Electro-Optic Ring Resonators in Integrated Optics

ELECTRO-OPTIC RING RESONATORS IN INTEGRATED OPTICS

FOR MINIATURE ELECTRIC FIELD SENSORS

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

in the Graduate School of The Ohio State University

Alexander Charles Ruege, B.S.E.E., M. S.

Graduate Program in Electrical and Computer Engineering

The Ohio State University

2011

Dissertation Committee:

Professor Ronald M. Reano, Advisor

Professor Betty Lise Anderson

Professor Fernando L. Teixeira

Alexander Charles Ruege

2011

ABSTRACT

This dissertation addresses two important aspects regarding the sensing of radio- frequency electromagnetic fields using integrated optical ring resonator devices. The first topic involves the theoretical design, fabrication and demonstration of a new field sensor based on electro-optically (EO) active integrated optical ring resonators. The second topic addresses the problem of enhancing the response from a single-mode ring resonator of a given ring waveguide loss through modifications in the device geometry.

The miniature integrated optical EO ring resonator sensor consists of low- dielectric constant polymers, is metal-free and is supported by a thin, flexible substrate.

The low-invasive platform is achieved through the development of a new fabrication process. The waveguide cores of the devices are constructed of polycarbonate doped with the EO chromophore Disperse Red 1 and are poled using the contact poling method.

The measured loaded quality factors of the poled EO rings are between 15,600 and

18,900.

The fields emanating from a microstrip resonator circuit at 3.9 GHz are measured.

It is determined that the measured modulation from the four-ring linear array is largest when the optical wavelength is biased on the steep slopes of the resonance lineshapes as theoretically predicted. Using electric field values obtained from electromagnetic simulations of the microstrip circuit, the EO coefficient is 0.72 pm/V. The sensitivity for ii electric fields in free-space field is 142.2 V / (m Hz0.5). The sensitivity is obtained for an off-resonance optical power of -9 dBm at an optical wavelength near 1550 nm, a photoreceiver conversion gain of 900 V/W, and a system impedance of 50 Ω. Also, sensing from asymmetric lineshapes due to the bistable effect in the ring resonators is also demonstrated. This EO field sensing demonstration is the first reported using EO ring resonator sensors built on a metal-free flexible integrated optics platform.

The second part of this dissertation addresses the problem of enhancing the response from a single-mode ring resonator of a given ring waveguide loss. A two-mode bus waveguide coupled to a single-mode ring resonator device is investigated. The Fano- shaped output lineshapes are shown to depend on the coupling coefficients, the input mode power distribution, and the relative phase difference of the two input modes.

Theoretical analysis and numerical parameter sweeps are used to determine optimal coupling coefficients to obtain maximum lineshape slope of the difference of the two mode power transmissions. The maximum lineshape slope that is theoretically obtainable from the device is 1.3 times that of an optimally coupled single-mode-coupled resonator with the same round-trip ring waveguide loss.

A device is fabricated in a polystyrene-silicon dioxide material system for demonstration purposes. Measurement results of the two-mode-coupled resonator device show that near-optimal coupling is achieved. The measured slope is found to be 1.28 times larger over an optimally coupled all-single-mode device. This work is the first experimental demonstration of enhanced lineshape slopes from the two-mode coupled ring resonator.

iii

DEDICATION

To my parents, for all their support.

ACKNOWLEDGMENTS

I would like to express my deepest gratitude to my advisor, Professor Ronald M.

Reano. His wonderful guidance, support and patience have enabled this work. I would also like to thank Professor Betty Lise Anderson and Professor Fernando L. Teixeira for their continuous encouragement and for their time dedicated as members of my dissertation committee.

I would also like to thank the director, Dr. Robert Davis, and the staff members at the Ohio State University Nanotech West cleanroom facilities. This research was possible through their support. Also, I would like to extend my gratitude to the faculty and staff at the ElectroScience Laboratory who have been continuously supportive in the pursuit of my degree.

Finally, I would like to extend my special thanks to members of my research group and the students of the ElectroScience Laboratory with whom I have had the pleasure to interact over the past years. The on-going discussion between members of my research group, Justin Burr, Galen Hoffman, Li Chen, Peng Sun and Michael Wood have greatly contributed to my personal and professional growth.

VITA

January 10, 1982 ………….. Born – Duncan Falls, Ohio

June, 2005 ………………… B.S. in Electrical Engineering, Ohio University, Athens, Ohio

June, 2007 ………………… M.S. in Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio

PUBLICATIONS

A. C. Ruege and R. M. Reano, “Sharp Fano Resonances From a Two-Mode Waveguide Coupled to a Single-Mode Ring Resonator,” Journal of Lightwave Technology, vol. 28, 2964-2968, 2010.

A. C. Ruege, L. Baas, T. E. Blue, R. M. Reano, “Geometries for the Sensitive Optical Detection of Photogenerated Carriers in Silicon,” IEEE Journal of Quantum Electronics, vol. 46, 818-826, 2010.

A. C. Ruege and R. M. Reano, “Multimode Waveguides Coupled to Single Mode Ring Resonators,” Journal of Lightwave Technology, vol. 27, 2035-2043, 2009.

A. C. Ruege and R. M. Reano, “Multimode Waveguide-Cavity Sensor Based on Fringe Visibility Detection,” Optics Express, vol. 17, 4295-4305, 2009.

FIELDS OF STUDY

Major Field: Electrical and Computer Engineering

TABLE OF CONTENTS

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... vi

Table of Contents ...... vii

List of Tables ...... xi

List of Figures ...... xii

List of Abbreviations ...... xviii

Chapter 1 Introduction ...... 1

1.1. Background ...... 1

1.2. Ring Resonator EM Sensors ...... 3

1.3. Goals and Contributions of this Dissertation ...... 6

1.3.1. Ring Resonator RF Field Sensor Demonstration ...... 6

1.3.2. Realization of Enhanced Lineshape Slopes ...... 8

1.4. Organization of the Dissertation ...... 10

Chapter 2 Waveguide Resonator Device Theory ...... 13

2.1. Dielectric Waveguides ...... 13

2.1.1. Effective Index Method ...... 15

2.1.2. Mode Solution of the Slab Waveguide ...... 16

vii 2.1.3. Waveguide Bends ...... 20

2.2. Single-Mode Bus Coupled Resonator Theory ...... 21

2.3. Resonator Arrays ...... 27

2.4. Two-Mode Bus Coupled Resonator Theory ...... 28

2.5. Generation of the Two Spatial Modes...... 33

2.6. Chapter Conclusions and Outlook...... 35

Chapter 3 Sensing with Ring Resonators...... 37

3.1. Electro-Optic Polymers ...... 37

3.2. Electro-optic Response ...... 39

3.3. Ring Resonator Sensor Response ...... 40

3.4. Optimization of Single Mode Bus Coupled Resonator for Sensing ...... 42

3.5. Sensor Arrays ...... 46

3.6. EO RF Field Sensing ...... 48

3.6.1. RF Bandwidth of Ring Resonator Sensor ...... 50

3.6.2. Invasiveness ...... 50

3.7. Optimization of the Two-Mode Coupled Resonator ...... 51

3.8. Chapter Conclusions and Outlook...... 55

Chapter 4 Design of Waveguide Resonator Devices ...... 58

4.1. Single-Mode Bus Coupled Resonator Design ...... 58

4.2. Two-Mode Bus Coupled Resonator Design...... 63

4.2.1. Mode Generator Design ...... 70

4.3. Chapter Conclusions and Outlook...... 73

Chapter 5 Fabrication Processes and Poling ...... 75

5.1. Single-Mode Bus Coupled Resonator for RF Sensing ...... 75

5.2. Poling Process ...... 84 viii 5.3. Fabrication of the Two-Mode Bus Coupled Resonator ...... 88

5.4. Chapter Conclusions and Outlook...... 91

Chapter 6 EO Sensor Experimental Results ...... 92

6.1. Laboratory Configuration for EO Sensing ...... 92

6.2. Microstrip Resonator ...... 95

6.3. Noise...... 103

6.4. Ring Resonator Optical Transmission Measurements ...... 106

6.5. EO RF Sensing Tests...... 110

6.6. Observed Bistability in Ring Resonator Transmission ...... 117

6.7. Discussion of the EO Sensing Measurements ...... 120

6.8. Chapter Conclusions and Outlook...... 125

Chapter 7 Two-Mode Bus Coupled Resonator Experimental Results ...... 127

7.1. Laboratory Configuration ...... 127

7.2. Two-mode Bus Coupled Resonator Device Characterization...... 130

7.3. Chapter Conclusions and Outlook...... 133

Chapter 8 Overall Conclusions and Future Work ...... 134

8.1. Overall Conclusions and Summary ...... 134

8.2. Future Work ...... 137

List of references...... 139

Appendix A Electro-Optic Polymer Theory ...... 149

A.1. Electro-Optic Polymers Theory ...... 149

A.2. EO Polymer Poling ...... 152

Appendix B Derivations of the Maximum Lineshape Slope ...... 154

B.1. Single-mode bus waveguide coupled to ring resonator ...... 154

A.2. Two-mode bus waveguide coupled to ring resonator ...... 157 ix Appendix C Teng-Man Ellipsometric EO Characterization ...... 159

C.1. Theory ...... 159

C.2. EO Characterization ...... 161

LIST OF TABLES

Table 1.1. Refractive indices and RF dielectric constants of materials used in EO RF sensor...... 7

Table 1.2. Refractive indices of the materials used in the two-mode device...... 9

Table 3.1. EO properties for EO polymers and inorganic crystals. The EO polymers are given as host polymer/chromophore...... 38

Table 4.1. Fabricated two-mode device dimensions...... 70

Table 6.1. Parameters determined from the four ring array spectra in Fig. 6.16...... 109

Table 6.2. Measured S parameters for the array and calculated normalized |Ey|...... 121

Table C.1. EO coefficients measured after heating trials of poled sample ...... 163

LIST OF FIGURES

Fig. 1.1. (a) Ring resonator coupled to one bus waveguide. (b) Optical power transmission of a ring waveguide resonator...... 4

Fig. 1.2. Resonance wavelength change due to optical path length change, where the intensity monitored at a single wavelength changes...... 5

Fig. 2.1. Dielectric waveguide geometry used for this dissertation...... 14

Fig. 2.2. Steps for calculating the propagation constant of the dielectric waveguide using the effective index method...... 16

Fig. 2.3. (a) Effective indices for the quasi-TE modes calculated by EIM and BPM. (b) Effective indices for the quasi-TM modes...... 19

Fig. 2.4. Electric field profiles of the quasi-TE0,0 and quasi-TE1,0 of a two-mode waveguide calculated by the beam propagation method. The arrows indicate the direction of the electric field vector...... 20

Fig. 2.5. Schematic of the single-mode bus coupled single mode resonator device...... 21

Fig. 2.6. Transmission of a single mode resonator for critical coupling and F = 50...... 26

Fig. 2.7. Schematic of a four element ring resonator array. The field transmission of each resonator is b0,n...... 27

Fig. 2.8. Transmission of a single resonator (N = 1), a five element array (N = 5) and a ten element array (N =10) with equally spaced resonances for rings with F = 50. The phase is relative to the first resonance for N = 1...... 28

Fig. 2.9. Schematic of the two-mode bus waveguide coupled to the single-mode ring resonator...... 29

Fig. 2.10 (a) The output mode transmissions for a1 = 0. (b) The output mode transmissions for a0 = 0...... 32

max Fig. 2.11 (a) The output mode transmissions for |a0| = |a1|, and δi = δi . (b) The output max mode transmissions for |a0| = |a1|, and δi = δi + π/2...... 33 xii Fig. 2.12. Mode generator device for controllably exciting the two modes of the two- mode waveguide...... 34

Fig. 3.1. Lineshape slope for a critically coupled resonator with F = 50...... 41

Fig. 3.2. Numerical and analytical calculations of the magnitude of the maximum lineshape slope as a function of coupling parameter, κ and several ring losses...... 43

Fig. 3.3. Maximum lineshape slopes for optimal coupling and critical coupling...... 45

Fig. 3.4. Maximum normalized lineshape slope for three different arrays with F = 50, 25 and 10. The slopes are normalized to the maximum slope of a single ring resonator. .... 46

Fig. 3.5. Simplified schematic of RF-optical test set-up...... 48

Fig. 3.6. (a) Optical power transmission for an optimally coupled ring resonator with finesse of 25. (b) Relative detected RF power at RF receiver for EO sensing...... 49

Fig. 3.7. The maximum slope of ΔB versus βL calculated from parameter sweep of Rc 2 2 and Sc. The maximum occurs for: (a) Rc = Sc = 1, (b) |a0| = |a1| , and (c) δi = κr1 - κr0 ± mπ/2 for odd m...... 52

2 2 Fig. 3.8. Optimized output mode power lineshapes for Rc = Sc = 1, |a0| = |a1| and δi = κr1 - κr0 + π/2 normalized to the total input power...... 53

Fig. 3.9 The difference, ΔB, of the optimized output mode power lineshapes. The maximum slope occurs at resonance where ΔB = 0...... 53

Fig. 3.10. Maximum lineshape slopes for the optimally coupled two-mode resonator device and the optimally coupled all-single-mode optimal coupling...... 55

Fig. 4.1. Effective indices for the first two quasi-TM spatial modes of a PC waveguide embedded in Cytop calculated by the effective index method and BPM...... 59

Fig. 4.2. Bend loss for bend radius for three different waveguide widths, w, calculated using BPM and simulated bend method...... 60

Fig. 4.3. Simulation of the ring coupling section to determine ring waveguide loss corresponding to straight coupling length where optimal coupling and critical coupling is obtained...... 61

Fig. 4.4. (a) Cross-section of the coupling section of the ring resonator. (b) Layout of the ring array. Two straight coupling lengths of 65 µm and 100 µm are used in unique arrays...... 62

Fig. 4.5. Normalized electric field profile of the fundamental TM mode of the PC/DR1 waveguide calculated by the beam propagation method...... 62

xiii Fig. 4.6. Effective index for PS core embedded in SiO2 for the first three quasi-TE spatial modes calculated by BPM for a 2-D cross-sectional waveguide...... 64

Fig. 4.7. Bend loss calculations using the simulated bend method in a 2-D waveguide. A width of 2 µm and a radius of 150 µm are chosen...... 65

Fig. 4.8. Coupling coefficients for a gap width of 0.5 µm and varying the coupling length calculated using three-dimensional BPM...... 66

Fig. 4.9. Coupling coefficients for a coupling length of 42.5 µm and varying the gap width calculated using three-dimensional BPM...... 67

Fig. 4.10. (a) Cross-section of the coupling section of the two-mode device. (b) Layout of the two-mode bus waveguide coupled to the single-mode ring...... 67

Fig. 4.11(a) Normalized amplitude of the electric field at a x-z cross-section inside the waveguide for quasi-TE0,0 mode input. (b) Amplitude of the electric field for only quasi- TE1,0 mode input...... 68

Fig. 4.12. (a) Normalized amplitude of the electric field for equal mode power input and max mode phases so that δi = δi is obtained. (b) . Normalized amplitude of the electric field min for equal mode power input and mode phases so that δi = δi is obtained...... 69

Fig. 4.13. Mode generator layout and design dimensions. “Input-1” is converted to the quasi-TE0,0 mode and “Input-2” is converted into the quasi-TE1,0 mode...... 71

Fig. 4.14 (a) Simulations results of the optimized mode generator for only the quasi-TE0,0 mode input, (b) only add waveguide input, and (c) both quasi-TE0,0 and add waveguide input...... 72

Fig. 5.1. (a)-(h). Fabrication process steps for the EO ring resonator sensors...... 76

Fig. 5.2 Cross-section of the developed PR showing the undercut obtained by the use of the LOR 2A layer...... 78

Fig. 5.3. (a) Cross-section SEM image of the etched channels in the LOR 5A. (b) Perspective SEM image etched channels at the coupling region of the resonator...... 79

Fig. 5.4 SEM image of ridges of PC/DR1 near the coupling section of the resonator device, after the LOR removal step...... 80

Fig. 5.5. Photomicrograph of several linear arrays of ring-racetrack resonators. The straight coupling length of the resonators is 65 µm...... 82

Fig. 5.6. Photomicrograph of single ring-racetrack resonator. The straight coupling length is 65 µm...... 82

xiv Fig. 5.7. Photomicrograph of the edge of released SU-8 film with PC/DR1 waveguides...... 83

Fig. 5.8. Three released SU-8 samples with PC/DR1 waveguide devices...... 84

Fig. 5.9. Sample to be poled on the hotplate with poling probes in contact with the two electrodes...... 85

Fig. 5.10. The measured current and hotplate temperature during the poling process as a function of time for a constant voltage of 200 V...... 86

Fig. 5.11. Ring resonator after poling the top Al electrode has been removed. The waveguides show no deformation, while the Cytop layer has become distorted due to flow...... 87

Fig. 5.12. (a) – (d) Fabrication process for the two-mode-coupled ring resonator devices...... 88

Fig. 5.13. (a) Etched channel in the SiO2. (b) Cross-section of PS filled channel...... 90

Fig. 6.1. Schematic for the testing configuration of the resonator array on the RF circuit...... 93

Fig. 6.2 Photograph of the RF microstrip resonator used for EO testing...... 95

Fig. 6.3. Measured magnitude of S11 of the RF resonator...... 96

Fig. 6.4 (a) Photograph of the EO sensor on the RF microstrip resonator showing the input and output fibers. (b) Detail photograph of the SU-8 substrate with EO ring resonators on RF resonator...... 97

Fig. 6.5. Photomicrograph of the ring arrays on top of the RF resonator. The microstrip lines are outlined in red. The SU-8 sample is outlined in white...... 98

Fig. 6.6. Simulated magnitude of S11 of the RF resonator...... 98

Fig. 6.7. (a) Normalized magnitude of the vertical field Ey at the first resonance at 1.9 GHz at 35 µm above the microstrip surface. (b) Normalized magnitude of the vertical field Ey at the second resonance at 3.9 GHz at 35 µm above the microstrip surface...... 99

Fig. 6.8. Simulations of the microstrip resonator at 3.90 GHz with and without an SU-8 slab...... 100

Fig. 6.9. Mean vertical electric field in ring resonator across microstrip. The locations and fields in each ring of the four-ring array are shown...... 101

Fig. 6.10. Phase of vertical electric field in ring resonator across microstrip. The locations and phases of each ring of the four-ring array are shown...... 101 xv Fig. 6.11. Measured S11 frequency response for the RF microstrip resonator in air, with optical devices on the SU-8 substrate and with a silicon sample of similar size to the SU- 8 sample...... 102

Fig. 6.12. Measurement of S21 magnitude noise level with laser directly connected to photodetector...... 104

Fig. 6.13. Noise levels measured with spectrum analyzer at 3 Hz bandwidth...... 106

Fig. 6.14. Normalized transmission spectra for a single ring-racetrack resonator...... 107

Fig. 6.15. Normalized transmission spectra of the two-ring array...... 108

Fig. 6.16. Normalized transmission spectra of the four-ring array...... 109

Fig. 6.17. Optical power transmission spectra for the S21 EO measurements...... 110

Fig. 6.18. Magnitude of S21 as the laser wavelength is swept across ring resonance of 1551.14 nm...... 111

Fig. 6.19. Phase of S21 as the laser wavelength is swept across the ring resonance at 1551.14 nm...... 112

Fig. 6.20. Measured S21 magnitude as a function of frequency near the second resonance of the RF resonator...... 113

Fig. 6.21. Measured optical power across resonance for the RF power sweep measurements...... 114

Fig. 6.22. Modulation signal measured at spectrum analyzer at a wavelength of 0.06 nm from resonance and an RF power of 11 dBm...... 114

Fig. 6.23. Measured RF power for three different bias wavelength points near ring resonance with best-fit lines...... 115

Fig. 6.24. (a) Four-ring array optical power spectrum, (b) measured |S21| and (c) S21 phase...... 116

Fig. 6.25. Measured resonance lineshapes for five different input powers...... 117

Fig. 6.26. Measured resonance wavelength change for varying optical powers...... 118

Fig. 6.27. Measured transmission spectra of a bistable resonance...... 119

Fig. 6.28. Measured magnitude of S21 for the bistable resonance depicted in Fig. 6.28. An RF power of 0 dBm is incident to the RF resonator...... 119

xvi Fig. 6.29. Calculated r33 values for the rings of the four-ring array. The solid horizontal lines denote the bounds for possible values of r33...... 122

Fig. 6.30. Electric field sensitivity calculated for ring R2 as a function of noise floor power...... 124

Fig. 7.1. Laboratory configuration. A 3 dB fiber coupler splits the light from a tunable laser into two output single-mode fibers (SMF). The two fibers are aligned to the input waveguides of the mode generator. Two fibers at the output couple light from the mode filter into two photodetectors, where the optical power is measured simultaneously. ... 128

Fig. 7.2. Optical micrograph of fabricated on-chip structure consisting of a mode generator, two-mode waveguide, single-mode ring, and mode filter...... 129

Fig. 7.3. Measured transmission spectra from two ring-racetrack resonators with radius equal to 150 µm...... 130

Fig. 7.4. (a) Measured output when only the TE0,0 mode is excited at the input. (b) Measured output when only the TE1,0 mode is excited at the input...... 131

Fig. 7.5. (a) Measured output for equal input mode power distribution and relative phase difference that maximizes the slope of the difference of the two mode power transmissions. (b) The difference of the two output mode powers...... 132

xvii

LIST OF ABBREVIATIONS

µm micro meter

µT micro Torr

Al aluminum

BPM beam propagation method

BW bandwidth

CdTe cadmium telluride

Cr chromium

CW continuous wave

DR1 Disperse Red 1

EDFA erbium doped fiber amplifier

EIM effective index method

EM electromagnetic

EO electro optic

ER extinction ratio

F finesse

FSR free-spectral range

xviii FWHM full-width at half-maximum

GaAs gallium arsenide

GHz gigahertz

HF hydrofluoric acid

ICP inductively coupled plasma

IF intermediate frequency

IR infrared

ITO indium tin oxide

LiNbO3 lithium niobate

LiTaO3 lithium tantalite

MHz megahertz mm millimeter mTorr millitorr

MZI Mach Zehnder interferometer nm nanometer

PC polycarbonate

PMMA Poly(methyl methacrylate)

PR photoresist

PS polystyrene

Q quality factor

RF radio frequency rpm rotations per minute

xix SEM scanning electron microscope

Si silicon

SiO2 silicon dioxide

TE transverse electric

Tg glass transition temperature

Ti titanium

TM transverse magnetic

UV ultraviolet

VNA vector network analyzer

CHAPTER 1

INTRODUCTION

1.1. Background

The sensing of electromagnetic (EM) fields via the linear electro-optic (EO) effect has been implemented and studied for several decades. EO sensors are based on a refractive index modulation of the sensor material due to an externally applied EM field.

