequency detuning is negative ( Δω = 2ω −ω −ω <0). To realize OPO in microresonators, this detuning Δω should be sufficiently small ( Δω ≈ 0 ) for phase-matching to occur[38]. It is also necessary that the detuning, Δω be less than the parametric gain bandwidth Ω = 4 P, where P is pump power, n is optical Kerr coefficient, n is linear refractive index[33]. Therefore, to achieve OPO, it is necessary to operate within these boundary conditions. However, there is one problem in exciting third order nonlinear phenomena, the third order nonlinear processes are competing with each other and they can coexist as a result observation of a pure. For example, in SiO2, the preferred process is stimulated Raman, and it can occur simultaneously with parametric oscillation in silica microcavities even with an optimized cavity size[39, 40]. The challenge is that the optical Kerr coefficient of silica is six orders of magnitude smaller than the Raman gain coefficient (n2 = 2.2×10-20 m 2 /W as compared to gR = 0.66×10 -13 m/W). The small Kerr coefficient results in a theoretical threshold value of OPO that is very closed to that for stimulated Raman[41, 42], leading to the concurrence of the two processes. Therefore it is extremely important to optimize the size, refractive index and the detuning of pump laser in order to get pure parametric oscillation. This optimization problem is not limited to silica. Resonators made of other materials, such CaF2, diamond and silicon, also suffer from the competing stimulated Raman emission[43-45]. In subsequent sections, I will present an approach for coating the surface of a spherical microcavity with gold nanorods using a dip coating procedure and demonstrate improved frequency comb generation using this device. The motivation for using gold nanorods to improve the nonlinear optical performance of the microsphere is both the ease with which this material 132 can be synthesized with high stability and their ability to behave as a multiple metallic nanosubtrate to individually hybridize the supporting modes. Additionally, the modal interaction and the performance of the hybrid plasmonic system are simulated by using 3D COMSOL multiphysics finite element method software. The design, the overall fabrication, and optical characterization of the hybrid microsphere acting as Kerr nonlinearity source are systematically demonstrated. We present the complete feasibility of our hybrid device with Q factors ~ 10 7 to generate parametric gain and Kerr-combs with threshold intensities significantly lower than both bare microdevices and higher Q factor silica microresonators. Furthermore, different concentrations of gold nanorods decorating the microsphere surface are related to the circulating intensity in the cavity at which bistability is achieved. These results demonstrate that under metal-dielectric interactions, these nonlinearities are feasible under very low incident power and relatively low Q factor. Finally, a new engineering method will be used to selectively excite only OPO combs or Raman Combs while other mechanism is suppressed. A. 2. Raman Scattering Due to inversion symmetry, silica does not exhibit second order nonlinearity. Therefore, the lowest order nonlinearity that one can observe in silica resonators is third order processes. On the other hand, the nonlinear coefficients of silica are low compared to other third order nonlinear materials; therefore, silica should not be a good choice for observation of nonlinear phenomena. However, high optical quality factors of silica resonators compensates for the low coefficients and one can observe nonlinear phenomena at low input power levels. One of these nonlinear phenomena that is non-instantaneous in nature is Raman scattering. Raman scattering is the direct result of the interaction of light with optical phonons. 133 The governing equations for Raman scattering are[8]: (A-1) 11 2 0 1 () 2 R ext R R R pu R dE E gE E dt ττ −− =− + + (A-2) Where Epu and ER, are Pump and Raman field intensities, respectively. Also, τext and τ0 are external coupling and intrinsic life times. In addition, gR is the Raman gain coefficient inside the cavity. By solving these two equations in steady state for input power, one can get: 22 00 (1 ) 11 () () () (1 ) pu R pu NL threshold eff pu R R pu R R pu nn K PM V K fg Q Q K π γ λλ + =+ (A-3) where Q0 values show the intrinsic quality factors for pump and Raman signal. Also, M is a value that takes the effect of back scattering into account. Furthermore, f is the spatial overlap function between the Raman and pump signal modes and is given by: 44 44 pu R pu R EEdA f EdA EdA =    (A-4) The threshold power is inversely squared dependent on the Quality factor ( 2 1 th P Q ∝ ). A. 3. Kerr nonlinearity As opposed to Raman nonlinearity, the fast (zero phase shift) nonlinear response of silica which appears as a change in refractive index is dependent on the intensity of interacting light. This phenomenon is called Kerr nonlinearity. The coefficient relating the change in refractive index to the intensity is usually shown with n2 and the governing equation is: 11 2 0 1 () 2 pu R ext pu pu R R p in pu dE EgEE s dt λ ττ κ λ −− =− + − + 134 02 () nI n n I =+ (A-5) Where the Kerr coefficient is related to nonlinear susceptibility through: (3) 2 0 3 8 n nc χ ε = (A-6) Due to inversion symmetry, the induced polarization has no second order term: (3) ii ijkljkl PE EEE χχ =+ (A-7) Since the polarization, term includes the phase change as well, it will result in parametric frequency conversion. Since the refractive index is changing with intensity, there is a modulation of refractive index due to propagation of two photons with different frequencies, which will result in a frequency shift of the third wave. This effect gives rise to parametric four wave mixing. By letting the parametric gain coefficient equal the cavity losses, we can get the threshold for the onset of the parametric oscillation. 