The refractive index modulation is detected using optical beams. EM sensors have been realized in devices utilizing free-space bulk optics, optical fiber-based and chip-based integrated optics. High spatial resolution, low invasiveness, large bandwidth and all- dielectric materials are characteristics of the optical sensor that can be realized through the use of such methods. Applications include near field mapping of antennas and radio frequency (RF) circuits [1-5] probing of high-speed microelectronic circuits [6-8] and electromagnetic compatibility and interference testing [9-11]. Sensors have also been implemented in RF-photonic links and receiver front-ends for reduced susceptibility to damage by high energy EM pulses [12]. Terahertz imaging has also been performed using electro-optic sensors [13].

Some of the first sensors based on the EO effect were based on a Mach-Zehnder interferometer (MZI) waveguide device. The output optical intensity was modulated by a 1 dipole antenna connected to electrodes on the MZI arms [14]. This method eliminated coaxial cables that otherwise would be a source of coupling and scattering of the sensed

RF field. Perturbation of the incident field may be greatly reduced by eliminating the attached antenna [15], [16]. Newer MZI sensor devices are completely devoid of all metal [17-19]. An additional EO sensing technique that was investigated at the same time as the MZI devices measured the optical polarization modulation in materials due to the EO effect. The internal fields of a microelectronic circuit have been mapped by measuring the polarization modulation of a laser beam in circuit substrates that exhibited the EO effect [5], [20-22]. External probes utilizing polarization modulation attached to optical fibers have also been fabricated and investigated [2], [23], [24]. Other types of sensors include waveguide mode cut-off sensors [25], Bragg grating sensors [26], Fabry-

Pérot resonators [27-29], resonant waveguide coupling sensors [30], and optical fiber- coupled ring resonators [31] have been demonstrated.

EO field mapping has also been investigated. In order to produce one- and two- dimensional field images, EO probes have been scanned over test structures [32]. The technique of polarization modulation in external probes has been used to carry out live field mapping [4]. Arrays of devices may also be implemented, where each element is interrogated through wavelength multiplexing. Two-element array of resonant-coupled waveguide sensors have been demonstrated [33]. The fabrication of an array of several

EO ring resonators affixed to an optical fiber has also been demonstrated [34]. The spatial resolution of the arrayed sensors is determined by the size of each sensor element.

High spatial resolution can be obtained by using integrated optical devices, where device footprints can be on the order of tens of square micrometers.

2 EO sensors have utilized inorganic EO crystals such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3), cadmium telluride (CdTe), and gallium arsenide (GaAs).

Polymers that exhibit the EO effect are also used. EO polymers have demonstrated larger

EO coefficients than inorganic crystals and have a lower dielectric constant than inorganic crystals [35]. EO polymers have also been shown to respond to fields up to the terahertz regime [13], [36]. Thus EO polymers with superior characteristics to inorganic materials have been extensively studied for use in RF field sensors.

As developments in fields such as high-speed microelectronics, novel antennas and terahertz imaging continues, it is evident that EO sensors with greater capability in terms of sensitivity, invasiveness, bandwidth, and spatial resolution will be required.

Sensors based on ring resonators constructed from EO polymers are thus investigated in this dissertation because of the potential for high sensitivity to RF fields, compact size, ability to be arrayed, and fabrication in a low-invasive planar integrated optical platform.

1.2. Ring Resonator EM Sensors

EO polymer modulators based on resonators have been widely reported [37-41].

EM sensors based on ring resonators are the one of the latest developments in EO field sensing techniques. A field sensor composed of an EO ring resonator fixed to an optical fiber was reported in 2007 [31]. Resonator EM sensors based on the plasma dispersion in silicon have also been investigated [42]. Because the device utilizes the plasma dispersion effect and not the EO effect, it requires metallic electrodes attached to a dipole antenna for field sensing. While having potential for high sensitivity to EM fields, the

3 device is intrinsically invasive because of the metal required for operation. It is thus clear that there is much work to be done using EO ring resonators as RF field sensors.

The ring resonator device is shown in Fig. 1.1(a). The device consists of a ring waveguide resonator and a straight bus waveguide. Laser light in the bus waveguide evanescently couples into the ring and generates resonant modes at particular laser light wavelengths. The optical transmission exhibits Lorentzian dips at the resonant wavelengths. A schematic of the power transmission of a ring resonator coupled to a single bus waveguide is shown in Fig. 1.1(b) as a function of wavelength. The resonance wavelength position occurs where the round-trip phase of the optical beam is an integer multiple of 2π. If the optical path length of the optical beam changes due to a change in refractive index of the resonator, the resonance wavelength will change. This change in resonance due to refractive index modulation is exploited in ring resonator sensing.

(a) (b) Fig. 1.1. (a) Ring resonator coupled to one bus waveguide. (b) Optical power transmission of a ring waveguide resonator.

Fig. 1.2. Resonance wavelength change due to optical path length change, where the intensity monitored at a single wavelength changes.

In RF sensing applications, the laser wavelength is fixed at a point on the steep slope of the resonance lineshape as depicted in Fig. 1.2. The refractive index of the ring resonator is modulated by the external electric field via the linear EO effect. The resonance wavelength changes due to the refractive index modulation. The output laser light intensity is thus modulated due to the lineshape slope of the resonance. The magnitude of the change is proportional to the lineshape slope at the bias wavelength and the magnitude of resonant wavelength change. A larger intensity change is therefore obtained from steeper lineshape slopes. The slope is determined by the coupling into the resonator and the optical loss of the resonator. Optimal coupling can be achieved through the design process of the ring resonators. The optical loss is determined by the device materials, design, and fabrication process.

The sensitivity to the externally applied electric fields in a ring resonator is thus proportional to the quality factor (Q) of the resonator. An EO polymer field sensor device with a Q on the order of 103 has been reported [31]. A Q on the order of 105 has

5 been demonstrated in EO polymer modulators [37]. Given a large Q, the optical beam passes through the sensing medium multiple times. In comparison to MZI devices with device lengths on the order of 1 cm, ring-resonator devices are much more compact due to this increase in interaction length.

1.3. Goals and Contributions of this Dissertation

The two main themes this research encompasses are as follows: (1) the demonstration of an RF field sensor based on ring resonators fabricated in an integrated optics platform using EO polymers and (2) the demonstration of a new device that exhibits enhanced lineshape slopes from a ring resonator not achievable with the geometry of a single-mode bus waveguide coupled to a single-mode resonator.

1.3.1. Ring Resonator RF Field Sensor Demonstration

The purpose of this research is to experimentally demonstrate RF sensing using ring resonators fabricated in an integrated optical platform using EO polymers. The goals of the work are as follows:

1. Design and fabricate poled EO ring resonators sensor devices with minimal invasiveness, high spatial resolution and large bandwidth.

2. Demonstrate sensing using linear arrays of resonators.

The device is based upon a single-mode ring coupled to a single-mode bus waveguide like that depicted in Fig. 1.1(a). The waveguide cores consist of 6 polycarbonate (PC) polymer doped with a commercially available EO chromophore,

Disperse Red 1 (DR1). The device is metal-free, uses the low dielectric constant flexible polymer SU-8 as the supporting substrate and is 30 µm thick. The refractive indices and dielectric constants of the materials used in the device are shown in Table 1.1. The cladding material is Cytop, a low-loss fluorinated polymer [43].

Refractive Dielectric Material Application index constant (RF) PC/DR1 Waveguide core 1.58 2.96 Cytop Waveguide cladding 1.33 2.0 SU-8 Substrate 1.57 3.2 Table 1.1. Refractive indices and RF dielectric constants of materials used in EO RF sensor.

In contrast to the ring-resonator coupled fiber in [31], the sensor demonstrated in this dissertation is built on an integrated optics platform. The waveguides devices are defined using a single lithography step. Thus the need for individual alignment of the resonators to the bus waveguide is eliminated, allowing for many-element arrays to be fabricated at the same time. Additionally, the device area is defined by photolithography. Thus dicing and cleaving is not required and waveguide end-facets are created by this technique.

Low perturbation to the sense field is enabled by the use of the metal-free thin polymer substrate. EO polymer MZI modulators [44] and non-EO active ring resonators

[45] on flexible substrates have also been demonstrated. The flexibility enables conformability of the optical devices to curved surfaces such as an aircraft or antenna.

The devices are also constructed on a thin flexible substrate in this dissertation. In

7 contrast to the MZI modulators of [44], RF sensing with resonant waveguide devices on a flexible polymer substrate is demonstrated.

In this dissertation, theoretical analysis of the resonator devices is first performed to determine the optimal coupling of the bus waveguide to the ring waveguide to give the largest lineshape slope given a ring waveguide with fixed optical loss. The theory is then used to design the devices to achieve near-optimal coupling. Single ring-resonators and resonator arrays are fabricated. EO sensing is demonstrated by placing the resonator devices on top of an RF microstrip resonator circuit that is resonant at 3.9 GHz. It is shown that the device is minimally perturbing by observing a small shift of resonance frequency of the microstrip resonator. To demonstrate EO sensing the optical wavelength is swept across the ring resonance wavelength. The EO response is shown to be highest when the optical wavelength is biased on the resonance lineshape. Sensing using an array device of four ring resonators coupled to the same bus waveguide is demonstrated.

1.3.2. Realization of Enhanced Lineshape Slopes

A limiting factor of the achievable sensitivity to EM fields of EO sensor devices based on the ring resonator is the loss of the resonator. Thus it is important to minimize the resonator loss. Given a fixed loss, modifications to the traditional ring resonator design can be done to realize larger lineshape slopes and thus improved sensitivity to EM fields. In this dissertation, enhanced lineshape slopes are obtained from a device based on the coupling of two bus waveguide spatial modes to a single-mode waveguide ring

8 resonator. This configuration is in contrast to the all-single mode devices where the bus waveguide is designed to support only one mode. A portion of this work has been presented in [46].

The goals of this work are as follows:

1. Determine optimal coupling conditions to obtain a lineshape slope larger than what is obtainable from an all-single-mode device given similar ring waveguide losses.

2. Design, build and test a proof-of-concept device demonstrating larger lineshape slopes.

Theoretical and numerical analysis of the device is performed to determine the optimal coupling conditions and input mode power distributions and phases. Fabricated devices consist of polystyrene (PS) cores with silicon dioxide (SiO2) cladding on silicon

(Si) substrate. The refractive indices of the materials are given in Table 1.2.

Refractive Material Application index PS Waveguide core 1.57 SiO2 Waveguide cladding 1.44 Si Substrate 3.48 Table 1.2. Refractive indices of the materials used in the two-mode device.

The two-mode coupling gives rise to asymmetric Fano-shaped resonances at the output [47]. It is demonstrated that if the coupling of the modes is optimized, the output lineshape slopes are larger than those obtained from the all-single-mode device. The output mode power distribution has been previously detected through the use of fringe visibility and has been used for biological sensing [48], [49]. In this work the mode powers are directly detected using on-chip mode filters [50]. The work in this 9 dissertation is also the first experimental demonstrations reported in literature of optimized lineshape slopes from an integrated optical device utilizing the two-mode coupling scheme.

Resonant devices that produce Fano transmission lineshapes may be manifested in several ways. In one realization, a single-mode resonator is coupled to two single-mode waveguides. The two modes of the two separated waveguides are excited. Such devices have been explored for optical switching [51]. The device is similar to add-drop dual- waveguide resonator filters, where modes are excited at two different waveguide inputs instead of one input [52]. Another device that produces Fano shaped output lineshapes is the ring-enhanced MZI investigated for applications in filters, and modulation [53-55].

In contrast to the two devices, in this work only a single bus waveguide is required to produce asymmetrical lineshapes. In applications involving highly arrayed resonators found in applications such as multi-channel multiplexing, many waveguide crossings or a multilevel approach are needed [56-58]. Two modes propagating in a single waveguide eliminates the need for many crossings.

1.4. Organization of the Dissertation

This dissertation is organized to demonstrate the successful development and testing of the ring resonator sensors beginning at fundamental theory and arriving at the final measurement results. This work consists of two major parts: the development of the theory to guide device design and the testing of the designed and fabricated devices.

10 The current chapter gives an introduction to EM field sensing, a description of the device principle and outlines the research goals described in this dissertation. In Chapter

2 the fundamentals of rectangular dielectric waveguides and their propagating optical modes are discussed. Evanescent coupling between modes of different waveguides is also introduced. This background is then used to derive equations for the optical transmission of the single-mode bus coupled resonator, arrays of resonators, and the two- mode bus coupled resonator. The theory treated in Chapter 2 is then used to construct a theoretical model for EO sensing using the resonator devices in Chapter 3. Fundamentals of EO polymers are introduced in Chapter 3 followed by the theoretical analysis of the ring response due to an applied electric field. It is shown that the magnitude of the transmission modulation due to the external field depends on the lineshape slope of the transmission spectra near the resonance wavelengths of the resonator. The lineshape slope depends on the loss of the ring resonator waveguide and the coupling of the bus waveguide mode and ring waveguide mode. Thus, in Chapter 3, the coupling condition between the bus waveguide and the ring resonator to obtain the largest lineshape slope for a resonator of a fixed loss are developed. It is also shown that given optimal coupling conditions and ring resonators of similar loss, the two-mode bus coupled resonator produces a larger transmission lineshape slope than the single-mode bus coupled resonator.

The second part of the dissertation addresses the design, fabrication and testing of the ring resonator devices. Chapter 4 illustrates the design of ring resonator sensors using the optimal coupling theory developed in Chapter 3. The dimensions of the rectangular waveguides are designed using the theory described in Chapter 2. The fabrication steps

11 of the two designs are documented in Chapter 5. The poling process for the EO field sensors is also detailed. In Chapter 6, the experimental results are given for the fabricated single-mode bus coupled resonator sensors. EO sensing of electric fields emanating from a microstrip resonator circuit resonant at 3.90 GHz is performed and confirmed. In Chapter 7, experimental results from the optical characterization of the two-mode bus coupled resonator device are given. Near-optimal coupling is experimentally demonstrated. Conclusions and a discussion of future work are treated in

Chapter 8.

CHAPTER 2

WAVEGUIDE RESONATOR DEVICE THEORY

The integrated optical ring resonator is an important element in a number of applications in telecommunications and sensing. The resonator is the key element in the

EO sensors developed in this dissertation. The operation of the sensor is based upon resonance wavelength modulation due to an applied electric field. In this chapter, the fundamentals of dielectric waveguides and propagating modes are first discussed. Next, waveguide coupling and all-single mode ring resonators are theoretically analyzed.

Finally, a two-mode bus coupled single-mode ring resonator device is theoretically analyzed and the equations describing the mode transmission are derived.

2.1. Dielectric Waveguides

Consider the dielectric waveguide geometry depicted in Fig. 2.1. The waveguide consists of a rectangular cross-section core with a refractive index of nc. The core is embedded in a cladding material of refractive index nclad. The top of the waveguide is surrounded by air of refractive index n0 = 1. The width of the core is w and the height is h. The waveguide extends into the z direction. Given nc > nclad > n0, light can be coupled and guided by the waveguide due to total internal reflection. 13

Fig. 2.1. Dielectric waveguide geometry used for this dissertation.

The guided EM fields that have a constant transverse distribution along the z axis of the waveguide are referred to as eigenmodes or modes of the waveguide. A number of propagating modes may exist in the waveguide of Fig. 2.1. The characteristics of the modes depend on the waveguide geometry and refractive indices. Maxwell’s equations are used to analyze the guided modes. In a charge-free, linear, and isotropic media,

Maxwell’s equations may be written as

H E   , 0 t

2 E H   0 n , t (2.1) D  0,

B  0.

E is the electric field intensity, D is the electric flux density, B is the magnetic flux density, and H is the magnetic field intensity. The free-space permittivity is ε0 and the permeability of free space is µ0. The general wave equation can be solved from Eq. (2.1) and may be given in two forms as [59]:

14  2E  2E    0 t 2 . (2.2)

 2 H  2 H    0 t 2

Solutions of the wave equation given the conditions imposed by the dielectric boundaries shown in Fig. 2.1 give rise to propagating modes in the waveguide, with propagation constants and electric field profiles. Plane wave propagation of the forms

E  Eexp j(t  z) (2.3) H  H exp j(t  z) are solutions to the wave equation, where ω is the angular frequency of the wave and β is the propagation constant of the wave. E and H are the vector complex amplitudes of the electric and magnetic fields, respectively. Numerical techniques are required to determine the mode propagation constants for the two-dimensional cross-section of the waveguide. However, approximations can be made that simplify the solutions to the wave equation.

2.1.1. Effective Index Method

Methods such as Kumar’s method [60] and Maractili’s method [61] can be used to obtain approximate solutions of the wave equation. The effective index method (EIM)

[62] can also be used to obtain approximate solutions by simpler techniques. EIM reduces the problem of determining the propagation constant of the mode of the two- dimensional waveguide into determining the propagation constants of two slab

15 waveguides generated from the original waveguide. The steps involved are depicted in

Fig. 2.2. The first slab waveguide is formed by extending the waveguide horizontally and to infinity. The top and bottom cladding refractive indices are n0 and nclad respectively. The propagation constant of the slab waveguide is determined and an effective index, neff, is calculated by

(2.4)   neff k , where k is the wavevector calculated by k = 2π/λ. The wavelength of light in free-space is λ. The effective index is then used as the core index in the next step, where the waveguide is extended to infinity in the vertical directions. The propagation constant solved from this final step is the approximate propagation constant of the original waveguide.

Fig. 2.2. Steps for calculating the propagation constant of the dielectric waveguide using the effective index method.

2.1.2. Mode Solution of the Slab Waveguide

Using EIM, the problem is reduced to solving two slab mode equations.

Assuming a slab waveguide geometry like that in step 2 of Fig. 2.2, the wave equation is reduced to 16 2 d Ex 2 2 2 2  (k n   )Ex  0 . (2.5) dy for an electric field polarized in the horizontal x direction. The polarization is called transverse electric (TE) in this case because the electric field lies in the plane that is perpendicular to the propagation direction. Ey, Ez and Hx are zero. For the transverse magnetic (TM) polarization, the electric field is polarized in the vertical y direction and

Ex, Hy and Hz are zero. For TM polarization, the magnetic field lies in the plane that is perpendicular to the propagation direction. The wave equation in this case is

d  dH   2  x   (k 2  )H  0.  2  2 x (2.6) dy  n dy  n

Ey is found from Hx by

 E y   H x . (2.7)  n 2 0 The normalized propagation constant, b, given as

2 2 neff  nclad b  2 2 . (2.8) nc  nclad can be determined by solving the dispersion equations for the TE and TM polarizations respectively [63]:

 b   b    2v 1 b  m  tan1 TE   tan1 TE  , TE      1 bTE   1 bTE  (2.9)  n2 b   n2 b    2v 1 b  m  tan1 1 TM   tan1 1 TM  TM  2   2   nclad 1 bTM   n0 1 bTM  .

The mode order m is an integer. The normalized frequency v is given by

17 v2  k 2h2 (n2  n2 )/ 4 1 clad (2.10) where the width of the slab waveguide is h. The parameter γ is defined as

2 2 nclad  n0   2 2 . (2.11) n1  nclad

Eq. (2.13) is transcendental and must be solved using numerical techniques such as

Newton’s method or the bisection method. Once the normalized propagation is found, the effective index and propagation constant can be found using Eqs. (2.8) and (2.4) respectively.

In this dissertation, the mode propagation constant for a two-dimensional waveguide geometry is also determined by using the beam-propagation method (BPM) software package BeamProp from RSoft, Inc. In BPM, the waveguide is assumed to slowly vary in the z direction, thus greatly reducing numerical solution of the wave equation of Eq. (2.2). When solving for the propagation constants of the modes the waveguide is assumed to be completely invariant in the z direction [64]. When designing the geometry of the waveguide and simulating the propagation of the modes, BPM is used in this dissertation. When solving for effective indices to fit to the characteristic equations of the ring resonator devices, EIM is utilized.

For demonstration purposes, assume the waveguide geometry of Fig. 2.1. The core material is PS and has a refractive index nc = 1.57. The height of the core is 1.5 µm.

The core is embedded in a silicon dioxide (SiO2) cladding and has a refractive index nclad

= 1.44. The top cladding is air. The effective indices are found by EIM and BPM as a function of waveguide width for the quasi-TE and quasi-TM modes. The modes for the two-dimensional cross-section are called quasi-TE because the fields Ey and Hx are

18 dominant. The Ex and Hy fields are dominant for the quasi-TM polarization. Fig. 2.3(a) shows the mode effective indices for the first three (m = 0, 1, 2) quasi-TE modes. Fig.

2.3(b) shows the mode effective indices for the first three quasi-TM modes. As the waveguide width increases more modes are supported in the waveguide. The cut-off width is the width at which a mode no longer propagates. For widths greater than the cut- off width, the BPM mode solutions and EIM solutions converge.

It is important in many optical waveguide devices that only one spatial mode propagates in the waveguide. Therefore the width and height must be designed so that only a single mode is supported. For example, for the quasi-TE modes of Fig. 2.3(a) the waveguide supports a single mode up to a width of 2 µm as calculated by BPM.

(a) (b) Fig. 2.3. (a) Effective indices for the quasi-TE modes calculated by EIM and BPM. (b) Effective indices for the quasi-TM modes.

Fig. 2.4. Electric field profiles of the quasi-TE0,0 and quasi-TE1,0 of a two-mode waveguide calculated by the beam propagation method. The arrows indicate the direction of the electric field vector.

Fig. 2.4 is a contour plot of the first two quasi-TE spatial modes of the PS waveguide for a width of 3 µm. The arrows indicate the direction of the electric field.

The field of the mode consists of a propagating wave inside of the core and evanescent waves that extend outside of the core. Note that for the quasi-TE0,0 mode, the field consists of a single lobe and for the quasi-TE1,0 mode, the field consists of two lobes.

2.1.3. Waveguide Bends

Waveguide bends are necessary structures in optical integrated circuits. For example, the ring resonator incorporates bends of a constant radius. A bent waveguide with a constant radius supports modes that are invariant in a cylindrical coordinate system. As the radius decreases in a bend, the mode is less supported and becomes a leaky mode. Energy is thus radiated into the cladding. In a ring resonator where keeping

20 the optical loss to a minimum is important, the bend radius must be optimized. The minimum radius of resonators is thus limited by the bend loss.

Bend loss can be determined by approximate closed-form analytical equations

[65] or by numerical techniques. In this dissertation, the bend loss is found by solving for the bend mode using the BPM mode solver from RSoft, Inc and EIM. A coordinate transformation that maps the refractive index distribution of a curved waveguide onto a straight waveguide is performed [66]. The method has been demonstrated to be accurate when the width of the waveguide is much larger than the radius of the bend.

2.2. Single-Mode Bus Coupled Resonator Theory

A schematic of a single ring resonator coupled to one bus waveguide is shown in

Fig. 2.5. Input light from the single-mode bus waveguide evanescently couples to the single-mode ring waveguide.

Fig. 2.5. Schematic of the single-mode bus coupled single mode resonator device.

21 The result of the interaction is observed at the output of the same bus waveguide. The coupling section and the ring waveguide can by analyzed separately to simplify the ring resonator transmission equation derivation.

When a waveguide is brought into the vicinity of another waveguide as in the case for the ring resonator, the propagating modes may couple and interfere. The amplitudes of the two modes, A1 and A2, along the propagation direction z of the directional coupler are determined by two differential equations [67]:

dA1   j 21 exp j(1   2 )A2 (z) dz , dA (2.12) 2   j exp j(   )A (z) dz 12 2 1 1

The coupling constants Κ12 and Κ21 are determined by the field overlap between the two modes at the coupling section. Using the coupled equations of (2.12) the energy transfer between waveguide modes can be determined for two symmetric or asymmetric waveguides and for different mode orders [68]. The coupling may also be solved by performing EM simulations of the coupling region with numerical methods such as the finite-difference time-domain method or BPM. Two methods to control the waveguide coupling are to vary the coupling length and the gap between the waveguides. Two straight coupling sections can be incorporated into the ring between the two 180o bends to increase the coupling length. Ring resonators of this configuration are traditionally called ring-racetrack resonators [69].

The coupling section can also be viewed as an EM device with several input and output ports related by a scattering matrix [70]. The coefficients of the scattering matrix

22 can be solved using numerical methods or analytical approaches. Assuming negligible back-reflections, the incoming modes and the outgoing modes can be related as

B   0 TB     , (2.13)    t   A   T 0A   where T is the matrix describing the coupling, A is the vector representing the mode complex amplitudes at the left side of the device depicted in Fig. 2.5 and B is the vector of the mode complex amplitudes on the output side. The subscript “+” denotes modes propagating toward the coupler. The subscript “-“ denotes modes propagating away from the coupler. Tt is the transpose of the matrix T. The independent ports can be realized by orthogonal modes of the same waveguide or by modes in spatially separated waveguides [70]. Assuming propagation in one direction the output modes are related to the input modes by

B  TA (2.14)   .

For the propagation of fields of one polarization, T is 2 x 2 for two coupled single-mode waveguides. This is the case for a single-mode bus waveguide coupled to a single-mode ring waveguide. T relates the inputs of the coupling section to the outputs by [71]:

b0   t  a0          . (2.15) br   t ar 

The quantities an and bn denote input and output complex amplitudes respectively and are depicted in Fig. 2.5. Subscripts with n = 0 or n = r refer to the fundamental mode of the bus waveguide and the fundamental mode of the ring waveguide respectively. The parameter κ is the coupling coefficient between the bus waveguide mode and the ring

23 waveguide mode. This parameter is a measure of the fraction of energy coupled from the bus waveguide into the ring waveguide. The parameter t is the transmission coefficient of a mode across the coupling section. The mode amplitudes are normalized such that their squared magnitudes correspond to the modal power. For lossless coupling, the matrix is unitary such that

| |2  | t |2 1. (2.16)

Due to the feedback of the ring waveguide, ar is related to br by ar  brtr , where the ring transmission, denoted tr, is

(2.17) tr  r exp( jr ).

The ring mode phase, denoted φr, is obtained from the ring circumference, Lr, and

propagation constant βr byr  Lr r . The ring field amplitude transmission coefficient

is the real parameter αr, given by r  exp(Lr  / 2) where the power attenuation coefficient in the ring is denoted by . Given Eqs. (2.15) and (2.17), the steady-state output field amplitude of the bus waveguide is

t   r exp( j r ) b0  a0  . (2.18) 1  r t exp( j r )

The ring field is

   br  a0  . (2.19) 1 r t exp( jr )

The normalized output power, T, is obtained from the square-magnitude of Eq. (2.18) and is

24 | b |2 (1 | t |2 )(1 2 ) T  0 1 r . 2 2 2 (2.20) | a0 | (1 | t | r )  4 | t | r sin (r / 2)

The resonance condition occurs for wavelengths corresponding to a ring phase that is an integer multiple of 2π:

2 2n    n L r eff r (2.21) r for integer n and resonance wavelength λr. The transmission spectra near resonance is a

Lorentzian dip. The extinction ratio depends on the coupling and ring loss. Critical coupling occurs when αr = |t| and is the condition such that the power lost in one round- trip of the ring resonator mode is equal to the coupled power into the ring resonator mode from the bus waveguide mode. The transmission is zero for critical coupling at resonance. If the resonator is under-coupled there is inadequate power coupling into the ring to obtain critical-coupling and thus |t| > αr.

The ring resonator may be characterized by the finesse, F and loaded quality factor, QL. The loaded quality factor is QL = λr/FWHM where FWHM denotes the full- width at half-maximum of the resonance lineshape. QL is a measure of the energy loss and storage of the resonator. The total energy lost is due to intrinsic energy loss in the ring resonator and the energy lost in the coupling. In terms of wavelength, the finesse is given by F = FSR/FWHM where FSR denotes the free-spectral range determined from the resonance condition of Eq. (2.12) and is

FSR  2 n L (2.22)  g r .

The group index is ng calculated by

25 dn n  n   eff . (2.23) g eff d

The finesse may also be derived in terms of the coupling and the ring waveguide loss and is given by

F  | t | / 1| t | (2.24) r  r .

The finesse and quality factor generally increase for decreasing optical loss in a resonator. The transmission as a function of φr is shown in Fig. 2.6 for a resonator with a finesse of 50. For the single-mode resonator, the FSR in terms of phase is 2π. For F = 50 at critical coupling, αr = |t| = 0.97.

Fig. 2.6. Transmission of a single mode resonator for critical coupling and F = 50.

26 2.3. Resonator Arrays

A schematic of a linear array consisting of four resonators coupled to a single bus waveguide is shown in Fig. 2.7. The dimensions of each resonator waveguide are unique so that the ring phase φn at a given wavelength is different for each resonator. Resonance wavelength separation is thus obtained because the resonance condition occurs for different wavelengths for each resonator. Each resonance of the individual resonators is addressed by tuning the input optical wavelength.

Fig. 2.7. Schematic of a four element ring resonator array. The field transmission of each resonator is b0,n.

The field transmission of a linear array of resonators is given by the product of the transmission, b0,n, of the individual resonators. A schematic of the power transmission for a single resonator (N = 1) and an array constructed of five resonators (N = 5) and an array of ten resonators (N = 10) is shown in Fig. 2.8. In this case, each critically-coupled resonator has a finesse of 50. The dimensions of each resonator are designed so that the resonance wavelengths are equally spaced within one FSR for a single resonator. The number of resonances that can be placed within an FSR at a spacing of the FWHM is equal to the finesse. A single resonance is affected by adjacent resonances in the FSR for

27 small resonance spacing, thus placing a limit on the number of resonators in an array.

Each resonator makes up one element of the spatial linear array in a sensing application.

2.4. Two-Mode Bus Coupled Resonator Theory

The two-mode bus waveguide coupled to the single-mode resonator is depicted in

Fig. 2.9. Two propagating modes of the two-mode bus waveguide couple and interfere with the fundamental mode of the single-mode ring at the coupling section. The output of the interference may also be determined by the use of the coupling matrix approach, where T of Eq (2.12) is now 3 x 3. The following system of equations describes the coupling region:

b0   t00 01 0r a0  b    t  a   1   10 11 1r  1  . (2.25) br  r0 r1 trr ar 

Fig. 2.9. Schematic of the two-mode bus waveguide coupled to the single-mode ring resonator.

The input mode complex amplitudes are denoted by a0, a1, and ar for the TE0,0, TE1,0, and ring modes, respectively. The corresponding output mode complex amplitudes are denoted by b0, b1, and br. The coupling of the TE0,0 and TE1,0 modes with the ring mode is determined by the coupling coefficients κmn which are schematically depicted in Fig.

2.9. The field profiles of the two spatial modes are of the same form as depicted in Fig.

2.4. The transmission coefficients of the modes through the coupling region are denoted by tmm. Subscripts with m = 0 or n = 0 refer to the TE0,0 mode, m = 1 or n = 1 refer to the

TE1,0 mode, and m = r or n = r refer to the ring mode. The mode amplitudes are normalized such that their squared magnitudes correspond to the modal power.

The device is similar to the single-mode device depicted in Fig. 2.5 by the fact that the two devices incorporate a single-mode ring resonator. The ring transmission, tr, for the two-mode device is also define by Eq. (2.17). The output mode amplitudes are determined by relating the ring transmission with the matrix of Eq. (2.25). The output modes complex amplitudes are

b0  t00a0 01a1 0rbrtr , (2.26)

29 b   a  t a   b t 1 10 0 11 1 1r r r , (2.27)

b  ( a   a ) /(1  t t ) r r0 0 r1 1 r rr . (2.28)

Ring resonances occur when the sum of the phase shift due to the ring outside of the coupling region and the phase shift at the ring-coupling section is an integer multiple of

2π.

Relationships between the magnitudes and phases of the coefficients of Eq. (2.25) may be found assuming that the coupling section is lossless. If the coupling section is lossless the coupling matrix is unitary [72]. The magnitudes of the coupling coefficients

2 2 are related by |κmn| = |κnm| . The relationships of the magnitudes of the coupling and transmission coefficients are determined by

2 2 2 t00  10   r0 1, (2.29)

2 2 2 t11   01   r1 1, (2.30) and

t 2   2   2  1. rr 0r 1r (2.31)

Following the derivation of [73], only four magnitudes of the coefficients are needed in order to completely determine all the magnitudes and phases of the coefficients if the matrix is unitary. The phases of five elements of the matrix may be arbitrarily set, obtained by changing the input and output reference planes of each mode. In this

derivation, the following phases are set to zero: t00  01  10  0r  r0  0.

The relationships between the phases and magnitudes of the coupling matrix may be found by [73]:

30  |  |2 |  |2  | t |2 |  |2  |  |2 | t |2  t  cos 1  0r 1r 00 01 01 11  11  2   2 | t00 || t11 ||  01 |   |  |2 | t |2  | t |2 |  |2  |  |2 |  |2  1  01 11 00 01 0r 1r  1r  cos    2 | t00 ||  01 ||  0r || 1r |  , (2.32)  |  |2 | t |2  | t |2 |  |2  |  |2 |  |2  1  0r 11 00 01 0r 1r   r1  cos    2 | t00 ||  01 ||  0r || 1r |   |  |2 |  |2  | t |2 |  |2  |  |2 | t |2  t  cos 1  01 1r 00 0r 0r rr  rr  2   2 | t00 ||  0r | | trr | 

Thus all the phases of the coefficients of the coupling matrix may be determined from the magnitudes. In order to obtain purely real phases from Eq. (2.32), a limitation is set on the magnitude of the coupling coefficients κ01:

2 2 | 0r || 1r | 1 1 | 0r |  | 1r |  |  | . (2.33) 01 2 2 | 0r |  | 1r |

If |κ01| is assumed as small as possible from Eq. (2.33), only the magnitudes |κ0r| and |κ1r| are required to completely determine the coupling matrix. The magnitudes of the coupling coefficients, |κ0r| and |κ1r| are determined by the physical geometry of the coupling section.

For the purposes of demonstration, the coupling coefficients are arbitrarily chosen and the output lineshapes described by Eq. (2.26) and Eq. (2.27) are found. Assume |κ0r|

= 0.2, |κ1r| = 0.25, |κ01| is minimized according to Eq.(2.33) and the round-trip ring loss is

2 αr = 0.92 dB. When only one input mode is excited, the lineshapes are Lorentzian. For a1 = 0, the normalized transmission is shown in Fig. 2.10(a). The normalized transmission is shown in Fig. 2.10(b) for a0 = 0.

(a) (b) Fig. 2.10 (a) The output mode transmissions for a1 = 0. (b) The output mode transmissions for a0 = 0.

The extinction ratios are determined by the coupling coefficients and the magnitude of αr.

Note that for the case of a single mode input, the ring acts as a mode generator near resonance. When one mode is input, both modes are excited at the output. When both input modes are excited, Lorentzian or asymmetrical Fano lineshapes may be obtained depending on the relative phase difference between the input modes, denoted by δi = a0

- a1. From Eq. (2.28), maximum power coupling into the ring for any input power

max distribution occurs for δi = δi = κr1 - κr0 + 2nπ, for n integer. Fig. 2.11(a) shows the

2 2 max output mode transmission for |a0| = |a1| = 0.5 and δi = δi . Minimum power coupling

min max max min occurs for δi = δi = δi + π. When δi = δi or δi = δi the output lineshapes are

max min Lorentzian. If δi is not equal to δi or δi , the lineshapes are both asymmetric as

max depicted in Fig. 2.11(b), where the input modes are of equal amplitude and δi = δi +

π/2. It is thus demonstrated that the form of the output lineshapes is strongly dependent on the input power distribution of the modes and the relative phase difference.

(a) (b) max Fig. 2.11 (a) The output mode transmissions for |a0| = |a1|, and δi = δi . (b) The output max mode transmissions for |a0| = |a1|, and δi = δi + π/2.

2.5. Generation of the Two Spatial Modes

In practice, power in the fundamental mode of a single-mode waveguide is coupled from an optical fiber or through free-space lenses. If the waveguide supports two spatial modes, it is difficult to control the mode power distribution and phases of the two modes simply by the coupling. An additional structure must be incorporated that excites the two modes with controllable amplitudes and phases from single mode waveguide inputs. Mode generating devices have been examined in the forms of mode- order converters [74] and asymmetric adiabatic couplers [50]. In these devices, higher order modes are excited from the single-mode inputs. In this dissertation, an asymmetric waveguide coupler similar to the device studied in [50] is used and is schematically depicted in Fig. 2.12.

Fig. 2.12. Mode generator device for controllably exciting the two modes of the two- mode waveguide.

A two-mode waveguide is evanescently coupled to a single mode “add” waveguide. The coupling section is designed such that the power in the “add” waveguide is only coupled into the second order mode of two-mode waveguide. This coupling is possible if the propagation constants of the two coupled modes are equal [50]. Thus the widths of the two waveguides must be designed to obtain this condition. The two-mode waveguide is fed by a single mode input via a tapered waveguide section. The taper is long enough so that no higher order modes are generated from the single-mode input amplitude a0. The second order mode input amplitude of the two mode waveguide, a1 is thus zero. Assuming lossless coupling, the outputs are related to the inputs of the ideal mode generator by the coupling matrix relationship:

ja b0  e 0 0 a0     j   b  0 0 e b a  1    1  . (2.34)    jc   ba   0 e 0 aa 

The phases due to the coupling are denoted by φa, φb and φc. When the propagation of the two modes is reversed through the coupling section the device acts as a mode filter.

34 The two spatial modes are separated into two separate single-mode waveguides. The mode filter is useful for measuring the mode power output from the resonator device.

2.6. Chapter Conclusions and Outlook

In this chapter, the fundamentals of rectangular dielectric waveguides and their propagating optical modes are discussed. Evanescent coupling between modes of different waveguides is also introduced. This background is used to derive equations for the optical transmission response of the single-mode bus coupled resonator, arrays of resonators, and the two-mode bus coupled resonator. The theory discussed in this chapter is a fundamental component used for further theoretical modeling, device design and device characterization presented in this dissertation. In Chapter 3, it is used to construct a theoretical model of EO sensing using the resonator devices. The design of the devices in Chapter 4 also requires the analysis presented in this chapter. This theory is also utilized for lineshape fitting of the measured optical transmission spectra of the two devices as demonstrated in Chapter 6 and 7.

Scattering matrix theory is used to relate the input and output mode amplitudes of the coupling region of the ring resonators. Transmission equations are derived by combining the coupling relationships and the feedback provided by the ring resonator.

This analysis technique is used for both the single-mode bus coupled resonator and the two-mode bus coupled resonator. The transmission spectrum as a function of ring phase of the single-mode bus coupled resonator is shown to be Lorentzian near the resonance condition. The output transmission spectrum of the two-mode bus coupled resonator

35 depends on the input mode power distribution and the relative mode phases. A discussion of the mode generator device, used with the two-mode bus coupled resonator is also given.

CHAPTER 3

SENSING WITH RING RESONATORS

In this chapter, the fundamentals of EO polymers are introduced. This theory is used to develop a model of the modulation in optical transmission due to an applied electric field for a EO single-mode bus coupled resonator. The results from Chapter 2 are used to obtain expressions for optimal coupling between the bus waveguide and the ring resonator. The optimal coupling condition occurs when the largest possible modulation is obtained given a ring with a fixed optical loss. This analysis guides the design of an

EO sensor based on the ring resonator. RF field sensing using the ring resonator devices is also discussed. A complete expression for the RF modulated power from an EO ring sensor is developed.

This chapter then demonstrates that an increased transmission modulation is achieved by the use of the two-mode bus coupled ring resonator device. Optimal coupling conditions are derived to obtain this increase in transmission modulation.

3.1. Electro-Optic Polymers

RF field sensing is enabled by the EO effect in the poled polymer making up the ring resonator waveguide core. EO polymers are organic compounds that exhibit the EO 37 effect. They consist of two parts: a linear optical polymer and dipolar chromophore molecules. In comparison to EO inorganic crystals, EO polymers have low dielectric constants and potentially larger EO coefficients. Thus EO polymers are ideal for applications in RF sensing. Table 3.1 illustrates several EO material parameters for the inorganic crystals LiNbO3 and GaAs and reported EO polymers. One of the first EO polymers studied was the DR1 chromophore dispersed in a PMMA matrix in a guest-host system. An EO coefficient of 2.5 pm/V was reported in 1987 [75]. Through the investigation of poling techniques and molecular engineering of EO materials, EO coefficients greater than 300 pm/V have been achieved [76]. In sensing applications, lower dielectric constants perturb the sensed fields less. Also, the EO coefficient, r33, of

EO polymers have the potential to be much greater than the coefficients obtained using inorganic crystals. Thus, EO polymers are a suitable material for use in EO sensors.

EO Refractive Dielectric EO material coefficient (pm/V) index constant (RF)

LiNbO3 εr11 = 43, r33 = 30.9 2.2 (λ = 633 nm) εr33 = 28 GaAs 13.2 r = 1.4 3.4 (λ = 1150 nm) 41 PMMA/DR1 [75] r = 2.5 1.52 2.3 (λ = 633 nm) 33 APC/CLD [77] r = 90 1.63 2.5 (λ = 1060 nm) 33 PMMA/AJL34 [76] r = 306 1.52 2.3 (λ = 1310 nm) 33 Table 3.1. EO properties for EO polymers and inorganic crystals. The EO polymers are given as host polymer/chromophore.

A guest-host system of the DR1 chromophore in a PC polymer (Poly (Bisphenol

A carbonate)) is used in the proof-of-concept devices demonstrated in this dissertation.

38 EO coefficients from systems of DR1 in PMMA from 1 pm/V to 10 pm/V have been demonstrated [78-81]. PC has also been used as the host polymer for DR1 [82]. The

o o glass transition temperature, Tg, of PC is 155 C, compared to 105 C for PMMA. Given the higher Tg, the PC/DR1 system will exhibit greater thermal stability of the polar order

[83]. Less relaxation of the EO coefficient will therefore occur over time compared to systems of PMMA/DR1.

The use of DR1 in this dissertation is for proof-of-concept purposes. It is commercially available and has been well characterized. It has also been used as a standard to measure against the characteristics of other EO chromophores. As indicated in Table 3.1 the EO coefficient of EO polymer systems incorporating the DR1 chromophore is much less than those obtainable with newer systems. The EO chromophores such as CLD and AJL34 were not commercially available at the time of this research. It is expected, however, that future research involving the topics presented in this dissertation will involve the optimization of the EO coefficient through EO polymer material investigations.

3.2. Electro-optic Response

Initially the polymer with incorporated chromophores does not exhibit EO activity. In order to activate the EO effect the orientation of the chromophores must be aligned through the poling process. In this dissertation, the contact poling method is used. At a temperature near Tg, the chromophores are able to move and are aligned by an applied static electric field. The chromophores are then locked in place when the EO

39 polymer is cooled below the Tg while the electric field is applied. The newly oriented chromophores break the centro-symmetry of the polymer and a non-zero EO coefficient is obtained. From the index ellipsoid, the refractive index modulation experienced by an optical field polarized in the y (TM) direction due to a change in the y-polarized field ΔEy is approximately

1 3 ny   2 nc r33Ey . (3.1)

The respective refractive index change for the TE-polarized optical field is

1 3 nx   2 nc r13Ey . (3.2)

It is also common to assume that the coefficient r33 is three times larger than r13 [84].

Thus it is advantageous to perform electric field modulation and sensing using the TM optical polarization. The derivation of Eqs. (3.1) and (3.2) is given in Appendix A.1.

3.3. Ring Resonator Sensor Response

Once the EO polymer has been poled, the refractive index will change according to Eq. (3.1) for TM polarized light. From the resonance condition of Eq. (2.21), a change in effective index of the ring mode incurs a change in resonance wavelength, λr by

d  r  r . (3.3) dneff neff

In EO sensing, nc is modulated by changes in the electric field ΔEy. The effective index change due to the core index change is proportional to the fraction of optical intensity in the waveguide core [85]. Define η as the change in neff for a change in nc:

40 dn   eff . (3.4) dnc

The effective index change is less than the core index change, thus η < 1. Given the ring resonance lineshape slope with respect to wavelength, S, defined as

dT S  , (3.5) dr the change in normalized transmission due to a change in electric field for the EO ring is

3 nc r33r S T  E y . (3.6) 2neff

S is the lineshape slope when the maximum transmission off-resonance is equal to unity.

The change in transmission due to a change in electric field is the detected signal and should be maximized. In order to maximize the change in transmission, S and r33 should therefore be maximized given the available materials and ring waveguide loss. The EO coefficient is optimized through EO material selection and the poling process.