2 22 2 2 2 00 00 (1 ) ( / 2) (1 ) () eff eff Kerr th nRn QK K P cCQK π ωω γω ξ λ − ++Δ + = Δ (A-8) Where neff and K are the effective refractive index and coupling parameters respectively. Also Δω=2 ωp- ωi- ωs is the detuning frequency from perfect phase matching conditions. Also C( ξ) is the back scattering coefficient. Furthermore, the nonlinear coefficient γ equals: 2 . NL eff n cA ω γ = where 44 44 pu R NL eff pu R EEdA A EdA EdA =    135 A. 4. Improvement of nonlinear response To date, the majority of efforts to improve threshold and the span of nonlinear response in ultra-high Q cavities have focused on optimizing the Q. An alternative strategy is to engineer the materials forming or coating the cavity. Hybrid optical microcavities comprised of an ultra- high Q cavity with a highly nonlinear nanomaterial coating represent a novel and broadly translatable strategy to improve the performance of frequency combs. In this section, I have demonstrated that the combination of gold nanorods coated with highly nonlinear material with ultra-high Q silica microcavities results in a reduction of the comb threshold. The mechanism and enhancement is further elucidated with finite element method modeling and can be explained in terms of the hybridization of the mode and its interaction with the hybrid cavity. Raman gain, Raman-assisted FWM, and anti-Stokes Raman are all observed, leading to a comb span of ~300 nm in the near-IR range, with incident intensity <1 GW cm -2 . For the nanorod concentrations studied, the required threshold for parametric oscillation ranged from 110 µW to 1 mW. Although the Q factors of the devices were decreased due to the nanoparticles, the thresholds were improved by 40 % and the comb span was increased by ~100 nm, verifying the nanomaterial enhancement. Optical frequency comb contains equally spaced lines that result in a broadband, coherent light source[9]. Since the spacing of the comb teeth is determined by optical modes that are accurately spaced, combs have found numerous applications, including spectroscopy, atomic clocks, microwave signal conversion, and pulse train generation. The initial optical frequency comb was demonstrated using femtosecond lasers[10-13]; however, this platform was rapidly replaced and commercialized with fiber-based mode locked laser combs. Recently, research has shifted to the development of whispering gallery mode optical microcavity-based combs. 136 Optical resonators are capable of selectively separating and constructively building up specific wavelengths of light, acting as optical amplifiers at those wavelengths. Because the amount of amplification is directly related to the cavity quality factor (Q) or the cavity finesse (F), frequency comb research has focused on high-Q and ultra-high Q microcavities fabricated from a range of materials using a variety of methods. In all cases, the comb generation relies on a nonlinear process known as parametric frequency conversion which is based on a third order nonlinear interaction and which results in four wave mixing (FWM)[14, 15]. For nonlinear materials the refractive index is dependent on the intensity of the propagating light (no+I·n2) where no is the refractive index, I is the laser intensity, and n2 is the Kerr coefficient of the resonator material. In addition, to create a true comb, a second process, in which the sidebands combine to generate additional signal and idler lines via FWM, is utilized. Clearly, this approach requires significant power, not only in the pump, but also in the sidebands, which was the original motivation for using ultra-high-Q cavities in this application. In this section, we introduce a strategy for improving the third order nonlinear effect and reducing the threshold for frequency comb generation in the near-IR (C- and L- telecommunication bands) via small molecule-coated gold nanoparticles (NPs). The method is demonstrated using silica ultra-high Q microsphere resonators as a test bed. Nonlinear optical parametric emissions are obtained with circulating intensities less than 0.03 GW cm -2 , which is over 10x lower than in previous work with SiO2 devices. The mechanism is based on the highly localized enhancement of the optical field by the nanoparticles that, in turn, maximize the interaction with the small-molecule coating. Notably, unlike previous work that leveraged plasmonic resonant behavior for enhancement, the observed effect does not arise from a 137 resonance behavior, but instead is a surface plasmon-polariton. Complementary finite element method modeling is performed to explain the observed experimental results. A.5. Theory To evaluate the nonlinear effect in the resonator, we define an effective nonlinearity that ( eff) is related to, but distinct from, the Kerr coefficient of the material. Specifically, eff takes into account the optical mode area of the cavity field (Aeff) and the wavelength according to: eff=2 n2/( Aeff). The optical mode area is dependent on the device diameter and other