Fig. 3.1. Lineshape slope for a critically coupled resonator with F = 50.

41 The lineshape slope S is maximized by minimizing the ring waveguide loss, ρ, optimizing the coupling parameter |t|, of the bus waveguide and biasing the optical wavelength at the steepest wavelength point of the lineshape slope. Fig. 3.1 depicts the lineshape slope, S as a function of relative ring phase for a critically coupled resonator and F = 50. In order to maximize S for a given ring resonator, the wavelength should be biased at the peaks shown in Fig. 3.1. Note the opposite signs of the local minima and maxima around the resonances.

3.4. Optimization of Single Mode Bus Coupled Resonator for Sensing

The ring waveguide loss depends significantly on the fabrication process and the waveguide materials. Sources of loss in the ring include surface scattering from rough sidewalls, material absorption and bend radiation. Surface scattering usually arises in dry etch processes during fabrication. The bend radiation loss can be kept to a minimum by the design of the bend radius. It is desirable to determine the optimal coupling that maximizes the lineshape slope for a given ring waveguide loss. Numerical and analytical studies of the characteristic equation of Eq. (2.20) can be performed to determine the optimal value of |t| for a given αr. A numerical study has been previously performed to determine the optimal coupling conditions given a ring with fixed loss [86]. However, it is desirable to have analytical approximations to guide the resonator design. The characteristic equation can be manipulated to derive analytical expressions for the slope and optimal coupling. Appendix B.1 details the derivations for the following equations assuming a resonator loss so that αr > 0.8 is obtained. At critical-coupling, the finesse is

42 7 for αr = 0.8. The magnitude of the maximum lineshape slope with respect to ring phase and assuming an off-resonance transmission of unity is derived as

2 2 dT 3 3r | t |1r 1 | t |   3 . (3.7) dr max 81r | t |

To achieve this slope, the wavelength must be biased so that the phase offset from resonance is obtained as

  1 3(1 | t | r ) r,max  2sin   . (3.8)  6 | t | r 

Eq. (3.8) indicates that the location to achieve the magnitude of the maximum slope is found on both sides of the resonance, which occurs at φr = 0. The maximum slope as a function of the coupling parameter κ is shown in Fig. 3.2 for three different round-trip

2 ring power transmissions (αr ).

Fig. 3.2. Numerical and analytical calculations of the magnitude of the maximum lineshape slope as a function of coupling parameter, κ and several ring losses.

43 The slope is calculated from the analytical model of Eq. (3.7) is and compared to numerically calculating the slope directly from Eq. (2.20). The analytical expression fits well with the numerically calculated maximum slope. Note that the slope as a function of the coupling has a peak at a given κ. The location and value of the peak and depends on the round-trip waveguide loss. Thus, the magnitude of the transmission coefficient |t| may be designed to obtain a maximum slope given a fixed ring waveguide loss. The coefficient |t| for maximum lineshape slope is derived as 3  1 | t | r . (3.9)  r  3

The maximum normalized lineshape slope for optimal coupling is derived from Eqs. (3.7) and (3.9). For low-loss rings, the slope can also be written in terms of ρLr:

dT 3r (3r  1)(r  3) 4 3  2  . (3.10) d max 9(1  r ) 9Lr

At this coupling condition, the extinction ratio of the transmission is 9 [86]. Also, |t| > αr from Eq. (3.9) which implies that the resonator is under-coupled with respect to the critically-coupled condition. For comparison, the maximum normalized slope for critical coupling is approximately

dT 3 3 r 3 3  2  . (3.11) d cc,max 8(1 r ) 8Lr

For αr ≈ 1, the slope for optimal coupling is 1.185 times larger than the slope for critical coupling. Fig. 3.3 shows the numerical and analytical maximum lineshape slopes for

2 optimal and critical coupling as a function of round-trip ring power loss, αr .

Fig. 3.3. Maximum lineshape slopes for optimal coupling and critical coupling.

The analytical solutions compare well with the numerical results. As expected, the lineshape slope increases for less loss.

To convert the lineshape slope with respect to ring phase to the lineshape slope with respect to wavelength, S, the slope is multiplied by the derivative dφr/dλ calculated from Eq. (2.21):

dT 2Lrng S  2 . (3.12) d r

From the calculation of Eq. (3.12), S is proportional to the inverse of the ring waveguide loss, ρ, for the optimally coupled resonator and the critically coupled resonator. For low- loss resonators (αr > 0.8), S does not depend on the length of the ring. This is in contrast to MZI sensors, where the response to the electric field is proportional to the length of the

MZI waveguides.

45 3.5. Sensor Arrays

As shown in Section 3.4 the response to an EM field is proportional to the lineshape slope of the resonance for a ring resonator. For a single resonator, the response depends on the optical loss. In ring resonator arrays, the interaction of the resonances in the transmission spectra will tend to lower the slope, thus degrading the sensitivity of the overall array. The number of resonators in an array must therefore be optimized so that a maximum amount of elements are in the array without significantly degrading the lineshape slope of each individual resonance. For arrays of N number of rings, with equally space resonances as depicted in Fig. 2.8 the maximum lineshape slope for rings of F = 50, 25 and 10 is shown in Fig. 3.4. Each curve is normalized to the maximum slope from a single-element array.

Fig. 3.4. Maximum normalized lineshape slope for three different arrays with F = 50, 25 and 10. The slopes are normalized to the maximum slope of a single ring resonator.

46 For F = 50, an array with 40 rings will degrade the response by half of the single-element response. An array with 20 rings degrades the response by half for F = 25. For F = 10, 9 rings reduces the response to half that of the single ring device.

There are several challenges in the fabrication and design of highly arrayed ring resonator sensors. The physical geometry for each resonator must be different so that the ring phase of each ring is unique at a given wavelength. One method to create resonance wavelength spacing in an array is to vary the total ring length of each resonator. In the design, the ring radius of a resonator may be kept constant while a straight section is added between the two halves of the ring to increase the length. From the resonance condition, in order to shift the resonance wavelength by one FSR, the length must be changed by ΔLr = λr/neff. At a wavelength of 1550 nm and neff = 1.5, ΔL = 1 μm. Thus, for two resonators with equally spaced resonances, the ring lengths must be different by

0.5 μm. For 15 resonators, the length of each resonator must be controlled by 0.065 μm to have equally spaced resonances. The waveguide cross-sectional dimensions may also be varied to achieve resonance wavelength separation due to the different effective indices of the rings. For example, assume a ring length of 0.75 mm, PC/DR1 cores and

Cytop cladding. The resonance will shift by one FSR if the height changes by 12 nm as calculated using EIM. Thus tight control of the waveguide dimensions must be maintained during the fabrication process to obtain controlled resonance wavelength spacing.

47 3.6. EO RF Field Sensing

In RF sensing, the output light from the ring resonators is directed into a high- speed photodetector that is connected to an RF receiver such as a spectrum analyzer or vector network analyzer (VNA). A simplified schematic of the RF test set-up is shown in

Fig. 3.5. Given an impedance of Z0 and a peak total optical power off resonance, Popt, the

RF power due to EO modulation is derived using Eq. (3.6) and is

2 GSP n 3 r E  P  opt c 33 y . rf 2 (3.13) 8Z 0 neff

The photoreceiver with conversion gain G is assumed to be composed of a photodetector and a transimpedance amplifier. The optical power is converted into an output voltage so that G is in units of V/W. For the single-mode resonator, the output RF power is proportional to ρ-2. From (3.13), it is also important to maximize the optical power. The maximum optical power is limited by the power damage limits of the components used in the test system.

Fig. 3.5. Simplified schematic of RF-optical test set-up.

(a) (b) Fig. 3.6. (a) Optical power transmission for an optimally coupled ring resonator with finesse of 25. (b) Relative detected RF power at RF receiver for EO sensing.

During sensing, the optical wavelength should be biased on the steepest point of the ring transmission slope to maximize the output RF power. Fig. 3.6(a) shows the relative transmission from an optimally coupled ring resonator with a finesse of 25. The

RF power during EO modulation as a function of ring phase is depicted in Fig. 3.6(b).

The peaks of the RF power correspond to the steepest points on the lineshape slope of the transmission. At resonance, the modulated RF power at the modulating frequency is zero. The phase of the signal may be detected if a VNA is used. The phase of the RF signal on one side of the resonance is 180o out of phase with the other side because of the opposite signs of the slope of the lineshape. A response of the form depicted in Fig.

3.6(b) will only occur for resonance modulation and demonstrates an adequate test to determine if EO modulation occurs in the sensor.

49 3.6.1. RF Bandwidth of Ring Resonator Sensor

The limiting factor in the RF bandwidth of the EO RF sensor is the optical ring resonator response. Responses from EO polymer modulators have been measured into the terahertz regime [79]. The resonant structure acts as a band-pass filter, with a bandwidth that is limited to the FWHM of the optical response. Because sensitivity improves with larger F and QL, larger bandwidth is obtained at the expense of the EO response. The bandwidth (BW) for the ring resonator is approximately given by [37]

BW  c (QLr ) , (3.14) where c is the speed of light. For example, for a ring resonator with QL = 10,000 at a wavelength of 1550 nm, the modulation bandwidth is 19 GHz. The resonator can also be operated at RF frequencies equal to a multiple of the FSR of the resonator [87]. For an

FSR equal to 2 nm, the sensor with QL = 10,000 can also be operated at a center frequency of 250 GHz with a bandwidth of 19 GHz. To mitigate this fundamental bandwidth limitation, multiple cavities have been coupled to achieve higher bandwidths in ring EO modulators [88].

3.6.2. Invasiveness

The presence of an EO sensor will disturb the RF field that is measured. In near- field sensing of devices such as antennas, the perturbation will distort the device operation and the radiation performance will be degraded. The performance of resonant

RF devices such as antennas, filters and resonators may be greatly reduced by materials

50 placed in the reactive near-field [2]. Thus small size, low dielectric constant and components free of metal are required for minimal invasiveness.

For integrated optical devices, the EO polymer waveguide structures are supported by a substrate, typically much larger than the waveguide devices themselves.

The presence of the substrate with a high dielectric constant will perturb the field.

Studies have been performed analyzing the effects of EO probes in an EM field demonstrating the invasiveness caused by high dielectric-constant EO materials such as

GaAs and LiTaO3 [89], [90]. Invasiveness is reduced at the cost of sensor response [2].

In this dissertation, the sensor device is metal-free, the total thickness is 35 µm and is composed of low-dielectric constant polymer materials as shown in Table 1.1.

3.7. Optimization of the Two-Mode Coupled Resonator

In the two-mode-coupled resonator, the additional spatial mode of the bus waveguide creates interference that affects the power coupled into and out of the ring.

The coupling coefficients, input mode powers, and relative phase difference required to give the largest lineshape slope for the two-mode-coupled resonator are determined numerically. Parameters are defined which relate the magnitude of coupling coefficients

2 |κ0r| and |κ1r| and the round trip power loss of the ring, 1 – αr . Let the power coupling

2 2 ratio be defined as Rc ≡ |κ0r| /|κ1r| , and the normalized power coupling sum be defined as

2 2 2 Sc ≡ (|κ0r| + |κ1r| )/(1 – αr ). The parameter Rc relates the magnitudes of the two coupling coefficients. The parameter Sc relates the two coefficients to the power lost in the ring.

The input mode power distribution and input phase difference for a given Rc and Sc are

optimized to obtain the maximum slope of the difference of the two output mode powers,

2 2 denoted by ΔB = |b0| - |b1| . Equations (2.26) and (2.27) are used to calculate ΔB as a function of ring mode phase, φr, using ρ = 6.5 dB/cm and Lr = 1.02 mm.

Fig. 3.7 shows the calculated maximum transmission lineshape slope of ΔB versus

φr for parameters Rc and Sc. The maximum lineshape slope, for the given ring loss and length, is found to be 6.51 rad-1. The shape of the contour lines in Fig. 3.7 demonstrates that the slope is more sensitive to changes in Sc than to changes in Rc. The following

2 conditions must be true to obtain the maximum lineshape slope: (a) Rc = Sc = 1, (b) |a0| =

2 |a1| , and (c) δi = κr1 - κr0 ± mπ/2 for odd m. For comparison, the maximum slope from

2 a single-mode ring resonator, with similar round-trip resonator loss (1 – αr ), optimally coupled to a single-mode bus waveguide is 5.01 rad-1 as calculated from Eq. (3.10).

2 2 Fig. 3.8. Optimized output mode power lineshapes for Rc = Sc = 1, |a0| = |a1| and δi = κr1 - κr0 + π/2 normalized to the total input power.

Fig. 3.9 The difference, ΔB, of the optimized output mode power lineshapes. The maximum slope occurs at resonance where ΔB = 0.

53 The optimized lineshapes of the two output modes and ΔB as a function of ring phase are shown in Fig. 3.8 and Fig. 3.9, respectively. The steepest point is located at resonance where ΔB = 0.

For the conditions of optimal coupling, when only one input mode is excited, the output mode lineshapes are like those depicted in Fig. 2.10. The extinction ratio of the output mode corresponding to the input mode is 6 dB. At resonance, the output mode power that is not excited at the input is equal to the output mode power that is excited at the input.

Under the conditions for optimal coupling, input mode power distribution and relative phase difference, the lineshape slope of the difference of the mode transmissions with respect to phase is

dB  1  r  . (3.15) d 2 L r max (1 r ) r

The derivation is given in Appendix B.2. For αr ≈ 1, the optimized lineshape slope of the two-mode device is 1.3 times larger than the optimized lineshape slope for the all-single- mode device and 1.54 times larger than the single mode critically-coupled resonator device.

Fig. 3.10 shows the numerical and analytical lineshape maximum slopes for optimal coupling, input mode power distribution and relative phase difference as a

2 function of the round-trip power loss, αr . For comparison, the maximum slope for the optimally coupled all-single-mode device is also shown. The analytical solutions compare very well with the numerical results.

Fig. 3.10. Maximum lineshape slopes for the optimally coupled two-mode resonator device and the optimally coupled all-single-mode optimal coupling.

3.8. Chapter Conclusions and Outlook

The results from this chapter are used in the following chapters to design, fabricate and test the ring resonator devices. The goal of this chapter is to derive equations that guide the design of sensitive ring resonator devices. Design equations are derived for optimal coupling between the ring resonator and the single-mode bus waveguide and the two-mode bus waveguide devices. Optimal coupling is achieved when the lineshape slope of the transmission spectra near resonance is maximized given a fixed ring resonator loss.

Fundamentals of EO polymers are introduced in this chapter followed by the theoretical analysis of the ring response due to an applied electric field. The response from an EO single-mode bus coupled resonator is treated first. It is shown that the magnitude of the transmission modulation due to the external field depends on the

55 lineshape slope of the transmission spectra near the resonance wavelengths of the resonator. The lineshape slope depends on the loss of the ring resonator waveguide and the coupling of the bus waveguide mode and ring waveguide mode. The coupling conditions between the bus waveguide and the ring resonator to obtain the largest lineshape slope for a resonator of a fixed loss are determined. This condition is used in the design process of the resonator devices, given in Chapter 4.

Sensor arrays of ring resonators coupled to the same bus waveguide are also discussed. It is found that the number of resonators in an array is limited by the finesse of each resonator. For a large number of array elements, the resonances of each resonator in the transmission spectra are affected by one another which results in the reduction of the lineshape slope.

Finally, a complete expression for the modulated RF power due to EO modulation in the ring resonator is developed. It is shown that the magnitude of the RF EO modulated power as a function of ring phase consists of two peaks at the steepest points of the optical power transmission spectra. A null in the RF power is present at the resonance wavelength. Because the sign of the slopes on either side of the resonance is opposite to the other side, the phase of the RF modulated power changes by 180o from one side of the resonance to the other side. This theoretical result can be used to confirm that resonance wavelength modulation is occurring.

In the next section of this chapter, an optimization of the two-mode bus coupled ring resonator is performed. It is shown that optimal coupling requires

2 2 2 |κ0r| = |κ1r| = 1 - αr  2. To produce the steepest possible lineshape slopes, the input mode power distribution must be equal and the relative phase difference must equal δi = 56 κr1 - κr0 ± mπ/2 for odd m. Asymmetric Fano lineshapes are produced at the output of the device. The slope of the difference of the two mode output power transmissions is

1.3 times larger than the slope from the optimized all-single-mode device given the same ring round-trip waveguide loss. This theoretical analysis is used to guide the design of the two-mode devices in Chapter 4.

CHAPTER 4

DESIGN OF WAVEGUIDE RESONATOR DEVICES

The optical waveguide design of the single-mode bus coupled resonator and the two-mode bus coupled resonator is performed in this chapter. Simulations of the waveguide devices are performed to determine the bend radius of the resonator for minimum loss. Simulations are also performed to determine the waveguide geometries for optimal coupling to obtain maximum lineshape slopes from the two devices.

4.1. Single-Mode Bus Coupled Resonator Design

The design of the EO ring resonator sensor devices requires single-mode operation, minimal bend loss and optimal coupling. The devices are designed for a laser wavelength near 1550 nm. The geometry of the bus and ring waveguides is consistent with the waveguide cross-section depicted in Fig. 2.1. The waveguides consist of cores of PC doped with DR1. The doping concentration of DR1 in PC is 20 weight percent.

The waveguide dimensions are designed to support only the fundamental spatial mode of the quasi-TM polarization. The side and bottom cladding is the fluorinated polymer

Cytop. The devices are supported by 30 µm thick SU-8, an epoxy based photoresist. The refractive indices of these three materials are shown in Table 1.1. 58 For a horizontally infinite slab waveguide consisting of a PC core with air top- cladding and Cytop bottom-cladding, the second order slab mode cut-off height is 1.25

µm as calculated by EIM. Therefore, a waveguide height of 1.0 µm is chosen so that only one spatial mode in the vertical direction can propagate. The effective index of the slab mode is 1.52 calculated by EIM. For a waveguide height of 1.0 µm, the effective indices of the first two modes for the two-dimensional PC/DR1 waveguide as a function of waveguide width are calculated using BPM. From the effective indices shown in Fig.

4.1, the second order quasi-TM mode cut-off width is 1.65 µm.

In order to determine the waveguide width, bend loss calculations are performed because the bend loss also depends on the waveguide width. The bend loss is calculated by using one-dimensional simulated bends using BPM and solving for the slab mode loss for several widths and varying bend radii.

Fig. 4.1. Effective indices for the first two quasi-TM spatial modes of a PC waveguide embedded in Cytop calculated by the effective index method and BPM.

Fig. 4.2. Bend loss for bend radius for three different waveguide widths, w, calculated using BPM and simulated bend method.

Fig. 4.2 shows the results of the calculations for widths w = 1.0 µm, 1.5 µm and 2.0 µm.

Note the bend loss is less for wider waveguides. A bend radius of 85 µm and waveguide width of 1.5 µm is chosen. The calculated loss is 5x10-4 dB/cm. The waveguide is single-mode at this width.

The coupling between the bus waveguide and ring waveguide is simulated using a ring bend radius of 85 µm, waveguide widths of 1.5 µm and a gap width separating the two waveguides of 1.0 µm. Three-dimensional BPM simulations of the coupling section are performed. A ring-racetrack geometry is used in the coupling design. The gap is chosen because it is within the fabrication capabilities of the photolithography system and is small enough so that adequate coupling can be achieved without using exceedingly long coupling lengths. The straight lengths are parallel to the bus waveguide.

Fig. 4.3. Simulation of the ring coupling section to determine ring waveguide loss corresponding to straight coupling length where optimal coupling and critical coupling is obtained.

Fig. 4.3 shows the ring waveguide loss corresponding to straight coupling lengths needed to obtain the optimal coupling condition of Eq. (3.9) and critical coupling.

The ring waveguide loss is expected to be between 5 dB/cm and 15 dB/cm. Two sets of resonators composed of straight coupling lengths of 65 µm and 100 µm are chosen to be fabricated. Optimal coupling is achieved for ring resonator losses of 9 dB/cm and

12 dB/cm for the two lengths respectively.

Linear arrays of two, four, eight and sixteen rings are also constructed in addition to single ring resonators. The resonators in the linear arrays are separated by a distance of 375 µm. The waveguide cross-section at the coupling section of the final design is shown in Fig. 4.4(a). The Cytop thickness of 3.7 µm is chosen so that the optical field will not interact with the SU-8 or the possible deformation in the Cytop caused by the poling process. The fundamental quasi-TM mode electric field profile for the PC/DR1 waveguide is calculated by BPM and is shown in Fig. 4.5. The layout of the ring array is 61 schematically depicted in Fig. 4.4(b). The devices are supported by the 30 µm thick SU-

8 film.

(a) (b) Fig. 4.4. (a) Cross-section of the coupling section of the ring resonator. (b) Layout of the ring array. Two straight coupling lengths of 65 µm and 100 µm are used in unique arrays.

Fig. 4.5. Normalized electric field profile of the fundamental TM mode of the PC/DR1 waveguide calculated by the beam propagation method.

62 4.2. Two-Mode Bus Coupled Resonator Design

The design of the two-mode bus waveguide device requires optimal coupling and

2 2 2 minimal bend loss. Optimal coupling requires |κ0r| = |κ1r| = 1 - αr  2 . The geometry of the bus and ring waveguides is also consistent with the waveguide cross- section depicted in Fig. 2.1. The waveguides consist of cores of PS. The side and bottom cladding is thermally grown SiO2. The substrate is 525 µm thick Si. The refractive indices of these materials are shown in Table 1.2. The waveguide dimensions of the ring are designed to support the fundamental spatial mode of the quasi-TE polarization. The dimensions of the bus waveguide are designed to support the quasi-TE0,0 and quasi-TE1,0 modes. The electric field mode profiles are similar to those shown in Fig. 2.4.

For a slab waveguide consisting of a PS core with air top-cladding and SiO2 bottom-cladding, the second order slab mode cut-off height is 1.65 µm as calculated by

EIM. Therefore, a waveguide height of 1.5 µm is chosen for the ring waveguide and the bus waveguide. The effective index of the slab mode is 1.52. For a waveguide height of

1.5 µm, the effective indices of the first three quasi-TE spatial modes for the two- dimensional PS waveguide as a function of waveguide width are calculated using BPM.

From the effective indices shown in Fig. 4.6, the second order quasi-TM mode cut-off width is 2.0 µm and the cut-off width for TE2,0 is 3.55 µm. A bus waveguide width of

3.0 µm is chosen.

Fig. 4.6. Effective index for PS core embedded in SiO2 for the first three quasi-TE spatial modes calculated by BPM for a 2-D cross-sectional waveguide.