geometrical properties as well as the refractive index and the wavelength ( ). Another quantity that shows the efficiency of second order process is the threshold for comb generation. The parametric threshold can be defined as the point when the Kerr-induced frequency shift equals half the cavity photon decay rate ( Δ Kerr= /2=n2 FPc/(2 nAeff)), where F is the cavity finesse, Pc is the power coupled into the cavity which is distinct from the power out of the laser and is the optical frequency. This relationship clearly shows the importance of coupled power and finesse on the threshold[9]. In order to have a better understanding of the interaction between the circulating optical field in the cavity and the nanoparticle, finite element method simulations using 3D COMSOL Multiphysics were performed. To allow direct comparison, the wavelength, nanoparticle properties, and resonant cavity properties were the same as those used in the experiments. In fig.A-1(a) I have shown that the circulating intensity can be coupled into the gold nanorods, forming surface plasmons at the dielectric-metal interface. Moreover, the presence of the particles covering the surface of the silica microsphere allows for the confinement of energy where maximum levels of energy density are distributed over the silica microsphere surface and the metal interface of the particle. 138 (a) (b) (c) (d) Figure A- 1 Simulation of TM mode at 1550nm. (a) field distribution near the gold nano particle at a distance of 15 nm. (b) and (c) field profile on the equatorial plane with and without gold nano-particle (d) maximum field enhancement of a gold nanoparticle vs. distance from the surface of the resonator. The aspect ratio of particle is 3.8 with a width of ~17 nm. In order get a deep insight into the local field enhancement mechanism, fig.A-1 shows the enhancement behavior in the presence and absence of a gold nanoparticle. Surprisingly, even though this is a non-resonant plasmon behavior, the optical field amplitude at the surface of the nanoparticle exceeds the optical field in the whispering gallery mode. This enhancement is the result of the formation of a strong and efficient hybrid whispering galley-plasmonic mode [16- 18] located between the silica microsphere and the gold surface. Notably, because this is not a plasmon resonant behavior, the nanoparticle behaves as a wavelength-independent localized 139 amplifier. Additionally, small organic molecules with the considerable Kerr coefficient are located precisely in this gap region. The efficiency of this process is strongly dependent on hybridization between the whispering gallery mode and the plasmonic mode of the nanoparticle lying within the evanescent tail of the optical cavity, and therefore, its proximity to the optical cavity surface is paramount. If the nanoparticle is moved away from the cavity surface, the enhancement is significantly decreased. Fig.A.1(d) presents the relationship between the sphere and the particle in terms of their relative distance interaction where, below 25 nm distance a significant boosting mechanism can be observed. The field around the gold nanoparticle could be enhanced from 4 to 24 times as compared to the field outside a bare resonator which indicates that the gold NPs still provide a relatively large enhancement factor at off resonant wavelengths.[18] For the case of our nanoparticles, the maximum enhancement at 1550nm is approximately10 times (fig.A-1d). To elucidate if a hybridized mode remains between the two surfaces or modifies the fundamental whispering gallery mode, we have run simulations for a range of distances from 1 to30 nm. Interestingly, we observed the fundamental mode is not affected and the hybridized mode remains between the two surfaces with intensity enhancement values higher than the maximum intensity of the whispering gallery modes. A.6. Characterization of off plasmonic resonance nano particle coated cavity The main parameter that is directly affecting the nonlinear process is the optical cavity Q, which is equal to / . To measure the cavity linewidth ( ), a cavity characterization set-up with a narrow linewidth laser centered at 1550nm is used as shown in fig.A-2. A low loss tapered optical fiber couples light from the laser into the cavity. 140 Figure A- 2:Experimental setup. 3D schematic of the experimental setup used for optically characterize the quality factor and frequency comb generation. For the case of our device, the resonance shows a symmetric linewidth of ( ) 4.81 ×10 -5 nm, which corresponds a quality factor of 3.2×10 7 . While this cavity still exhibits high Q values, usually silica microspheres shown Q-factor values in the order of 1×10 8 -10 9 . In this case, the performance is reduced from the bare microcavity. This decrease is due to both intrinsic material absorption and scattering losses. For the NP concentrations studied in this work, the Q factors ranged from 2×10 7 to 7×10 7 . In order to produce comparable results across the devices, maintaining similar Q factors and device geometries was critical. A. 7. Observation of parametric frequency comb generation from coated devices As we explained in the previous section, the largest nonlinear process in silica is the third order nonlinearity where a photon of the pump laser is absorbed to create the signal and idler photons. In this nonlinear interaction, the corresponding signal and idler frequencies, governed by energy conservation 2 ωpump= ωsignal+ ωidler, are