In order to determine the ring waveguide width, bend loss calculations are performed. The bend loss is calculated by using one-dimensional simulated bends using

BPM and solving for the slab mode loss for several widths and varying bend radii. Fig.

4.7 shows the results of the calculations for widths w = 1.5 µm, 2.0 µm and 2.5 µm. At w

= 2.0 µm, the ring waveguide is single-mode. A bend radius of 150 µm and waveguide width of 2.0 µm is chosen. The calculated bend loss is 0.01 dB/cm.

The coupling between the two-mode bus waveguide and ring waveguide is simulated by three-dimensional BPM. A ring-racetrack geometry is also used in the coupling design. From previous work in a similar material system, the ring waveguide loss is expected to be in the range of 6.0 dB/cm to 8.5 dB/cm [49]. For a ring of radius

150 µm with two straight coupling lengths of 50 µm the coupling coefficients for optimal coupling are between |κ0r| = |κ1r| = 0.26 and 0.30 for losses of 6.0 dB/cm and 8.5 dB/cm.

Fig. 4.7. Bend loss calculations using the simulated bend method in a 2-D waveguide. A width of 2 µm and a radius of 150 µm are chosen.

To obtain coupling coefficients between these values, simulations are performed varying the coupling length and gap width between the two waveguides. The simulated mode amplitudes at the output of the two-mode waveguide are required to determine the coupling coefficients. The amplitudes are determined by taking the overlap integral of the output field with the normalized field of the corresponding mode of which the amplitude is to be found. The individual mode fields are normalized so that the power in each is unity.

First, a gap width of 0.5 µm is chosen and the coupling length is varied. The coupling coefficients of the coupling section are determined in the BPM simulations by measuring the output powers in the modes when individual modes are excited at the input. The coupling coefficients |κ0r|, |κ1r|, |κ01| and |κ10| are shown in Fig. 4.8 for straight coupling lengths of 20 µm to 60 µm. From Fig. 4.8 |κ01| ≈ |κ10| for all coupling lengths, as predicted in Chapter 2. 65

Fig. 4.8. Coupling coefficients for a gap width of 0.5 µm and varying the coupling length calculated using three-dimensional BPM.

At a straight coupling length of 42.5 µm, |κ0r| = |κ1r| = 0.34. The equality fulfills the condition Rc = 1 required for optimal coupling. In order to reduce the magnitude of the coupling, the coupling length is fixed at 42.5 µm and the gap is varied in simulation.

As observed from the results of the simulation depicted in Fig. 4.9, the coupling coefficients both decrease for increasing gap width. At a gap width equal to 0.6 µm, |κ0r|

= 0.28 and |κ1r| = 0.29.

The nominal design of the two-mode bus coupled to the single-mode ring resonator is depicted in Fig. 4.10(a). The chosen gap width is 0.6 µm. The two-mode waveguide width is 3.0 µm. The single-mode ring waveguide width is 2.0 µm. The ring device is schematically depicted in Fig. 4.10(b). The coupling length of 40 µm is chosen from the simulation results of the coupling section.

Fig. 4.9. Coupling coefficients for a coupling length of 42.5 µm and varying the gap width calculated using three-dimensional BPM.

Fig. 4.10. (a) Cross-section of the coupling section of the two-mode device. (b) Layout of the two-mode bus waveguide coupled to the single-mode ring.

To illustrate the field coupling inside of the coupling region for the optimized design, the results of three-dimensional BPM simulations are given in Fig. 4.11. Fig.

4.11(a) shows the normalized |Ex| field when only the quasi-TE0,0 mode is excited at the input to the bus waveguide. 67

(a) (b)

Fig. 4.11(a) Normalized amplitude of the electric field at a x-z cross-section inside the waveguide for quasi-TE0,0 mode input. (b) Amplitude of the electric field for only quasi- TE1,0 mode input.

The field values are taken on an x-z plane that passes through the vertical center of the waveguides. The single lobe at the input of the bus waveguide is indicative of fundamental mode propagation. Fig. 4.11(b) shows the results when the quasi-TE1,0 mode is excited at the input to the bus waveguide. The quasi-TE1,0 mode has two lobes in the bus waveguide. At the outputs of both simulations, the field amplitude inside the ring for the two simulations is approximately equal, indicating equal coupling constants.

(a) (b)

Fig. 4.12(a) shows the results of the three-dimensional BPM simulations when the quasi-TE0,0 mode and the quasi-TE1,0 are excited with equal powers at the input of the bus waveguide. The alternating lobes in the bus waveguide are due to the beating pattern formed from the interference of the two modes with different propagation constants. The

max phases of the two inputs are set so that δi = δi is obtained for Fig. 4.12(a). The output amplitude of the field inside the ring is maximized. Fig. 4.12(b) depicts the simulation

min results for equal input amplitudes and with the phases such that δi = δi is obtained.

The two coupling coefficients are approximately equal, so there is nearly complete

69 cancellation of the field inside the ring waveguide and very little power is coupled into the ring.

To mitigate for fabrication errors, several devices with different dimensions are included in the fabrication process. Table 4.1 documents the different dimensions of the resonator devices that are fabricated.

Straight coupling Bus waveguide Ring waveguide Gap Device length width width width 1 30 µm 3.0 µm 2.0 µm 0.6 µm 2 40 µm 3.0 µm 2.0 µm 0.6 µm 3 55 µm 3.0 µm 2.0 µm 0.6 µm 4 30 µm 2.4 µm 1.4 µm 1.2 µm 5 40 µm 2.4 µm 1.4 µm 1.2 µm 6 55 µm 2.4 µm 1.4 µm 1.2 µm Table 4.1. Fabricated two-mode device dimensions.

4.2.1. Mode Generator Design

The mode generator is also designed using three-dimensional BPM. A schematic of the device is shown in Fig. 4.13. The waveguide heights are equal to 1.5 µm. The two-mode waveguide widths and the single-mode coupled “add” waveguide widths are designed so that the effective index of the quasi-TE1,0 mode is equal to the effective index of the fundamental mode of the “add” waveguide. The effective indices are equal for a two-mode waveguide width of 3.5 µm and the “add” waveguide width of 1.4 µm, obtained from Fig. 4.6. A straight coupling waveguide is used to increase the coupling of the modes. A 150 µm-long linearly tapered waveguide connects the input of the two- mode waveguide to the output of a single-mode waveguide of width 2.0 µm.

Fig. 4.13. Mode generator layout and design dimensions. “Input-1” is converted to the quasi-TE0,0 mode and “Input-2” is converted into the quasi-TE1,0 mode.

At the output of the mode generator, a 150 µm-long linearly tapered waveguide is used to connect the two-mode waveguide of the mode generator to the 3.0 µm wide two-mode bus waveguide. The tapered waveguides are long so that no higher order modes are excited. The gap width separating the two-mode waveguide and the “add” waveguide is

1.2 µm. From three-dimensional BPM simulations, the optimal straight coupling length is 170 µm. For this design, the mode conversion loss, from “Input-1” to the quasi-TE0,0 mode is 0.03 dB. The mode conversion loss from “Input-2” to the quasi-TE1,0 mode is

0.3 dB. To mitigate for fabrication errors, mode generators composed of three different coupling lengths of 140 µm, 170 µm, and 200 µm are fabricated. The mode filter located at the output of the two-mode-coupled single-mode resonator has the same dimensions as the generator. The mode filter acts to transfer the power of the two modes of the two- mode waveguide to two separate single mode waveguides.

Fig. 4.14(a)-(c) are the simulation results of the optimized mode generator structure using three-dimensional BPM. The normalized |Ex| field values are taken on an x-z cross-section that passes through the center of the waveguides. In Fig. 4.14 (a), the quasi-TE0,0 mode in the two-mode waveguide is excited at the input. No power is 71 observed to couple into the single-mode add waveguide. In Fig. 4.14 (b), power is input to the add waveguide. This power is coupled into the quasi-TE1,0 mode of the two-mode waveguide. The two parallel lobes at the output of the two-mode waveguide are indicative of the TE1,0 excitation. Very little power is observed at the output of the add waveguide, indicating that most power is coupled out of this waveguide and into the quasi-TE1,0 mode.

(a) (b) (c) Fig. 4.14 (a) Simulations results of the optimized mode generator for only the quasi-TE0,0 mode input, (b) only add waveguide input, and (c) both quasi-TE0,0 and add waveguide input.

72 Fig. 4.14(c) depicts the simulation results for the excitation of the two modes simultaneously with equal amplitudes. The presence of the two modes does not affect the total coupling, noted by the fact that little power is observed at the output of the add waveguide.

4.3. Chapter Conclusions and Outlook

In this chapter, the design process of the single-mode coupled resonator field sensor and the two-mode bus coupled device is illustrated. The design process utilized the ring resonator theory developed in the preceding chapters. A description of the fabrication of these designed devices is detailed in Chapter 5.

For the EO ring sensor, the ring waveguide and bus waveguide are designed to support only the fundamental spatial mode. This design is performed using EIM and

BPM simulations. A ring radius of 85 µm is used. The optical power loss due to the bend radius is simulated to be less than 10-3 dB/cm. Two sets of resonators composed of straight coupling lengths of 65 µm and 100 µm are chosen to be fabricated so that near- optimal coupling may be achieved for a range of ring waveguide losses. Arrays of 2, 4, 8 and 16 resonators coupled to the same bus waveguide are also designed.

The design process of the two-mode bus coupled resonator is also detailed in this chapter. Using BPM simulations, the bus waveguide dimensions are designed to support only the quasi-TE0,0 and quasi-TE1,0 modes. The ring waveguide is designed to support only the fundamental mode. The ring radius is designed to be 150 µm so that a simulated bend loss of 0.01 dB/cm is achieved, according to simulations. The coupling region is

73 2 2 2 designed so that the condition |κ0r| = |κ1r| = 1 - αr  2 is approximately achieved for

αr = 0.92. The mode generator and mode filter devices are also designed with the aid of

BPM simulations.

CHAPTER 5

FABRICATION PROCESSES AND POLING

This chapter illustrates the fabrication processes used to construct the ring resonator EO sensor and the two-mode bus coupled sensor. The poling process of the EO sensor is also illustrated in this chapter. Relationships developed from Chapter 3 are used to design the waveguide dimensions and layout of the devices as documented in Chapter

The fabrication process of the EO ring resonator is designed to fulfill two requirements: (1) perform vertical field poling with electrodes as close as possible to the waveguides and (2) fabricate a completely metal-free device. As demonstrated in this chapter, these two requirements are met.

5.1. Single-Mode Bus Coupled Resonator for RF Sensing

The fabrication process for the single-mode bus coupled resonators is designed so that vertical poling of the fabricated waveguides may take place and so that the metal-free waveguide devices may be released from the substrate. The process is shown schematically in Fig. 5.1. The process begins with the thermal growth of a 4 μm thick

SiO2 layer on 100 mm diameter single crystal <100> silicon wafers. 75

Fig. 5.1. (a)-(h). Fabrication process steps for the EO ring resonator sensors.

Next 100 nm of chromium (Cr) is deposited by electron-beam evaporation on the wafer.

The deposition rate is 0.15 nm/s at a pressure of 4 µTorr. The Cr serves as a bottom poling electrode. Next, lift-off resist, LOR 5A, from MicroChem is spin-coated on the wafer to obtain an LOR thickness of 1.6 µm. The thickness is obtained by performing spin-coating of the LOR 5A three times. The first layer is spun at a spin speed of 1,200 rotations per minute (rpm) and is held for 30 seconds. The wafer is then baked on hotplate at 275 oC for five minutes. Another LOR 5A layer is spin-coated on top of the previous layer using the same parameters as the first coating. The wafer is again baked at

275 oC for five minutes. A third layer of LOR 5A is spun at 2,000 rpm. The wafer is baked at 275 oC for 30 minutes. A total thickness of 1.6 µm is obtained as measured by a

NanoSpec spectroscopic reflectometry film thickness measurement tool. Next, a layer of the lift-off resist LOR 2A is spin-coated at 3,000 rpm for 30 seconds. The wafer is then

76 baked at 135 oC for two minutes on a hotplate. The thickness of the LOR 2A layer is 180 nm. A film of positive-tone photoresist, Shipley S1813, is spin-coated at 6,000 rpm for thirty seconds on top of the LOR 2A layer. The wafer is baked at 115 oC for 1 minute on a hotplate. The thickness of the photoresist is 1.0 µm.

The wafer is exposed to ultraviolet (UV) light for 2.4 seconds under vacuum and in hard contact with the device photomask. The photomask is a 5 inch square quartz plate with Cr features. Cr is present on the photomask in locations where the waveguides will be later in the fabrication process. The intensity of the UV light is 15 mW/cm2. The patterns are developed in Shipley Microposit MF-319 developer for 45 seconds. This development process removes the exposed S1813 and etches the LOR 2A to leave the unexposed S1813 with an undercut. The lift-off resists LOR 2A and LOR 5A are etched in the MF-319. The dissolution rate depends on the baking temperature and baking time after spin-coating the films. The LOR 5A layer is not etched by the MF-319 developer because it is baked at a higher temperature and longer time. Profiles suitable for lift-off are now on top of the LOR 5A film. A cross-section of the PR is shown in the scanning electron microscope (SEM) image of Fig. 5.2. A 50 nm layer of electron-beam evaporated SiO2 is deposited at a rate of 0.15 nm/s and a pressure of 4 µTorr. The cross- section at this step is schematically shown in Fig. 5.1(a). The S1813 is lifted-off by placing the sample in acetone in an ultra-sonic cleaner for 15 seconds.

Fig. 5.2 Cross-section of the developed PR showing the undercut obtained by the use of the LOR 2A layer.

After the acetone lift-off, the samples are cleaned in 2-proponal baths. Openings in the

SiO2 on top of the LOR 5A are present where waveguides will be located in subsequent fabrication steps.

Channels in the LOR 5A film are etched by inductively coupled plasma ething- reactive ion etching (ICP-RIE) using the patterned SiO2 as a hard mask. A Plasma-

Therm ICP-RIE tool is used for the channel etching. Small samples cleaved from the wafer are supported by a 100 mm diameter silicon carrier wafer in the etching chamber.

Helium back-side cooling is used. The RIE power is 100 W. The ICP power is 250 W.

The chamber pressure is 5 mT. Oxygen gas at a flow rate of 20 sccm is used. The D.C. voltage that develops across the RIE electrodes during the etch process is 320 V. Etching is performed in 30 second steps with the ICP-RIE power applied, with subsequent 45 second cooling steps with no power applied. Samples are etched for a total time of 4.5 minutes. The exposed LOR 5A is etched to the Cr electrode. The cross-section after the etch process is depicted in Fig. 5.1(b).

(a) (b)

Fig. 5.3. (a) Cross-section SEM image of the etched channels in the LOR 5A. (b) Perspective SEM image etched channels at the coupling region of the resonator.

The sample is placed in 10:1 hydrofluoric acid (HF, buffered oxide etchant) for 45 seconds to remove the SiO2 hard mask. An SEM cross-section image of the etched channel is shown in Fig. 5.3(a). A perspective view of two etched channels in the LOR is shown in the SEM image of Fig. 5.3(b). Next, diluted LOR 2A (50% in cyclopentanone) is spin-coated on the sample at 1,500 rpm for 45 seconds. The sample is baked at 170 oC for 3 minutes on a hotplate. This step is performed to partially fill the vertical ridges in the channel sidewall, which will reduce sidewall scattering in the final waveguides. After spin-coating the diluted LOR 2A, a thin layer of LOR 2A is left on the bottom of the channels. The sample is then etched for 15 seconds using the same ICP-RIE recipe for channel etching to remove this layer. Next, the PC/DR1 solution is spin-coated on the sample at 1,200 rpm for 1 minute. The solution consists of PC and DR1 dissolved in cyclopentanone. To create the solution, PC pellets are dissolved in cyclopentanone at 10 weight percent. After the PC is completely dissolved, DR1 is added to the solution. The amount of DR1 is 20 weight percent of the total solid content in the solution. After the 79 PC and DR1 have dissolved, the solution is filtered using a 0.20 µm nylon membrane syringe filter. After spin-coating the PC/DR1 solution, the sample is baked at 140 oC for

5 minutes on a hotplate. The PC/DR1 film fills the channels and a layer is left on top of the LOR 5A.

The sample is next etched in the ICP-RIE tool to remove the top slab of PC/DR1 and expose the LOR 5A. The recipe is the same as the channel etching recipe. The total power-on time for etching is 2 minutes. The LOR 5A is exposed after the etch process.

The cross-section at this step is depicted in Fig. 5.1(c). The sample is then placed in an

MF-319 bath for 15 minutes to remove the LOR 5A. PC/DR1 ridges on top of the Cr electrode remain. An SEM image of ridges of PC/DR1 near the coupling section of the resonator device is shown in Fig. 5.4.

Next, the Cytop is spin-coated twice on the sample at 3,000 rpm for 30 seconds.

Fig. 5.4 SEM image of ridges of PC/DR1 near the coupling section of the resonator device, after the LOR removal step.

80 After each of the two spin-coat steps, the sample is baked at 60 oC for 5 minutes and 100 oC for 5 minutes. The thickness of the Cytop is 3.7 µm as measured using the profilometer. The cross-section at this step is shown in Fig. 5.1(d). The sample is next etched for 3 seconds in an RIE tool (Technics 800-II) at a power of 100 W, a chamber pressure of 100 mT and an oxygen gas flow rate of 10 sccm. The etch process promotes adhesion of materials to the Cytop surface. The top poling electrode is next deposited by electron-beam evaporation of 250 nm aluminum (Al) at a deposition rate of 0.15 nm/s and a pressure of 4 µTorr. The sample is placed under a shadow mask that defines the top electrode patterns during the evaporation step. The dimensions of the top electrodes are approximately 1 cm x 0.5 cm.

The sample is then poled by applying a voltage between the two poling electrodes as shown schematically in Fig. 5.1(e) and is documented in the next section. After poling, the Al electrode is removed by placing the sample in an MF-319 bath for 30 minutes. SU-8 2025 is spin-coated on top of the Cytop at 3,500 rpm for 2 minutes. The sample is baked at 60 oC for 4 minutes on a hotplate. The sample is then exposed to UV light with the device mask for 50 seconds. This photolithography step defines the size and shape of the SU-8 substrate. A post-exposure bake process is performed at 60 oC for

4 minutes. The SU-8 is developed in an SU-8 developer bath for 5 minutes. The thickness of the patterned SU-8 is 30 µm. This step is depicted in Fig. 5.1(f). Next, the sample is etched in the RIE tool. The SU-8 is used as an etch mask during the dry etch of

Cytop and PC/DR1 waveguides. The sample is etched for 15 minutes at a power of 100

W, 100 mT pressure and an oxygen flow-rate of 10 sccm. The cross-section at this step is depicted in Fig. 5.1(g).

Fig. 5.5. Photomicrograph of several linear arrays of ring-racetrack resonators. The straight coupling length of the resonators is 65 µm.

The waveguide in- and out-coupling facets are defined at this etch step. The resonator devices of the unreleased films are shown in the photomicrograph of Fig. 5.5. The image depicts a single element device, a two element array, a four element array, and the first six elements of the eight element array.

Fig. 5.6. Photomicrograph of single ring-racetrack resonator. The straight coupling length is 65 µm.

Fig. 5.7. Photomicrograph of the edge of released SU-8 film with PC/DR1 waveguides.

The straight coupling lengths shown in the image are 65 µm long. A single ring- racetrack resonator is shown in Fig. 5.6. Finally, the etched sample is released from the

Si substrate in a 49% HF acid bath for 15 minutes. The device at this step is depicted in the schematic of Fig. 5.1(h). The coupling end-facet of a PC/DR1 waveguide on a released SU-8 substrate is shown in the photomicrograph of Fig. 5.7. Tapered optical fibers are brought into close proximity to the end facet in order to in- and out-couple laser light from the devices. A photograph of three released samples of different sizes is shown in Fig. 5.8. The size of a single device is also depicted in the figure. The released devices are flexible and transparent to visible light.

Fig. 5.8. Three released SU-8 samples with PC/DR1 waveguide devices.

5.2. Poling Process

Poling takes place by applying a high voltage between the Cr and Al electrodes on a heated sample at step (e) shown in Fig. 5.1. The sample is placed on a hotplate at room temperature. Connection between the electrodes and a Keithley 2400 SourceMeter voltage source is made using Suss MicroTec probe-heads. A photograph of a sample placed on the hotplate with poling probes is shown in Fig. 5.9. The silver reflective area on the sample is the top Al electrode. The probe tips are rounded by applying solder to the ends of wire tips. It is found that using rounded probe tips reduced the likely-hood of electric breakdown occurring at the probe tip connection points to the electrodes. The

Keithley 2400 and hotplate are connected to a data acquisition computer to record the voltage, current and hotplate temperature during the poling process.

Fig. 5.9. Sample to be poled on the hotplate with poling probes in contact with the two electrodes.

The resistance between the electrodes is tested to ensure they are not shorted together before the poling process. Defects in the Cytop and PC/DR1 film may create a connection between the two electrodes. It is not possible to pole a sample if there is a short connection between the electrodes. The contact poling method discussed in

Appendix A.2 is followed for the poling of the PC/DR1 devices. Fig. 5.10 shows the current and temperature as a function of time for the poling of PC/DR1 waveguides and

3.7 µm thick Cytop. The voltage is held constant at 200 V from 0 to 30 minutes. The magnitude of the electric field inside the waveguide when the voltage is first applied is 31

MV/m. The measured current is zero when the voltage is initially set to 200 V. The electrical current increases with temperature and continues to increase when the temperature is constant at 150 oC. The hotplate is cooled after five minutes at 150 oC.

The current also decreases as the temperature decreases. The temperature dependence of the resistivities of the materials in the stack is one probable cause of the temperature- dependent current flow. The voltage source is disconnected from the sample once the 85 sample has cooled to room temperature. Spikes in the current indicate when dielectric breakdown occurs on the sample. Breakdown has been found to occur mostly at the edges of the Al electrode. A permanent short develops due to the electric breakdown in some cases and it is no longer possible to pole the sample. Fig. 5.10 shows a full poling process without permanent shorts occurring.

It is found that the when the Al electrode is placed directly on the PC/DR1 waveguide the PC/DR1 will deform and flow against the Al electrode. The optical loss will be very large for the distorted PC/DR1 and reduce the sensing capability of the ring resonators. The thick layer of Cytop is used to prevent the waveguides from distorting.