equidistant from the pump. The new nonlinear frequency generation is governed by wave vector phase matching and energy conservation. The 141 energy and momentum conservation are satisfied respectively via the detuning frequency mechanism[19]. When the signal and idler angular modes coincide with the resonator modes, the phase-match criterion is satisfied intrinsically (via modulation instability) in the cavity by considering the phases of all the circulating optical fields. In addition, the signal and idler photons can interact with each other, resulting in higher order sidebands referred to as Kerr frequency combs[20-22]. To ensure parametric processes, measurements were carried out with a ~130 µm of diameter spheres which guarantee dispersion- compensated properties[21-23]. The parametric gain and the Kerr combs of the cavity are characterized using the set-up shown in fig.A-2. In fig.A-3, we have shown an example of both signal and idler modes that are coupled back into the tapered fiber and detected in the Optical Spectrum Analyzer. (a) (b) Figure A- 3:(a)Experimental observation of a generated frequency comb. As a result of cascaded degenerate and non-degenerate optical parametric oscillation a frequency comb is generated. (b) Dependence of OPO on the taper- resonator gap. The third order nonlinear emissions observed in Fig. 3 (a) are visualized by pumping the device at 1550.312 nm. The lowest obtained threshold for the nanoparticle coated microsphere was 450 ±15 µW, which is approximately a factor of 25 % to 40% lower than our plain silica 142 device and others silica microresonators with Q factors in the same range[14, 20-22, 24]. Fig.A-3 shows the generated frequency comb when the micro-cavity supports high levels of circulating power. This bistable behavior in the transmission demonstrates that the third order nonlinear response is governed by both the electronic Kerr and thermal change responses[25]. As the circulating power increases, the generated signal and idler sidebands show a linear evolution (above the threshold) with a correlation factor of 0.95 and a conversion efficiency of 65%. Since the coupling distance represents a critical parameter for the threshold power and OPO gain relation[20-23], fig.A-3(b) inset shows the dependence of the required threshold as a function of the relative coupling between the taper and the microsphere. The gap = 0 nm in fig.A.3(b) represents an over-coupled position while the consecutive relative distances are respectively referred to as critical and under-coupled positions. 435 µW of threshold power is obtained for values around 30 nm of relative gap distance in the under-coupled regime. A.8. Gold Nanoparticle Enhancement at off Plasmonic Wavelengths In order to comprehensively study the mechanism underlying the comb formation in these hybrid devices, we compared a device coated with gold nano rods (coated in a solution of 0.125 mM gold nano rods) with a bare sphere. To more easily compare the performance of the different devices, the circulating optical intensity will be used as the metric, instead of input optical power. Optical intensity removes experimental variables such as coupling and device geometry variations, allowing a more unbiased analysis to be performed. Fig.A-4 shows the evolution of the Kerr frequency combs in two silica microspheres, one coated in solution with gold nano rods with the concentration of 0.125 mM gold nano rods and the second one is a bare sphere. The individual spectra for each microcavity are chosen to highlight 143 key stages in the comb formation. All the measurements were reproduced, and the results shown are representative. Both devices exhibit Raman emission around 1650nm (fig.A-4). However, the threshold for Raman is significantly lower when the PEG-coated nanoparticles are coated on the coated device. As a result, because the basic mechanism for optical frequency comb generation is Raman-assisted four-wave-mixing, the threshold for frequency comb generation is also significantly reduced. For example, in a non-functionalized microsphere with 1.05 GW/cm 2 of circulating optical intensity, only Raman is present. However, in a PEG-functionalized nanoparticle coated microsphere with 0.03 GW/cm 2 of circulating intensity, both Raman and OPO are present. (a) (b) Figure A- 4:Optical frequency comb formation in: (a) bare microsphere and (b) coated microsphere with gold nanorod concentrations of 0.125 mM. The Kerr comb generation is enhanced by the presence of gold nanorods decorating the surface of the devices. The performance is mainly governed by Raman-assisted FWM emissions. As can be observed in fig.A-4, new emissions arise around the 1450 nm region, which correspond to the anti-Stokes signal of the Raman contribution and their corresponding assisted FWM at that region[26]. In order for the parametric emissions to appear at very low input powers, there must be a complementary nonlinear interaction enhancing the third order nonlinear coefficient of the 144 cavity. The FEM modeling showed an increased optical intensity at the surface of the metal nanoparticles, which is precisely where PEG molecules were located. Previous work has shown that PEG has a large third order non-linear coefficient as compared to silica [27, 28]. Therefore, the PEG molecules can increase the effective third order nonlinearity of the cavity. It is important to note that although the optical parametric oscillation depends on phase-matching conditions, at these