It is also important that the Tg of Cytop is less than the Tg of the PC/DR1 waveguides. It has been found that when the PC/DR1 flows at a lower temperature than the over-layer material, small cavities in the PC/DR1 develop which also increases the waveguide loss.

No cavities in the waveguide developed when using the Cytop film.

Fig. 5.10. The measured current and hotplate temperature during the poling process as a function of time for a constant voltage of 200 V.

Fig. 5.11. Ring resonator after poling the top Al electrode has been removed. The waveguides show no deformation, while the Cytop layer has become distorted due to flow.

Fig. 5.11 shows a resonator after poling has taken place and the Al electrode has been removed. The PC/DR1 shows no deformation. The Cytop deformed as indicated by the darker areas around the coupling section. This deformation occurred because the

o temperature increased above the Tg of Cytop (108 C). The Cytop flowed against the more rigid Al electrode. The thickness of the Cytop is designed so that the optical field does not interact with the top surface of the Cytop. Thus the optical field will not experience excess loss from the Cytop deformation.

In parallel with the fabrication of the ring resonator devices, poled films of

PC/DR1 are also tested in a commonly used ellipsometric configuration [91] detailed in

Appendix C. A 1.3 µm PC/DR1 thick layer is poled at 155 oC by a field of 77 MV/m for

8 minutes. An EO coefficient equal to 1.7 pm/V is measured using the ellipsometric technique. It is also determined that after poling, applying heat to the sample degrades the EO coefficient. Directly after poling, a sample is heated at 65 oC for 15 minutes without a static electric field applied. The EO coefficient is reduced by 66% after the

87 heating as measured by the ellipsometric technique. Using this technique, poling is confirmed to take place.

5.3. Fabrication of the Two-Mode Bus Coupled Resonator

The fabrication process for the PS two-mode bus waveguide device is similar to the poled PC devices and is depicted in Fig. 5.12(a)-(d). The process begins with the thermal growth of a 4 µm thick SiO2 layer on 100 mm diameter single crystal silicon wafers. Lift-off resist from MicroChem (LOR 2A) is spin-coated on the wafers at a speed of 3,000 rpm for 45 seconds. The wafers are baked on a hotplate at 135 oC for 2 minutes. Shipley S1813 is spin-coated on the LOR layer at 4,000 rpm for 30 seconds.

The wafers are subsequently baked at 115 oC for 1 minute on a hotplate.

Fig. 5.12. (a) – (d) Fabrication process for the two-mode-coupled ring resonator devices.

88 The sample is next exposed to UV light for 2.4 seconds with the device photomask under vacuum and in hard contact. The intensity of the UV light is 15 mW/cm2. The patterns are developed in MF-319 developer for 1 minute. The exposed areas of the PR are removed during the development. This development etched the LOR to leave the S1813 with an undercut to facilitate a metal lift-off. A 20 nm thick nickel

(Ni) film is deposited onto the patterned resist and SiO2 surface by electron-beam evaporation with a 5 nm thick adhesion layer of titanium (Ti). The deposition pressure is

5 µTorr. The deposition rate for both metals is 0.1 nm/s. The cross-section at this step is depicted in Fig. 5.12(a). The metal on the resist is subsequently lifted off in a N-

Methylpyrrolidone solvent bath and cleaned in acetone and 2-proponal baths. The wafers with the metal patterns are cleaved into four equal sized samples and baked at 300 oC for

10 minutes on a hotplate, improving adhesion of the metal to the substrate. Channels are anisotropically etched in a Lam 490 plasma etcher system using the Ti/Ni film as a hard mask. A gas flow of 100 sccm SF6 and 30 sccm He is used. The RF power is 500 W at a pressure of 375 mTorr. The etch rate of the SiO2 is 3.5 nm/s. Fig. 5.13(a) is an SEM image of an etched channel in SiO2. The cross-section after the etch step is schematically shown in Fig. 5.12(b). The etched samples are next cleaned in a 3:1 mixture of concentrated sulfuric acid (H2SO4) and hydrogen peroxide (H2O2) for 30 minutes at 120 oC. The cleaning step also removes the Ti and Ni metal films. LOR-2A is then spin- coated on the etched channels at 6,000 rpm for 30 seconds and baked at 180 oC for 30 minutes on a hotplate. The thickness of the LOR in the planar areas of the SiO2 is 80 nm.

Fig. 5.13. (a) Etched channel in the SiO2. (b) Cross-section of PS filled channel.

Next a solution of PS in cyclopentanone (20 wt%) is spin coated on the samples at

1,500 rpm for 1 minute and baked at 160 oC for 30 minutes. Before spin-coating, the solution is filtered through a 0.20 µm nylon membrane syringe filter. It is found that the

LOR-2A layer beneath the PS changes the properties of the spin-coated PS so that the top of the PS film above the waveguides is planar after baking. Without the thin LOR layer, the surface of the PS is nonplanar above the etched SiO2 channels. The thickness of the

PS above the unetched SiO2 is 1.5 μm. The result of this step is depicted in Fig. 5.12(c).

The thick PS slab is next etched in the Plasma-Therm ICP-RIE etching tool. The RIE voltage is 75 V. The ICP power is 300 W. O2 and CHF3 gasses are used at flow rates of

20 sccm and 5 sccm respectively. The chamber pressure is 5 mTorr. The etch rate of the

PS is 4.8 nm/s. The samples are then cleaved at the input waveguides side and output waveguides side of the devices to provide suitable fiber-coupling facets. The final step is depicted in Fig. 5.12(d). An SEM micrograph of the PS waveguide with a thin slab left on top of the waveguide is shown in Fig. 5.13(b).

90 5.4. Chapter Conclusions and Outlook

In this chapter, the fabrication process for the EO single-mode bus couple ring resonator sensor is given. The poling process is also described. Poled ring resonator devices are constructed on a silicon substrate. The ring waveguide devices with a Cytop cladding and an SU-8 coating are released from the substrate. The final device is completely metal free and is constructed of polymers with dielectric constant values less than 4. The next chapter details the experimental results obtained from these fabricated devices. EO field sensing is demonstrated and the device is shown to minimally perturb the electric field emanating from the tested microstrip RF circuit.

The fabrication details for the two-mode bus coupled resonators are also discussed in this chapter. The devices are successfully fabricated in the PS and SiO2 material system. In Chapter 7, the experimental results obtained from the fabricated devices are given.

CHAPTER 6

EO SENSOR EXPERIMENTAL RESULTS

In this chapter, RF field sensing using the EO ring resonator sensors is demonstrated. The laboratory configuration is first discussed. The ring resonator devices on SU-8 substrate are tested on an RF microstrip resonator circuit. The VNA supplies the

RF power and detects the modulated power from the ring resonators. Simulations of the

RF circuit are performed to determine the electric field magnitude above the circuit where the sensor device is placed. Characterization of a multi-resonator array is performed.

6.1. Laboratory Configuration for EO Sensing

The set-up for EO field sensing is shown in Fig. 6.1. The VNA (Anritsu

37247D) is used to supply RF power to an RF microstrip circuit. The RF power is amplified by a 30 dB 2 GHz – 8 GHz amplifier (Minicircuits ZVE-8G) connected to port

1 of the VNA. When less RF power is required, the amplifier is removed from the system. The VNA is calibrated using a 50 Ω load, short and open standard terminations.

A one-path, two-port calibration is performed and corrects for four forward-direction error terms. 92 Light from a near-infrared (IR) continuous wave (CW) tunable laser (Agilent

81682A) is amplified by an erbium-doped fiber amplifier (EDFA, MPB EFA-P21F). The output light is guided by Corning SMF-28 single-mode optical fiber and is coupled into the waveguide devices. Input and output optical fibers are tapered in order to improve the coupling efficiency between the fiber and the waveguides. The input and output fibers are tapered to a diameter of 2.0 µm by a wet chemical etch [92]. The fibers are butt-coupled against the waveguide facets during measurements. Butt-coupling is required to stabilize the input and output laser power coupling during the EO measurements.

The polarization of the input light is set by an in-line fiber polarization controller.

Fig. 6.1. Schematic for the testing configuration of the resonator array on the RF circuit.

93 Before coupling light into the waveguide devices, the polarization of the input light is set by focusing the output light from the tapered fiber through a bulk-optical linear polarizer and into a photodetector. The polarizer is set so that only vertically polarized (TM) light will pass through to the photodetector. The fiber polarization controller is then adjusted so that a maximum transmission through the polarizer is obtained. Once the polarization is configured, the optical ring resonator devices on the SU-8 substrate are fixed on top of the RF circuit with small pieces of polyimide adhesive tape.

A 20 dB fused fiber coupler is used to direct 99% of the output light from the ring resonators to the high speed photoreceiver (New Focus Model 1544) that has a conversion gain of G = 900 V/W. The RF output of the photoreceiver is connected to port 2 of the VNA. The second output of the fiber coupler directs 1% of the input optical power into a slow-speed photodetector. The detector is used to monitor the optical power transmission through the resonator devices. A computer is used to control the laser and

VNA and is used to collect amplitude and phase transmission data from the VNA.

During the VNA testing of the EO response, the RF power transmission is measured by recording the magnitude and phase of S21. The VNA can be set to CW mode, where RF power at a single frequency is output at port 1 and is detected at port 2. The RF frequency of the VNA can also be swept to measure the RF transmission spectra of S21.

Because the magnitude of S21 is the relative power transmission from port 1 to port 2, the measured S21 is proportional to the quantity calculated from Eq. (3.13):

(6.1) | S21 |dB  Prf ,dB  PVNA,dB. where PVNA is the power output from the VNA at port 1 and Prf is the RF power due to

EO modulation from Eq. (3.13). This modulated power is due to the RF power output 94 from the VNA and any amplification input to the microstrip resonator. Given Eq. (3.13), the knowledge of the ring parameters and r33, the electric field inside of the resonator may be calculated from Eq. (6.1). The phase of S21 is a measure of the phase of the electric field modulating the ring resonator refractive index with respect to the output RF phase of the VNA.

6.2. Microstrip Resonator

A microstrip resonator circuit is used to characterize the EO sensing capability of the optical devices at RF frequencies. A photograph of the circuit is shown in Fig. 6.2.

The resonator is a one port device and consists of a 50 Ω input line coupled to a second

50 Ω microstrip line that is 55 mm long. The width of the microstrip line connected to the input connector is 3.2 mm. The gap separating the two lines is 0.5 mm. The circuit is connectorized with an SMA female microstrip-to-coaxial transition connector. The circuit is constructed on a Rogers Duroid 5880 substrate that is 1.143 mm thick and has a copper ground plane. The dielectric constant of the substrate is 2.2. The S parameters of the RF resonator are measured using the VNA.

Fig. 6.2 Photograph of the RF microstrip resonator used for EO testing.

95 Fig. 6.3 shows the measured magnitude of the return loss. The first resonance of the device occurs at 1.94 GHz. The second resonance occurs at 3.90 GHz. Note that the return loss is minimum at the second resonance. Thus most of the RF power output from the VNA is being delivered to the resonator at this frequency. The electric field magnitude on the RF coupled line will be largest at this second resonance, thus sensing will be performed at 3.90 GHz.

A photograph of the RF resonator with the EO sensor sample and input and output fiber is shown in Fig. 6.4(a). The tapered optical fibers are brought over the RF resonator and moved into position with manual x-y-z translation stages. A detailed photograph of the EO sensor on the microstrip circuit is shown in Fig. 6.4(b). The sample is 6 mm long,

1.2 mm wide and 35 µm thick. It is positioned on the edge of the coupled microstrip line, where the electric field is expected to be largest at the resonance frequencies.

Fig. 6.3. Measured magnitude of S11 of the RF resonator.

(a) (b) Fig. 6.4 (a) Photograph of the EO sensor on the RF microstrip resonator showing the input and output fibers. (b) Detail photograph of the SU-8 substrate with EO ring resonators on RF resonator.

The photomicrograph of Fig. 6.5 shows the ring resonators directly above the microstrip line outlined in red. Note that the SU-8, outlined in white, is transparent to visible light, which allows accurate positioning of the ring resonators over the RF devices. The device depicted has four arrays of four resonators each. The ring resonators labeled RA, RB, RC and RD have straight coupling lengths of 100 µm and are 1.3 mm away from the edge of the coupled line.

The RF resonator structure is simulated using HFSS (ANSYS, Inc.), a finite- element method software package in order to determine the magnitude of the vertical electric field, Ey, above the circuit. The simulated S11 as a function of frequency is shown in Fig. 6.6. The similarities between the measured and simulated S11 show that the simulation accurately models the RF resonator.

Fig. 6.5. Photomicrograph of the ring arrays on top of the RF resonator. The microstrip lines are outlined in red. The SU-8 sample is outlined in white.

Fig. 6.6. Simulated magnitude of S11 of the RF resonator.

A contour plot of |Ey| at the first resonance frequency of 1.94 GHz is shown in

Fig. 6.7(a) at 35 µm above the circuit. The plot is normalized to the maximum field. A contour plot of |Ey| at the first resonance frequency of 3.90 GHz is shown in Fig. 6.7(b) at

35 µm above the circuit. The plot is also normalized to the maximum field. The sensor

98 device is not included in the simulation because it is assumed that the perturbation to the electric field is insignificant. The maximum fields are located at the ends of the coupled lines at both frequencies. At the first resonance, a single null occurs in the center of the coupled line and the electric field is at maximum at the ends. In Fig. 6.7(b), there are two nulls in the electric field and the field is maximum on the ends and in the center of the coupled line. The largest field for the second resonance is located on the coupled line nearest to the input of the microstrip line.

The simulated electrical field values at the second resonance are numerically averaged over a path of the same geometry as the fabricated ring resonator to determine the average electric field experienced by a ring.

99 Assuming insignificant perturbation of the electric fields by the sensor, the vertical RF

field in the polymer material is E y, p  E y / r, p where Ey is the field in the absence of dielectric material. Simulations of the microstrip resonator at 3.90 GHz are performed with and without a slab of material located on top of the microstrip line near the point of the largest electric field as exemplified in Fig. 6.7(b). The small dielectric slab simulates

50 µm thick SU-8 with PC/DR1 where εr = 3. The magnitude of Ey is shown in Fig. 6.8 as a function of vertical distance from the top of the microstrip line. As expected, the electric field magnitude inside the SU-8 is approximately 3 times less than the field in the same location in the absence of the slab. The data is normalized to the maximum field value from the simulation without the slab.

Fig. 6.9 shows the mean electric field |Ey| inside of the ring for different positions

Fig. 6.8. Simulations of the microstrip resonator at 3.90 GHz with and without an SU-8 slab.

100

Fig. 6.9. Mean vertical electric field in ring resonator across microstrip. The locations and fields in each ring of the four-ring array are shown.

Fig. 6.10. Phase of vertical electric field in ring resonator across microstrip. The locations and phases of each ring of the four-ring array are shown.

101 on the coupled microstrip line for an RF input power of 1 W. The distance from the edge of the coupled microstrip line is 1.3 mm, similar to the actual location of the rings RA,

RB, RC and RD. |Ey| is largest near the edges of the microstrip line near 0 mm and 3 mm. The fields experienced in each ring labeled in Fig. 6.5 are also shown. Fig. 6.10 shows the phase of Ey inside of the ring for different positions on the coupled microstrip line. The phases of Ey for the rings labeled in Fig. 6.5 are also shown.

The perturbation of the S parameters of the microwave circuit by the sensor is a measure of the invasiveness of the sensor. Using the VNA, the magnitude of the return loss near the second resonance frequency of the RF circuit is measured and is shown in

Fig. 6.11. In air, the minimum return loss of the second resonance at 3.9 GHz is -8.2 dB.

The resonance shifts by -2.8 MHz when the SU-8 sample is placed on the end of the coupled line.

Fig. 6.11. Measured S11 frequency response for the RF microstrip resonator in air, with optical devices on the SU-8 substrate and with a silicon sample of similar size to the SU- 8 sample.

102 The minimum S11 of the resonance is now -7.5 dB. For comparison, a 0.5 mm thick silicon sample of similar area to the SU-8 sample is placed at the same location as the

SU-8 sample. The second resonance frequency shifts by -113 MHz. The minimum S11 of the resonance is -1.7 dB. The corresponding resonance frequency shifts indicate that

EO sensors based the SU-8 substrate are much less invasive than those based on higher dielectric constant materials such as silicon.

6.3. Noise

There are two major sources of unwanted signals in the EO characterization system. RF power that is radiated from the circuit may be coupled through the photoreceiver. This signal can be attenuated by surrounding the photoreceiver with RF absorber material. It has also been reported that the laser source can be directly modulated by a nearby RF radiating source [19]. To eliminate this unwanted noise signal, the investigators separated the RF device under test and the laser by 50 meters using long optical fibers. In this work, an isolation system is constructed to attenuate the noise signals.

The noise signal due to direct laser modulation by the RF circuit is investigated in the laboratory. The tests are performed to determine the noise level at different optical output powers. In this work, the VNA and laser are shielded with metal plates and RF absorber material. The experiments performed represent the EO test configuration.

However, the ring resonators are bypassed by connecting the output fiber of the EDFA directly to the photoreceiver. Thus only the RF power received due to the laser

103 modulation is measured. The 30 dB RF amplifier is used in this test and the VNA output is set to 0 dBm so that the total power to the RF resonator is 30 dBm. The laser output is varied and the magnitude of S21 is measured at the second resonance frequency of 3.9

GHz.

Fig. 6.12 shows the measured magnitude of S21 for optical powers from -9 dBm to

0 dBm at the photoreceiver. The measurements are performed with and without the isolation system in place. The intermediate frequency (IF) bandwidth of the VNA is set to 10 Hz and 50 averages per data point are performed. At a laser power of 0 dBm, the measured S21 is -85 dB without isolation. With isolation in place, the measured S21 is -94 dB. The measured data is fitted to best-fit lines using linear regression. The slopes of the best fit lines are 2.1 dB/dB and 2.2 dB/dB for the measurements with and without the isolation system respectively.

Fig. 6.12. Measurement of S21 magnitude noise level with laser directly connected to photodetector.

104 The measured slopes indicate that the RF modulated power is nearly proportional to the square of the optical power. When the 30 dB RF amplifier is removed from the system the measured RF power decreases by 30 dB for both cases.

The minimum noise level in the receiver system with no laser power and no RF power is determined by the fundamental limitations of the receiver equipment. Two significant noise sources in the RF photonics system are shot noise and thermal noise.

The thermal noise power at temperature T is given by PRF,T = kBT for a 1 Hz minimum system bandwidth where kB is Boltzmann’s constant. It is due to thermal vibrations of charges in resistive elements in the receiver electronics. Thermal noise is considered to be white noise. At room temperature, the noise limit at a system bandwidth of 1 Hz is -

174 dBm. At 3 Hz it is -169 dBm, at 10 Hz it is -164 dBm.

The noise due to the high speed photoreceiver is characterized by its noise- equivalent power (NEP). The NEP is defined as the equivalent laser optical power that gives a signal-to-noise ratio (SNR) of unity per Hz0.5 at the output of the detector. The

NEP is due to a combination of shot noise and thermal noise in the photoreceiver and is considered to be white noise. Therefore, the NEP also depends on the minimum RF

2 system bandwidth. The RF noise due to the NEP is given as PRF ,NEP  (NEP G) (2Z 0 ) at 1 Hz bandwidth. The specified NEP of the photoreceiver is 33 pW Hz-1/2. For a bandwidth of 3 Hz, the RF noise power is -136 dBm. At 10 Hz, the RF noise power is -

130 dBm. Fig. 6.13 shows the noise RF power measured with a spectrum analyzer at a center frequency of 3.90 GHz and a resolution bandwidth of 3 Hz.

105

Fig. 6.13. Noise levels measured with spectrum analyzer at 3 Hz bandwidth.

The photoreceiver is connected directly to the spectrum analyzer. The laser and RF sources are off. The measured noise with the photoreceiver on is between -148 dBm and

-136 dBm. This level is considered the minimum possible noise level of the RF system and corresponds with the predicted noise level due to the NEP.

6.4. Ring Resonator Optical Transmission Measurements

The transmission spectra of three different ring-racetrack resonator arrays on the released SU-8 substrate are first measured so that the ring waveguide loss can be determined. For each ring the straight coupling length is equal to 100 µm. Thus the total ring length is Lr = 734 µm. The dimensions of each ring are nominally the same. Fig.

6.14 shows the normalized transmission spectrum for a single ring-racetrack resonator.

106

Fig. 6.14. Normalized transmission spectra for a single ring-racetrack resonator.

The FWHM of the lineshape is 0.12 nm, or 15 GHz. The finesse, F, and QL is 18 and

13,000 respectively. By fitting the parameters |t| and αr of Eq. (2.20) to the data, the ring waveguide loss, ρ, is 13.8 dB/cm. EIM is used in the fitting to determine the ring waveguide phase. The coupling parameter is found to be |t| = 0.95.

Fig. 6.15 shows the normalized transmission spectrum for an array of two ring resonators. The FSR for both resonances is 2.1 nm. The FWHM of the two resonances lineshapes are 0.10 nm, or 12.5 GHz. F and QL are 21 and 15,500 respectively. From fitting the two resonances to Eq. (2.20), the ring waveguide loss, ρ, for the ring resonator resonance at 1553.87 nm is 15.6 dB/cm. The coupling parameter is |t| = 0.96. The ring waveguide loss is 13.5 dB/cm for the second resonance at 1554.1 nm. The coupling parameter is also |t| = 0.96. In the fitting of the two resonances, it is assumed that the ring waveguide loss is different and the coupling length is the same. Making this assumption removed the ambiguity of |t| and αr.

107

Fig. 6.15. Normalized transmission spectra of the two-ring array.

The different losses may be attributed to the Cytop deformation during poling as depicted in Fig. 5.11.

The dimensions of the individual ring resonators in the arrays are nominally the same. However, due to fabrication differences in the ring resonators, resonance wavelength separation is obtained as observed in Fig. 6.15. One source of this resonance wavelength separation is differences in waveguide height of the two resonators. The waveguide height may be different due to non-uniform spin-coated thickness at the step depicted in the fabrication process of Fig. 5.1(c). A waveguide thickness difference on the order of 1.5 nm causes the resonance wavelength separation as observed in the transmission spectra of the two ring array.

Fig. 6.16 shows the normalized transmission spectrum for an array of four ring resonators. The FSR for each resonator is 2.1 nm. The different extinction ratios indicate different losses for the different rings.

108

Fig. 6.16. Normalized transmission spectra of the four-ring array.

The resonance wavelength, fitted loss ρ, and coupling parameter |t|, FHWM, F and QL are documented in Table 6.1.

λ Loss, ρ FWHM Ring r α |t| F Q (nm) dB/cm r (GHz) L 1 1551.9 10.0 0.919 0.960 11.1 24.2 17,500 2 1552.4 11.0 0.911 0.960 10.2 26.2 18,900 3 1552.6 13.4 0.893 0.960 11.8 22.7 16,400 4 1552.9 10.0 0.919 0.960 12.3 21.7 15,600 Table 6.1. Parameters determined from the four ring array spectra in Fig. 6.16.

The extinction ratios of the resonances of the four-ring array indicate that the coupling is between optimal coupling and critical coupling. For ring 1 and 4, αr = 0.926.

From the equation for optimal coupling, Eq. (3.9), the optimal coupling parameter |t| is

0.958. Thus near-optimal coupling is achieved for these two rings where |t| is measured as 0.960. Also, the coupling parameters correspond well with the simulated predictions

109 shown in Fig. 4.3. The FWHM of the four resonators are between 11.1 GHz and 12.3

GHz. These values are the approximate expected RF bandwidth of the devices

6.5. EO RF Sensing Tests

The four-ring array depicted and highlighted in Fig. 6.5 is tested in the EO characterization set-up. The EO modulation from a single resonance is first measured.

During the test, the VNA output power is set to 0 dBm. The RF amplifier is used so that

30 dBm of RF power is applied to the RF resonator. The RF frequency of the VNA is set to a constant value of 3.9 GHz. The optical power input to the ring resonator devices is

+14.5 dBm as set by the EDFA. The laser wavelength is swept across a single ring resonance and the S21 magnitude and phase for each wavelength point is measured.

Fig. 6.17. Optical power transmission spectra for the S21 EO measurements.

110 Fig. 6.17 shows the optical power transmission spectra for a wavelength sweep across a single resonance at 1551.12 nm. The laser wavelength is stepped by 0.01 nm and is held constant for 2.5 seconds at each wavelength point. The fiber-to-chip coupling changes over time and accounts for the noise in the optical power data. The VNA averages 7 data points for each wavelength point. The VNA IF bandwidth is 10 Hz.

Fig. 6.18 shows the magnitude of S21 as a function of laser wavelength. Two peaks in the data are observed and occur at the steepest points on the lineshape of Fig.

6.17. The value of |S21| at the peak at 1551.2 nm is -93 dB. The signal level away from resonance is -110 dB, which is due to the direct laser modulation and the direct RF coupling into the photodetector. The noise level measured for similar conditions but when the RF output is terminated into a 50 Ω load and the laser power off is measured to be -122 dB.

Fig. 6.18. Magnitude of S21 as the laser wavelength is swept across ring resonance of 1551.14 nm.

111

Fig. 6.19. Phase of S21 as the laser wavelength is swept across the ring resonance at 1551.14 nm.

|S21| is also at a minimum when the laser wavelength is at the ring resonance wavelength. The phase of S21 is shown in Fig. 6.19. At ring resonance, a phase shift of approximately 180o is observed. This phase shift is illustrated in the plot.

The magnitude of S21 is also measured as a function of RF frequency at a constant laser wavelength. When the RF frequency is not at the resonance frequencies, the return loss is near -1 dB. Therefore, a significant portion of the incident power to the resonator is reflected back to the RF amplifier. The RF amplifier is removed from the set-up so that it will not be damaged when the RF frequency is outside of resonance. The laser wavelength is biased on the steepest part of the lineshape slope of the ring resonance.

The EDFA output power is increased so that -2 dBm of optical power is incident at the photoreceiver. The S21 data is averaged over three RF frequency scans. Fig. 6.20 depicts the measured magnitude of S21 from 3.65 GHz to 4.1 GHz. The signal at resonance is -97 dB, and is 13 dB higher than the noise level off-resonance.

112

Fig. 6.20. Measured S21 magnitude as a function of frequency near the second resonance of the RF resonator.

The EO response from the ring resonator is also measured as a function of RF input power at three different wavelength bias points on the ring resonance. A spectrum analyzer (Agilent E4407B) is used so that the absolute detected RF power is directly measured. The wavelength bias points on the ring resonance are shown in Fig. 6.21. The bias points are 0.01 nm, 0.06 nm, and 0.10 nm away from resonance. The wavelength is held constant at each of the three bias points. The VNA is used as the RF source in CW mode at an RF frequency of 3.9 GHz. The spectrum analyzer sweep bandwidth is set to

100 Hz. The center frequency is 3.90 GHz. The spectrum analyzer resolution bandwidth is set to 3 Hz. No averaging is used. The RF power is varied from -13 dBm to +11 dBm and the peak RF power of the spectrum measured by the spectrum analyzer is measured.

Fig. 6.22 shows the RF spectrum for a modulation signal for a bias point of 0.06 nm from resonance and at an RF power of 11 dBm.

113

Fig. 6.21. Measured optical power across resonance for the RF power sweep measurements.

Fig. 6.22. Modulation signal measured at spectrum analyzer at a wavelength of 0.06 nm from resonance and an RF power of 11 dBm.

114

Fig. 6.23. Measured RF power for three different bias wavelength points near ring resonance with best-fit lines.

Fig. 6.23 shows the peak RF power detected at the spectrum analyzer for the three different wavelength bias points. The data is fit to best-fit lines by a linear regression.

The largest four input RF powers are used for the linear regression. At low powers the detected RF power is constant at the noise level near -135 dBm. The slopes of the lines are 0.96 dB/dB, 1.02 dB/dB and 1.1 dB/dB for the bias points at 0.06 nm, 0.10 nm and

0.01 nm respectively.

Next, the VNA is used to measure the EO response from the four rings in the array. The laser wavelength is swept across the resonances of the four rings and the magnitude and phase of S21 at 3.9 GHz is recorded. The incident RF power to the RF resonator is 30 dBm using the RF amplifier. The VNA averaging and wavelength step configuration is the same as the data taken for the single resonance shown in Fig. 6.17.

Fig. 6.24(a) shows the transmission power spectrum of the array. Fig. 6.24(b) depicts the magnitude of S21 and Fig. 6.24(c) shows the phase of S21 for the four rings.

115

Fig. 6.24. (a) Four-ring array optical power spectrum, (b) measured |S21| and (c) S21 phase.

116 Note that near each of the four resonances, two peaks in the magnitude of S21 and phase shifts of ~180o are observed. The different resonances are labeled R1-R4 in Fig. 6.24(a)-

(c).

6.6. Observed Bistability in Ring Resonator Transmission

When the optical power input to the rings is increased, the resonance lineshapes are observed to be asymmetric. This asymmetry is due to an optical power dependent ring waveguide refractive index. Bistable ring resonator devices are based on this effect

[93], [94]. The resonance wavelength also depends on the input power. Fig. 6.25 shows five resonance lineshapes for five different input powers. The resonance wavelength shift for relative input power is shown in Fig. 6.26. The change in resonance is approximately linear for changes in input optical power.

Fig. 6.25. Measured resonance lineshapes for five different input powers.

117

Fig. 6.26. Measured resonance wavelength change for varying optical powers.

Modulation is also observed for the asymmetric lineshapes. The output power is increased so that a maximum optical power of 2 dBm is received at the photoreceiver.

An RF power of 0 dBm is input to the RF resonator. The VNA averaging is the same as the data taken for the single resonance shown in Fig. 6.17. The laser wavelength is stepped by 0.005 nm. Fig. 6.27 is the optical power transmission measured for a laser wavelength sweep across an asymmetric resonance. Fig. 6.28 depicts the measured magnitude of S21 as a function of laser wavelength. As observed, |S21| is at a minimum near resonance and reaches a peak of -105 dB at a relative wavelength of 0.1 nm from resonance. |S21| decreases for laser wavelengths further away from resonance. It is not possible to bias on the steep low-wavelength side of the resonance.

118

Fig. 6.27. Measured transmission spectra of a bistable resonance.

Fig. 6.28. Measured magnitude of S21 for the bistable resonance depicted in Fig. 6.28. An RF power of 0 dBm is incident to the RF resonator.

119 6.7. Discussion of the EO Sensing Measurements

The S21 data from the measurements of the single resonance of Fig. 6.18 are similar to the prediction depicted in Fig. 3.6(b). The measured |S21| in Fig. 6.18 shows two maxima near the steepest wavelength points on the resonance lineshape. The phase of S21 as shown in Fig. 6.19 also corresponds with the theoretical prediction that the phase will change by 180o from one side of the resonance to the other side due to the opposite signs of the lineshape slope of the resonance. For this measurement, the maximum optical power measured off-resonance depicted in Fig. 6.18 is -9 dBm. From the noise measurements of Fig. 6.12, the noise power due to direct laser modulation is predicted to be -112 dBm with 30 dBm of RF power input to the RF resonator. The noise power is thus 19 dB less than the maximum modulation power shown Fig. 6.18. The predicted noise level is similar to the power levels indicated in Fig. 6.18 at wavelengths far from the resonance wavelength. The noise power of the VNA with port 1 terminated into a 50 Ω load and with the laser power off is -122 dB. Thus, the RF input power must decrease by 29 dB so that the EO modulation signal and the noise level are equal. When the RF power is decreased, the noise due to the direct laser modulation linearly decreases as well.

The RF spectrum measurements of Fig. 6.20 also indicate that the modulation is highest at the RF resonance frequency. As depicted in Fig. 6.23 the detected RF power is linear with the input power to the RF resonator and the response is strongest near the steepest point on the resonance lineshape. From this data presented in this dissertation, it is thus concluded that the ring resonator refractive index is modulated via the EO effect by the electric fields from the RF resonator. 120 The S21 measurements from the four-ring array may be used to calculate relative electric field magnitudes and phases. Calculations of the relative fields do not require knowledge of the EO coefficient r33. If the ring resonators have equal r33 and dimensions, the measured RF power, from Eq. (3.13), is proportional to the square of the

2 2 electric field, and S: Prf  S E . It is evident from the optical power data of Fig.

6.24(a) that the lineshape slopes of each resonance are not equal. Using EIM to calculate the ring mode phase the lineshapes are fitted to the data of Fig. 6.24(a). The normalized lineshape slope, S, of each resonance is then calculated by fitting Eq. (2.20) using EIM to the optical power spectrum shown in Fig. 6.24(a). Table 6.2 shows the magnitude and phase of S21, the calculated normalized slope S and the mean normalized calculated vertical electric field |Ey| experienced by the ring resonator.

Resonance |S | S phase Norm. slope, Norm. Ring 21 21 wavelength (nm) (dB) (deg) S (nm-1) calculated field R1 1550.8 -89.0 47.8 10.9 1.00 R2 1551.1 -92.8 99.4 12.1 0.62 R3 1551.5 -91.1 29.4 7.5 0.95 R4 1551.7 -91.7 16.3 11.6 0.71

Table 6.2. Measured S parameters for the array and calculated normalized |Ey|.

At the time of the measurement, no system was in place to determine which resonance wavelength corresponds with a physical resonator. However, the range of the normalized calculated electric field values are within the range of the expected range of the simulated field, shown in Fig. 6.9. A mechanism may be put in place to determine the location of each resonator. For example, an IR camera attached to a microscope

121 positioned over the ring resonators may be used to observe the scattered light when the wavelength is at a ring resonance [95].

An estimation of the EO coefficient, r33 can be made from the measured data.

The expected r33 value is less than 1 pm/V as determined from the ellipsometric measurements given in Appendix C. The EO coefficient can be calculated from the knowledge of the magnitude of the electric field inside the ring obtained from simulations using Eq. (3.13). The data obtained from the measurement of the four-ring array is used to calculate the EO coefficient assuming that r33 is equal for each ring in the array due to the similar poling conditions.

From EIM, η = 0.8 and neff = 1.43. The maximum transmission power is Popt = -9 dBm from Fig. 6.20. At an input RF power of 30 dBm to the microstrip resonator,

Fig. 6.29. Calculated r33 values for the rings of the four-ring array. The solid horizontal lines denote the bounds for possible values of r33.

122 the average field in the ring resonator is between 4.2 kV/m and 8.7 kV/m depending on the ring location as shown in Fig. 6.9. Using the measured values of the magnitude of S21 tabulated in Table 6.2 and the lineshape slope S for each ring, r33 is calculated using Eq.

(3.13) for the range of electric field values. The results of the calculations are shown in

Fig. 6.29. Under the assumption that r33 is equal for all four rings, the range of possible values are bounded between 0.70 pm/V and 0.75 pm/V, as depicted in Fig. 6.29 by the black horizontal lines. The mean r33 is 0.72 pm/V. The predicted value of r33 is close to the expected value in the ellipsometric configuration.

Using r33 = 0.72 pm/V, the sensitivity to fields in free-space is calculated. The sensitivity is defined as the minimum detectable electric field magnitude for an SNR of 1.

The noise level depends on the measurement equipment, noise sources and minimum system bandwidth. From Fig. 6.22 the minimum detectable RF power at a spectrum analyzer bandwidth of 3 Hz is -130 dBm. The noise generated by the photoreceiver is the main source of this noise and is considered to be Gaussian. The minimum noise of the

VNA at 10 Hz bandwidth is -122 dB for 0 dBm RF output. The sensitivity is the minimum electric field divided by the square-root of the minimum RF system bandwidth

[96].

The sensitivity is calculated for the most sensitive ring of the array, R2, given S =

-1 12.1 nm , r33 = 0.72 pm/V, G = 900 V/W, Popt = -9 dBm, Z0 = 50 Ω, as a function of receiver noise floor power. The sensitivity is shown in Fig. 6.30. At a noise floor of -130 dBm, the sensitivity to electric fields in free-space is 56.6 V/(m Hz0.5). This noise floor corresponds to the noise floor measured using the spectrum analyzer. At a noise floor power of -122 dBm, as measured with the VNA, the sensitivity is 142.2 V/(m Hz0.5).

123

Fig. 6.30. Electric field sensitivity calculated for ring R2 as a function of noise floor power.

From Eq. (3.13), the sensitivity depends on many factors that may vary according to the sensor system. The sensitivity is given for an optical bias power of -15.5 dBm (-9 dBm power off-resonance), at an optical wavelength of 1550 nm, a photoreceiver conversion gain of 900 V/W, and a system impedance of 50 Ω. If the bias power is increased by 9 dB, the free-space sensitivity is 17.7 V / (m Hz0.5) for a noise floor of -122 dBm.

The bistability effect observed in the rings at high input powers is nonlinear in origin. The refractive index of the ring depends on the optical power in the ring.

Because the ring power that may be calculated from Eq. (2.28) is nonlinear with respect to laser wavelength, the phase will also be nonlinear. It is observed in Fig. 6.25 that at the highest input power, the low-wavelength side of the resonance is very sharp. Also, as the optical input power increases, the resonant wavelength decreases. The measured data is thus consistent with a thermal origin of the bistability effect. The thermo-optic

-4 o -1 coefficient of PC is dn/dT = -0.9 x 10 C [97]. For increasing ring temperatures the 124 resonance wavelength of the ring decreases due to the thermo-optic effect. For higher optical powers, there is greater heating of the ring. One source of this heating may be due to material absorption of the laser light. Thermo-optic effects in rings respond slowly to external changes in temperature. At fast wavelength sweep speeds, the bistable effect is less significant [98]. It is expected that the same mechanism occurs when the refractive index is modulated at RF frequencies. Thus, it is expected that the EO modulation will not be proportional to the slope of the lineshape slope as it is for the linear ring phase modulation. Further work may be performed to examine this effect.

6.8. Chapter Conclusions and Outlook

This chapter demonstrates successful EO sensing using the fabricated EO ring resonator field sensors. This work represents the first reported demonstration of field sensing using ring resonators in a completely metal-free, all-dielectric integrated optics flexible platform. The design process presented in Chapter 4 which was developed from the theory in Chapter 2 and Chapter 3 is successfully implemented. Assuming an EO coefficient of 0.72 pm/V as calculated using RF field simulations and from the four-ring array data, the sensitivity for electric fields in free-space field is 142.2 V / (m Hz0.5).

The all-polymer device is shown to minimally perturb the RF fields emanating from the microstrip resonator by observing the resonance shift. EO sensing is demonstrated by measuring the modulated RF power and phase as a function of wavelength near the resonance wavelength. The noise in the measurement system is also characterized. In the experiments, the maximum power from the EO modulation is 19 dB

125 higher than the measured and predicted noise signal level. A frequency sweep near the second RF resonance of the microstrip resonator shows that the modulation is largest at resonance. It is also demonstrated by observing that the largest modulated power occurs at the steepest point on the resonance lineshape, as predicted by theory. The response from a four-ring array was also measured. At each resonance in the transmission spectra, modulation was observed to occur at each resonance. Finally, it is observed that as the optical power input to the devices increases, asymmetric lineshapes result in the power transmission spectra. Sensing is also performed using these bistable-type lineshapes.

126

CHAPTER 7

TWO-MODE BUS COUPLED RESONATOR EXPERIMENTAL

RESULTS

The testing and experimental results of a two-mode bus waveguide coupled to a single-mode ring resonator are given in this section. The two modes of the bus waveguide are excited via coupling optical power from fibers at two inputs of the device chip. The output mode powers are measured as a function of wavelength, mode power distribution and mode relative phase differences. The slope of the difference of the two measured mode powers with respect to wavelength is then measured. Near-optimal coupling of the two modes and the ring resonator is demonstrated.

7.1. Laboratory Configuration

The laboratory configuration is depicted in Fig. 7.1. A photomicrograph of the fabricated chip is shown in Fig. 7.2. A 3-dB fused fiber coupler is used to split the power from a tunable near-IR laser into two single-mode fibers. The laser power input to the 3- dB fiber coupler is 8 dBm. The fibers are aligned to the two single-mode inputs of the on-chip mode generator.

127

The polarization of the light guided by the two fibers is adjusted using two polarization controllers. The relative phase difference between the two bus waveguide modes is controlled via an off-chip free-space delay line adjusted using a piezo-electric controller.

At the output facets of the mode filter, two fibers are aligned to the output waveguides to detect the power output from the mode filter. The optical powers from the two fibers are measured simultaneously using a power meter. Cleaved single mode fibers are used to couple light to and from the chip.

A phase drift of several degrees per minute is observed between the two input fibers in the laboratory. This drift may be attributed to temperature fluctuations [99]. In order to stabilize and control the relative phase difference, a system consisting of an adjustable length GRIN-lens coupled free-space delay line is used. A portion of light incident at the fibers at the input of the chip is reflected due to the refractive index difference between the fiber core and air.

128

Fig. 7.2. Optical micrograph of fabricated on-chip structure consisting of a mode generator, two-mode waveguide, single-mode ring, and mode filter.

This reflected light in the two fibers propagates back through the system to the 3 dB fiber coupler where they interfere. A photodetector at the fourth output of the fiber coupler is used to detect the result of the interference. If the relative phase difference between the two input fibers changes, the power incident at the photodetector changes. The signal is fed back through a proportional-integral-derivative controller in software to adjust the length of the free-space delay line via a piezo-actuator. Phase stabilization suitable for the characterization of the on-chip devices is achieved using this configuration.

All-single mode ring resonator devices are also fabricated on the same chip to enable characterization of the ring waveguide loss. Note that the parameters αr and |t| in

Eq. (2.20) may be interchanged to give identical lineshapes. To determine the two parameters unambiguously for this experiment, the transmission spectra of two resonators comprised of two different coupling lengths are measured. Two ring race-track resonators incorporating straight coupling lengths of Lc = 20 µm and Lc = 40 µm are fabricated on the test chip. The width of the waveguides and the radii of the resonators are equal to the width and radii of the resonator in the two-mode device. Fig. 7.3 shows the measured transmission spectra of the two resonators.

129

Fig. 7.3. Measured transmission spectra from two ring-racetrack resonators with radius equal to 150 µm.

The ring waveguide loss, ρ, should be equal for two rings of equal radius. From fitting

Eq. (2.20) using EIM to the measured transmission data, the ring loss is 6.5 dB/cm for both rings. The transmission coefficient |t| for Lc = 20 µm and Lc = 40 µm is 0.91 and

0.83 respectively.

7.2. Two-mode Bus Coupled Resonator Device Characterization

Measurements from the two-mode bus coupled resonator with dimensions corresponding to device 2 of Table 4.1 are performed. The gap width separating the bus waveguide from the ring is 0.6 µm. The fabricated ring radius is 150 m. Straight coupling section lengths equal to 40 µm are used. Fig. 7.4(a) is the normalized transmission of both outputs when only the TE0,0 mode is excited at the input. The data is normalized to the total output power detected off-resonance.

130

(a) (b) Fig. 7.4. (a) Measured output when only the TE0,0 mode is excited at the input. (b) Measured output when only the TE1,0 mode is excited at the input.

Fig. 7.4(b) shows the normalized transmission of both outputs when only the TE1,0 mode is excited. The extinction ratio for the TE0,0 mode is 5.8 dB and the extinction ratio for the TE1,0 mode is 5.9 dB. The measured extinction ratios demonstrate that the coupling coefficients are nearly optimal, and thus Rc ≈ Sc ≈ 1 are obtained.

The mode generation and filtering efficiency can also be measured from Fig.

7.4(a) and (b). Far from resonance wavelengths, the power in the bus waveguide is not efficiently coupled to the ring waveguide. Ideally, at an off-resonance wavelength, all of the power input to “input-1” should be detected at the output of the mode filter at

“output-1” and no power should be detected at “output-2”. The same is true for “input-

2.” From Fig. 7.4(a) at an off-resonance wavelength of 1562.25 nm, the power at

“output-1” is -23.5 dBm. The detected power at “output-2” is -47.0 dBm. Fig. 7.4(b) shows the output power detected when power is only excited at “input-1”. At a wavelength of 1562.25 nm, the detected power at “output-1” is -52.5 dBm. The detected power at “output-2” is -23.0 dBm. The measurements demonstrate that there is efficient 131 mode generation and filtering and there is low cross-talk of the two modes. The difference of 0.5 dB could be due to the mode generators, the filters, or the fiber-to-chip coupling.

Both inputs are excited with equal power and the input relative phase difference is adjusted to obtain a maximum lineshape slope of the output mode power difference. Fig.

7.5(a) shows the output lineshapes near the resonance wavelength. The data is normalized to the total output power summed from “output-1” and “output-2” detected off-resonance. The difference is shown in Fig. 7.5 (b). The measured maximum lineshape slope of 27.1 nm-1 corresponds to 6.44 rad-1, in good agreement with the 6.51 rad-1 calculated numerically. As calculated in Section 3.7, the maximum lineshape slope for an optimally coupled all-single mode resonator with a similar ring waveguide is 5.0 rad-1, which is 1.28 times less than the measured device.