nanoscale dimensions the phase-matching considerations are not affected, and the optical parametric signals can be emitted and supported in the hybrid cavity at very low circulating optical power [29]. The performance enhancement is observed not only in the threshold needed for OPO but also in the frequency comb span. In a non-functionalized device, a span ~200 nm is observed when ~ 4 GW/cm 2 is circulating. This span is consistent to other devices with similar performance [22, 23]. In contrast, when the PEG-coated nanoparticles are present, the comb span increased to ~300nm with better distribution throughout the range of analysis. Notably, these emissions are obtained with peak intensities 10 times lower than previous publications [20-23]. This premise is based on the optical performance of the device, which presented Q factors in the range of 10 7 . Additionally, considering the uniformity of the low frequency comb, it is possible that the comb easily extends beyond 1750nm; however, the working range of the instrumentation used in the present measurement was limited to 1700nm. Nevertheless, this range would be comparable to combs generated by other high χ 3 materials [30, 31]. The threshold decreases from 1mW to 110 µW (0.4 GW cm -2 to Q 0.025GW cm -2 ) as we coat the device with gold nanoparticles. When compared to a plain silica device, these values represent an enhancement of 35 with respect to both the silica device studied here and to previously published devices with similar characteristics[22]. 145 To rigorously isolate the mechanism giving rise to the observed enhancement, a second measurement using non-functionalized metal nanoparticles was performed. In this measurement, the particles were covered with the surfactant CTAB. The presence of CTAB is critical for the nanoparticle growth and stabilization when the seed-growth method is used. As such, unlike the PEG, its presence is required. The same concentration of CTAB-NPs was used as with PEG-NPs to coat the microspheres (0.125 mM). Devices coated with CTAB-NPs show weaker OPO nonlinear signals than those with a PEG-NPs coating layer. This supports the significance of PEG molecules functionalized the gold nanoparticles as fundamental element of this hybrid MRs-PEG-NPs configuration. The nonlinear behavior observed from MRs-CTAB-NPs configuration can be explained in terms of the inherent properties of metallic structures where weak signals can be enhanced which entails that those weak parametric signals were transferred to the particles and there were locally boosted via photon-plasmon interactions[32]. A. 9. Selective comb generation The majority of efforts in the field of resonator-assisted frequency combs have been focused on balancing high Q with high n2 as well as dispersion engineering. After the initial successes with SiO2 devices, the field quickly shifted to crystalline cavities that offered improvement in both metrics, notably a nearly 100x increase in Q. However, these devices are fabricated using mechanical polishing methods. An alternative approach is to create a hybrid cavity, comprised of multiple materials, enabling an increase in the n2 while maintaining the ability to fabricate devices using lithographic techniques. 146 Hybrid cavities leverage the advantages of two distinctly different optical material systems to develop an otherwise unattainable property. While there are many possible architectures, one vision is a semiconductor or dielectric UHQ cavity with a monolayer coating of a highly nonlinear small molecule. Nonlinear optical organic molecules are an emerging class of materials for nonlinear photonics. Because of the ultrafast molecular electronic polarization, organic molecules exhibit very large third-order nonlinearities and fast optical response[46, 47]. High speed all-optical signal processing can be achieved in silicon-organic hybrid waveguides by using organic molecules as active cladding materials. Optical loss and speed limitation caused by large two-photon absorption of silicon are overcome in silicon-organic hybrid systems [48, 49]. In this section, we have developed a strategy for creating oriented monolayers of small molecules on the surfaces of UHQ silica microcavities and verified the method using 4-[4- diethylamino(styryl)]pyridinium (DASP) and chloromethyl phenyl silane (CPS). Depending on the molecule, we show selective excitation of either OPO or Raman, at the expense of the other behavior. The observed enhancement (or quenching) behavior is the result of the high OPO or Raman coefficient of the two small molecules. Complementary finite element method modeling is performed to study the optical field interaction with the small molecule layers. By equating theoretical parametric and Raman thresholds in a resonator under critical coupling condition[33, 40],[41] we introduced a useful figure-of-merit parameter: p≈ 1.54 , where λ is the pump wavelength, gR is Raman gain coefficient, n2 is Kerr coefficient, and ke is the percentage of effective optical field in hybrid system (in single- component system, ke =1). When p<1, the parametric threshold is lower than the Raman threshold, and OPO is preferred. When p>1, the Raman threshold is lower than the parametric threshold, and stimulated Raman is preferred. When p=1, it means OPO and stimulated Raman 147 will co-exist. Because the p value is a function of the characteristic (gR and n2) of a given material, it is useful to evaluate if a material is preferable for parametric oscillation. A small p value (p ≪1) is preferred to avoid the concurrence of stimulated Raman. For silica, p≈1.1. The silica whispering gallery mode optical cavities are fabricated from optical fiber using a previously detailed method[50]. The device diameters were approximately 120 μm. To form a self-assembled and oriented monolayer of the two small molecules, the surface chemistry process developed by a group member and shown in fig.A-6 is performed. Specifically, the density of the hydroxyl groups on the silica surface is increased with an O2 plasma treatment. Then, a phenylene layer is grafted to the surface using CPS. Finally, the DASP layer is grafted to the surface. DASP was chosen for the present work because the n2 value is five orders larger than that of silica[51]. Notably, unlike spin coating or dip coating methods, this technique results in the formation of a signal monolayer of molecules that are oriented with the optical field. This approach allowed direct comparison between the silica microspheres with a phenylene monomolecular layer and the DASP layer (n2,phenylene is negligible compared to n2,DASP). By extracting exact geometries from microscopic images, finite element method (FEM) modeling of the optical mode profile is performed to determine the interaction of the optical field with the small molecule monolayer. The simulations showed that approximately 11% of the optical intensity is contained in the evanescent tail and is able to interact with the approximately 2 nm thick monolayer. Additionally, the presence of the monolayer does not change or distort the optical mode profile due to its negligible size and similar refractive index to silica. Thus, it is expected that the optical cavity can directly and efficiently interact with the monolayer. 148 Figure A- 5:Optical mode profile and schematic structure of the hybrid microspheres. a, FEM simulation of the optical mode of in the microsphere with radius of 60 μm (left). The mode profile at the cross section of the device (right) indicates about 11% of the optical field extends out of the silica surface, and is able to interact with the ~ 2 nm monomolecular layers. b, diagram of four wave mixing in active third order nonlinear χ(3) medium. c, schematic structure of bare silica sphere, hybrid silica sphere grafted with chloroomethyl phenyl silane (CPS) monolayer (blue color), and hybrid silica sphere grafted with diethylamino-styryl-pyridium (DASP) monolayer (red color). To verify this hypothesis and to investigate the effect of surface monomolecular layers on the parametric oscillation behavior of the spheres, a 1550 nm narrow linewidth tunable continuous-wave (CW) diode laser was used to pump the microspheres. The light from the laser was evanescently coupled into and out of the cavities using a tapered optical fiber waveguide. The coupling efficiency was optimized by controlling the distance between the taper-waveguide with the microspheres by a nano-stepping 3-D stage. The output signal was split, with one portion going to an oscilloscope and the other going to an optical spectrum analyzer. To measure the Q values, the transmission spectra are recorded by the oscilloscope using the cavity characterization set-up. The Q is calculated by fitting the spectra to a Lorentzian and using the expression Q = λ/ δλ, where δλ is the full width at half-maximum (FWHM) determined for the fit. Owing the minimal optical loss (absorption and scattering loss) caused by the 149 monomolecular layers, the hybrid microspheres maintained ultrahigh Q values at ~1550 nm. As shown in fig.A-6, the bare-silica and IPS-silica hybrid micromicrospheres exhibited ultra high Q values of 1 × 10 8 at ~1550 nm, while DASP-silica hybrid microspheres showed only a slightly lower Q values of 0.8 × 10 8 . Such high Q organic hybrid devices would ensure the effective nonlinear optical interaction between the evanescent optical field with the organic gain medium on the surface. Figure A- 6:Comparison between different resonators coated with different small molecules. As illustrated in the figure by coating the resonator with a thin layer of small molecules the quality factor does not drop drastically. The threshold power P for parametric oscillation based on FWM can be estimated by the equation as[41, 43] P ≈ 1 .54 ( ) (A-9) where λP is the pump wavelength, V is optical mode volume, n is the linear refractive index and n2 is the Kerr coefficient. Q0 and QL are the intrinsic and loaded quality factors, respectively. To experimentally determine the threshold for OPO, the output power of the first sideband emission was measured as a function of pump power. 150 Figure A- 7:Measurement scheme. Light from the 1550 nm tunable diode laser is coupled into the microsphere using an optical fiber taper. The optical signal was split by a 90/10 beamsplitter (BS), with 90% of optical signal is coupled into the optical spectrum analyzer (OSA) to capture the output emission signal, and 10% of the optical signal to a photodiode (PD) to monitor the laser transmission signal by Oscilloscope (O-Scope). Typical observed output spectra above the thresholds from different spheres (CPS-silica and DASP-silica) are shown in fig.A-8. For silica, stimulated Raman around 1650 nm appeared first at low input power. Under higher input power, extremely weak non-equidistant parametric emissions from 1500 nm to 1580 nm were also observed. It is mainly due to Raman-assisted FWM between the SRS photons and