(a) (b) Fig. 7.5. (a) Measured output for equal input mode power distribution and relative phase difference that maximizes the slope of the difference of the two mode power transmissions. (b) The difference of the two output mode powers.

132 7.3. Chapter Conclusions and Outlook

This chapter illustrates the results of the optical characterization of the two-mode bus coupled ring resonator. Near-optimal coupling and lineshape slopes corresponding to the predicted values are successfully demonstrated. Two measurements are performed that show near-optimal coupling is achieved. First, only a single mode is excited in the bus waveguide. As predicted in Chapter 3, when optimal coupling is achieved, the extinction ratio of the excited mode at the output is 6 dB. Measured extinction ratios of

5.8 dB and 5.9 dB are measured for the quasi-TE0,0 and quasi-TE1,0 modes respectively.

Second, the two input modes are excited with equal amplitudes. The relative phase difference between the two modes is adjusted to achieve maximum lineshape slope of the difference of the two mode outputs. The measured maximum lineshape slope of 27.1 nm-

1 corresponds to 6.44 rad-1. This measured slope is in good agreement with the 6.51 rad-1 calculated numerically in Chapter 3 for a waveguide loss of 6.5 dB/cm.

The measurement results represent the first experimental demonstrations of enhanced lineshape slopes using the two-mode coupling scheme. These devices can be made electro-optically active and fabricated on the all-polymer substrate as demonstrated in this dissertation. Thus larger lineshape slopes and increased sensitivity to RF fields may be obtained. The system can also be simplified by placing the power splitter and phase control on-chip at the input of the mode generator.

133

CHAPTER 8

OVERALL CONCLUSIONS AND FUTURE WORK

8.1. Overall Conclusions and Summary

This dissertation addressed several important aspects regarding the sensing of EM fields using miniature integrated optical resonator devices. The first topic addressed by this dissertation is the fabrication and demonstration of an EO polymer ring resonator RF sensor. First, the design considerations for a sensor based on a ring resonator coupled to a single-mode waveguide was investigated. The optimal coupling that gives the largest lineshape slope for a fixed ring waveguide loss was theoretically determined using the theoretical basis developed in this dissertation. The fabrication process developed for the device led to a metal-free all-polymer flexible platform for the integrated optical devices.

The devices consist of polycarbonate polymer doped with the EO chromophore Disperse

Red 1 waveguide cores with Cytop cladding. The devices are supported by a 30 µm thick flexible SU-8 substrate. Ring waveguides losses between 10 dB/cm and 13.8 dB/cm were measured. Near-optimal coupling was achieved for an array of four resonators.

The fields emanating from an RF microstrip resonator circuit at 3.9 GHz were measured using the fabricated and poled EO resonators. The invasiveness of the sensor was determined by observing the shift in the second RF resonance in return loss 134 measurements caused by the presence of the sensor device. The shift was found to be -

2.8 MHz for the all-polymer sensor, compared to a silicon sample of the same size that caused a shift of -113 MHz in the second RF resonance.

To demonstrate sensing, the laser wavelength was swept across ring resonances and the modulated RF power is measured by the VNA. Sensing using a four-ring linear array is demonstrated. Near each resonance, two peaks in the modulated RF power are observed. It is shown that the modulation is largest when the wavelength is biased on the steep slopes of the resonance lineshapes. This effect is predicted in theoretical calculations. Also, the phase of the RF signal on the low wavelength side of the resonance is approximately 180o out of phase with the phase on from the high wavelength side of the resonance. This phase change is also predicted in theoretical calculations.

Thus it is concluded that sensing via the EO effect is occurring.

Assuming electric field values obtained from simulation, the electro-optic coefficient r33 is 0.72 pm/V as calculated from the four-ring array data. This value is similar to values obtained for poled PC/DR1 films measured in an ellipsometric configuration. The sensitivity for electric fields in free-space field is calculated and is

142.2 V / (m Hz0.5). The sensitivity is given for a VNA noise level of -122 dBm, an off- resonance optical power of -9 dBm, at an optical wavelength near 1550 nm, a photoreceiver conversion gain of 900 V/W, and a system impedance of 50 Ω.

Relative electric field values are calculated from the measured modulated RF power and the lineshape slope of each resonance from the four-ring array. Spatial field mapping could not be performed due to the lack of a mechanism to link a resonance

135 wavelength with the spatial location of each resonator. Sensing from asymmetric lineshapes due to the bistable effect in the ring resonators is also demonstrated.

The second topic of this dissertation addressed the problem of increasing the lineshape slope from a single-mode ring resonator for a given ring waveguide loss. A two-mode bus waveguide coupled to a single-mode ring resonator device was investigated. The Fano-shaped output lineshapes are shown to depend on the coupling coefficients, relative power distribution, and relative phase difference of the two input modes. Theoretical analysis and numerical parameter sweeps were used to determine optimal coupling coefficients for maximum lineshape slope of the difference of the two mode power transmissions. The maximum lineshape slope that is theoretically obtainable from the device is 1.3 times that of an optimally-coupled single-mode-coupled resonator with the same round-trip ring waveguide loss.

A device was fabricated in a polystyrene-silicon dioxide material system by a photolithographic process. The two modes were excited using on-chip mode generators.

The transmissions of the two modes were measured via on-chip mode filters that separated the two output modes into two different single mode waveguides. The waveguide loss was determined to be 6.5 dB/cm. Measurement results of the two-mode- coupled resonator device show that near-optimal coupling is achieved. A 1.28 times increase in lineshape slope over an optimally coupled all-single-mode resonator of the same waveguide loss was experimentally determined.

In summary, the following items have been demonstrated in this dissertation:

1. The first reported EO RF sensing demonstrations based on ring resonators in a completely metal free, all-polymer and flexible integrated optics platform.

136 2. Development of a new fabrication process was developed in order to obtain the vertically poled EO devices on the all-polymer substrate.

3. RF sensing using a linear four-ring resonator array addressed by wavelength multiplexing.

4. RF sensing using bistable-type resonance lineshapes.

5. Given optimal coupling between a two-mode bus waveguide to a single-mode ring resonator, the lineshape slope from the transmission of the device is theoretically 1.3 times larger than an optimally coupled all-single-mode device of similar ring resonator loss.

6. The first reported experimental demonstrations of a resonant device demonstrating

1.28 times larger lineshape slope compared to optimally coupled single-mode bus coupled resonators with similar ring loss.

8.2. Future Work

There is much work to be done involving the devices studied in this dissertation.

Future work involves the following tasks:

1. Investigate the effects of bistability on sensing. This testing will involve measuring the EO modulation as a function of input optical power.

2. Investigate other EO polymers and optimize the poling process to produce sensors that are more sensitive to an applied electric field.

3. Investigate mechanisms to determine the physical location of a ring from the ring resonance so that field mapping can be performed. One example is to use an IR camera

137 attached to a microscope positioned over the ring resonators to observe the increase in scattered light when the wavelength is at a ring resonance.

4. Increase the number of ring resonators in the linear array in order to perform higher resolution spatial field mapping.

5. Incorporate EO polymers in the two-mode bus coupled resonator so that EO sensing with sharper lineshapes can be performed.

6. Simplify the two-mode bus coupled resonator system by placing the power splitter and phase control on-chip at the input of the mode generator.

138

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148

APPENDIX A

ELECTRO-OPTIC POLYMER THEORY

A.1. Electro-Optic Polymers Theory

The EO effect in materials arises from a non-zero second-order nonlinearity term of the power series expansion of the optical polarization. The power series expansion of the polarization, P, in the ijk coordinate system with electric field E can be expressed by

(1) (2) (3) P   0 ij E j   0 ijk E jEk   0 ijkl E jEk El  ... , (A.1) where χ(1) represents the linear susceptibility, χ(2) is the second-order nonlinearity, and χ(3) is the third-order nonlinearity. The susceptibilities χ(i) are tensors of rank 1 + i. The material must exhibit overall statistical alignment of dipole molecules to obtain a non- zero χ(2). The material thus cannot have a center of inversion symmetry.

The polarizability, pI, of the individual nonlinear molecules will interact with an applied electric field, affecting the overall polarization of the material. If it is assumed that the chromophores can be treated as independent non-interacting units, the molecular induced polarization in the I direction of the local coordinate system can be expressed as

[100]

149 0 pI  I IJ EJ  IJK EJ EK  IJKLEJ EKEL .... (A.2)

The subscripts I, J, and K refer to the local coordinate system of the molecule. The ground-state dipole moment is μ0. The term α is the linear polarizability, β is the first- order molecular hyperpolarizability and is a measure of how easily the electric field induces a dipole in the chromophore. γ is the second order hyperpolarizability. The frequency dependencies in the parameters of Eq. (A.2) are not included for simplicity.

In order to relate the molecular expression of Eq. (A.2) and the macroscopic expression Eq. (A.1) the chromophore number density, N, and local field factors, f, must be taken into account. The local field factors account for the fact that the applied electric fields are affected by the local environment of the chromophore. The macroscopic susceptibility can then be related to molecular polarizability by [100]

 (2)  Nf f f  ijk i j k ijk . (A.3)

The term <β> represents the average of the individual hyperpolarizabilities over all the orientations of the individual chromophores in the material. This term depends on the electro-static interactions of the chromophores and the poling efficiency.

The externally applied electric field is related to the material refractive index in the EO polymer through a tensor relationship. The EO coefficients are the tensor elements. For EO poled polymers three coefficients are non-zero: r13, r51 and r33 and r13

= r51 [100]. Thus the EO tensor rik (i = 1, 2,3, k = 1, 2, 3, 4, 5, 6) of the poled polymer is

[84]

150  0 0 r13   0 0 r   13 

 0 0 r33  rik    (A.4)  0 r13 0  r 0 0   13   0 0 0  where r33 is the EO coefficient in the direction of the poling field. The EO coefficient, r33, is related to the hyperpolarizability by [101]

3 4 r33  2Nf cos  n (A.5) where is the acentric order and represents how well the individual chromophores are oriented in the same direction. The product of the local field factors is denoted by f and the EO polymer refractive index is n. Eq. (A.5) indicates that for increasing the number of chromophore molecules in the material and for increasing molecular alignment, the nonlinear response increases.

The change in refractive index given a change in electric field is determined from the equation for the index ellipsoid of the poled polymer. The index ellipsoid for the EO polymer is given by

 1   1   1  1  x'2   r E   y'2   r E   z'2   r E   2 13 z'   2 13 z'   2 33 z'   no   no   ne  , (A.6)

 2y' z'r33E y'  2z' x'r13E x' where x’, y’, and z’ are the directions of the principal axes of the material. Ex’ Ey’ and Ez’ denote the applied electric field amplitudes in the x’, y’ and z’ directions respectively.

The ordinary refractive index and extraordinary refractive index, no and ne are approximately equal to the refractive index of the EO polymer core, nc. In the coordinate

151 system of the waveguide defined in Fig. 2.1, the direction y is parallel to the z’ direction.

From the index ellipsoid, the refractive index change experienced by an optical field polarized in the y (TM) direction due to a change in the field ΔEy is approximately

1 3 ny   2 nc r33Ey . (A.7)

The respective refractive index change for the TE-polarized optical field is

1 3 nx   2 nc r13Ey . (A.8)

A.2. EO Polymer Poling

Room-temperature photo-assisted poling [78], all-optical poling [102] and static field poling [103] have been employed to achieve alignment of the chromophore molecules. In photo-assisted poling, energy is provided by optical pumping to the EO polymer and the chromophores become mobile. The chromophores are then aligned by a static electric field applied to the polymer. All-optical poling occurs by the interference of two optical beams in the EO polymer. In static field poling, a strong constant field is applied across the polymer while the temperature of the sample is increased to the glass transition temperature (Tg). At Tg, the chromophores are mobile and can be aligned to the applied field. In the case of static field poling, larger fields lead to greater chromophore alignment and a larger r33. The field is thus limited by the dielectric breakdown field of the EO polymer which is on the order of 100 MV/m [104].

There are two methods for static field poling: contact poling and corona poling.

In corona poling, electrical breakdown of the atmosphere above the heated polymer is obtained by a highly charged thin wire. Positive ions are driven to the sample resting on a grounded plate, generating a field across the polymer. In contact poling, the electric 152 field is applied by electrodes close to the EO polymer. Contact poling is the method utilized in this work.

A schematic of the poling process is shown in Fig. A.1. The sample is placed on a hotplate at room temperature and connections are made from the electrodes to the voltage source. The voltage is set to the poling voltage. The temperature is then increased to near the Tg of the EO polymer. The sample is cooled after a length of time.

Once room temperature is reached, the poling voltage is reduced to zero and the sample is removed from the hotplate.

Fig. A.1. Schematic representation of the poling temperature and voltage as a function of time during the EO polymer poling.

153

APPENDIX B

DERIVATIONS OF THE MAXIMUM LINESHAPE SLOPE

B.1. Single-mode bus waveguide coupled to ring resonator

In order to determine the maximum slope from the single-mode bus waveguide coupled to the single-mode ring resonator, the zeros of the second derivative of Eq. (2.20) are first found. The zeros of the second derivative are located at the relative ring phases at which the maximum slope occurs. The first derivative of Eq. (2.20) with respect to sin(φr/2) is

2 2 dT 8(sin r / 2) r | t |  r 1| t | 1  . (B.1) 2 2 d sin( r / 2)  r | t | 1  4 r | t | (sin r / 2)

The second derivative with respect to sin(φr/2) is

2 2 2 dT 8 r | t |  r 1| t | 1   d 2 sin( / 2) 2 2 r  r | t | 1  4 r | t | (sin r / 2) . (B.2) 2 2 2 2 2 128(sin  r / 2) r | t |  r 1| t | 1 2 3  r | t | 1  4 r | t | (sin r / 2)

By letting Eq. (B.2) equal zero and solving for sin(φr/2), the location for maximum slope is obtained as

154

3  r | t | 1 sin( r / 2)   . (B.3) 6  r | t |

Eq. (B.3) indicates that the location for the magnitude of the maximum slope is found on both sides of the resonance, which occurs at φr = 0. By inserting Eq. (B.3) into the first derivative, the magnitude of the maximum slope with respect to for sin(φr/2) for any combination of αr and |t| is

2 2 dT 3 3 r | t |1  r |1 t |   3 . (B.4) d sin( r / 2) max 41  r | t |

To obtain the maximum slope with respect to φr the chain rule is applied. Assuming small φr, so that cos(φr/2) = 1, the maximum slope is approximately

dT dT d sin( / 2)  r (B.5) d r max d sin( r / 2) d r max . 2 2 3 3 r | t |1 r |1 t |   3 81 r | t |

For low-loss resonators and near-critical coupling, the point of maximum slope is near resonance and thus φr is small.

From numerical simulations it was determined that for optimal coupling, the extinction ratio (ER) is equal to 9 for low loss, under-coupled resonators [86]. The extinction ratio is given as the ratio of the maximum transmission to the minimum transmission of the ring resonator output spectrum and is

2  r | t | 1 ER  2 . (B.6)  r  | t |

To determine the accuracy of the assumption that ER = 9 for optimal coupling, a numerical parameter sweep of αr and |t| is performed. 155

Fig. B.1. The extinction ratio for obtained for maximum lineshape slope at optimal coupling calculated numerically.

Given a value of αr, the value of |t| is determined to give the maximum slope from Eq.

(B.5). The ER for optimal coupling conditions is depicted in Fig B.1 as a function of the

2 round-trip power loss αr . As expected, the ER approaches 9 as the round-trip ring

2 waveguide loss αr approaches zero. Letting ER = 9 and solving Eq. (B.6) for |t|, the condition for optimal coupling is obtained as

3 1 | t | r . (B.7)  r  3

Using Eq. (B.7) with the equation for the maximum slope, the maximum slope for optimal coupling is therefore

dT 3 (3 1)(  3) r r r .  2 (B.8) d r max 9(1 r )

The maximum slope can be found for critical coupling by letting αr = |t| and evaluating the maximum slope equation. Thus the maximum slope for critical coupling is

156 dT 3 3 r .  2 (B.9) d r cc,max 8(1 r )

The equations for maximum slope may also be written in terms of ring waveguide loss and the ring total length. From Section 2.2 the ring waveguide loss is related to the

field transmission by r  exp(Lr  / 2) . Assuming low round-trip ring waveguide loss the following approximation is obtained:

 r 1 2  . (B.10) (1 r ) Lr

A.2. Two-mode bus waveguide coupled to ring resonator

To derive an analytic expression for the maximum slope of the optimized two- mode bus waveguide device, it is assumed that the optimal coupling conditions, mode power distribution and relative phase difference found in the first part of Section 3.7 are true for any waveguide loss. Near resonance, it is assumed that the two mode output transmission difference, ΔB, is of the form of the Fano resonance cross-section [105]:

  B  F r . 2 2 (B.11) F r where ΓF is defined as the Fano lineshape half-width. For the two-mode bus coupled ring resonator the FWHM is obtained from the finesse, given by F = 2π/FWHM. For the two- mode bus coupled ring resonator, the finesse may be written as

F    r | trr | 1 r | trr |. (B.12)

At the optimal coupling conditions, |trr| = αr. Thus the lineshape ΓF is

2 F  1 r   r . (B.13)

157 To determine the lineshape slope, the first derivative of Eq. (B.11) is found:

2 2 dB F F  r   . (B.14) d 2 2 2 r F  r 

From Section 3.7, it was determined that the maximum slope is found at resonance, φr =

0. The maximum optimized slope is derived as

dB 1  r   2 . (B.15) d r F 1 r

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APPENDIX C

TENG-MAN ELLIPSOMETRIC EO CHARACTERIZATION

C.1. Theory

To characterize the EO coefficient of the poled polymer, an ellipsometric technique, commonly called the Teng-Man technique after the authors of the original paper [91] is used. A schematic of the optical set-up is shown in Fig. C.1. The inset shows the EO polymer sample. A film of the unpoled EO polymer is placed between two planar electrodes on a glass substrate. The electrodes serve as poling electrodes and EO modulation electrodes. One electrode is transparent and electrically conductive and is deposited on a glass substrate. A common material used is indium-tin oxide (ITO). The other electrode is placed onto the top surface of the polymer stack and is reflective. The sample is first poled using the process depicted in Fig. A.1.

In the optical set-up, a free-space beam output from the laser-coupled fiber is directed through the ITO-coated glass substrate and through the EO polymer at angle θ.

The beam is reflected by the reflective electrode and directed through a quarter-wave plate, polarizer and photodetector. The polarization of the input beam is set to 45o to the plane of incidence by the input polarizer and the polarization controller.

159

Fig. C.1. Teng-Man configuration for EO coefficient characterization.

This polarization is such that the polarization of light parallel to the plane of incidence is equal to the polarization perpendicular to the plane of incidence. A phase bias is created between the parallel polarized field and the perpendicular polarized fields by the quarter- wave plate. The output polarizer is cross-polarized to the input polarizer. A voltage source applies a voltage between the two electrodes, creating an electric field in the EO polymer and modulating the refractive index of the polymer. The polarization of the laser beam is modulated and is converted to an amplitude modulation by the output polarizer. The ratio of the modulation intensity to the optical intensity is theoretically determined by the following equation [106]:

2 Im 4 r33E nsin   2 2 1 2 sin . (C.1) Ic 3 d (n  sin )

The modulation intensity is Im. The optical intensity is Ic. The applied electric field in the EO polymer is E. The separation between the two electrodes is d. The refractive 160 index of the polymer is n and the phase bias created by the quarter-wave plate is Γ. The

EO coefficient r33 may thus be determined by measuring the modulated optical intensity.

It is assumed that r33 = 3r13 in the derivation of Eq. (B.1).

C.2. EO Characterization

In parallel with the fabrication of the ring resonator devices, poled films of

PC/DR1 were also tested in the Teng-Man ellipsometric configuration. The configuration shown in Fig. C.1 was constructed and samples with PC/DR1 films were tested. A photograph of the laboratory set-up is shown in Fig. C.2. A 200 nm thick ITO film is used for the transparent electrode and is sputter-coated onto pre-cleaned 1 mm thick glass slides. PC/DR1 is spin-coated onto the ITO. The top electrode is evaporated onto the top surface of the polymer and is reflective. Unpoled samples were tested first in order to determine that no other modulation sources were present and to confirm that the EO effect was present after poling.

The sample is placed in the Teng-Man configuration immediately after poling. A modulating voltage signal is applied to the electrodes. The output signal from the photodetector is measured by a lock-in amplifier. Unpoled samples were measured and determined to produce a modulation signal similar to when no voltage was applied to the

EO polymer, indicating that no EO modulation was taking place.

A sample with a 1.3 µm PC/DR1 layer between the ITO and evaporated 200 nm thick Cr electrodes was poled at 155 oC by a field of 77 MV/m for 8 minutes.

161

Fig. C.2. Photograph of the Teng-Man set-up for EO characterization.

A 10 V amplitude signal modulated at 5 kHz was applied to the electrodes in the Teng-

Man configuration. The incident angle was set to θ = 45o and the phase bias was set to Γ

o -5 = 90 . The ratio Im/Ic was measured to be 5x10 . The signal was found to be linearly proportional to the applied voltage amplitude. From Eq. (C.1), the EO coefficient was measured to be 1.7 pm/V. This value is similar to other poled r33 values in the literature that use DR1 as the EO chromophore measured in the Teng-Man configuration.

Tests were also performed to determine the stability of the EO coefficient during heating cycles after poling. If a poled sample is heated to near the Tg of the polymer, the chromophores will tend to relax, reducing the EO coefficient. A sample was poled at 155 o C by a field of 45 MV/m for 5 minutes. The r33 measured immediately after poling was

1.5 pm/V. The sample was then heated for 15 minutes at different temperatures. Table

C.1 documents the subsequent heating trials performed on the same sample.

162 o Trial Temperature ( C) r33 (pm/V) 1 No heating 1.5 2 65 1.0 3 100 0.7 4 125 0.7 5 150 0.5 Table C.1. EO coefficients measured after heating trials of poled sample

The data of Table C.1 indicate relaxation of the EO coefficient occurs for all heating cycles. This effect is important to note since heating steps occur after the waveguide poling step in the fabrication process. The sample is heated for a total time of 8 minutes at 60 oC after poling for the SU-8 photolithography step. A reduction of approximately

66% of the EO coefficient is thus expected from the heating step.

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