pump photons. No obvious increased parametric emission was found by increasing the Q value of the base-silica spheres (from 0.9×10 8 to 1.8 ×10 8 ). As indicated by the figure-of-merit parameter (p = 1.1), the Raman threshold is slightly lower than parametric threshold for these bare-silica resonator. For CPS-silica, the silica microspheres grafted with an organic phenylene monomolecular layer, SRS emission also dominates the output spectra. It is interesting to find that the weak parametric emission in bare-silica spheres was suppressed. Changes in Q value of the IPS-silica microsphere (from 1.0×10 8 to 1.8 ×10 8 ) did not affect the suppression behavior. Compared to bare-silica with same Q value (1.8 ×10 8 ), the Raman threshold slightly decreased. This can be ascribed to the slightly enhanced Raman gain over parametric gain due to the enhanced the 151 hyperpolarizabity and Raman coefficient by the surface asymmetric organically-modified silica[52]. The absence of parametric process is consistent with calculated figure-of-merit parameter value (p = 1.5, larger than 1). (Because the n2 of the surface phenylene molecules is only 9 × 10 -20 to 13 × 10 -20 m 2 /W [53], the surface molecular layer does not enhance the overall Kerr coefficient of CPS-silica.) (a) (b) Figure A- 8:Output spectra from different microspheres pumped by a 1550 CW diode laser. Surprisingly, as shown in fig.A-8(b), sole parametric oscillation emissions (signal/idle photon pairs) surrounding the pump wavelength at ~1550 nm were observed in DASP-silica hybrid microsphere (Q = 0.7×10 8 ), but no SRS emission (around 1650 nm) was found. With increasing the input pump power, the intensity of the signal/idle photon pairs increase dramatically. As the size of the all the spheres are kept constant (~120 μm) and monomolecular 152 layers are ultrathin (~ 2 nm), the effective mode area ( A ) of and effective refractive index of the spheres are assumed to remain constant. Thanks to the high Kerr nonlinearity value (n2(DASP) = 2.54 × 10 -17 to 3 ×10 -15 m 2 /W, 1.0×10 3 to 1.2 × 10 5 × n2(silica)) of the surface DASP monolayer[51], the effective parametric gain bandwidth of the DASP-silica: Ω = 4 () P is thus enhanced by two to four orders larger of magnitude over that of bare silica ( Ω ), where Pe is the effective power of the evanescent field (Pe = 0.11×P). the improved parametric gain bandwidth ensures that the condition for FWM is fulfilled: Ω ≫ ∆ω. In addition, the calculated figure-of-merit parameter p is about 3.1× 10 -2 to 2.6 × 10 -4 , which is ≪ 1. Therefore, FWM-based OPO dominates in DASP-silica hybrid microspheres, while the competing the Raman process is completely excluded. (a) (b) Figure A- 9:Experimental results and energy level diagram of parametric oscillation. Fig.A-9 shows the optical parametric oscillation output spectra generated from DASP- silica hybrid microspheres. A single pair of signal/idler photons with equal output power initially appeared (fig.A-9a), which can be attributed to optical parametric oscillation solely induced by the surface Kerr gain via degenerate FWM. Moreover, in most cases, primary Kerr frequency combs with a spacing of 3.8 nm were observed, with multiple subsidiary signal/idler photons 153 along with the first pair of signal/idler photons (fig.A-10b). (The formation of Kerr frequency combs has been previously ascribed to the degenerate FWM with consequently cascaded non- degenerate FWM.) The idler output power increase exponentially with increasing the input power. To evaluate the impact of the surface Kerr monomolecular layer on the primary frequency comb generation, the measured output power of first idler photons was plotted versus the peak circulating pump intensity in the spheres. As clearly shown in fig.A-10(c), the measured maximum output power of the first idler was amplified more than 100-folds in DASP-silica under much lower circulating pump intensity, compared to bare-silica. (Considering the effective evanescent field intensity (0.1 times of peak intensity) that contributed to the surface Kerr monolayer, the threshold intensity for FWM in the monolayer can be calculated to be ~0.03 GW/cm 2 based on the measured result.) Note that in the DASP functionalizedsilica devices not only were the first pair of signal/idler photons generated, but also the well-structured subsidiary photon pairs. No favorable equidistant photon pairs were observed in our bare-silica spheres at the input powers studied. In conclusion, we have demonstrated an engineering method to selectively control Kerr optical parametric oscillation in organic/silica hybrid microresonators pumped by a CW laser. By integrating a monomolecular layer of NLO molecule DASP on the surface of silica microspheres, we have shown sole Kerr parametric oscillation with more than 100-fold enhancement in the organic/silica hybrid microspheres compared to bare-silica spheres. Primary Kerr frequency combs have also been demonstrated in the DASP-silica hybrid microspheres, owing to the highly enhanced effective Kerr gain interaction with the evanescent optical field. Additionally, we have also demonstrated the effective control between sole SRS emission to sole Kerr parametric oscillation in the hybrid microsphere by changing the optically-active molecules. 154 This organic hybrid strategy is highly applicable to other geometries of resonant cavities and photonic structures. 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Abstract (if available)

Abstract Due to high speed and large capacity of optical devices there is an ever increasing demand in fabrication and integration of cost effective optical devices that could be used for many applications such as sensing , data storage , medical applications , optical processing, and military applications . Light has the capability to propagate at extremely high speeds that no other carrier can achieve (c=3×108m/s). This high speed makes it the best candidate for signal transmission. However, unlike electronic devices that work with electrons as carriers and require electron controlling mechanisms such as resistance, potential, and current, optical devices must process optical signals. This necessitates the development of optical signal manipulation techniques. The most powerful factor in optical device design is refractive index manipulation. Refractive index can be controlled by the spatial shaping of a material or by doping atoms with different densities. In this thesis, I have investigated the design, fabrication, and characterization of whispering gallery mode optical resonators for applications in telecommunications. First, I have studied the wave nature of light and the equations governing propagation of light in dielectric devices. Next, I have studied how we design and fabricate Whispering gallery mode resonators, including both spheres and toroidal resonators. Finally, I have shown several interesting applications of whispering gallery mode resonators, such as thermal response, frequency combs, and cavity optomechanics.

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Asset Metadata

Creator Soltani, Soheil (author)

Core Title Fabrication and characterization of yoroidal resonators for optical process improvement

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 05/07/2018

Defense Date 03/21/2017

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

Tag OAI-PMH Harvest,optical design,optical resonator,wave optics,whispering gallery mode resonators

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Armani, Andrea M. (committee chair), Tambe, Milind (committee member), Wang, Han (committee member), Wu, Wei (committee member)

Creator Email soheil.soltani86@gmail.com,soheilso@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-500566

Unique identifier UC11268137

Identifier etd-SoltaniSoh-6315.pdf (filename),usctheses-c40-500566 (legacy record id)

Legacy Identifier etd-SoltaniSoh-6315.pdf

Dmrecord 500566

Document Type Dissertation

Format application/pdf (imt)

Rights Soltani, Soheil

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA