optimization of wideband fiber optic hydrophone probe for ... · manseta, adil mudassir, gaurav...

Optimization of wideband fiber optic hydrophone probe

for ultrasound sensing applications

A Thesis

Submitted to the Faculty

of

Drexel University

by

Rupa Gopinath Minasamudram

in partial fulfillment of the requirements for the degree

of

Doctor of Philosophy

June 2010

iii

Dedications

to my parents and husband

iv

Acknowledgements

I would like to sincerely express my gratitude to the following people for

their immense support towards the completion of this work. Firstly, I would like to

thank my advisor, Dr. Afshin S. Daryoush from the bottom of my heart, for his

constant guidance, co-operation, and encouragement to help me face challenges

encountered both in the research work as well as my graduate student life. This

thesis work wouldn’t have been possible without his advice, patience and

motivation.

I would like to thank to Dr. Peter Lewin immensely for his guidance in

helping me understand the acoustics aspects of this work, improving my writing and

presentation skills. I also thank him for agreeing to be on the dissertation

committee.

I would like to sincerely thank Dr. M. El-Sherif from Photonics Labs Inc.

for his inputs, which helped me better appreciate the nature of thin films and Finite

Element Analysis. I also would like to thank Dr. El-Sherif for consenting to be on

my committee.

I am thankful to Photonics Labs Inc. for their contribution in the process

development of the etched and coated fiber samples. I am grateful to Dr Lalit

Bansal, Dr Vasileios Nasis and other members of Photonics Labs for their excellent

help with the fabrication of the fiber samples.

v

I am thankful to Dr Adam Fontecchio and Dr Gary Freidman for their

inputs and for agreeing to be on the dissertation committee.

I thank Dr Philip Bloomfield for his assistance with the acoustic transducer

design aspect, Brent Boyd and Mark Schiber from the Drexel machine shop for

their help in designing mechanical holders and Dr Edward Basgall for his help with

the sputter coater. I also thank Dr Sumet Umchid and Karthik Srinivasan for their

assistance in the initial stages of this work. Assistance from Yuhaan and Chris

Bawiec with the acoustic measurements is appreciated.

My student life would not have been enjoyable without my friends Khushali

Manseta, Adil Mudassir, Gaurav Gandhi, Karthik Srinivasan, Ebraheem Sultan and

Piyush Arora. Their presence and words of wisdom made the roughest days

cheerful.

I am eternally indebted to my parents and my husband for all their love,

prayers, patience, support and sacrifice. Lastly, I thank the Almighty and seek His

blessings.

vi

TABLE OF CONTENTS

Acknowledgements .............................................................................................. iv

LIST OF TABLES ................................................................................................ x

LIST OF FIGS..................................................................................................... xii

Abstract................................................................................................................ xx

Chapter 1: Introduction ....................................................................................... 1

Chapter 2: Background and Motivation............................................................. 4

2.0 Introduction: ................................................................................................... 4

2.1 Fiber optic acoustic sensors: .......................................................................... 5

2.1.1 Intensity Modulated Sensors:............................................................................ 6

2.1.1.1 Reflection type: .............................................................................................. 6

2.1.1.2 Transmission Type:........................................................................................ 8

2.1.2 Phase modulated acoustic sensors: .............................................................. 12

2.1.2.1 Extrinsic interferometric phase modulated sensors: .................................... 14

2.1.2.2 Internal interferometric phase modulated sensors: .................................... 20

2.1.3 Frequency/Wavelength Modulated sensors .................................................... 27

2.1.3.1 Indirect frequency modulated acoustic sensors with heterodyne detection: 28

2.1.3.2. Direct wavelength modulated sensors: ....................................................... 30

2.1.4 Acousto-optic Sensor Parameters ................................................................... 34

2.2 Noise cancellation in fiber optic hydrophone sensors: .............................. 36

2.2.1 Common mode noise rejection by signal processing:..................................... 39

2.2.2 Common mode noise rejection by differential amplifier:............................... 40

2.2.3 Common mode noise rejection by anti-parallel photo-diodes: ....................... 41

2.3 Numerical modeling of optical waveguides: ............................................... 43

2.3.1. Finite Element Method (FEM): ..................................................................... 45

2.3.2. Finite Difference Method (FTD): .................................................................. 48

2.3.3 Beam Propagation Method (BPM): ................................................................ 52

2.4 Summary: ...................................................................................................... 54

Chapter 3: Analytical modeling......................................................................... 57

3.0 Introduction: ................................................................................................. 57

3.1 Plane wave propagation at two material interface: ................................... 58

vii

33.1.1 Reflection and Transmission coefficient of plane wave at boundary: .......... 59

3.1.2 Transmission line equivalent theory: .............................................................. 63

3.2 Analytical model of uncoated fiber: ............................................................ 64

3.3 Extraction of complex refractive index of thin (2nm-35nm) gold films: . 68

3.3.1 Need for extraction of complex refractive index: ........................................... 69

3.3.2 Fabrication: ..................................................................................................... 71

3.3.3 Experimental set-up, results and discussion: .................................................. 72

3.4 Analytical model of coated fiber:................................................................. 77

3.4.1. Assuming compressible water and incompressible gold: .............................. 80

3.4.2. Assuming incompressible water and compressible gold: .............................. 81

3.4.3. Combined water and thin gold film compression:......................................... 82

3.5 Summary........................................................................................................ 82

Chapter 4: Numerical modeling ........................................................................ 84

4.0 Introduction................................................................................................... 84

4.1 Numerical model of standard single mode fiber with step index: ............ 85

4.1.1 Simulation set-up for electromagnetics module: ............................................ 85

4.1.2 Simulation set-up for coupled acousto-optic analysis: ................................... 89

4.2. Impact of fiber optic sensor tip geometries: .............................................. 93

4.2.1 Uncoated Cylindrical etched fiber sensor: ...................................................... 93

4.2.2 Uncoated linear tapered fiber sensor: ............................................................. 99

4.2.3 Uncoated exponential tapered fiber sensor: .................................................. 103

4.3 Numerical model of thin film gold coated fiber sensors:......................... 108

4.3.1 Effect of gold coating on cylindrical etched fiber sensors:........................... 112

4.3.2. Effect of gold coating on linear tapered fiber sensors: ................................ 116

4.3.3. Effect of gold coating on exponentially tapered fiber sensors:.................... 118

4.4 Summary: .................................................................................................... 123

Chapter 5: Experimental results ..................................................................... 125

5.0 Introduction: ............................................................................................... 125

5.1 Measurement Set-up:.................................................................................. 125

5.1.1 Acoustic Sub-system:.................................................................................... 125

5.1.2 Fiber optic sub-system at 980nm: ................................................................. 126

5.1.3 Fiber optic sub-system at 1550nm: ............................................................... 127

5.2 Mechanical holder assembly:..................................................................... 129

viii

5.3 Acoustic measurements using reference PVDF needle hydrophone:..... 130

5.4 Acoustic measurements with fiber optic hydrophone probes: ............... 133

5.4.1 Responsivity improvement measurements: .................................................. 133

5.4.2 Noise cancellation measurement: ................................................................. 144

Fig 5. 9: Experimental set-up for noise cancellation using balanced detection..... 144

5.4.3 Frequency domain response to burst acoustic signal at 5 MHz:................... 147

5.5 Summary: .................................................................................................... 150

Chapter 6: Conclusions and Recommendations for Future Work .............. 152

6.0 Introduction: ............................................................................................... 152

6.2. Recommendations for Future work:........................................................ 154

REFERENCES.................................................................................................. 158

Appendix A-1: LIST OF EQUIPMENT & COMPONENTS ....................... 165

Appendix A-2: HE 11 mode in Single Mode Fiber .......................................... 166

Appendix A-3: Extracted values of refractive index of thin film gold ......... 169

Appendix A-4: Extraction of photo-elastic constants of thin gold films ...... 170

Appendix A-5: Acoustic to Electrical analogy................................................ 172

Appendix A-6: Design of HIFU transducer and verification using PiezoCAD

............................................................................................................................. 173

Appendix A-7: Characterization of passive optical link components .......... 181

Appendix A-8: Characterization of optical active link components ............ 182

Appendix A-9: Photo-detector PDB130 C specifications .............................. 184

Appendix A-10: Mechanical holder design .................................................... 187

Appendix A-11: Laser Diode Mount ............................................................... 195

Appendix A-12: Sputter coater holder design................................................ 196

Appendix A-13: Ted Pella sputter coater performance specifications ........ 198

ix

Appendix A-14: Single stage Single ended inverting amplifier design ........ 199

Appendix A-15: Raman Images of fabricated fiber samples ........................ 202

Appendix A-16: Static reflectance in air of coated fiber sensors ................. 204

Appendix A-17: Reflectance from cylindrically etched fiber model ............ 205

Vita ..................................................................................................................... 206

x

LIST OF TABLES

Table 3. 1: Summary of complex refractive index data of thin (2-35nm) gold films

at 980nm................................................................................................................... 76

Table 3. 2: Refractive index data of 20nm and 35nm thick gold films at 1480nm

and1550nm............................................................................................................... 76

Table 4. 1 Responsivity performance comparison of cylindrical etched fiber sensors

.................................................................................................................................. 97

Table 4. 2 Responsivity performance comparison of linear tapered fiber sensors as

function of taper angle ........................................................................................... 102

Table 4. 3 Responsivity performance comparison of exponential tapered fiber

sensors.................................................................................................................... 106

Table 4. 4 Responsivity performance of coated straight cleaved fiber sensor....... 110

Table 4. 5:Responsivity performance of coated 7 degree linear tapered fiber sensor.

................................................................................................................................ 116

Table 4. 8 Responsivity performance of 7 degree exponential tapered fiber sensor

................................................................................................................................ 119

Table 5. 1: Pressure to voltage responsivity performance of thin film coated fiber

samples................................................................................................................... 133

Table 5. 2: Static reflectance of straight cleaved fiber samples............................ 135

Table 5. 3: Static reflectance of uncoated cylindrically etched fiber samples....... 136

Table 5. 4: Static reflectance of thin film coated cylindrically etched fiber samples

................................................................................................................................ 136

xi

Table 5. 5: Static reflectance of uncoated linearly tapered fiber samples: (taper

angle 3-5 degrees) .................................................................................................. 137

Table 5. 6: Static reflectance of thin film coated linearly tapered fiber samples:

(taper angle 3-5 degrees)........................................................................................ 138

Table 5. 7: Pressure to voltage responsivity performance of fiber optic probes at 980

nm .......................................................................................................................... 138

Table 5. 8: Pressure to voltage responsivity performance of fiber optic probes at

1550 nm ................................................................................................................. 139

Table 5. 9: Estimation of coating thickness from coating time based on static

reflectance measurement........................................................................................ 142

Table 5. 10 Noise cancellation performance of the fiber optic probes at 980nm.

Noise power of the photo-detector under no modulation = -112 dBm. ................. 145

Table 5. 11: Noise cancellation performance of fiber optic probes at 1550nm. Noise

power of the photo-detector under no modulation = -112 dBm . .......................... 146

Table A-16. 1: Static reflectance performance of thin film coated fiber sensors .. 204

xii

LIST OF FIGURES

Fig 2. 1: Reflection type fiber optic acoustic sensor with intensity detection [10] ... 6

Fig 2. 2: Experimental set-up of single mode intensity modulated fiber optic

hydrophone [11]......................................................................................................... 8

Fig 2. 3: Schematic of Transmission type intensity modulated fiber optic acoustic

sensor. ........................................................................................................................ 9

Fig 2. 4: Transmission type hydrophone using Schlieren technique [13]................ 10

Fig 2. 5: Principle of intensity modulated total internal reflection pressure sensor

[14]........................................................................................................................... 11

Fig 2. 6: Mach Zehnder interferometer using free space optics .............................. 12

Fig 2. 7: Michelson interferometer using free space optics ..................................... 13

Fig 2. 8: Acoustic pressure sensor using Mach- Zehnder Interferometric detection

[16]........................................................................................................................... 14

Fig 2. 9: Schematic of optical structure wound on the mandrel hydrophone [16]... 14

Fig 2. 10: Multilayer cylindrical fiber optic phase modulated acoustic sensor [17] 17

Fig 2. 11: Embedded interferometric phase modulated acoustic sensor [19] .......... 18

Fig 2. 13: Concept of Fabry Perot interferometer [23] ............................................ 20

Fig 2. 14: FP based fiber optic acoustic sensor [25]. ............................................... 22

Fig 2. 15: Schematic of Fabry Perot based phase modulated sensor [25] ............... 22

Fig 2. 16: Concept of multi-layer structure interferometer...................................... 24

Fig 2. 17: Fiber optic multilayer hydrophone, i=1….N, L=Low index Layer, H =

high index layer, p = Pressure Pulse [27] ................................................................ 25

Fig 2. 18: Phase modulated sensor using heterodyne detection [29]....................... 28

xiii

Fig 2. 19: Heterodyne detection using coated fiber optic hydrophone [30]. ........... 29

Fig 2. 20: Schematic of Fiber Bragg Grating sensor [31]........................................ 30

Fig 2. 21: Implementation of DBR fiber laser structure [35] .................................. 31

Fig 2. 22: Schematic of optical hydrophone employing Distributed Bragg Reflector

fiber sensor [38] ....................................................................................................... 32

Fig 2. 23: RIN cancellation by signal processing [9]............................................... 39

Fig 2. 24: RIN cancellation by differential amplifier [40]....................................... 40

Fig 2. 25: RIN cancellation using balanced photo-detector [41]. ............................ 41

Fig 2. 26: Signal subtraction using anti-parallel photo-diodes ................................ 42

Fig 2. 27: Concept of meshing in Finite Element Method....................................... 47

Fig 2. 28: Concept of Finite Difference approximation........................................... 49

Fig 2. 29: Meshing and using Finite Difference approximation.............................. 50

Fig 2. 30: Illustration of the concept of BPM. ......................................................... 53

Fig 3. 1: Plane wave reflection and transmission at boundary for normal incidence

.................................................................................................................................. 59

Fig 3. 2: (a) Plane waves at boundary between different media (b) Transmission line

equivalent model of waves at two dielectric interface............................................. 62

Fig 3. 3: Transmission line analogue model of uncoated fiber................................ 64

Fig 3. 4: Reflectance vs Pressure amplitude of uncoated fiber................................ 67

Fig 3. 5: Dynamic Responsivity of uncoated fiber sensor in terms of dB per MPa 67

Fig 3. 6: Experimental set-up for extraction of complex refractive index of thin (2 -

35nm) gold films...................................................................................................... 72

xiv

Fig 3. 7: Reflectance (dB) vs coating thickness (nm) of coated fiber sensors at

(blue) 980nm, (red) 1480nm and (black) 1550nm wavelength. .............................. 74

Fig 3. 8: Extracted (a) real and (b) imaginary parts of index of refraction of thin

sputtered gold film as a function of coating thickness at (blue) 980nm, (red)

1480nm and (black) 1550nm. (Error bars of the extracted results for three samples

are indicated by + sign)............................................................................................ 75

Fig 3. 9: Transmission line analogue of metal coated fiber..................................... 77

Fig 3. 10: Improvement in responsivity vs coating thickness considering water

compression only ..................................................................................................... 80

Fig 3. 11: Improvement in responsivity vs coating thickness considering thin film

gold compression only ............................................................................................. 81

Fig 3. 12: Improvement in responsivity vs coating thickness considering water and

thin film gold compression ...................................................................................... 82

Fig 4. 1: (a) Geometry of straight cleaved uncoated fiber (b) Geometry of straight

cleaved thin film gold coated fiber. ......................................................................... 86

Fig 4. 2 Mesh structure of uncoated single mode fiber with step index profile ...... 87

Fig 4. 3: Power density profile of uncoated unetched single mode fiber ................ 91

Fig 4. 4: Geometry and mesh structure of a Graded Index (GRIN) single mode

fiber. ......................................................................................................................... 92

Fig 4. 5: Power density profile of uncoated unetched GRIN single mode fiber...... 92

Fig 4. 6: Geometry, mesh structure and acoustic boundary conditions of etched

GRIN single mode fiber model................................................................................ 94

Fig 4. 7 RF boundary conditions of etched GRIN single mode fiber model. .......... 94

xv

Fig 4. 8: Power density profile of 6 µm etched GRIN single mode fiber model..... 95

Fig 4. 9: Power density profile of 8 µm etched GRIN single mode fiber model..... 95

Fig 4. 10: Power density profile of 10 µm etched GRIN single mode fiber model. 96

Fig 4. 11: Power density profile of 12 µm etched GRIN single mode fiber model. 96

Fig 4. 12: Pressure to voltage responsivity performance of etched cylindrical fiber

sensors as function of etched tip diameter. .............................................................. 98

Fig 4. 13: Geometry, mesh structure and boundary conditions of uncoated 7 degree

linear tapered fiber sensor. ....................................................................................... 99

Fig 4. 14: Power density profile of 7 degree linear tapered GRIN single mode fiber

model...................................................................................................................... 100


model...................................................................................................................... 100


model...................................................................................................................... 101


model...................................................................................................................... 101

Fig 4. 18: Geometry, mesh structure and boundary conditions of exponential

tapered GRIN fiber model ..................................................................................... 103

Fig 4. 19: Power density profile of 7 degree exponential tapered GRIN single mode

fiber model ............................................................................................................. 104

Fig 4. 20: Power density profile of 15 degree exponential tapered GRIN single

mode fiber model. .................................................................................................. 104

xvi


mode fiber model. .................................................................................................. 105


mode fiber model. .................................................................................................. 105

Fig 4. 23 Plot of relative responsivity, dB of uncoated linearly (red) and

exponentially (blue) tapered fiber sensors as function of taper angle. Reference: -

282 dB re 1 V/µPa.................................................................................................. 107

Fig 4. 24: Geometry, mesh structure and boundary conditions of GRIN thin film

coated fiber. Inset shows the mesh structure and boundary condition in gold coated

region. .................................................................................................................... 108

Fig 4. 25: Power density profile of a straight cleaved 5 nm gold coated fiber sensor

................................................................................................................................ 111

Fig 4. 26: Geometry, mesh structure and boundary conditions of etched 5 nm coated

fiber sensor............................................................................................................. 112

Fig 4. 27: Power density profile of 5nm coated 6 micron etched fiber sensor ...... 113

Fig 4. 28: Power density profile of 5nm coated 8 micron etched fiber sensor ...... 114

Fig 4. 29: Power density profile of 5nm coated 10 micron etched fiber sensor .... 114

Fig 4. 30: Power density profile of 5nm coated 12 micron etched fiber sensor .... 115

Fig 4. 31:Geometry, mesh structure and boundary conditions of coated 6 micron

etched fiber sensor ................................................................................................. 115

Fig 4. 32: Power density profile of 5nm coated 7 degree linear tapered fiber sensor

................................................................................................................................ 116

xvii


................................................................................................................................ 117

Fig 4. 34 : Power density profile of 5nm coated 30 degree linear tapered fiber

sensor. .................................................................................................................... 118

Fig 4. 35: Geometry, mesh structure and boundary conditions of 7 degree

exponential coated fiber sensor.............................................................................. 119

Fig 4. 36 : Power density profile of 5nm 7 degree exponential taper sensor......... 120

Fig 4. 37: Power density profile of 5nm coated 15 degree exponential taper sensor

................................................................................................................................ 120


................................................................................................................................ 121

Fig 4. 39: Improvement in responsivity, dB of 6 µm cylindrically etched sensor vs

gold coating thickness (2-30nm). Reference: -282 dB re 1V/µPa. ........................ 122

Fig 5. 1: Experimental set-up at 980nm optical wavelength ................................. 126

Fig 5. 2: Experimental set-up at 1550nm optical wavelength. .............................. 128

Fig 5. 3: Acoustic holder set up, (Left) 3 D linear translator assembly, (Right) HIFU

transducer and sensor holder assembly depicting needle hydrophone (in center with

black cable) and holes for as many as four optical fiber sensors (two on either side

of needle hydrophone with yellow jackets). .......................................................... 129

Fig 5. 4: Needle hydrophone output at 1.5 MHz and 5 MHz, 60Vpp excitation to

transducer, needle hydrophone tip 1 cm from holder surface................................ 130

Fig 5. 5: Needle hydrophone output at 1.5 MHz and 5 MHz, 60Vpp excitation to

transducer, needle hydrophone tip 1 mm from holder surface. ............................. 131

xviii

Figure 5. 6: Needle hydrophone 1D and 2D scan data at 1.5 MHz and 5 MHz. ... 132

Fig 5. 7: Responsivity improvement, dB vs coating time, sec (ref: -282 dB re

1V/µPa). ................................................................................................................. 134

Fig 5. 8: Improvement in responsivity, dB vs coating thickness. Data indicated by

blue line: simulation, red square: Experiment. Ref = -282 dB re 1V/µPa. ............ 140

Fig 5. 9: Responsivity improvement, dB vs coating thickness, nm (Blue:

Simulation, Red: experimental data with errorbar)................................................ 142

Fig 5. 10: Experimental set-up for noise cancellation using balanced detection... 144

Fig 5. 11: Frequency response of PVDF needle hydrophone ............................... 147

Fig 5. 12: Frequency response of straight cleaved uncoated FOHP ...................... 148

Fig 5. 13: Frequency response of 4-5nm coated fiber sensor (# 17 T) .................. 148

Fig 5. 14 : Frequency response of 6-7 nm coated fiber sensor (# 12 C)................ 149

Fig A-2. 1: Propagation constant of the HE11 mode vs wavelength. ..................... 166

Fig A-2. 2: Electrical field amplitude profile of HE11 mode in single mode fiber at

980nm (linear plot). ............................................................................................... 167

Fig A-2. 3: Electrical field amplitude profile of HE11 mode in single mode fiber at

980nm (logarithmic scale). .................................................................................... 167

Fig A-2. 4: Power density profile of HE11 mode in single mode fiber at 980nm. 168

Fig A-6. 1: Geometry and mesh structure of focused transducer model. .............. 173

Fig A-6. 2: Z displacement profile of focused transducer at resonant frequency of

1.59 MHz ............................................................................................................... 176

Fig A-6. 3: Electrical impedance of focused transducer at fundamental resonance.

................................................................................................................................ 176

xix

Fig A-6. 4: Pressure distribution of focused transducer at 1.5 MHz ..................... 177

Fig A-6. 5: 2D linear plot of pressure field at the focus of transducer, focal length =

35 mm .................................................................................................................... 177

Fig A-6. 6: Electrical input impedance of the transducer at fundamental and 3rd

harmonics. .............................................................................................................. 179

Fig A-6. 7: Voltage to pressure transfer function of transducer at fundamental and

3rd

harmonic ........................................................................................................... 179

Fig A-9. 1: Common mode noise rejection performance of PDB 130-C

photodetector [64].................................................................................................. 185

Fig A-9. 2: Noise vs frequency performance of PDB 130C photo-detector [64] .. 185

Fig A-9. 3: Responsivity performance of PDB 130C photo-detector [64]. ........... 186

Fig A-11. 1: Layout of laser diode mount with bias tee ........................................ 195

Fig A-11.2: Realization of laser diode mount........................................................ 195

Fig A-14. 1: Schematic of single ended amplifier ................................................. 199

Fig A-14. 2: Simulated gain performance of amplifier vs frequency .................... 199

Fig A-14. 3: Layout for single ended amplifier design.......................................... 200

Fig A-14. 4: Experimental characterization of amplifier gain. .............................. 200

Fig A-14. 5: Realization of the amplifier............................................................... 201

Fig A-15. 1: Straight cleaved fiber sample ............................................................ 202

Fig A-15. 2: Linearly tapered fiber sample (5 degree taper angle)........................ 202

Fig A-15. 3: Cylindrically etched fiber sample. .................................................... 203

Fig A-15. 4: Geometry of fiber sample #18 C. ...................................................... 203

xx

Abstract

Rupa Gopinath Minasamudram

Under the supervision of Afshin S Daryoush, PhD

Acoustic characterization of medical ultrasound devices is needed for

optimization of image quality in diagnostic applications and to ensure their safety

and effectiveness in therapeutic applications. New generation of acoustic

transducers operating at fundamental frequency 15 MHz are being developed and

FDA requires that as many as 8 harmonics are considered for real-time pressure-

time waveform measurements in dispersive nonlinear medium. Therefore,

hydrophone probes are required to perform characterization of the acoustic output

of these devices at least up to 100 MHz in terms of frequency response.

The primary goal of this thesis is to develop a Fiber Optic Hydrophone

Probe (FOHP) for spatial averaging free characterization of ultrasound field till 100

MHz. Spatial averaging free design of the sensor is based on optimization of fiber

geometry to achieve an active fiber dimension of the order of 7 µm to be

comparable with half of the acoustic wavelength at 100 MHz. An innovative aspect

of this work includes the development of a semi-empirical model for extraction of

complex refractive index at optical wavelengths of 980 nm, 1480 nm and 1550 nm

and stress-strain relationship of thin film gold for thickness ranging from 2nm-

35nm. These are indispensable in modeling and optimization of 100 MHz FOHP in

calculation of optimized pressure to voltage responsivity.

xxi

For responsivity optimization, a novel multi-physics numerical model based

on the Finite Element Method (FEM) was employed to solve electromagnetic,

mechanics, and acoustics performance of the FOHP. The model and the selection of

its input parameters, including coupled acousto-optic interaction of thin film gold,

are based on published physical parameters and accurate extraction of various fiber

parameters.

Optimization results indicate that cylindrically etched FOHP with 6 µm tip

diameter and 5 nm gold coating provides the highest responsivity performance of -

234 dB re 1V/ µPa. The experimental verification of the thin film coated FOHP

using 1 MPa pressure amplitude, produced unprecedented voltage responsivity

between -234 and -254 dB re 1V/µPa or 2V/MPa and 200 mV/MPa, respectively.

The optimum detection sensitivity of around 0.3 kPa is achieved by Relative

Intensity Noise cancellation of 10 dB using balanced optical photo-detector.

1

Chapter 1: Introduction

This thesis deals with the design and optimization of a wide band, spatial

averaging free fiber optic hydrophone probe (FOHP) for characterization of

ultrasound fields in the frequency range of 1-100 MHz for use in applications

relevant to theragnostics. Therapeutic and diagnostic applications of ultrasound

have experienced rapid growth within the past decade. Diagnostic imaging of breast

is routinely performed in the 12-15 MHz frequency range. High Intensity

Therapeutic Ultrasound (HITU) machines are now commercially available and have

gained attention in the treatment of liver tumor, fibroids, and prostate cancer [1, 2].

The existing AIUM/NEMA standards and FDA guidelines require the

acoustic output characterization using hydrophone probes calibrated to eight times

the center frequency of the imaging transducer [2-5]. Thus, the ultrasound field

generated by imaging transducers should be characterized by a calibrated

hydrophone probe having bandwidth on the order of 100 MHz. In addition to

diagnostic applications, the characterization of high intensity (up to 10,000 W/cm2)

fields is crucial for optimizing tissue ablation and minimizing collateral tissue

damage [3-7].

This work describes the development of a novel finite element method

(FEM) model that was used to optimize the design of 100 MHz bandwidth, spatial

averaging free Fiber Optic Hydrophone Probe (FOHP). Such probes are capable of

measuring the ultrasound field in terms of pressure-time (p-t) waveform. The p-t

waveform is the key parameter from which all other ultrasound field characteristics

such as intensities, total power and energy are derived. Currently, in ultrasound

2

metrology, the p-t waveform measurements are performed using hydrophone

probes. The active element in a majority of these probes is made of piezoelectric

polymer (PVDF); however, these probes are not capable of faithful reproduction of

the temporal characteristics of the measured field due to finite (~ 500 µm) aperture

size of the sensitive element area. Such aperture size is about 33 times of the

acoustic wavelength at the highest frequency of interest (i.e., 100MHz) and

introduces spatial averaging errors already at frequencies beyond 3 MHz. In order

to eliminate the effects of spatial averaging, the hydrophones should be able to

sample the field with at least half-wavelength resolution, which at 100 MHz in

water medium would require an active sensor aperture size on the order of 6-7 µm

[8]. Therefore to perform characterization of acoustic fields in the frequency range

up to 100 MHz without introducing spatial averaging error, it is clear that there is a

well defined need for a rugged hydrophone probe with sub-millimeter spatial

resolution.

To design a sub-millimeter resolution hydrophone probe, a single mode

fiber optic hydrophone based on intensity modulation principle was considered. The

specific aims of this thesis are to improve and optimize pressure to voltage

responsivity and sensitivity (minimum detectable pressure) performance of single

mode Fiber Optic Hydrophone Probe by:

• Using novel down-tapered nm scale gold coated fiber sensor.

• Obtaining Signal to Noise Ratio (SNR) improvement by canceling the

dominant laser Relative Intensity Noise (RIN).

3

The thesis is organized as follows: Chapter 2 provides the background

literature survey and motivation for this research. Analytical transmission line based

modeling of thin (2-35nm) film gold coated fiber optic hydrophone probes and

extraction of complex index of refraction of thin (2-35 nm) sputtered gold films is

presented in Chapter 3. Chapter 4 describes in detail the numerical modeling and

optimization of fiber optic hydrophone probe using Finite Element Method

(FEM).Chapter 5 describes the experimental set-up and reports the measurement

results of the fabricated fiber optic hydrophone probes. Conclusions of this work

and suggestions for future work are outlined in chapter 6.

4

Chapter 2: Background and Motivation

2.0 Introduction:

This chapter provides the background survey and motivation for this work. Having

appreciated the need for a wide-band fiber optic based acoustic sensor, it is now

fitting to review some of the relevant works reported in literature. This chapter is

organized as follows: In section 2.1, various acousto-optic sensors presented in

literature are described and compared in terms of their performance (i.e. pressure to

voltage responsivity, sensitivity, bandwidth, etc.).Understanding the advantages and

drawbacks of the existing acousto-optic sensors is vital in making the choice of the

appropriate sensing technique to measure the incident pressure signal. As stated in

chapter 1, the intensity modulation scheme is chosen here for the development of

the fiber optic hydrophone probe. A brief review of the hydrophone terminologies is

presented at the end of this section. In section 2.2, three optical intensity noise

cancellation techniques used in fiber optic hydrophone systems are described.

Appropriate choice of noise cancellation technique is important to enhance the

sensitivity of the fiber optic hydrophone probe. In order to optimize the responsivity

performance of these sensors, it was important to understand the acousto-optic

interactions which contribute to the responsivity. Predicting the behavior of a fiber

optic acoustic sensor required the use of a numerical modeling technique. Section

2.3 provides an overview of the different numerical techniques developed for

solving partial differential equations, namely, Finite Element Method (FEM), Finite

Difference Method (FDM) and Beam Propagation Method (BPM). Their

performance (memory, model geometry complexity) comparison is presented and

5

the FEM is chosen as the numerical technique for design and optimization of the

FOHP.

2.1 Fiber optic acoustic sensors:

In the past two decades, the fiber optic communication industry has

revolutionized the telecommunication industry by providing increasingly high

bandwidth services at decreasing costs. These developments have also driven the

fiber optic sensor technology in parallel. The use of fiber optics in acceleration,

temperature, pressure, acoustics, vibration, strain, humidity, viscosity, refractive

index measurements and a host of other sensor applications, has been explored.

Optical fibers have following advantages over conventional acoustic sensing

techniques: (1) Immunity to electro magnetic interference (2) Small sensing area (3)

Small physical dimensions, light weight. (4) Large bandwidth (5) High resistance to

high temperature, corrosion by chemicals, adverse climatic conditions and hence

can be used in hazardous environments.

An electric wave traveling in a medium in the positive z-direction can be

expressed by the basic equation given below:

)cos(),( oo kztEtzE θω +−= (2.1)

Where,

oE is electric field amplitude in V/m,

ω is angular frequency in rad/s,

k is the wavenumber in per meter,

and oθ is initial phase in radians.

6

In optical sensing, the physical quantity being sensed interacts with the

fiber and directly or indirectly modulates one or more of the above parameters

associated with electromagnetic field in/around the fiber. Accordingly we can

classify acoustic fiber optic sensors as intensity modulated sensors,

frequency/wavelength modulated sensors and phase modulated sensors.

Fig 2. 1: Reflection type fiber optic acoustic sensor with intensity detection [10]

2.1.1 Intensity Modulated Sensors:

In these sensors, the impingent acoustic pressure modulates the intensity of

detected light. These sensors can be further divided as reflection type, transmission

type or total-internal reflection based intensity modulated sensors.

2.1.1.1 Reflection type:

In reflection type sensors, the incident pressure induces a change in the refractive

index of the sensing medium surrounding the sensing fiber. This in turn modulates

the density of the water medium through which the acoustic wave propagates,

changing the refractive index of water. This leads to a change in the Fresnel back-

7

reflectance at the fiber-water interface. The intensity of back-reflected light is thus

modulated by incident acoustic pressure.

The Fresnel reflection at the fiber water interface is given by

R = 2

2

)(

)(

wc

wc

nn

nn

+

−. (2.2)

The responsivity or voltage sensitivity is given by

p

n

n

R

p

n

n

R

p

R w

w

c

c ∆

∆

∆

∆+

∆

∆

∆

∆=

∆

∆, (2.3)

where,

4104.1 −=∆

∆X

p

nw per MPa is the change in refractive index of water with

pressure[9]. 6105 −=∆

∆X

p

nc per MPa is the change in refractive index of silica fiber

with pressure [9]. Since the compressibility of water dominates the responsivity, the

compressibility of fiber core is ignored for a 3.6% error in results.

This principle was demonstrated by Staudenraus et al using a 100/140 µm

multimode straight-cleaved fiber at 800nm optical wavelength [9]. The incident

optical signal was split into two halves and coupled to the sensing fiber. The

sensing fiber was placed in the vicinity of the ultrasonic field. The back-reflected

modulated signal was intensity detected using a 20 MHz bandwidth photo-detector.

Positive pressure amplitudes of as much as 31 MPa were reported by this technique.

Similar cost effective assembly, as shown in Fig 2.1 was demonstrated using

100/125µm straight cleaved graded index multimode fiber at 850nm in [10].

Responsivity of -302 re 1 V/µPa and sensitivity of 0.9 MPa was achieved using a p-

8

i-n photo-detector with 50 MHz bandwidth. [11] reported a similar scheme using

single mode fiber with 10 µm core sensing diameter. 50 mW of optical power at

980nm wavelength was used as the interrogating signal. As seen from Fig 4.2, the

modulated signal was intensity detected using a 1 GHz wideband APD resulting in

a sensitivity of -287.3 dB re 1 V/µPa.

Fig 2. 2: Experimental set-up of single mode intensity modulated fiber optic hydrophone [11]

2.1.1.2 Transmission Type:

In transmission type sensing the intensity of the transmitted light is modulated by

the incident pressure [12]. Two single mode fibers are placed co-axially, with their

straight cleaved ends facing each other, at a 2-3 µm distance of separation as shown

in Fig 2.3. The fiber on the left is rigidly held in the ferrule, while the fiber on the

right is free to vibrate. Acoustic wave incident at the junction causes vertical

displacement of the free fiber. As a result the distance between the fibers changes,

9

Acoustic wave

Optical

fiber

Light INLight OUT

Ferrule

Acoustic wave

Moving

fiber

Optical

fiber

Acoustic wave

Optical

fiber

Light INLight OUT

Ferrule

Acoustic wave

Moving

fiber

Optical

fiber

in turn changing the light coupling efficiency. Maximum light is coupled when

cores of the two fibers are perfectly aligned while no light is coupled when the

displacement is greater than the core diameter. The transmitted light intensity is

Fig 2. 3: Schematic of Transmission type intensity modulated fiber optic acoustic sensor.

thus modulated by the incident pressure amplitude. The fiber used in this case is a

single mode fiber with 4.5 µm core diameter at 620 nm optical wavelength. A

sensitivity of 80 dB re 1 µPa is obtained over an acoustic frequency range of 100 Hz

to 1 kHz [12]. A modification to the above approach is the Schlieren technique

presented in [13]. In this case, the sensitivity of the moving hydrophone is improved

by employing a diaphragm as shown in Fig 2.4. Multimode fibers with 200 µm core

diameter are used as the interrogating fibers. Incident light at 633 nm is passed

through GRIN rod lens and incident on a movable grating structure connected to a

diaphragm. The light which passes through the grating structure is focused into the

10

output multimode fiber using the GRIN rod lens at the output. The amount of light

intensity coupled to the output depends on the spacing between the gratings and the

period of the grating. The incident acoustic pressure displaces the diaphragm, this

Fig 2. 4: Transmission type hydrophone using Schlieren technique [13].

in turn changes the spacing between the gratings and hence modulates the output

light intensity. The minimum detectable pressure in this case is reported to be 60 dB

re 1 µPa while the responsivity of the sensor is -178 dB re 1 V/µPa over the

frequency range of 100 Hz to 5 KHz [13].

Another modification to the above type of sensor includes the use of

frustrated total internal reflection at the edge of multimode fibers [14]. The fibers

are polished and placed at such an angle such that all the modes undergo total

internal reflection at the fiber-air-fiber interface. By bringing the fibers close to one

11

another , as illustrated in Fig 2.5, the amount of light coupling into the fiber can be

increased.

Fig 2. 5: Principle of intensity modulated total internal reflection pressure sensor [14]

Any vertical displacement of one of the fibers violates the above condition and

changes the amount of light coupled to the other fiber. The incident acoustic

pressure modulates the vertical displacement of the fibers and hence modulates the

intensity of the transmitted light. This sensor has a sensitivity of 80 dB re 1 µPa

over 100Hz to 10 kHz frequency range. The transmission type hydrophones have

large sensing areas and are more suited for deep-sea acoustic sensing applications.

Intensity modulation schemes are highly desirable due to simplicity in

construction. They are less sensitive to temperature and spurious phase noise effects

than phase modulated pressure sensing schemes. However, these schemes are

subjected to high loss of optical energy since in reflection at the fiber end or in

coupling between the fibers. Thus responsivity of these systems is typically lower in

comparison to the phase modulated sensors.

12

2.1.2 Phase modulated acoustic sensors:

This section discusses phase modulated acoustic sensors; in which the phase of the

interrogating signal is modulated by the incident acoustic wave. The change in

phase is detected using interferometric techniques. When two coherent light beams,

shifted apart in phase superimpose, they undergo constructive and destructive

interference to form an interference pattern.

Fig 2. 6: Mach Zehnder interferometer using free space optics

Mathematically, let us consider linearly polarized waves with their electric fields as

[15];

).cos( 11111 θω +−= trkE,t)r(E o (2.4.a)

).cos( 22222 θω +−= trkE,t)r(E o (2.4.b)

Where 1oE , 2oE are the electric field amplitudes

k is the wavenumber, per meter.

When these two waves superimpose on each other, the resultant intensity is given

by

LASER

LENS

Mirror

Mirror

BEAM-SPLITTER

BEAM-SPLITTER

Detector

De

tecto

r

SIGNAL PATH

REFERENCE PATH

LASER

LENS

Mirror

Mirror

BEAM-SPLITTER

BEAM-SPLITTER

Detector

De

tecto

r

SIGNAL PATH

REFERENCE PATH

LASER

LENS

Mirror

Mirror

BEAM-SPLITTER

BEAM-SPLITTER

Detector

De

tecto

r

SIGNAL PATH

REFERENCE PATH

13

φcos2 2121 IIIII ++= (2.5)

Where,

2121 )( εεφ −+−= rrk (2.6)

TEI

2

11 = , T

EI2

22 = are the time averaged intensities of the two waves.

21,εε is the initial phase angles of the waves.

The third term in equation (2.3) is the interference term which is modulated by the

acoustic wave in interferometric sensors. The formation of an interference pattern

requires the use of highly coherent source and hence such systems use single mode

laser diodes as the source. The interferometer can be inbuilt within the fiber or

external to the fiber. Depending on the placement of the interferometer within the

fiber sensor system, these sensors can be further classified as (1) Extrinsic

interferometric phase modulated sensors. (2) Intrinsic interferometric phase

modulated sensors.

Fig 2. 7: Michelson interferometer using free space optics

LASER

LENS

Mirror

Mirro

r

SIGNAL PATH

REFERENCE SIGNAL

Detector

BEAM-SPLITTER

LASER

LENS

Mirror

Mirro

r

SIGNAL PATH

REFERENCE SIGNAL

Detector

BEAM-SPLITTER

14

2.1.2.1 Extrinsic interferometric phase modulated sensors:

As the name suggests, in such sensors the interferometer is external to the fiber. The

phase detection is done using interferometric sensing. The two popular

Fig 2. 8: Acoustic pressure sensor using Mach- Zehnder Interferometric detection [16]

Fig 2. 9: Schematic of optical structure wound on the mandrel hydrophone [16]

15

configurations which have been reported in literature are based on Michelson and

Mach-Zehnder interferometers [15]. Light from a coherent source is split into two

arms using the beam-splitter or coupler and hence these are amplitude splitting

interferometers. One arm acts as the reference arm and is isolated from the acoustic

field. The other arm is the sensing arm and is placed in the sensing environment.

Fig 2.6 and Fig 2.7 show the two configurations. Mach-Zehnder interferometer uses

two mirrors to produce 180 degrees phase shift each and two beam-splitters to split

and combine the signals respectively, while Michelson interferometer uses only a

single beam-splitter for dividing and combining the signals. The signals from the

two arms of the interferometer superimpose at the beam-splitter and an interference

fringes are formed at the detector. Any change in the optical path length between

the two arms of the interferometer, changes the phase in the interference term of

equation (2.3). This is manifested in the form of displacement of fringes in the

interference pattern. A displacement of one fringe corresponds to a phase shift of

2π. Thus, the fringe displacement can be calibrated in terms of change in phase and

the incident pressure amplitude can be estimated. It is to be noted that the length of

the 2 arms must be within the coherence length of the laser source to observe this

effect.

Fig 2.8 shows a Mach-Zehnder interferometric based phase modulated

pressure sensor implemented using single mode optical fibers. In this case, the

sensing is performed by spool of fiber wound in the form of a coil as illustrated in

Fig 2.9. Application of pressure to this sensing fiber coil changes the physical

length of the fiber as well as the refractive index of sensing fiber material due to

16

strain-optic effect. This is turn leads to an optical path length difference between the

two arms of the interferometer, leading to phase shift and subsequent fringe

displacement. Thus the incident acoustic pressure modulates the phase and the

fringe pattern [16]. The relationship of phase change on pressure can be

mathematically written as follows.

nLβφ = (2.7)

Where,

φ = Phase of the optical signal

β = Wave-number of the optical signal

n = Refractive index of fiber core

L = Physical length of fiber sensor

p

nL

p

Ln

p ∆

∆+

∆

∆=

∆

∆ββ

φ (2.8)

The first term represents the change in physical length of the fiber while the second

term represents the change in refractive index of the fiber by the incident acoustic

pressure due to strain-optic effect [16]. The amount of phase change induced by the

strain optic effect depends on the strain-optic co-efficients and compliance of

sensing material (in this case, silica). The change in the refractive index of the fiber

is given as;

)2)(21(2

11112

3ppn

En +−=∆ µ (2.9)

Where,

1112 , pp = Pockel coefficients

17

E = Young’s modulus

µ = Poisson’s ratio of the fiber material.

Thus the phase sensitivity of the device to applied pressure can be improved by

using a larger length of fiber sensor or by using materials with higher compliance

(small Young’s modulus). Due to low compliance of silica, a long length of fiber is

needed for improved sensitivity. Sensitivity of 92 kPa has been reported using bare

fiber sensors [16].

Fig 2. 10: Multilayer cylindrical fiber optic phase modulated acoustic sensor [17]

[17] demonstrates the improvement in phase sensitivity of interferometric sensors

by employing a multilayer cylindrical structure surrounding the optical fiber

cladding as shown in Fig 2.10. A factor of 7 dB improvement in sensitivity was

obtained over that of the bare fiber performance, by using a 2 layer structure

consisting of silicon rubber and hytrel surrounding the optical fiber. Sensitivity can

also be enhanced by wrapping the fiber around a mandrel (cylinder) of suitable

material [18]. A mandrel of low Young’s modulus when subject to pressure, its

length changes thus causing stretching or compression of the fiber wound around it.

Thus, the mandrel with higher compliance helps to amplify the change in phase.

The sensitivity improvement obtained by this structure depends on mandrel

18

geometry and properties of the mandrel material. A modification to the above

structure is the embedded single mode fiber acoustic sensor suggested in [19, 20].

The configuration shown in Fig 2.11 is based on Mach Zehnder interferometer.

Fig 2. 11: Embedded interferometric phase modulated acoustic sensor [19]

The coupler at the input splits the signal to the sensing and reference fiber while the

coupler at the output combines the resultant phase modulated signal. The sensing

fiber is coated with a suitable polymer and wound in the form of coil and molded on

to a polyurethane mandrel with low Young’s modulus to improve sensitivity. The

reference fiber is wound to an aluminum mandrel which is rigid to acoustic pressure

in order to isolate the reference fiber from any strain effects. Sensitivity in the range

of -328 to -338 dB re 1V/ µ Pa has been reported over a frequency range of 0.75 to

10 kHz using this scheme.[21] uses the Michelson interferometer for detecting

phase modulation as shown in Fig 2.12. The sensor has been implemented using

free space optic components. The beam splitter helps to split the signal to reference

and sensing arms. Silicon rubber block is placed in the path of the beam of the

sensing arm and is exposed to acoustic pressure. The high compliance of silicone

19

rubber helps to enhance the sensitivity in this scheme. A voltage sensitivity of -205

dB re 1 V/ µPa and a minimum detectable pressure of as low as 22 dB re 1 µPa was

achieved using a 10cm long silicone rubber block [21].

Fig 2. 12: Michelson Interferometer based phase modulated pressure sensor [21]

The major disadvantage associated with the technique is that the system is subjected

to phase changes with respect to temperature changes in addition to pressure

changes. This leads to uncertainty in measured pressure value and is only useful at

frequencies higher than rate of thermal fluctuations of the sensing arm. Phase

modulation techniques are subject to random phase fluctuation due to temperature

drifts, environmental conditions and hence are limited in performance by phase

noise. Temperature drifts can be compensated by using a push-pull configuration

and tunable resonant cavity techniques, making the implementation complex [22].

In case of free space optics based systems, alignment to obtain interference patter is

a cumbersome task. Large lengths of fibers, in tens of meters are required to

achieve high sensitivity. Such large sensing dimensions of the mandrel fiber sensors

20

make them unsuitable for ultrasound sensing applications in the range of 1-100

MHz.

2.1.2.2 Internal interferometric phase modulated sensors:

In this case the interferometer is embedded within the fiber itself, making the size of

the sensor more suited for ultrasonic sensing applications. In this regard, Fabry-

Perot (FP) interferometers have been extensively studied in literature. Fig 2.13

explains the concept of a Fabry Perot interferometer [23].

Fig 2. 13: Concept of Fabry Perot interferometer [23]

In principle, the device consists of two, plane parallel, highly reflecting surfaces

separated by a finite distance. When this distance between the two mirrors is varied,

it forms an interferometer formed by the optical path length modulation of the

waves traveling back and forth within the resonator. The phase difference between

the waves reflected from the surfaces of the two mirrors is given by [23];

θλ

πφ 2

4+=

nL, (2.10)

where

n = refractive index of the Fabry-Perot medium

21

L = length of the cavity

λ = incident optical wavelength

θ = phase change at the reflection from mirror.

The phase change θ is relatively small when compared to that induced by the length

of the cavity. Ignoring the second term, the ratio of the reflected power to the

incident power is given by;

)2/(sin1

)2/(sin2

2

φ

φ

F

F

P

P

i

r

+= , (2.11)

where

F = Coefficient of finesse of the interferometer =

2

21

2

− r

r

r = reflection co-efficient at the mirror surface.

Highly reflecting surfaces can be obtained by using thin semi-transparent metallic

films such as aluminum, silver or gold or by using dielectric films such as TiO2.The

thickness of coating controls the reflectivity of mirrors and hence of finesse the

interferometer, whereas the distance between the mirrors controls the length of the

resonant cavity. These two parameters together determine the sensitivity of phase

modulated sensors.[24,25,26] report the development of a FP based optical

hydrophone for ultrasound sensing applications till 50 MHz. The interferometer is

created by using partially reflecting gold films at the tip of a single mode optical

fiber at 1550 nm. The reflectivity of front and back mirrors were chosen to be 75%

and 98% respectively for optimized sensitivity performance. The reflectivity of

these sputtered films was controlled by controlling the coating thickness. These

mirrors were spaced by using a 10 µm layer of Parylene-C. The low Young’s

22

Pressu

reP

ressure

modulus associated with Parylene, enhances the phase sensitivity of this sensor.

Detailed construction of the sensor is shown in Figs 2.14 and 2.15.

Fig 2. 14: FP based fiber optic acoustic sensor [25].

Fig 2. 15: Schematic of Fabry Perot based phase modulated sensor [25]

The incident light undergoes multiple reflections between the two gold mirrors to

form a resonant structure. The incident acoustic pressure modulates the length of

the polymer spacing, thereby forming an interferometer. The operating point of the

laser is chosen to be at the maximum slope of the interferometer transfer function

23

for maximum sensitivity. Based on equation (2.8), the acoustic phase sensitivity in

this case is given by

)(4

kFE

nL

pl

λ

πφ=

∆

∆, (2.12)

where

E = Young’s modulus of Parylene-C

)(kFl = A function describing the distribution of stress across Parylene-C

This stress distribution function affects the frequency response of the sensor.

Thicker polymer layer improves the sensitivity but has limited broadband nature

due to multiple reflections of acoustic wave within Parylene. The voltage

responsivity of these sensors varies in the range of 209 mV/MPa to 580 mV/MPa

[26]. The sensitivity of the probe was calculated to be 15 kPa over a 20 MHz

measurement bandwidth. However the three reported samples have large probe to

probe variation in responsivity performance. The frequency response indicates a

resonance at 25 MHz due to probe diameter of 150 microns. Though the sensor

provides a better responsivity and sensitivity performance when compared to the

intensity modulated sensors reported earlier, there are two main problems. The

interferometric sensing is highly sensitive to temperature and environmental

vibration effects. Any change in the optical phase leads to shifting of the operating

point on the interferometric transfer function. This immediately changes the

responsivity and dynamic range of the sensor. In order to overcome the effect of

thermal drifts, tunable lasers with computer aided feedback control has been

employed by the system, making the measurement procedure complex. The

interferometer transfer function has to be re-calibrated every time there is a change

24

in the operating point. Secondly, the non uniform frequency response beyond 25

MHz occurs from acoustic wave diffraction effects due to probe dimensions of

about 150 µm.

Fig 2. 16: Concept of multi-layer structure interferometer

The next category of intrinsic interferometric sensors employs Fabry Perot

filters formed by Multi-layer structures as shown in Fig 2.16. Fabry Perot filters

are essentially band pass filters obtained by a specific arrangement of alternating

stacks of dielectric layers with high and low index of refraction. It is well known

that when a plane wave encounters a change in the medium, part of the incident is

reflected and the remaining is transmitted (assuming no absorption). The amount of

power being reflected and transmitted depends on the refractive indices of the two

media. When light is incident on a stack of dielectric coating, some portion of the

light gets reflected and transmitted at each layer interface. These reflected beams

nL

nL

nL

nH

nH

nH

Air

Glass substrate

nL

nL

nL

nH

nH

nH

Air

Glass substrate

25

superimpose to form an interferometer or filter. The filtering characteristic of this

structure depends on the refractive indices, length of the various layers and the

specific arrangement of these hi-lo layers. The Fabry-Perot filter typically consists

of central λ/2 layer of either high or low refractive index followed by an

arrangement of λ/4 layers of high and low index on either side. The finesse or

selectivity of this band pass filter depends on the number of layers and the choice of

the refractive index of the high and low index layers.

Fig 2. 17: Fiber optic multilayer hydrophone, i=1….N, L=Low index Layer, H = high index

layer, p = Pressure Pulse [27]

A multi-layer Fabry Perot filter implemented by Koch et al is shown in Fig

2.17. Two high-reflection subsystems, both consisting of several λ/4 layers, are

connected by a central λ/2 spacer layer which acts as the Fabry-Perot cavity at an

optical wavelength of 631nm. The sensor consists of 19 dielectric layers with

alternating hi-low refractive indices of n = 2.3 (Nb2O5) and n = 1.48 (SiO2) [27].

The total length of this sputter coated multilayer structure is 1.9 µm. The principle

of ultrasound measurement is based on the phase modulation caused by elastic

deformation of the multilayer structure by the incident acoustic field and the

26

resultant change in index of refraction of the dielectric layers by elasto-optic effect.

This phase modulation is intensity detected in terms of change in optical

reflectance, ∆R from the interferometric transfer function.

The effective reflection co-efficient at the input of a multilayer structure can

be written in terms of the characteristic matrix, M as

r = 22121121110

2212112111

mYmmYYmY

mYmmYYmY

NNo

NNoo

++

++

+++

−−+ (2.13)

M =

2221

1211

mm

mm = ∏

=

N

i

iM1

where Mi is the characteristic matrix of the ith

layer.

Mi =

)cos()sin(

/)sin()cos(

iiiii

iiiii

dkndknjY

Ydknjdkn, (2.14)

where

Yi = optical admittance of the ith

layer,

iidn = optical thickness of the ith

layer, and

id = physical thickness of the ith

layer.

The total input reflectance is thus a function of the optical phase shift through each

layer and expressed as:

R = f )( iidkn (2.15)

The responsivity of this sensor is given as:

p

ddknf

p

ndknf

p

R i

ii

i

ii∆

∆+

∆

∆=

∆

∆)(').(' (2.16)

The first term represents the change in refractive index of the ith

due to elasto-optic

effect. This is dependent on elasto-optic constants of the dielectric material and is

given by equation (2.9). The second term represents physical deformation of the ith

27

layer. The responsivity performance can be enhanced by suitable choice of

dielectric materials. The system is operated at maximum sensitivity point

(maximum slope of interference transfer function).Using this approach, a voltage

responsivity of 3 - 4 mV/MPa is obtained till a frequency of 15 MHz [28]. The

frequency response shows a strong resonance peak at 24 MHz. [27] demonstrated

by numerical modeling that the frequency response was strongly influenced by the

propagation of radial waves introduced by lateral strain as well as vibration at the

fiber tip in addition to longitudinal waves. [28] suggests that the resonance peak can

be reduced by destroying the radial symmetry at the fiber tip. As discussed earlier,

phase interferometric systems are highly sensitive to temperature and the works

reported in [27, 28] do not use any control loop to compensate for thermal drifts.

Thus, intrinsic FP cavity structures provide a 20-30 dB higher responsitivity

performance in comparison to the intensity modulated sensors [26]. However, the

operating point has to be stabilized at the maximum slope point on the interference

transfer function. Periodic nature of the interference transfer function, limits the

linearity or dynamic range of such sensors.

2.1.3 Frequency/Wavelength Modulated sensors

In this section, the wavelength modulated acoustic sensors are discussed. Here, the

incident pressure amplitude modulates the wavelength or frequency of the incident

light. These are further classified as indirect and direct frequency modulated

sensors.

28

2.1.3.1 Indirect frequency modulated acoustic sensors with heterodyne

detection:

Indirect frequency modulated sensors are essentially phase modulated sensors,

where modulation of rate of optical phase results in frequency modulation of optical

signal. The phase modulated sensors discussed up to this point is based on detection

of fringe displacement and intensity detection based using homodyne detection.

Fig 2. 18: Phase modulated sensor using heterodyne detection [29].

Homodyne detection is a process which involves mixing of a reference signal with a

sensor signal of the same frequency/ wavelength. Another technique which has

been reported in literature is based on heterodyne detection in which the sensor

signal is mixed with a reference signal of a different frequency/ wavelength.

A heterodyne detection technique using external Bragg’s cell, an acousto-optic

modulator is reported in [29]. As depicted in Fig 2.18, the incident optical

frequency of is modulated using the Bragg’s cell driven at a frequency of 11 MHz.

The Braggs cell shifts the frequency (wavelength) of the laser source by 11 MHz,

29

MHzfo 11+ while the un-shifted frequency component is incident on the sensing

fiber. The sensing fiber is wound in the form of a coil and placed in the acoustic

environment to be sensed. As discussed earlier, the incident pressure modulates the

phase of light proportional to acoustically induced strain and change in refractive

index, resulting in frequency modulation of the signal. This modulated signal from

sensing fiber, so ff + and frequency shifted signal are combined at the output beam-

splitter and detected by the photo-detector. The output of the photo-detector, 11

MHz ± sf , serves as an input to the frequency discriminator, output of which is

proportional to the modulation frequency, sf and hence to the incident pressure

amplitude. A pressure sensitivity of 26 dB re 1 µPa has been obtained over the

frequency range of 1-1400 Hz.

Fig 2. 19: Heterodyne detection using coated fiber optic hydrophone [30].

30

Koch used the above heterodyne interferometry for ultrasound detection till 20

MHz [30]. The sensing was done by a 100 micron diameter fiber with metal coating

at the tip as shown in Fig 2.19. The incident acoustic pressure, compresses the front

end of the fiber creating an optical path length change. This leads to a phase

modulation and subsequently frequency modulation of the incident beam.

2.1.3.2. Direct wavelength modulated sensors:

The most common type of wavelength modulated sensors makes use Fiber Bragg

Grating (FBG) structures. A repetitive array of diffracting elements, that has the

effect of producing periodic perturbations in the phase, amplitude or both of the

emergent wave is said to be a grating [15]. Based on the refractive index profile and

the period of the perturbations, light at a particular wavelength interferes

constructively producing a high finesse structure. If the periodicity of the structure

satisfies the Bragg condition at a certain wavelength, this wavelength is known as

the Bragg wavelength and given by,

dn effB 2=λ (2.17)

Where,

d = periodicity of the grating.

Fig 2. 20: Schematic of Fiber Bragg Grating sensor [31]

31

These grating structures are written into the fiber using etching or photo

lithographic techniques. When acoustic wave is incident on the grating structure,

both refractive index and grating period change due to elasto-optic effects [31]. This

change in refractive index in turn shifts the Bragg wavelength resulting in

wavelength modulation. Fisher et al implemented a FBG structure of 0.5mm length

using heterodyne detection in the frequency range of 76 KHz to 1.9 MHz at 830nm

[32]. [31] reports a grating sensor designed at 780nm Bragg wavelength with a

grating length in the range of 0.6mm- 20mm as shown in Fig 2.20. A sensitivity of

81 dB re 1 µPa has been obtained in the range of 0.01 – 3 MHz. [33] employs

grating sensors in the reflection and transmission mode, at a Bragg wavelength of

1550nm for ultrasound detection up to 3 MHz. The sensor has a sensitivity of 120

dB re 1 µPa with 70 dB dynamic range. Fiber Bragg grating sensors fixed to rubber

diaphragms for enhanced sensitivity in underwater sensing applications have been

studied in [34]. [35] describes a fiber grating written into an Erbium doped fiber for

enhanced sensitivity performance at 980nm used in submarine detection.

Fig 2. 21: Implementation of DBR fiber laser structure [35]

32

Fig 2. 22: Schematic of optical hydrophone employing Distributed Bragg Reflector fiber sensor

[38]

The responsivity or sensitivity of grating sensors can be enhanced by coating the

grating region with a material of lower Young’s modulus. The idea is to amplify

small changes in the axial length of the grating leading to improvement in

sensitivity. This concept has been demonstrated in [36] by using polymer coating.

The reported responsivity varies from -195 dB re 1V/µPa to -220 dB re 1 V/µPa in

the frequency range from 5-20 KHz depending on the material and geometry of

coated grating structure.

Another category which has been explored is wavelength modulate sensor is

the Distributed Bragg reflector (DBR). In [37] Beverini et al used a DBR

structure formed as shown in Fig 2.21 for deep sea sensing applications. Two Bragg

gratings with the same reflection characteristics were written in a fiber and spaced

apart by an Erbium doped fiber medium. This structure acts as an active medium

when pumped at a wavelength of 980nm producing a very narrow linewidth of

reflected signal. Thus this structure is suggested to have a higher sensitivity when

compared to DFB structures. This wavelength modulated sensor is employed in a

33

Mach-Zehnder interferometric configuration for detection. Extremely high

reponsivity of 76 mV/Pa and sensitivity of 0.7 mPa has been reported over the

acoustic frequencies of 10-100 KHz using this technique.

The above concept has been extended to the ultrasonic frequency sensing range by

Guan et al in [38] as shown in Fig 2.22. Instead of interferometric sensing, the

detection principle takes advantage of the modulation of the birefringence between

the two orthogonal modes of the fiber grating. The Bragg wavelengths are slightly

different for the two orthogonal polarization modes resulting in a beat frequency.

The incident acoustic pressure modulates the pitch of the grating there-by

modulating this beat frequency and is detected using a spectrum analyzer. In [38]

two 1550nm Er-Yb doped grating structures each of length 10mm and 3mm

respectively are written inside a single mode fiber. The separation distance between

the two gratings is about 10 mm and results in a dual polarized signal. A coupler

along with the photo-detector monitors beat frequency between both the

polarization modes. The minimum detectable pressure level was calculated to be

164 dB re 1 µPa and 158 dB re 1 µPa at 10 and 20 MHz, respectively

Like intrinsic FP and multilayered phase modulated sensors, the FBG and

DBR based wavelength modulated sensors offer high responsivity and sensitivity

performance. However, these schemes are also highly sensitive to environmental

vibrations, strains and thermal variations. In [31], the authors have indicated that

the frequency response is non-uniform possibly due to the reflection of acoustic

waves inside the grating structure. Demodulation circuit is more complicated in

comparison to simple intensity detection, in that the wavelength modulation is

34

converted to phase modulation using interferometric technique. This makes the

measured result more dependent on environmental conditions and thermal drifts.

The length of the gratings and distributed nature of such sensors restricts their use

in high spatial resolution applications.

2.1.4 Acousto-optic Sensor Parameters

Having reviewed the various acousto-optic sensors reported in literature, it

is now essential to choose the sensing mechanism based on certain performance

criteria. For a hydrophone to faithfully characterize ultrasounds encountered in

theragnostic applications, it has to meet certain performance requirements These

specifications are briefly outlined as follows:

Voltage responsivity: This is the transfer function of the hydrophone specified by

the ratio of voltage measured at the output of the hydrophone to the input pressure

amplitude. It is to be noted that this is also known as Voltage sensitivity in acoustics

and measured in mV/MPa or dB re 1 V/µPa. It is required that the responsivity is of

the order of -268 dB re 1V/µPa in other to make them comparable to the

commercial PVDF hydrophone performance.

Sensitivity or minimum detectable pressure: This is the value of the minimum

input pressure amplitude which provides a signal to noise ratio of 3 dB (in terms of

power) at the detector. The sensitivity is determined by the noise floor level of the

hydrophone. It is expressed in Pa or dB re 1 µPa.

Linearity or 1 dB compression point: This is the value of pressure amplitude for

which the output stops increasing by 1 dB for every 1 dB in the input pressure

amplitude. For diagnostic applications, the hydrophone has to be linear till 10 MPa

35

[30], whereas for therapeutic applications the linearity upto 75 MPa is desired. It is

expressed in Pa.

Dynamic Range: This is the range of pressure values from minimum detectable

pressure to the 1 dB compression pressure, measured in units of dB.

Spatial Averaging Free Bandwidth: This is the frequency at which spatial

averaging is introduced by the sensor and depends on the dimensions of the sensor.

Typically, spatial averaging is introduced for acoustic wavelengths smaller than to

twice the active probe length. For having spatial averaging free performance till 100

MHz, the maximum active sensing dimension should be 7.5 µm. It is measured in

Hz.

Overall sensor bandwidth: This is the frequency at which the responsivity drops

by 3 dB from its maximum value (in terms of power). This bandwidth depends on

the receiver electronics bandwidth as well on the spatial averaging free bandwidth,

which ever is the limiting factor. It is expressed in Hz.

Table 2.1 summarizes the performance of various schemes for ultrasound

sensing available in literature. The wavelength modulated sensors offer best

sensitivity performance. However, the large interaction lengths restrict the spatial

averaging free bandwidth below 1 MHz, making them unsuitable as point receivers

for ultrasound sensing applications. This limitation is overcome by the intrinsic

interferometric phase modulated pressure sensors, which have sensing dimensions

in microns. These sensors exhibit better responsivity and sensitivity in comparison

to intensity modulated sensors. The disadvantage associated with this scheme is the

effect of thermal drift and environmental vibration on the performance of the

36

sensor. External control circuit is required to compensate against temperature

effects, making the sensing process challenging. Another concern is the non-

uniform frequency response due to propagation of acoustic waves in the radial

direction of the probe. This limits the use of these sensors for ultrasound

characterization till 100 MHz. Intensity modulated sensors are simple to implement

and are more robust to thermal fluctuations. Using single mode fiber sensors, with

10 µm active area, the spatial averaging free bandwidth can be extended to around

75 MHz. The disadvantage associated with intensity modulated sensors is the poor

responsivity and sensitivity. In order to have performance comparable to that of the

commercial PVDF needle and PVDF membrane hydrophones, the responsivity has

to be boosted by at least 20 dB. The sensitivity is determined by the noise floor of

the optical hydrophone. Improvement in sensitivity can be achieved by reduction of

the noise component.

The next section discusses the various sources of noise and briefly reviews

some of the noise cancellation techniques for fiber optic hydrophone reported in the

literature.

2.2 Noise cancellation in fiber optic hydrophone sensors:

Before reviewing the noise cancellation schemes, it is important to understand the

sources of noise in the acousto-optic receiver. Noise is a random unwanted signal

which interferes with or masks the information signal, making the detection process

difficult. The noise floor determines the lower end of the dynamic range of the

receiver. In order to reproduce the signal faithfully, the receiver exhibit high signal

to noise ratio.

37

Table 2.1: Performance summary of acousto-optic sensors

Sensing technique Detection technique Voltage Responsivity Spatial Averaging

free BW Sensitivity

Intensity modulation using

multimode fiber [10]

Intensity detection of

back-reflected signal

-302 dB re 1V/µPa

7-10 MHz

239 dB re 1 µPa

Intensity modulation using

single mode fiber [42]


back-reflected signal

-288 dB re 1V/µPa

75 MHz

Inrtinsic Fabry Perot phase

modulated sensor [24]

Intensity detection

-253 dB re 1V/µPa

24 MHz

203 dB re 1 µPa

Multilayer phase modulated

sensor [28]

Intensity detection

-284 dB re 1V/µPa

25 MHz

-

Wavelength modulated fiber

Bragg grating sensor [31]

Intensity detection

---

< 0.5 MHz

81 dB re 1 µPa

Wavelength modulated

Distributed Bragg Reflector

fiber sensor [38]


beat frequencies

----

< 0.22 MHz

164 dB re 1 µPa

38

kTGBI t 42

>=<

The three most important sources of noise in the optical receiver are as

follows:

(i) Thermal Noise: Thermal noise is caused by random collision of carriers in

the resistive element of the circuit. It is also known as Jonhson’s noise or

white noise .The noise power spectral density is given by

(2.18)

where

k = Boltzmann constant = 1.38 X 2310 J/K

T = Temperature

G = Conductance

B = measurement bandwidth

(ii) Shot Noise: This is caused by random emission of photo-induced electrons

or incident photons. The photo-detector, the laser diode as well as the back

end amplifiers contribute to shot noise. Noise power spectral density is

given by

, (2.19)

where

q = charge of an electron

IDC = DC photocurrent at the photo-detector.


(iii) Relative Intensity Noise (RIN): This characterizes the random intensity

fluctuations of the source caused by the quantum nature of emission of

BqII DCsh 22

>=<

39

photons. The RIN of the laser source is specified as the ratio of mean square

intensity fluctuation to the average intensity and given by

2

2

DC

INR

I

IRIN

><= (2.20)

The associated RIN noise power spectral density is,

BIRINI DCRIN

22.>=< , (2.21)

where

IDC = DC photocurrent at the photo-detector.


In intensity modulated schemes, relative intensity noise is the dominant source of

noise. In order to enhance the sensitivity of the fiber optic hydrophone probe,

reduction of intensity noise is essential. Relative noise cancellation schemes

suggested in literature are based on the concept of cancellation of common mode

intensity noise. Three such configurations are discussed below.

2.2.1 Common mode noise rejection by signal processing:

Fig 2. 23: RIN cancellation by signal processing [9]

40

Staudenraus et al implemented a crude form of RIN cancellation by utilizing the

signal processing feature of oscilloscope [9] as illustrated in Fig 2.23. The input

optical power from the laser is split into two at arms 2 and 3 of the optical coupler.

Arm 2 is connected to the fiber optic sensor probe which is placed in the ultrasonic

field. The sensor is a multimode intensity modulated type. Arm 3 of the coupler is

connected to the photo-detector which contains RIN noise signal and is termed as

the ‘noise detector.’ Arm 4 of the coupler contains the information signal as well as

the RIN noise signal. Subtraction of the signals from arms 3 and 4 cancels the

common mode RIN noise. The efficiency of noise cancellation depends on

matching of the two photo-detectors.

2.2.2 Common mode noise rejection by differential amplifier:

Fig 2. 24: RIN cancellation by differential amplifier [40]

Koch et al implemented RIN cancellation using differential amplifier and free space

optics components as shown in Fig 2.24. The input optical signal is split and

coupled to the sensor and reference arm using the beam splitter. The reference arm

41

collects the noise signal and is fed to the non-inverting input of amplifier, A. The

sensor is a multi-layered coated phase modulated hydrophone placed in the acoustic

field to be sensed. The back-reflected information signal is given to the inverting

terminal of the amplifier. Out of phase combination of the two signals, cancels the

common mode noise signal [40]. The amount of noise cancellation achieved by this

technique depends on the matching of the photo-detectors and the Common Mode

Rejection Ratio (CMRR) of the differential amplifier.

2.2.3 Common mode noise rejection by anti-parallel photo-diodes:

Fig 2. 25: RIN cancellation using balanced photo-detector [41].

Beard et al implemented the RIN cancellation using balanced photo-detector [41].

The common mode rejection is performed by anti-parallel photodiodes as shown in

Fig 2.26. The set-up for RIN cancellation is depicted in Fig 2.25. The signals

incident on the two photo-detectors are the reference signal, which contains the

noise and the sensor signal which contains information as well as noise signal. The

42

sensor in this case is a FP interferometric phase modulated sensor. The photo

currents from two well matched photo-detectors are subtracted resulting in the

cancellation of the common mode relative intensity noise and the information signal

is amplified by the trans-impedance stage.

Fig 2. 26: Signal subtraction using anti-parallel photo-diodes

Based on the literature reviewed in sections 2.1 and 2.2 of the chapter, it is clear

that in order to design a spatial averaging free, wideband fiber optic hydrophone

probe till 100 MHz, fiber probe dimensions must be of the order of 7 microns.

Intensity modulated scheme as reported by Lewin et al in [42] has been chosen as

the sensing technique as it is less sensitive to thermal fluctuations and

environmental effects. Though simple in construction, the responsivity needs to be

improved by at least 20 dB to make these sensors applicable. Naturally, this would

require a design optimization of the fiber sensor tip to boost responsivity while

providing spatial averaging free performance. Optimization of the fiber sensor

design involves several critical steps such as modeling the waveguiding

characteristic of the fiber sensors with different tip geometries, studying the effects

43

of thin film coating and modeling the interaction of acoustic waves with the optical

field. Accurate modeling of these phenomena requires the use of numerical

methods. The next section briefly reviews the theory of optical waveguide analysis

and existing numerical methods for the same.

2.3 Numerical modeling of optical waveguides:

This section reviews the various numerical techniques used for optical waveguide

analysis. Light is essentially an electromagnetic wave and its propagation is

governed by the Maxwell’s equations expressed below [43]:

t∂

∂−=×∇Β

Ε

t∂

∂+=×∇

DJΗ (2.22)

0.

.

=∇

=∇

B

D νρ

Where,

E = electric field intensity

H = magnetic field intensity

D = electric field density

B = magnetic field density

νρ = electric charge density

J = current density

Solving the above equations for a homogenous, isotropic, source free medium,

results in the following,

44

t∂

∂−=×∇Β

Ε

t∂

∂=×∇

DΗ (2.23)

0.

0.

=∇

=∇

B

D

Taking the curl of the first two expressions leads to time harmonic wave equations

for electric and magnetic fields expressed below,

0

0

2

22

2

22

=∂

∂−∇

=∂

∂−∇

t

t

ΗΗ

ΕΕ

µε

µε

(2.24)

Using the phasor notation of electric and magnetic fields, the above expressions are

reduced to Helmholtz wave equations given by.

0

0

22

22

=+∇

=+∇

HH

EE

k

k (2.25)

Where, k = µεω is the wave-number

Solution to the above 3D Helmholtz equations, subject to appropriate boundary

conditions models the propagation characteristics of the waveguide. The 3D

Electro-magnetic (EM) equations can be solved by the following methods [44, 45]:

• Analytical techniques: Analytical techniques make simplifying assumptions about

the geometry of the waveguide in order to apply a closed-form solution. These are

useful when the nature of the fields can be anticipated. However, most EM analysis

problems are too complex to be approximated using this approach. Nevertheless,

analytical solutions are very important as they provide qualitative physical insight

45

for complex problems, useful in initial design. They act as a good reference for

verifying numerical test results.

• Asymptotic techniques: Asymptotic techniques involve expansion of partial

differential as an infinite series, and taking any initial partial sum provides an

asymptotic formula for that equation. Inclusion of higher order terms provides a

more accurate solution than the simplified analytical formulae. Geometrical optics,

Ray tracing, and quasi-static approximation fall under the above category.

• Numerical techniques: Numerical techniques attempt to solve fundamental field

equations directly, subject to the boundary constraints posed by the geometry.

Numerical techniques require more computation than analytical techniques or

asymptotic techniques, but are very powerful EM analysis tools. Without making a-

priori approximations about field interactions, numerical techniques analyze the

entire geometry provided as input. They calculate the solution to a problem based

on a full-wave analysis and provide highly accurate results for complex geometries

where use of analytical methods would result in significant errors.

The three most common numerical methods used for numerical modeling of

optical waveguides are: (1) Finite Element Method (FEM). (2) Finite Difference

Method (FTD). (3) Beam Propagation Method (BPM).

2.3.1. Finite Element Method (FEM):

The concept of the finite-element method is that although the behavior of a function

may be complex over a large region, a simple approximation may be used to solve

it over a small region and the results can be summed to give the wave solution. The

total geometry to be modeled is thus divided into a number of small non-

46

overlapping regions called “elements” [46]. The field equation to be solved is

approximated by a specific expression over each element. In one approach, this

expression is a function of the complex function which is to be evaluated. This is

called a functional and this approach is called Variational method. For example,

assuming, that the wave is traveling in the positive z direction with propagation

constant β, the Helmholtz wave equation for electric or magnetic field , Ф reduces

to ,

( ) 022

2

2

2

2

=Φ−+∂

Φ∂+

∂

Φ∂βk

yx (2.26)

The functional, )(Φ= fI is chosen such that when the functional becomes

stationary, it leads to the field solution [43]. That means, solving

0=Iδ (2.27)

is equivalent to solving equation (2.26).

In the second approach, an approximation of the actual wave solution is solved over

each element.

( ) Rkyx

=Φ−+∂

Φ∂+

∂

Φ∂ 22

2

2

2

2

β (2.28)

R is the residual error between the approximate solution and the actual solution.

Iteratively this residual error is iteratively forced to zero over the region to be

analyzed. Thus,

daRA

.∫W = 0 (2.29)

Where W is the weight associated with the residue. This is called the Galerkin

method.

47

Fig 2. 27: Concept of meshing in Finite Element Method

Thus, the first step in finite-element analysis is to divide the geometry over which

the wave equations have to be solved, into smaller elements as shown in Fig 2.27.

For 90% and higher accuracy of the results, the size of the element should at least

be 1/10th

of the incident wavelength [47]. Smaller the mesh size, higher is the

accuracy of the result. This however requires enormous computational resources. In

order to consume lower memory; the elements can be small where geometric details

exist and much larger elsewhere. Triangular and square meshes are popularly used

mesh shapes. Triangular meshes are widely used for complex geometries [46].

Once the meshing is done, equation (2.27) or equation (2.29) is solved over

each element. In each element, the field Φ is expressed in terms of a linear or

quadratic function, called the shaping function, N of the field. The corners of the

elements are called nodes. The goal of the finite-element analysis is to determine

the value of the field at the nodes, using the shape function and values from the

neighboring nodes. The computations are based on building matrices whose order

depends on the mesh shape and the shape function. Contributions of individual

element are summed to solve the overall matrix. The Dirichlet or Neumann

48

boundary conditions are applied to outer boundary of the region under analysis. The

final eigenvalue matrix has the form [43, 49],

[ ] [ ] 0)( 2 =Φ− BA λ , (2.30)

where

A and B are matrices which are a function of shaping polynomial N.

222 βλ −= k is the propagation constant.

Solution to the above matrix is the solution to the Helmholtz wave equations.

The major advantage that finite element methods have over other EM

modeling techniques is the fact that the electrical and geometric properties of each

element can be defined independently. This permits the problem to be solved with a

large number of small elements in regions of complex geometry and fewer, larger

elements in relatively open regions. Thus it is possible to model configurations that

have complicated geometries and many arbitrarily shaped dielectric regions in a

relatively efficient manner. Smaller the mesh size, greater is the accuracy of the

solution. However, smaller mesh dimensions consumes a lot of memory and also

increases computation time [48].

2.3.2. Finite Difference Method (FTD):

In this method, the region to be analyzed is discretized into smaller region. The

finite difference approximation is applied to the wave equation being solved over

each region [43,50]. The finite difference approximation is discussed below.

49

Fig 2. 28: Concept of Finite Difference approximation

Consider a 1 dimensional function, continuous and smoothly varying as shown in

Fig 2.28. The Taylor series expansion for the values of the function at h1 and h2 can

be written as follows:

))0(()0("!2

1)0('

!1

1)0()( 2

222 fHfhfhfhf ++−=− (2.31.a)

))0(()0("!2

1)0('

!1

1)0()(

2

111 fHfhfhfhf +++=+ (2.31.b)

Where, H (f (0)) is higher order terms of the Taylor series expansion.

Subtracting and adding the above 2 equations gives the approximation for first and

second derivatives of the function at the origin respectively.

))0(()()(

)0('21

21 fEhh

hfhff +

+

−−= (2.32.a)

))0(()(

))0()()()((2)0("

2121

212112 fEhhhh

fhhhfhhfhf +

+

+−−+= (2.32.b)

Where, E (f (0)) is the error due to higher order terms.

f(0)f(-h2)

f(h1)

-h2 h10x

f(0)f(-h2)

f(h1)

-h2 h10x

50

The above equations are known as finite difference approximations [43,50]. These

are then applied to over each node of the element and the field at a node is

evaluated based on the value of the field at adjacent nodes. For example, let us

consider the geometry as shown in Fig 2.29 over which the solutions of the wave

equation have to be evaluated. The first step in FTD is to divide the region to be

analyzed into smaller elements of rectangular or square shape, forming M X N

elements mesh.

Fig 2. 29: Meshing and using Finite Difference approximation

The finite difference approximation is used to evaluate the field Ф at a node

),( qp yx as below:

0)()(... ,

22

,,11,1,,1 =−++++−+++ +−+− qpqpqpqpqpqp kdcbadcba φβφφφφφ (2.33)

Where, a, b, c and d are functions of distances d1, d2, d3 and d4. Evaluating the

expression for all the nodes, and applying Dirichlet and Neumann boundary

(x p,yq )

(x p,yq+1 )

(x p+1,yq )

(x p,yq-1 )

(x p-1,yq )

d1

d2

d3

d4

(x p,yq )

(x p,yq+1 )

(x p+1,yq )

(x p,yq-1 )

(x p-1,yq )

d1

d2

d3

d4

51

conditions on the outermost boundaries, the global matrix is created leading to the

eigenmatrix as shown below [43,50]:

][ 2 φβφ =A (2.34)

FTD solves the stationary Helmholtz wave equations using the phasor

representation. Finite Difference Time Domain (FDTD) method directly solves the

wave equations directly in the time harmonic representation as shown in equation

2.24. Both space and time variables are quantized in this case. Finite difference

approximations are used to evaluate the space and time derivatives. Inputs are time-

sampled analog signals. The region being modeled is represented by two

interleaved grids of discrete points. One grid contains the points at which the

magnetic field is evaluated. The second grid contains the points at which the

electric field is evaluated. The electric field values at time t, are used to find the

magnetic field values at time t + ∆t and vice versa. At each time step, the electric

and magnetic fields are alternately calculated through the grid. Time stepping is

continued until a steady state solution or the desired response is obtained. Since

both space and time variables are quantized, the required computer storage is

enormous. Execution time is proportional to the electrical size of the volume being

modeled and the grid resolution (mesh dimensions). Absorbing elements are used at

the outer boundary of the lattice in order to prevent unwanted reflection of signals

that reach this boundary. Anisotropic materials to be modeled and non-homogenous

materials can thus be easily modeled. The disadvantage of this method is the shape

of the mesh is rectangular. Arbitrary mesh shapes are not possible. Hence accuracy

suffers while modeling objects possessing cylindrical or circular geometry [48].

52

2.3.3 Beam Propagation Method (BPM):

Beam propagation method is a technique based on solving Helmholtz wave

equations using slow varying envelope approximation [43]. The field solution of a

wave propagating in the positive z direction with propagation constant β is

expressed in terms of a slowly varying envelope as below:

zjezyxAzyx β−=Φ ),,(),,( (2.35)

Substituting the above in equation (2.26) and using the Fresnel approximation that

02

2

=∂

∂

z

A, we get

Aky

A

x

A

z

Aj )(2 22

2

2

2

2

ββ −+∂

∂+

∂

∂=

∂

∂ (2.36)

The goal of BPM is to solve above equation at each discrete step along the direction

of propagation. Knowing the field at position z, A(x, y, z) the field at the next step z

+ ∆z, A (x, y, z +∆z) is evaluated. Once the field A(x, y, z) is computed, translation

through a distance of ∆z is manifested in the form progression of phase of the

slowing varying signal. This process is iterated in the direction of propagation as

shown in Fig 2.30. This is implemented using either Fast Fourier Transforms (FFT-

BPM) or Finite Difference Method (FD-BPM) or Finite Element Method (FE-

BPM) [43]. In FFT, the field is represented in terms of its Fourier basis functions

and the problem is solved in the frequency domain. Since discretization is

performed only along the direction of propagation, less computer memory is

required for storage. As a result, the computational speed is higher. Drawback is

that this technique is not useful in modeling scenarios where the Fresnel

approximation does not hold good. Presence of reflecting waves and evanescent

53

waves also poses a problem as the method cannot differentiate between an

evanescent mode and a propagating mode. Thus this is not useful for modeling

scattering waves [48].

Fig 2. 30: Illustration of the concept of BPM.

As stated earlier, design and optimization of the fiber optic hydrophone is a

complex process involving acousto-optic interactions. This requires the use of

software that can model acoustics and EM equations and couple the impact of one

physical phenomenon on the other. Hence COMSOL Multiphysics, an FEM based

software is chosen as the simulation and design tool for this work [51]. COMSOL is

capable of modeling any physical process described with Partial Differential

Equations. Geometry of the structure and its constituent material properties can be

specified by the user. CAD imports can also be used to specify geometry. A

particular advantage of this package which makes it attractive for our application is

its multiphysics coupling capability, enabling equations from various fields such as

structural mechanics, high frequency electromagnetics, and acoustics to be linked

A (x, y, z)A (x, y, z+∆z) A (x ,y ,z+2∆z)

∆z ∆z

A (x, y, z)A (x, y, z+∆z) A (x ,y ,z+2∆z)

∆z ∆z

54

and solved all in the same model and all at the same time. Thus acoustic pressure

effects and its interaction on the electromagnetic radiation at the fiber tip and inside

the fiber can be effectively modeled. This can further be used to predict the fiber tip

geometry which will yield optimum hydrophone responsivity.

2.4 Summary:

This chapter presented a classification of the various acousto-optic sensors

presented in literature. As stated earlier, the wavelength modulated sensors offer

best sensitivity performance. However, the large interaction lengths restrict the

spatial averaging free bandwidth below 1 MHz, making them unsuitable as point

receivers for ultrasound sensing applications. This limitation is overcome by using

intrinsic interferometric phase modulated pressure sensors, which have sensing

dimensions of the order of microns. These sensors exhibit higher (20-30 dB)

responsivity and sensitivity in comparison to intensity modulated sensors but are

sensitive to thermal drifts and environmental vibrations. External control circuitry is

required to compensate against temperature fluctuations, making the detection

process complicated. Another concern is the non-uniform frequency response with a

resonance at 25 MHz which sets a limitation on the bandwidth. Intensity modulated

sensors are simple to implement and are more insensitive to thermal fluctuations in

comparison to interferometric sensors. Using single mode fiber sensors, with 10 µm

active area, the spatial averaging free bandwidth can be extended to around 75

MHz. The disadvantage associated with intensity modulated sensors is the poor

responsivity (-302 dB re 1 V/µPa) and sensitivity. In order to have performance

comparable to that of the commercial PVDF needle and PVDF membrane

55

hydrophones, the responsivity has to be boosted by at least 20 dB. The intensity

modulation scheme was chosen for the development of the fiber optic hydrophone

probe as these fiber optic sensors had desirable probe dimensions (~ 7 microns) for

avoiding spatial averaging error till 100 MHz. Accordingly, the contributions of this

thesis are as follows:

• Improving responsivity of fiber optic hydrophone sensor by increasing

optical source power, using thin (2-35nm) film gold coating, and

identifying optimum geometry for optimum coating thickness.

• Improving sensitivity of fiber optic hydrophone by employing RIN

cancellation technique to reduce RIN dominated receiver noise

floor.

Three distinct optical intensity noise cancellation techniques used in fiber

optic hydrophone systems were discussed to improve the sensitivity of the fiber

optic hydrophone probe. Finally, a brief review of the different numerical

techniques developed for solving partial differential equations was presented. To

gain insight into the complex acousto-optic interactions contributing to the

responsivity performance of the probe which in turn serves as a guideline in the

optimization process of the fiber optic hydrophone probe a multi-physics analysis

and geometry optimization is to be conducted. The commercially available

multiphysics software from COMSOL Inc (Sweden) that uses Finite Element

Method (FEM) was selected due to its ability to simultaneously solve multiple

physics equations of electromagnetic for optics, acoustics, and mechanics, while it

56

handles complex geometries (fiber end-face) with greater accuracy when compared

to the other techniques.

57

Chapter 3: Analytical modeling

3.0 Introduction:

As discussed in chapter 2, for achieving a spatial averaging free bandwidth

of 100 MHz, single mode reflection based acoustic sensors with active dimensions

of the order of 7 microns are required. In order to make the responsivity

performance of these sensors comparable to that of that of the commercially

available PVDF needle and PVDF membrane hydrophones, the responsitivity

requires to be boosted by a factor of 20 dB at least. It was conceived that a thin

layer of metallic gold coating at the tip of the fiber sensor could enhance the p-v

responsivity by increasing the reflectance from the fiber sensor tip. In order to gain

an initial understanding of the impact of thin gold coating on the responsivity

performance of the fiber sensors, an analytical model was required. Accordingly,

this chapter deals with the analytical modeling of the nanometer gold coated and

uncoated fiber optic sensors based on transmission line theory.

The chapter is organized as follows: Section 3.1 outlines the behavior of

plane waves at two material interfaces and gives a brief introduction to the

transmission line analogue technique. Section 3.2 presents the analytical

transmission lien model of the uncoated fiber optic hydrophone probe which serves

as a reference for further analysis. Review of the data in literature revealed that the

thin film optical constants differ by almost 100% from the bulk optical constants of

gold and that the optical properties are dependent on several factors such as the

thickness of the film, the optical wavelength, the deposition technique, the substrate

properties and the nature of the deposited film. Moreover, to the best of the author’s

knowledge, the complex optical constants of sputtered gold films with thicknesses

58

below 20nm at the optical wavelengths of interest (here, 980nm, 1480nm, and

1550nm) are not available. These are the wavelengths at which high (1 W) power

semiconductor sources are available. In order to correctly model the behavior of the

gold coated fiber optic hydrophone sensors, it was crucial to determine the thin (2-

35nm) film optical constants of gold. Section 3.3 explains the extraction procedure

in detail and presents the extracted optical constants at wavelengths of 980nm,

1480nm, and 1550nm. Section 3.4 extends the analytical model to the coated fiber

sensors taking into account the extracted values of complex index of refraction of

thin film gold. In addition to the compression of water by incident acoustic

pressure, the impact of compression of thin gold by the incident acoustic pressure

on the fiber sensor responsivity is evaluated.

3.1 Plane wave propagation at two material interface:

When a plane wave traveling in a homogenous unbounded medium

encounters a sudden discontinuity, part of the energy is reflected and the remaining

energy is transmitted into the second medium. This is similar to what happens to the

wave in a guided medium such as transmission line. Any discontinuity in the

impedance of the medium causes part of the energy to be reflected, giving rise to a

reflected wave. The remaining energy gives rise to the transmitted wave. In case of

load mismatch to the line’s characteristic impedance, this remaining energy is

delivered to the load. Thus it can be seen that the above two scenarios are analogous

to each other. The behavior of plane waves at a boundary can thus be modeled

using transmission line analogue. This chapter deals with analytical modeling of

both coated as well as uncoated optical fiber sensors based on transmission line

59

equivalent model. The transmission line analogy based on plane wave

approximation is valid to represent the linearly polarized modes in a single mode

fiber. The model assumes that the core refractive index is nearly same as that of the

cladding. The model also assumes that the core is infinite in extent and geometry of

the fiber is ignored.

Fig 3. 1: Plane wave reflection and transmission at boundary for normal incidence

33.1.1 Reflection and Transmission coefficient of plane wave at boundary:

The linearly polarized modes in the fiber optic waveguide can be modeled as plane

waves as an initial approximation. As shown in Fig 3.1, a planar interface separates

two homogenous, lossless, isotropic media. Medium I is characterized by (µ1,ε1)

while Medium II is characterized by (µ2,ε2). Let us assume that the wave is

propagating in the +z direction. Thus the propagation unit vector for incident wave

is given by ∧

ik =∧

z .This wave sees a sudden discontinuity at the interface and is

partially reflected. The reflected wave travels in the direction opposite to that of the

incident wave and has a propagation unit vector given by ∧

rk = -∧

z in the negative z

Incident wave

Reflected wave

Transmitted wave

Medium I

η1

Medium II

η2

Z=0

Incident wave

Reflected wave

Transmitted wave

Medium I

η1

Medium II

η2

Incident wave

Reflected wave

Transmitted wave

Medium I

η1

Medium II

η2

Z=0

60

direction. The transmitted wave has same direction as that of the incident wave,

∧

tk =∧

z .

The phasor form of electric and magnetic fields for the three waves can be

represented as follows [52]:

Incident wave: jkz

oii eEz−

∧

= xE )(~

jkz

oii eEz−

∧

= 1

)(1

~

XzHη

= jkzoi eE −

∧

1ηy

Where wave number in medium I, 1k =k = µεω .

Reflected wave: jkz

orr eEz+

∧

= xE )(~

jkz

orr eEz+

∧

−= X )(1

)(1

~

zHη

= jkzor eE +

∧

1ηy-

Where wave number in medium I, 1k =k = µεω .

Transmitted wave: jkz

ott eEz−

∧

= xE )(~

jkz

ott eEz−

∧

= X 1

)(2

~

zHη

= jkzot eE −

∧

2ηy

Where wave number in medium II, 2k =k = µεω .

The total field in medium I is a summation of incident field and reflected

field while the total field in medium II is the transmitted field.

Field in medium I:

=+= )()()(~~

1

~

zzz ri EEE )( jkz

or

jkz

oi eEeE+−

∧

+x

=+= )()()(~~

1

~

zzz ri HHH )(1

1

jkz

or

jkz

oi eEeE+−

∧

−η

y where 1k =k = µεω .

61

Field in medium II:

jkz

ott eEzz−

∧

== xEE )()(~

2

~

== )()(~

2

~

zz tHH jkzot eE −

∧

2ηy where 2k =k = µεω .

Applying boundary conditions for ~~

, HE at z = 0, the tangential component

of electric field is always continuous along the boundary. Since the boundary is

source free (no current sources), the tangential component of the magnetic field is

also continuous at the boundary. As no free charges or currents exist at the

boundary, only tangential components of the reflected and transmitted fields are

present.

Hence,

)0()0( 2

~

1

~

EE = , )0()0( 2

~

1

~

HH =

Therefore,

t

o

r

o

i

o EEE =+ (3.1)

211 ηηη

t

o

r

o

i

o EEE=− (3.2)

Solving (3.1) and (3.2) simultaneously yields,

i

o

r

o EE

+

−=

12

12

ηη

ηη, i

o

t

o EE

+=

12

22

ηη

η

The reflection coefficient ( Γ ) at the boundary is the ratio of reflected electric field

to the incident electric field.

Thus, ==Γi

o

r

o

E

E

+

−

12

12

ηη

ηη. (3.3)

62

Z01 Z02

Z=0

Incident wave

Reflected wave

Transmitted wave

Transmission line I

Transmission line II

Z01 Z02

Z=0

Incident wave

Reflected wave

Transmitted wave

Transmission line I

Transmission line II

.

Incident wave

Reflected wave

Transmitted wave

Medium I Medium II

Z=0

η1 η2

Incident wave

Reflected wave

Transmitted wave

Medium I Medium II

Z=0

η1 η2

Fig 3. 2: (a) Plane waves at boundary between different media (b) Transmission line equivalent

model of waves at two dielectric interface

The transmission coefficient (τ) at the boundary is the ratio of transmitted electric

field to the incident electric field.

Thus, ==i

o

t

o

E

Eτ

+ 12

22

ηη

η. (3.4)

For a non- magnetic medium, the intrinsic impedance of the medium is given

by r

o

ε

ηη = , where rε = relative permittivity of the medium. The refractive index

of a non-magnetic material is given by n ≈ rε . Substituting in equation (3.3) and

(3.4), the reflection co-efficient and transmission co-efficient in terms of refractive

index of the medium can be given as

=Γ

+

−

21

21

rr

rr

εε

εε=

+

−

21

21

nn

nn (3.5)

=τ =

+ 21

12

rr

r

εε

ε

+ 21

22

nn

n (3.6)

63

3.1.2 Transmission line equivalent theory:

Transmission line analogue approach offers a simplistic technique to model

the effect of dielectric materials on the medium. As seen in Fig. 3.2a, the two media

are separated at the planar boundary at z = 0. The transmission line equivalent

circuit is shown in Fig. 3.2b. As seen, intrinsic impedance of different media are

represented in terms of characteristic impedance of transmission lines

( 101 η≡Z , 202 η≡Z ), the electric field is represented in terms of voltage on the line

(~~

VE ≡ ), and the magnetic field is analogous to current on the line (~~

IH ≡ ).

Material properties such as rr εµ , and refractive index ‘n’ of the medium are thus

expressed as impedance of the transmission line. A denser medium with a high

value of refractive index has a low value of intrinsic impedance and is denoted as a

line of larger width. On the other hand, a rarer medium is indicated by a smaller

width line. As already known from the transmission line theory, a sudden change in

the width of the transmission line causes some portion of the incident energy to be

reflected and the remaining is transmitted to the second line or the load. This is

precisely what happens to a plane wave which sees a sudden discontinuity in the

material medium in which it propagates. The energy is partly reflected and partly

transmitted. The amount of reflection depends on the relative refractive index

mismatch of the two media. Larger the mismatch, higher is the amount of

reflection. With these basic quantities being defined, the reflection and transmission

co-efficient at various dielectric interfaces can be easily calculated.

64

Incident wave

Reflected wave

core

0 0

n

η Z =

water

0 L

n

η Z =

Incident wave

Reflected wave

water

0 L

n

η Z =

Incident wave

Reflected wave

water

0 L

n

η Z =

in Γ in Γ

≡ core n water n

in Γ in Γ

≡

Incident wave

Reflected wave

n core

Fig 3. 3: Transmission line analogue model of uncoated fiber

3.2 Analytical model of uncoated fiber:

Fig. 3.3 shows the transmission line equivalent model of the single mode

fiber. The model assumes infinite cladding region which is valid when the dominant

mode is well guided in the core region. The model also assumes that the refractive

index difference between the core and cladding regions is negligible (∆ ~0.001).The

effects of finite cross-sectional sensing area as well as the tip geometry effects are

ignored. Therefore only the effect of dielectric materials on the propagation of light

in the fiber is modeled. Core refractive index of the single mode fiber, coren is

considered to be 1.41 at incident optical wavelength of 980nm while refractive

index of water, watern is considered to be 1.33.

The fiber core is replaced by a transmission line of characteristic

impedance,coren

Z 0

0

η= .Water is replaced by a load of impedance,

water

Ln

Z 0η= .

Reflection occurs due to refractive index mismatch at the core-water interface. The

reflection coefficient at the fiber core-water interface is given by

65

watercore

watercore

in

corewater

corewater

L

L

in

nn

nn

nn

nn

ZZ

ZZ

+

−=Γ

+

−

=

+

−=Γ

00

00

0

0

ηη

ηη

The reflectance (R) for the TEM at normal incidence is given as,

R = *ininΓΓ = | inΓ |2

R =

2

watercore

watercore

nn

nn

+

−

(3.8)

The return loss is expressed in logarithmic scale of base ten as,

R (dB) = 20log| inΓ |= 20logwatercore

watercore

nn

nn

+

− (3.9)

As noted earlier, application of ultrasound causes a change in the density and

hence refractive index of water. This in turn causes a change in the reflection co-

efficient at the core-water interface, in turn modulating the reflectance looking into

the fiber. We are interested in evaluating the responsivity of the sensor which is

defined as the ratio of change in reflectance to the applied pressure amplitude,

expressed in units of dB per MPa. The responsivity can be calculated by

differentiating equation (3.8) with respect to pressure as follows:

dP

d

dP

d

dP

dR in

in

in

in

ΓΓ+

ΓΓ=

*

*

. (3.10)

The responsivity can be also expressed as a function of compression of water and

fiber core by the incident acoustic pressure as:

66

dP

dn

dn

dR

dP

dn

dn

dR

dP

dR w

w

c

c

+= . (3.11)

The change in refractive index of water with respect to pressure is a linear

relationship given by 14104.1 −−= MPaXdP

dnw [11].The compressibility of fiber core

is a factor of 100 lower than that of water and given by 16106.1 −−= MPaXdP

dnw .

Ignoring the refractive index of core change with respect to pressure for a 3% error

in the result, equation (3.10) reduces to:

2)(

)/(2

wc

wc

nn

dPdnn

dP

dR

+

−= (3.12)

Fig. 3.4 shows the reflectance performance of an uncoated fiber sensor as a function

of incident pressure amplitude. It can be seen that the relationship is linear. The

slope of the plot of Fig. 3.4 yields the dynamic responsivity of the uncoated fiber in

terms of dB per MPa shown in Fig. 3.5. It can be seen that the dynamic responsivity

remains constant as a function of pressure amplitude. Considering a photodiode

with responsivity of 0.65 A/W at 980nm (see Appendix A-9), with a 5 kΩ trans-

impedance gain, the pressure to voltage responsivity of an uncoated optical fiber

hydrophone was evaluated to be -282 dB re 1 V/µPa. The typical pressure to

voltage sensitivity of the PVDF based hydrophone probes is around -260 to -268 dB

re 1 V/µPa. An 18 dB improvement in responsivity performance of the fiber optic

hydrophone makes it comparable to the PVDF based hydrophones and it is to be

achieved through coating of the fiber tips.

67

100

101

102

-60

-55

-50

-45

-40

-35

Pressure, MPa

Ref

lect

ance

, dB

100

101

102

-56.5

-56

-55.5

-55

-54.5

-54

Pressure, MPa

Fib

er R

esp

on

siv

ity

, d

B p

er M

Pa

Fig 3. 4: Reflectance vs Pressure amplitude of uncoated fiber

Fig 3. 5: Dynamic Responsivity of uncoated fiber sensor in terms of dB per MPa

68

In order to an initial understanding of the responsivity performance of the

thin film gold coated fiber sensors, a transmission line based analytical modeling

was pursued. One of the most important input parameters to the model was the

complex index of refraction of thin film gold. Several works reporting refractive

indices of thin gold films with thicknesses ranging from 20nm to 200nm are

available in literature. Closer examination of the reported data revealed that the

optical constants of thin films are dependent on factors such as fabrication

technique, coating thickness, incident optical wavelength, polarization of incident

wave, substrate properties and nature (island, continuous, discontinuous) of the

deposited film. A brief review of some of the data reported in the literature is

presented in the next section. The section also outlines the extraction procedure for

optical constants of thin gold films at optical wavelengths of 980nm, 1480nm and

1550nm, with thicknesses ranging from 2nm – 35nm deposited by using sputtering

technique.

3.3 Extraction of complex refractive index of thin (2nm-35nm) gold films:

Before getting into the details of the extraction procedure it is important to

understand the need for such a process given that there are several works reporting

refractive indices of thin gold films available in literature. The review below

focuses on reports which present refractive indices of gold films at the optical

wavelengths of interest (i.e. 980nm, 1480nm and 1550nm). These complex index of

refraction values at these wavelengths are particularly important because at these

wavelengths high (1W) power semiconductor optical sources are available, which

69

are subsequently used for development of the high sensitivity fiber optic

hydrophone probe (FOHP) (See chapter 5).

3.3.1 Need for extraction of complex refractive index:

Theye et al reported the complex refractive index values of thin film gold

for thicknesses ranging from 15 nm to 25 nm in the spectral range of 0.5 to 6 eV

(for optical wavelengths spanning from 200 nm to 2500 nm) by measuring both the

transmission and reflection of incident light intensities [53]. Similar technique was

used by Johnson et al for determining refractive index of 35 nm thick gold film

fabricated by vacuum deposition for optical wavelengths spanning from 200 nm to

2500 nm [54]. The values of refractive indices in the spectral range of 980 nm to

1550 nm ranged from 0.22-j6.35 to 0.56-j11.21. Refractive indices of evaporated

gold films with 16 nm to 60 nm thicknesses were reported to lie in between 1-j8 and

0.3-j8.75 and in between 1-j9.25 and 0.3-j10.5 at telecommunication wavelengths

of 1310 nm and 1550 nm respectively [55]. In the same work, Lee et al observed

that for film thicknesses below 20 nm, the real part of refractive index increases and

the imaginary part decreases beyond the bulk value due to presence of small air

gaps (micropores) in the films at such thicknesses. Lin et al [56] presented the

optical constants for a 100nm thick gold film with nanostructure (pitting) on the

surface, in the optical wavelengths stretching from 400 nm-1100 nm. The complex

refractive index varied from 1.5-j2 at 400 nm to 0.3-j7 at 1100 nm. The impact of

structure of thin films on the refractive index of gold was also studied by Al Maroof

et al in [57], in which the performance of 20nm homogenous gold film to that of a

20nm mesomorphic gold film obtained by removing aluminum atoms from AuAl2

70

was compared. The mesomorphic gold structure consisted of numerous voids with a

surface roughness of ± 20nm. The values for refractive index of this structure were

determined to be 1.4-j2 and 1.4-j3 as opposed to the bulk values of 0.4-j7 and 0.5-j9

at 980nm and 1550nm respectively. Heavens et al presented the measured values of

refractive indices of evaporated films with thicknesses ranging from 1 nm to 30nm

deposited on quartz substrate in [58] for the optical wavelengths of 450nm, 600nm

and 700nm. Similarly, the refractive indices of 1 nm – 22 nm thick evaporated films

on glass were determined using ellipsometric technique in [59] for wavelengths

spanning from 400 nm to 1000 nm. Based on the above review, two observations

were made. First, there was inconsistency (50% and higher) in the reported values

optical constants of thin films, summarized in Table 3.2. It was understood that this

discrepancy arose from the fact that the optical properties were not only dependent

on the optical wavelength and the coating thickness but also on the film deposition

technique, nature of substrate and nature of the deposited film (homogenous or

inhomogenous). Second, the refractive indices of sputtered films for thicknesses

from 2 nm – 35nm were not available. Hence these values had to be extracted for

sputtered films using a semi-empirical method described in detail below.

The first step in the extraction process was the fabrication of the sputtered

fiber sensors exhibiting consistent (within 2%) sample to sample reflectance

performance for coating thicknesses ranging from 2nm to 35nm. This step was

extremely important in order to have higher certainty in the extracted results. Next,

numerical models of straight cleaved uncoated and thin film gold coated sensors

with coating thicknesses from 2-35 nm were created using COMSOL Multi-physics

71

(See chapter 4). The indices of refraction of thin film gold were determined by

tuning the values of the real and imaginary values of the gold film, such that the

numerical reflectance matched with those measured experimentally.

3.3.2 Fabrication:

In this section, a step by step description of the fabrication of thin film gold

coated fiber samples for extraction of the complex refractive index in the range

from 2 nm- 35 nm is provided. As already mentioned, this step is crucial in

obtaining samples which exhibit uniform (within ± 0.5 dB) reflectance

performance, thereby reducing the uncertainty in the extracted values of optical

constants. FC/APC connectorized optical fiber jumpers (FIS S37A7AS3FISC) with

mechanical reliability and excellent return loss were cut into two halves and cleaved

using Fujikura CT-30 cleaver at the bare fiber end. The cleaved fibers were then

examined under a microscope in terms of cleave quality (cleave angle and any

surface damage) and rejects were re-cleaved until identical flat cleaved surfaces

were attained. The cleaved fibers were then coated using Cressington 208 HR

sputter coater. Three fiber samples, along with two AFM grade mica slides

(www.tedpella.com), were simultaneously placed at concentric locations from the

center of the plasma field in the vacuum chamber to ensure uniformity (within 2%)

of fiber samples in terms of their reflectance values. Au films were deposited on

unheated substrates at Ar pressure of 0.04 mbar. The coating time was controlled by

the Cressington thickness controller 2050, consisting of a lead zirconate titanate

(PZT) sensor that was placed at the center of the vacuum chamber. The shift in the

oscillation frequency of the PZT sensor served as a measure of the coating thickness

72

Laser

Source

Optical

power

Meter,

EXFO

3 dB

optical

coupler

Air/ water/ 10%

Isopropyl

alcohol

FC/APC

connector

Sensing

FiberReference

Fiber

Laser

Source

Optical

power

Meter,

EXFO

3 dB

optical

coupler

Air/ water/ 10%

Isopropyl

alcohol

FC/APC

connector

Sensing

FiberReference

Fiber

within accuracy of ± 0.5 nm and was sensed by the thickness controller, which in

turn limited the coating time accordingly. The tooling factor was set to 2.2, which is

the ratio of the distance between the target and PZT sensor to the distance between

the target and the fiber sample tip. The density of gold target was set to 19.3 Kg/m3

[60]. At least three fiber samples were fabricated for each desired coating thickness

in the range of 2.5 nm to 35nm.

Fig 3. 6: Experimental set-up for extraction of complex refractive index of thin (2 - 35nm) gold

films

3.3.3 Experimental set-up, results and discussion:

As the number of prototype samples was limited, the results discussed in the

following are based on coating thicknesses set for values of 2.5nm, 3.5nm, 5.0nm,

6.7nm, 8.0nm, 10.0nm, 13.5nm, 18.0nm, 22.5nm, 25.0nm, 30.0nm, and 35.0nm

using the PZT thickness sensor. Three samples of uncoated and coated fiber sensors

were prepared to conduct statistical performance analysis and calculate the expected

73

error bar in the extraction results. Experimental set-up to measure back-reflectance

of the fabricated fiber sensors is shown in Fig 3.6. Single mode laser sources with

external optical isolators (Ascentta, Inc) were used at wavelengths of 980nm

(Lumics, Inc LU0975M400), 1480nm (JDSU Inc. acquired from Dovebid auction),

and 1550nm (Eudyna FLD5F7CZ) respectively. The input optical power to the fiber

sensors was set at 1 mW (0 dBm) using current and temperature controller units

(ILX Lightwave LDC 3900, Thorlabs LDC 8005 and TED 8040). This optical

power was split into half using the 3 dB optical coupler (Ascentta, Inc) with

insertion loss of 0.26 dB and uniformity of 0.4dB. One of the output arms of the

coupler was connected to the above fabricated coated fiber sensors and immersed in

the medium being sensed (here, air, water and isopropyl alcohol), whereas, the

other arm was terminated directly in the same medium. All the fibers jumpers were

terminated in with FC-APC (angle polished) connectors, which had a return loss of

greater than 50 dB to minimize any back-reflections from fiber interconnections.

The back-reflected light from the coated fiber sensor was collected through the 3 dB

optical coupler and measured by a calibrated optical power meter (EXFO FPM

500). The reflectance from the fabricated fiber sensors was then determined by

calculating the ratio of the reflected optical power to the input optical power

(1mW). The measurement procedure was carried out for 3 or more samples of every

coating thickness for each of the three sensing media. The reflectance

measurements were repeated for the entire set of samples over a period of a week,

in order to ensure repeatability of the results. Once this was done, the average

74

reflectance was calculated for each coating thickness. This average back-reflectance

plotted in Fig 3.7 was used as an input to the numerical model.

Fig 3. 7: Reflectance (dB) vs coating thickness (nm) of coated fiber sensors at (blue) 980nm,

(red) 1480nm and (black) 1550nm wavelength.

The effective refractive indices of core and cladding were extracted from the

average reflectance measurement values of uncoated straight cleaved fiber samples.

The refractive indices were determined to be 1.41, 1.44, and 1.47 for the core region

and 1.4078, 1.4378, and 1.4678 for the cladding at the wavelengths of 980nm,

1480nm, and 1550nm respectively. Subsequently, these values were used as the

input parameters for the numerical model of coated single mode fiber (see chapter

4) for extraction of complex index of refraction of gold films. The complex index of

refraction of gold (i.e. ‘n’ and ‘k’ value) was varied till the reflectance from the

numerical model matched with those obtained experimentally for each sensing

medium (here, air, water and isopropyl alcohol).

75

0 5 10 15 20 25 30 35 402

4

6

8

10

12

14

Coating thickness, nmImag

inar

y p

art

of

com

ple

x r

efra

ctiv

e in

dex

of

gold

Fig 3. 8: Extracted (a) real and (b) imaginary parts of index of refraction of thin sputtered

gold film as a function of coating thickness at (blue) 980nm, (red) 1480nm and (black)

1550nm. (Error bars of the extracted results for three samples are indicated by + sign).

These extracted real parts of the complex index of gold ‘n’ and the extinction

coefficients ‘k’, are plotted in Fig 3.8 along with their estimated error bars. The

0 5 10 15 20 25 30 35 400

1

2

3

4

5

Coating thickness,nm

Rea

l p

art

of

com

ple

x r

efra

ctiv

e in

dex

of

go

ld.

a

76

error bars represent the difference between the maximum and minimum of extracted

‘n’ and ‘k’ values from the mean value for 3 fiber samples. In this analysis complex

index of refraction of fiber, water, air, and alcohol was ignored since the loss

induced is practically insignificant (less than 0.01 % error).

Table 3. 1: Summary of complex refractive index data of thin (2-35nm) gold films at 980nm

Table 3. 2: Refractive index data of 20nm and 35nm thick gold films at 1480nm and 1550nm

n-jk at 980 nm Coating

thickness [54]

Evapo-

rated films

[57]

[59]

Evapo-

rated films

Current

work

Sputtered

films

%

deviation

(n, k)

35 nm 0.22-j6.35 - - 0.30-j4.20 26%,34%

20 nm - 0.40-j7.00 0.60-j6.80 0.50-j5.00 20%,28%

20 nm

(mesomorphic) - 1.40-j1.50 - - -

~ 15 nm - - 1.40-j7.50 0.85-j5.88 39%,22%

~ 5 nm - - 2.80-j6.90 2.85-j6.15 2%,11%

~ 3 nm - - 3.80-j4.80 3.06-j5.69 19%,19%

~ 2 nm - - 4.70-j4.00 3.16-j5.02 33%,25%

n-jk at 1480 nm n-jk at 1550 nm Coating

thickness [54] [57] Current

work

[54] [57] [55] Current

work

35 nm 0.43-

j9.52

0.40-

j7.25

0.56-

j11.20

0.4-

j10.50

0.50-

j5.60

20 nm - 0.60-

j8.00

0.61-

j7.55 -

0.50-

j9.00

0.5-

j9.60

0.65-

j6.00

20 nm

(Meso-

morphic)

- 1.40-

j2.50 - -

1.40-

j3.00 - -

77

Table 3.1 summarizes the values of complex refractive index of thin gold films in

the range of 2 – 35 nm available in literature and extracted in this work at 980 nm

wavelength. Table 3.2 compares the ‘n’ and ‘k’ values for 20 nm and 35 nm thick

films at 1480 nm and 1550nm. It can be seen that the values extracted here are

within the 35 % deviation from the values reported by other works. This reiterates

the fact that the optical properties of thin films are indeed dependent on the coating

techniques, nature of the substrate and nature of the deposited film. These complex

index of refraction data are indispensable in modeling of coated fiber optic

hydrophone probes pursued in section 3.4.

3.4 Analytical model of coated fiber:

In the section, the analytical transmission line model of thin film gold coated

fiber optic sensors is presented. The analytical expressions are derived and the

responsivity performance is modeled based on extracted values of thin gold films

obtained in the previous section. The impact of compressibility of thin film gold on

the responsivity performance of the fiber optic sensor is predicted.

Fig 3. 9: Transmission line analogue of metal coated fiber

≡ n

c

Incident wave

w n

d

in Γ Reflected wave

n d

d

c

o

ncZ

η=

d

o

ndZη

=w

o

nwZη

=

inΓ

Incident wave

Reflected wave

d

c

o

ncZ

η=

d

o

ndZη

=w

o

nwZη

=

inΓ

Incident wave

Reflected wave

78

Fig. 3.9 shows the transmission line analogue model of a gold coated optical

fiber. Again, the fiber core is replaced by a line of impedance,c

cn

Z 0η= .Water is

replaced by a load of impedance,w

wn

Z 0η= .The gold coating of thickness ‘d’ is

represented by a transmission line of characteristic impedance, d

dn

Z 0η= and length

d. In addition to the reflection at the metal-water interface, additional reflection

occurs from the core-metal coating. Core refractive index of the single mode fiber,

cn is considered to be 1.41 while refractive index of water, wn is taken as 1.33. The

thin gold coating has a complex refractive index, n d = n – j k where n is the real

term and represents the phase constant of the wave.

The input impedance as seen from the fiber core is given by,

dZZ

dZZZZ

wd

dw

dinγ

γ

tanh

tanh

+

+= (3.11)

where γ =

−

λ

π ).(2 kjnj is the complex propagation constant.

The complex reflection co-efficient in this case is given by,

inΓ =

+

−

cin

cin

ZZ

ZZ (3.12)

Equation (3.11) can be re-written in terms of refractive indices of the material as,

inZ =

djnk

nn

djnk

nn

n

wd

dw

d

λ

πηη

λ

πηη

η

)(2tanh

)(2tanh

00

00

0

++

++

. (3.13)

79

Substituting equation (3.13) in equation (3.11), a simplified form of reflection co-

efficient in terms of refractive index of the materials is obtained and given by the

equation,

dnnnnnn

dnnnnnn

dcwwcd

dcwwcd

inγ

γ

tanh)()(

tanh)()(2

2

+++

−+−=Γ (3.14)

The effective reflectance (R) is given by,

R = *ininΓΓ

The return loss is expressed as,

R.L = 10 log(R) = 10 log ( *ininΓΓ ) (3.15)

The dependence of reflectance on pressure can be found by differentiating equation

(3.15) with respect to pressure as follows,

dP

d

dP

d

dP

dR in

in

in

in

ΓΓ+

ΓΓ= *

*. . (3.16)

It can be noted from equation (3.14) that the overall responsivity of the gold coated

structure is dependent on three parameters, namely, the compressibility of fiber core

with pressure, the compressibility of water with pressure and the compressibility of

thin gold film with pressure. Mathematically, this dependence can be given as,

(3.17)

The third term of Equation (3.17) can be further expanded in terms of

change in the real and imaginary terms of the refractive index of thin film gold as

follows,

(3.18)

P

d

dP

n

nP

n

ndP

d inw

w

inc

c

inin

∂

∂

∂

Γ∂+

∂

∂

∂

Γ∂+

∂

∂

∂

Γ∂=

Γ

d

k

kj

d

n

nd

g

g

ing

g

inin

∂

∂

∂

Γ∂+

∂

∂

∂

Γ∂=

∂

Γ∂

80

0 5 10 15 20 25 30 350

5

10

15

20

25

30


Imp

rov

emen

t in

res

pon

siv

ity

, d

B

Responsivity improvement of gold coated FOHP using peicewise TL model

Impact of water compression

As noted earlier, the compressibility of the fiber core with pressure is ignored with

respect to that of water and thin gold film compressibility. The following 2 cases

arise.

Fig 3. 10: Improvement in responsivity vs coating thickness considering water compression

only

3.4.1. Assuming compressible water and incompressible gold:

In this case, P

n

P

d w

∂

∂<<

∂

∂, where

P

nw

∂

∂= 1.4 X 10

-4 per MPa. Equation (3.16) can be

modified as,

P

n

n

R

P

n

n

R

dP

dR w

w

in

in

in

w

w

in

in

in∂

∂

∂

Γ∂

Γ∂

∂Γ+

∂

∂

∂

Γ∂

Γ∂

∂Γ= ......

*

*

* (3.19)

Where,

22

2

]tanh)()([

]tanh)(tanhtanh[2

dnnnnnn

dnnnndndnn

ndwcwcd

wcdcdwd

w

in

γ

γγγ

+++

−−+=

∂

Γ∂ (3.20)

81

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35


Impro

vem

ent

in r

esp

onsi

vit

y,

dB


Impact of gold compression

Fig 3. 11: Improvement in responsivity vs coating thickness considering thin film gold

compression only

The improvement in responsivity in given as the ratio of responsivity of coated

sensor to the responsivity of uncoated fiber sensor. The improvement in

responsivity for this case is shown in Fig. 3.10

3.4.2. Assuming incompressible water and compressible gold:

In this case, P

n

P

d w

∂

∂>>

∂

∂. Assuming

P

d

∂

∂= 10 pm per MPa, the equation (3.17)

reduces to,

p

d

ddP

d inin

∂

∂

∂

Γ∂=

Γ (3.21)

The improvement in responsivity for this case is shown in Fig. 3.11

82

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35


Impro

vem

ent

in r

esponsi

vit

y,

dB


Impact of gold compression

Impact of water compression

Total improvement in responsivity

Fig 3. 12: Improvement in responsivity vs coating thickness considering water and thin film

gold compression

3.4.3. Combined water and thin gold film compression:

The overall improvement in responsivity including compressibility of water and

that of thin film gold is presented by equation (3.17). The expected improvement in

responsivity as a function of coating thickness is shown in Fig. 3.12. The maximum

improvement in responsivity is obtained for coating thicknesses around 4-5 nm.

3.5 Summary

This chapter discussed in detail the analytical modeling of uncoated fiber

sensor and thin (2-35 nm) film gold coated fiber optic sensors using transmission

line analogy. The chapter also provided a detailed procedure for extraction of

refractive index of thin films based on a semi-empirical technique. This technique

was needed because a closer analysis of the literature data revealed inconsistencies

(50%) in the values of optical constants and led to the conclusion that the optical

83

constants of thin films have to be determined for each individual case (coating

technique, substrate properties, optical wavelength). The extraction results were

crucial in performing the analytical modeling of coated fiber optic hydrophone

sensors and in predicting the achievable improvement in responsivity for coating

thicknesses in the range of 2 nm-35 nm.

The responsivity of the uncoated fiber sensor was predicted to be about -55

dB per MPa and expected to be constant with respect to pressure. The effect of

water compressibility and the gold compressibility on the responsivity of the thin

film gold coated sensors was modeled. Ignoring the compression due to gold, it is

seen that as much as 23 dB improvement in responsivity is achievable due to

enhanced reflection from the metal layer. Introduction of compressibility of thin

gold film by incident acoustic pressure predicted as much as 30 dB improvement in

responsivity for coating thicknesses of around 4-5 nm. It is seen that for thickness

below 15nm, the achievable improvement in responsivity is dominated by the gold

compression effect. This indicates that the magnitude of compressibility of thin

gold film (or change in refractive index of thin film gold) is greater than or of the

order of water compression (refractive index change) with respect to pressure.

Above 15 nm thickness, the effect of water compression dominates, which means

that the compressibility of gold is smaller in comparison to that of water. The

analytical model results obtained here serve as a guideline for the verifying the full-

wave numerical modeling results and for further optimization of the fiber sensor

design to be discussed in the next chapter.

84

Chapter 4: Numerical modeling

4.0 Introduction

Having established an initial understanding of the voltage to pressure

responsivity performance of the uncoated and coated fiber sensors using the

analytical transmission line based model, the full wave numerical modeling of the

fiber optic hydrophone sensors was pursued. The analytical model did not consider

factors such as finite dimensions of the core, fiber sensor tip geometry, and optical

power density distribution at the sensing tip. The subsequently developed numerical

model discussed here addressed all of the deficiencies of the transmission line one

and included the impact of tip geometries. Additionally, it was also required to

model the impact of acoustic pressure distribution on the compressibility of thin

gold films and its effect on the fiber optic probe’s responsitivity. As mentioned

earilier, the Finite Element Method (FEM) based commercial software, (COMSOL

Multiphysics, FEMLAB. Inc.,) was chosen due to its ability to solve coupled multi-

physics equations simultaneously [51].

This chapter deals with the numerical full-wave modeling of optical fiber

hydrophone sensors and is organized as follows. Section 4.1 describes a step by step

procedure to set up the numerical model of a standard single mode fiber. This

numerical model was used as a part of the semi-empirical method, to extract the

complex refractive index of thin gold films as described in chapter 3. Modeling was

performed by considering a step index profile as well as a graded index profile for

the core region. The rest of the chapter discusses the optimization procedure for the

fiber optic hydrophone probe. Section 4.2 models the impact of the fiber sensor tip

geometries; namely, straight cleaved sensor, cylindrically etched sensor, linearly

85

tapered sensor and exponentially tapered sensor on the responsivity of the FOHP.

Section 4.3 outlines the modeling procedure for the thin film gold coated fiber optic

sensors. The impact of thin film coating thickness on the above considered fiber tip

geometries is evaluated for film thicknesses ranging from 2 nm to 30 nm.

4.1 Numerical model of standard single mode fiber with step index:

4.1.1 Simulation set-up for electromagnetics module:

This section gives a detailed account of the single mode fiber model set-up

procedure using COMSOL. The RF (Radio Frequency)/Photonics module was used

for this purpose. The choice of geometry, the mesh assignment and the boundary

conditions are described below.

Geometry:

As discussed in chapter 2, in FEM analysis, the region to be modeled is

discretized using a mesh structure. By rule of thumb, in order to have less than 10

% uncertainty in the results, the minimum mesh size should be limited to 1/10th

of

the optical wavelength [47]. Use of a three dimensional model would require

around 3 million meshes and 16 GB of memory. To reduce the memory

requirement by a factor of two, circular symmetry of the optical fiber was used. The

machine which was used for computation was a Dell Optiplex 745 with 2 GB

memory capacity. The simulation ran out of memory when the number of mesh

elements exceeded half a million. So, the dimensions of the fiber sensor geometry

had to be carefully chosen to meet this requirement.

86

core core

cladding

Z

r

Water Water

cladding

cladding

cladding

Thin film gold

coating

Impedance boundary Impedance boundary


Imped

ance b

oundary

Imped

ance b

oundary

Mat

ched

boundar

yM

atch

ed b

oundar

y

Mat

ched

boundar

yM

atch

ed b

oundar

y

Port

Port

10 µm 10 µm

50 µm50 µm

25 µm 25 µm15 µm 15 µm

core core

cladding

Z

r

Water Water

cladding

cladding

cladding

Thin film gold

coating



Imped

ance b

oundary

Imped

ance b

oundary

Mat

ched

boundar

yM

atch

ed b

oundar

y

Mat

ched

boundar

yM

atch

ed b

oundar

y

Port

Port

10 µm 10 µm

50 µm50 µm

25 µm 25 µm15 µm 15 µm

Fig 4. 1: (a) Geometry of straight cleaved uncoated fiber (b) Geometry of straight cleaved thin

film gold coated fiber.

The 2D geometries of the considered straight cleaved coated and uncoated fiber-

optic structures are shown in Fig.4.1. The optical fiber length of 25 µm was

considered along the z-axis and included 15 µm length of the sensing medium. A

core diameter of 10 µm was considered and the cladding region diameter was

selected to be 50 µm. Again, these lengths were specifically chosen in order to limit

the number of mesh elements to less than half a million. The 2 Dimensional

Helmholtz wave equations for electric and magnetic fields, given were solved over

all the regions.

The Helmholtz equations for an isotropic, homogenous, source-free material were

given by,

0222 =+∇ EknE i (4.1.a)

87

100

nm

100

nm

80 nm 80 nm

300

nm

0222 =+∇ HknH i (4.1.b)

Fig 4. 2 Mesh structure of uncoated single mode fiber with step index profile

Where, ni is the index of refraction for each medium. The values of the effective

refractive index of core, cladding and water medium were considered to be 1.41,

1.4078 and 1.33 respectively at 980nm optical wavelength (see chapter 3). The core

and cladding refractive index values were extracted using the procedure outlined in

chapter 3. After construction of geometry, the mesh structure was generated.

Mesh Generation:

Fig 4.2 depicts the mesh structure of the coated fiber sample with inset rendering

the detailed meshing in the coated section. As stated earlier, to reduce uncertainty in

the numerical results, the mesh size of at least 1/10th

of the incident wavelength was

employed, where for shortest wavelength of interest (here, 980 nm) the resolution

88

corresponds to a mesh dimension of around 98 nm. Hence, triangular meshes with

resolution of 80 nm and 100 nm were employed in the core and cladding region

respectively. A finer mesh size of 100 nm was used in the sensing region near the

fiber core interface while a coarse mesh structure of 300 nm was considered

everywhere else in the sensing medium. The next step was to apply appropriate

boundary conditions.

Boundary conditions:

Application of appropriate boundary conditions is the most crucial step in creating a

more accurate model. Fig 4.2 shows the assigned boundary conditions for the

uncoated single mode fiber model. The port boundary condition was used on the

left hand side boundary of the core. This port excited the dominant mode (HE11) in

the fiber (see appendix A-2). The port provided an input of 1 W to the fiber core

and served as a reference plane, yielding the reflection co-efficient (reflectance) at

the input of the fiber sensor. The reflection co-efficient was calculated as,

∫∫ −

=Γ11

11

.EE

).EE(E.Where, (4.2)

E = Total electric field.

E1 = Incident electric field.

The impedance boundary condition was given by,

( ) 0=+×∇×i

EHn

η

φ Where, (4.3)

ηi = characteristic impedance of the medium.

This boundary condition, also known as the ‘absorbing boundary’ was used at all

external boundaries of the sensing medium and at cladding boundaries lying along

89

the r axis of the fiber to avoid unwanted reflections from these artificially imposed

limitations on the size of the structure. At left hand boundary of the fiber cladding,

matched boundary condition given by,

( ) φβ EjEn i=×∇× (4.4)

Where, βi = propagation constant of the wave in the cladding.

This sets the condition that the field propagates along z direction with the

propagation constant, βi.

Finally, continuity condition was imposed at all interior boundaries given by,

0)(ˆ21 =−× HHn

rr (4.5)

Where, H1 and H2 are the magnetic fields in the media at interface.

4.1.2 Simulation set-up for coupled acousto-optic analysis:

In order to evaluate pressure to voltage responsivity of optical fiber sensor,

the acoustics module of COSMOL was coupled to the RF module. The acoustics

module solved the linear acoustic wave equation in the water medium as,

0))/(()/1(.(2

0

2 =−∇−∇ pcp so ρωρ (4.6)

Where,

p = Pressure field.

oρ = Density of water = 1000 Kg/ m3.

sc = Acoustic velocity in water = 1500 m/s.

ω = Angular frequency for 1.5 MHz acoustic frequency.

The input acoustic excitation was provided by defining the pressure boundary

condition on the right hand side boundary of the water medium shown in Fig 4.1.

90

The pressure amplitude was varied from 1 MPa to 5 MPa in steps of 1 MPa in order

to evaluate the reflectance as a function of pressure amplitude. Radiation

boundary condition was specified over the remaining boundaries of the water

medium to simulate ‘absorbing boundaries’ as discussed earlier.

The pressure field distribution resulting from this acoustic simulation was

then coupled to the RF module. Coupling was achieved by defining the refractive

index of water (nw) as a variable dependent on the pressure distribution, given by,

pp

nnn ow .

∆

∆+= . Where, (4.7)

p = pressure amplitude distribution (in MPa)

=on static index of refraction of water = 1.33

4104.1 −=∆

∆X

p

n per MPa [11].

The remaining parameters for the fiber simulation set-up in the RF module were

kept untouched. The resultant solution yielded the performance of reflectance as a

function of acoustic pressure. At this point, a quantity termed as fiber dynamic

responsivity is introduced. The fiber dynamic responsivity defined as the ratio of

change in reflectance to the change in incident pressure amplitude was calculated

from slope of the reflectance vs pressure plot. The unit of dynamic responsivity was

given by dB/MPa.

Fig 4.3 shows the power density profile of the dominant mode in the

standard single mode fiber on a linear scale. The static reflectance of the single

mode fiber was -30.65 dB while the dynamic responsivity was -55 dB per MPa.

91

Fig 4. 3: Power density profile of uncoated unetched single mode fiber

This result matched closely with the analytical results presented in section 3 and the

measurement results, and established the validity of the numerical model. This

formed the reference result for the optimization procedure.

The next step towards modeling a more realistic single mode fiber was to

consider the fiber with graded index profile of refractive index of core. As seen in

Fig 4.4, the graded index profile was created by dividing the core region into

smaller regions and assigning different refractive index. The difference in the

refractive index between adjacent graded index regions was 0.035 %.

92

Fig 4. 4: Geometry and mesh structure of a Graded Index (GRIN) single mode fiber.

Fig 4. 5: Power density profile of uncoated unetched GRIN single mode fiber.

1.4078

1.4083

1.4089

1.4095

1.4078

1.41

1.40951.4089

1.4083

1. 33

Impedance boundary

Impedance boundary

Imp

edan

ce bo

un

dary

Po

rtM

atch

ed

bo

un

dar

yM

atch

ed

bo

un

dar

y

1.4078

1.4083

1.4089

1.4095

1.4078

1.41

1.40951.4089

1.4083

1. 33

1.4078

1.4083

1.4089

1.4095

1.4078

1.41

1.40951.4089

1.4083

1. 33

Impedance boundary

Impedance boundary

Imp

edan

ce bo

un

dary

Po

rtM

atch

ed

bo

un

dar

yM

atch

ed

bo

un

dar

y

93

The geometry and the refractive indices of the graded index straight cleaved fiber

are shown in Fig 4.4 along with the boundary conditions. The mesh structure was

identical to those discussed earlier. The static reflectance of the single mode fiber

was -30.71 dB while the dynamic responsivity was -55.14 dB per MPa. Fig 4.5

represents a linear plot of the power density profile of a GRIN single mode fiber.

This indicates that the results of the GRIN profile fiber closely match with those

obtained from the effective step index single mode fiber. Once these base-line

simulations were performed, the design optimization was started.

4.2. Impact of fiber optic sensor tip geometries:

In this section, the fiber optic hydrophone probe design optimization

procedure is outlined. Firstly, the impact of four different fiber tip geometries

namely, uncoated unetched straight cleaved fiber sensor, uncoated cylindrical

etched fiber sensor, uncoated linear tapered sensor and uncoated exponential

tapered sensor on the overall responsivity performance of the hydrophone is

discussed. In that, the effect of varying etch diameters on the performance of

cylindrical etched sensors is modeled. Also, the responsivity performance of

tapered sensors is evaluated for different taper angles. Secondly, the effect of thin

film gold coating thickness on the fiber responsivity is studied. In that, it is shown

that the compressibility of thin gold film by the incident acoustic pressure

dominates the responsivity performance of the coated fiber sensor.

4.2.1 Uncoated Cylindrical etched fiber sensor:

The geometry and mesh structure of the cylindrical etched fiber sensor with 6 µm

core diameter is shown in Fig 4.6. The mesh sizes are indicated in nanometers. The

94

pressure and radiation boundary conditions are used as indicated in the Fig.4.7. The

pressure amplitude was changed from 1 MPa to 5 MPa at acoustic frequency of 1.5

MHz.

Fig 4. 6: Geometry, mesh structure and acoustic boundary conditions of etched GRIN single

mode fiber model.

Fig 4. 7 RF boundary conditions of etched GRIN single mode fiber model.

200 nm

200 nm

200 nm

200

nm

80 nm120 nm

Radiation boundary

Radiation boundary

Rad

iation b

oundary

Rad

iation b

oundary

Pressu

re boundary

6 µm

200 nm

200 nm

200 nm

200

nm

80 nm120 nm

Radiation boundary

Radiation boundary

Rad

iation b

oundary

Rad

iation b

oundary

Pressu

re boundary

6 µm

6 µm

Po

rt B

ou

nd

ary

Mat

ched

Bo

un

dary

Mat

ched

Bo

un

dar

y Impedance Boundary

Impedance Boundary

Imp

edan

ce B

ou

nd

ary

6 µm

Po

rt B

ou

nd

ary

Mat

ched

Bo

un

dary

Mat

ched

Bo

un

dar


Impedance Boundary

Imp

edan

ce B

ou

nd

ary

95

Fig 4. 8: Power density profile of 6 µm etched GRIN single mode fiber model.


96



97

As stated earlier, the solution of the acoustics module was coupled to the RF

module. The boundary conditions used in the RF module are shown in Fig 4.7. The

linear power density profile of the etched structure is shown in Fig 4.8. The

cylindrical etched diameter was varied from 6 µm to 12 µm in steps of 2 microns.

The dynamic responsivity results are summarized in table 4.1. The linear power

density plots of the 12 µm diameter, 10 µm diameter and 8 µm diameter are shown

in Fig 4.9, Fig 4.10 and Fig 4.11 respectively.

Table 4. 1 Responsivity performance comparison of cylindrical etched fiber sensors

Comparison of the static reflectance performance of the fiber sensors from table 4.1

indicated that the single mode unetched uncoated fiber sensor had the highest static

reflectance. The value of reflectance remained at around -31 dB so long as the

etching is limited to cladding region. In this case most of the optical power is

confined to the core as seen in Figs 4.9 and 4.10. The static reflectance starts

reducing as the etching extends deeper into the core region. This is due higher

leakage of power outside the core region as seen from Fig 4.8. For the same

reasons, the dynamic responsivity performance is highest in case of unetched fiber

and then the value decreases as the fiber is etched further into the core.

Fiber Sensor Geometry Static

Reflectance, dB

Dynamic responsivity in

dB per MPa

Unetched Uncoated fiber -30.85 dB - 55.0 dB per MPa

Uncoated 12um etched fiber -30.94 dB - 55.0 dB per MPa




98

6 8 10 12 14 16 18 20-25

-20

-15

-10

-5

0

5

Cylindrically etched tip diameter, µm

Imp

rov

emen

t in

sen

siti

vit

y,

dB

Fig 4. 12: Pressure to voltage responsivity performance of etched cylindrical fiber sensors as

function of etched tip diameter.

The dynamic fiber responsivity can be used to calculate the pressure to

voltage sensitivity of the fiber optic hydrophone probe, in terms of mV/MPa , using

the following relationship;

p-v responsivity (mV/MPa) = η x G x D.R. (4.8)

Where, η is the responsivity of the photo-detector in A/W, G is the transimpedance

gain in ohms, and D.R. is the dynamic responsivity in per MPa and given as,

D.R = Pin x 2α x10(dynamic fiber responsivity/10)

.

Where, α is the insertion loss of the fiber sensor geometry, Pin is the input optical

power and p is the acoustic pressure amplitude, x indicates the multiplication

opertion. For the photo-detector considered here, Thorlabs PDB 130C with a

responsivity of 0.65 A/W at 980 nm and trans-impedance gain of 5 Kohm, the p-v

responsivity was calculated and plotted as function of etched cylindrical fiber

diameter in Fig 4.12. The responsivity of the uncoated unetched straight cleaved

99

fiber sensor was evaluated to be -282 dB re 1 V/µPa. However, in order to avoid

spatial averaging the till 100 MHz, the desirable tip dimensions were around 6-7

µm. Using the values from Table 4.1 in equation 4.8, it is seen that at such tip

dimensions, the responsivity drops by as much as 22 dB to a value of -304 dB re 1

V/µPa. Hence in order to make such probes comparable in responsivity

performance to those of the straight cleaved fiber sensors, their responsivity needs

to be boosted by about 40 dB. The fiber sensors considered henceforth have sensing

tip diameters of 6 µm.

4.2.2 Uncoated linear tapered fiber sensor:

In this section, the linearly tapered fiber sensor tip geometries were modeled. The

geometry, mesh structure and RF boundary condiitons of an uncoated linearly

tapered fiber sensor is shown in Fig 4.13.The acoustic boundary conditions are

similar to those shown in Fig 4.6.

Fig 4. 13: Geometry, mesh structure and boundary conditions of uncoated 7 degree linear

tapered fiber sensor.

200 nm

200 nm

200

nm

200

nm

80 nm

120 nm

6 µm

Port

Boundar

yM

atch

ed B

oundar

yM

atch

ed B

oundar


Impedance Boundary

Imped

ance B

oundary

α

200 nm

200 nm

200

nm

200

nm

80 nm

120 nm

6 µm

Port

Boundar

yM

atch

ed B

oundar

yM

atch

ed B

oundar


Impedance Boundary

Imped

ance B

oundary

200 nm

200 nm

200

nm

200

nm

80 nm

120 nm

6 µm

Port

Boundar

yM

atch

ed B

oundar

yM

atch

ed B

oundar


Impedance Boundary

Imped

ance B

oundary

α

100

.

Fig 4. 14: Power density profile of 7 degree linear tapered GRIN single mode fiber model.

Fig 4. 15: Power density profile of 15 degree linear tapered GRIN single mode fiber model

101



102

The pressure amplitude was varied from 1 MPa to 5 MPa at the acoustic frequency

of 1.5 MHz in steps of 1 MPa.The incident optical power was set to 1W at

wavelength of 980 nm. The taper angle (α) is indicated in Fig 4.13 as the angle

formed by the axis of the fiber and the tapered section. The values of taper angles

used were, 7 degrees, 15 degrees, 30 degrees and 40 degrees. Linear plots of the

power density profiles of the 7 degree, 15 degree, 30 degree and 40 degree tapered

sensors are shown in Figs 4.14, 4.15, 4.16and 4.17 respectively.

Table 4. 2 Responsivity performance comparison of linear tapered fiber sensors as function of

taper angle

The fiber dynamic responsivity performance and static reflectance as a function of

taper angles are summarized in Table 4.2. It is seen that the static reflectance as

well as the dynamic responsivity of the fiber sensors increases as the taper angle

increases. For taper angles nearing 0 degrees, which represents the cylindrically

etched case, the performance approaches that of a cylindrically etched fiber sensor

which means that there is a decrease in the static reflectance as well as dynamic

responsivity. As the taper angle increases, higher amount of optical power is

Fiber Sensor Geometry Static

Reflectance, dB

Dynamic responsivity

in dB per MPa

Uncoated 7 degree linear tapered

fiber sensor

-33.37 dB - 60.0 dB per MPa

Uncoated 15 degree linear

tapered fiber sensor

-32.94 dB - 59.3 dB per MPa



-32.36 dB

- 58.0 dB per MPa



-32.17 dB

- 57.6 dB per MPa

103

contained in the core region, the responsivity increases behavior approaches that of

the straight cleaved fiber sensor (i.e. taper angle of 90 degrees).

4.2.3 Uncoated exponential tapered fiber sensor:

In this section, fiber sensors having an exponential tapered structure are considered.

The RF boundary conditions used with this fiber sensor geometry are shown in Fig

4.18. The responsivity performance of the exponentially tapered fiber sensors was

simulated as a function of different amounts of exponential taper. Four such cases

of exponential tapers were considered here, namely, 7 degrees, 15 degrees, 30

degrees and 40 degrees. A higher taper angle serves as an indication of a quicker

transition to the core region at the tip. The geometry and mesh structure of uncoated

exponential tapered fiber sensor with 7 degree exponential taper is shown in Fig

4.18.

Fig 4. 18: Geometry, mesh structure and boundary conditions of exponential tapered GRIN

fiber model

200 nm

200 nm

200

nm

200

nm

80 nm

120 nm

6 µm

Po

rt B

ou

nd

ary

Mat

ched

Bo

un

dar

yM

atch

ed B

ou

nd

ary Impedance Boundary

Impedance Boundary

Imp

edan

ce Bo

un

dary

200 nm

200 nm

200

nm

200

nm

80 nm

120 nm

6 µm

Po

rt B

ou

nd

ary

Mat

ched

Bo

un

dar

yM

atch

ed B

ou

nd

ary Impedance Boundary

Impedance Boundary

Imp

edan

ce Bo

un

dary

104

Fig 4. 19: Power density profile of 7 degree exponential tapered GRIN single mode fiber model

Fig 4. 20: Power density profile of 15 degree exponential tapered GRIN single mode fiber

model.

105


model.


model.

106

Table 4. 3 Responsivity performance comparison of exponential tapered fiber sensors

The power density profile of the 7 degree, 15 degree, 30 degree and 40 degree

exponentially tapered fiber sensor are shown in Figs 4.19- 4.22. The static

reflectance and dynamic responsivity performance as a function of degree of

exponential taper are summarized in Table 4.3. Again, as the degree of taper

increases, the static reflectance as well as the dynamic responsivity performance of

the fiber sensor increases, due to higher confinement of the optical power within the

core region. Therefore, it is desirable that the transition to the fiber end face is

faster.

The pressure to voltage responsivity or sensitivity of the linearly tapered and

exponentially tapered fiber sensors is shown in Fig 4.23. Ideally, a uniform linear

(adiabatic) tapering process causes transfer of energy from the dominant mode to

the cladding modes along the taper length. The resultant tapered fiber exhibits

minimal losses due to conservation of power in the fiber. Any disturbance in the

tapered region, causes leads to coupling of energy from the dominant mode to the

leaky modes, resulting in loss of power as depicted in Fig 4.23.

Fiber Sensor Geometry Static Reflectance,

dB

Dynamic responsivity in

dB per MPa

Uncoated 7 degree exp

tapered fiber

-33.60 dB - 67.0 dB per MPa


tapered fiber

-32.80 dB - 64.0 dB per MPa


tapered fiber

-32.62 dB - 60.0 dB per MPa


tapered fiber

-32.02 dB - 58.0 dB per MPa

107

0 10 20 30 40 50 60 70 80 90-30

-25

-20

-15

-10

-5

0

Taper angle, degrees

Rel

ativ

e re

spo

nsi

vit

y,

dB

Fig 4. 23 Plot of relative responsivity, dB of uncoated linearly (red) and exponentially (blue)

tapered fiber sensors as function of taper angle. Reference: - 282 dB re 1 V/µPa.

It is seen that for smaller taper angles (below 40 degrees), the exponentially tapered

sensor provides a higher decrease in responsivity when compared to a

corresponding linearly tapered sensor. This degradation is because the

exponentially tapered structure introduces greater change (perturbation) in the

electro-magnetic field inside the core that results in a greater leakage of power from

dominant mode to the leaky modes, when compared to that of the linearly tapered

sensor. As the taper angle increases, the responsivity improves and approaches the

performance of an unetched straight cleaved fiber for taper angle of 90 degrees.

From the discussion in this section, it is clear that the dynamic responsivity

reduces when the tip dimension is reduced below core diameter. In order to boost

the responsivity by at least 40 dB, a thin layer of metallic gold (2nm – 30nm coating

thickness) was considered at the uncoated structures discussed in this section. The

impact of gold coating thickness on the static reflectance and the effect of gold

compressibility on the dynamic responsivity is evaluated in the subsequent section.

108

4.3 Numerical model of thin film gold coated fiber sensors:

Fig 4. 24: Geometry, mesh structure and boundary conditions of GRIN thin film coated fiber.

Inset shows the mesh structure and boundary condition in gold coated region.

200 nm

200 nm

80 nm

100 nm

Radiation boundary

Radiation boundary

Match

ed b

oundary

Match

ed B

oundary

Pressu

re boundary

Impedance boundary

Impedance boundary

Port

watern

coren

claddingn

claddingn

300 nm

goldn

200 nm

200 nm

80 nm

100 nm

Radiation boundary

Radiation boundary

Match

ed b

oundary

Match

ed B

oundary

Pressu

re boundary

Impedance boundary

Impedance boundary

Port

watern

coren

claddingn

claddingn

300 nm

goldn

~ 2-20nm

Pressure

Free

boundary Fixed

boundary

109

This section describes the detailed modeling procedure of thin film gold

coated fiber optic hydrophone sensor. Coupled equations from 3 modules in

COMSOL, namely, Acoustics, Structural Mechanics and RF/Photonics, were

solved simultaneously. The geometry, mesh structure and boundary conditions for a

thin film gold coated straight cleaved sensor are shown in Fig 4.24.

As discussed earlier, the acoustic module solved acoustic wave equation

and computed pressure distribution over the water region. Plain strain analysis was

performed in order to study the effect of pressure on the compressibility of thin film

gold. The boundary conditions used for the strain analysis are indicated in the inset

of Fig 4.24. The right hand side boundary of the gold film was set to be free to

move, while the left hand side boundary was fixed to the fiber core. The density of

gold was set to the bulk gold value of 19300 kg/m3 and the Poisson’s ratio was set

to 0.44 [60]. The Young’s modulus of thin gold film was varied as a function of

coating thickness. As seen in the case of optical constants of thin film gold, the

elastic constants of thin film gold also differed from the bulk values by several

orders of magnitude. Since these values were unavailable for gold films with 2nm-

30nm thickness, they had to be extracted from experimental results. As mentioned

in Chapter 3, these values of Young’s modulus were evaluated chosen based on the

assumption such that a pressure of 1 MPa produces a displacement of about 1

picometer. The values of Young’s modulus for various coating thickness have been

listed in Table A-4 (see appendix A-4). The resulting strain distribution is used to

calculate the change in the refractive index of gold through photo-elastic effect [61].

110

Assuming that the gold film is isotropic, this change in the refractive index

produced by applied strain is given by [61],

pSn

ng2

3

0−=∆ . Where, (4.7)

=on Refractive index of thin film gold under zero stress (pressure) condition.

p = photo-elastic constant of thin film gold.

S = Strain (displacement per unit length).

The photo-elastic constants of thin film gold are once again dependent on the film

thickness. Since no data was available in literature, these values had to be calculated

from the extracted results of refractive indices of gold. The detailed calculations and

corresponding values of the photo-elastic constants are discussed in appendix A-4.

Table 4. 4 Responsivity performance of coated straight cleaved fiber sensor

Initially, the refractive index of thin film gold was considered to incompressible

with respect to pressure variation. Later, the effect of compressibility of gold was

taken into consideration. The performance of straight cleaved fiber sensor for

Coating

thickness, nm

Dynamic responsivity with

water compression only

Dynamic responsivity with

water and gold compression

30nm - 52 dB/MPa -51 dB/MPa

20nm -50 dB/MPa -46 dB/MPa



7 nm -43 dB/MPa -27 dB/ MPa

5 nm -45 dB/MPa - 21 dB/MPa

3 nm -54 dB/ MPa - 23 dB/MPa

2 nm -54 dB/MPa - 28 dB /MPa

111

different coating thicknesses is summarized in Table 4.4 by taking into account both

compressible and incompressible gold coating. By considering incompressible gold

layer, only 12 dB in dynamic responsivity is achieved at around 7nm.This is due to

enhanced reflectance from the metallic gold coated end-face.

Fig 4. 25: Power density profile of a straight cleaved 5 nm gold coated fiber sensor

However, when the compressibility of thin gold film by the incident acoustic

pressure is accounted for, as much as 34 dB improvement in dynamic responsivity

is achieved at around 4-5 nm. This shows that for film thicknesses below 10 nm, the

improvement in responsivity is dominated by the thin film compressibility of gold

112

by the incident acoustic pressure. The power density profile of a 5 nm gold film

coated straight cleaved fiber optic sensor is shown in Fig 4.25.

4.3.1 Effect of gold coating on cylindrical etched fiber sensors:

In this section, the effect of thin (2-30 nm) film gold coating on the responsivity

performance of cylindrically etched fiber sensors is modeled. The geometry, mesh

structure and boundary conditions for a 6 µm cylindrically etched coated fiber

sensor are shown in Fig 4.24.The effect of gold coating on various etched tip

diameters was modeled considering coating at the tip as well as on the sides of the

etched tip.

Fig 4. 26: Geometry, mesh structure and boundary conditions of etched 5 nm coated fiber

sensor.

200 nm

200 nm

200 nm

200 nm

80 nm

120 nm

Radiation boundary

Radiation boundary

Match

ed B

oun

dary

Match

ed b

oun

dary

Pressu

re bo

un

dary

6

µm

Po

rt

200 nm

200 nm

200 nm

200 nm

80 nm

120 nm

Radiation boundary

Radiation boundary

Match

ed B

oun

dary

Match

ed b

oun

dary

Pressu

re bo

un

dary

6

µm

Po

rt

113

The cylindrically etched tip diameter was then varied from 6 µm to 12 µm in steps

of 2 µm . The power density profiles of a 5 nm coated structure are shown in Figs

4.27, 4.28, 4.29 and 4.30 for tip etched tip diameter of 6 µm, 8 µm,10 µm and 12

µm respectively.

Fig 4. 27: Power density profile of 5nm coated 6 micron etched fiber sensor

Table 4. 5: Responsivity performance of 6 µm etched coated fiber sensor

Coating thickness,

nm

Dynamic responsivity of cylindrical

etched coated sensor

30nm - 38 dB/MPa

10nm - 29 dB/MPa

7 nm - 27 dB/ MPa

5 nm - 22 dB/MPa

3 nm - 25 dB/MPa

2 nm - 28 dB /MPa

114



115

200 nm

200 nm

200

nm

200

nm

80

nm

120

nm

Radiation boundary

Radiation boundary

Match

ed b

oundary

Match

ed b

ound

ary

Pressu

re boundary

6 µm

Port

200 nm

200 nm

200

nm

200

nm

80

nm

120

nm

Radiation boundary

Radiation boundary

Match

ed b

oundary

Match

ed b

ound

ary

Pressu

re boundary

6 µm

Port


Fig 4. 31:Geometry, mesh structure and boundary conditions of coated 6 micron etched fiber

sensor

116

Table 4. 6:Responsivity performance of coated 7 degree linear tapered fiber sensor.

4.3.2. Effect of gold coating on linear tapered fiber sensors:


Coating thickness,

nm

Dynamic responsivity of 7 degree

taper coated sensor

30nm - 39 dB/MPa

10nm - 31 dB/MPa

7 nm - 25 dB/MPa

5 nm - 23 dB/MPa

3 nm - 25 dB/MPa

2 nm - 35 dB/ MPa

117

The effect of gold coating on linearly tapered fibers with different taper angles is

evaluated in this section. The geometry, mesh structure and boundary conditions for

a 7 degree tapered sensor with thin film gold coating is shown in Fig 4.31. Once

again, the coating is considered on the tip as well on the sides of the linearly tapered

tip. The power density profiles for taper angles of 7 degrees, 15 degrees, and 30

degrees are plotted in Figs 4.32, 4.33 and 4.34 respectively. The dynamic

responsivity performance of the 7 degree linearly tapered sensor is summarized in

Table 4.7 as a function of coating thickness in the range from 2-30 nm.


118

Fig 4. 34 : Power density profile of 5nm coated 30 degree linear tapered fiber sensor.

From the simulation results, it can be seen that as much as 33 dB improvement in

dynamic responsivity over that of a corresponding uncoated fiber sensor is obtained

for thin film coating thickness of around 5 nm. It is seen that due to the presence of

thin film coating at the fiber end-face, the amount of power reflected into the core

region increases, when compared to a corresponding uncoated case. Thus it is

expected that such sensors would exhibit enhanced reflectance performance in

comparison to the uncoated ones.

4.3.3. Effect of gold coating on exponentially tapered fiber sensors:

This section outlines the effect of gold coating on exponentially tapered fiber

sensors with different degrees of taper. The geometry, mesh structure and boundary

conditions for a 7 degree exponentially tapered sensor is shown in Fig 4.35. Taper

angles of 7 degrees, 15 degrees, and 30 degrees were considered for coating

119

thicknesses in the range from 2nm - 30nm. The dynamic responsivity performance

as a function of coating thickness is summarized for exponentially tapered angle of

7 degrees in table 4.7.

Table 4. 7 Responsivity performance of 7 degree exponential tapered fiber sensor

Fig 4. 35: Geometry, mesh structure and boundary conditions of 7 degree exponential coated

fiber sensor

Coating thickness, nm Dynamic responsivity of 7 degree

taper coated sensor

30nm - 39 dB/MPa

10nm - 38 dB/MPa

7 nm - 33 dB/MPa

5 nm - 27 dB/MPa

3 nm - 31 dB/MPa

2 nm - 35 dB/ MPa

200 nm

200 nm

200 nm

200 nm

80 nm

120 nm

Radiation boundary

Radiation boundary

Match

ed b

ou

nd

aryM

atched

bo

un

dary

Pressu

re bo

un

dary

6 µm

Po

rt200 nm

200 nm

200 nm

200 nm

80 nm

120 nm

Radiation boundary

Radiation boundary

Match

ed b

ou

nd

aryM

atched

bo

un

dary

Pressu

re bo

un

dary

6 µm

Po

rt

120

Fig 4. 36 : Power density profile of 5nm 7 degree exponential taper sensor


121


The power density profiles for 5nm coating thickness are plotted in Figs 4.35

through 4.38 for exponentially tapered angles of 7 degrees, 15 degrees and 30

degrees respectively. It can be seen that higher optical power is reflected back into

the core region when compared to the corresponding uncoated fiber sensors. The

exponential fiber sensor however has a greater leakage of power from the core into

the surrounding due to non-uniform tapering of the waveguide. This represents the

more realistic scenario , since it is very difficult to obtain step discontinuities in

etched fiber structures and perfectly uniform taper in case of a linearly tapered fiber

structure.

122

0 5 10 15 20 25 300

10

20

30

40

50


Imp

rov

emen

t in

Sen

sitv

ity

, d

B

Fig 4. 39: Improvement in responsivity, dB of 6 µm cylindrically etched sensor vs gold coating

thickness (2-30nm). Reference: -282 dB re 1V/µPa.

Fig 4.39 shows the plot of improvement in p-v responsivity of a thin film

coated fiber optic hydrophone probe with 6 micron cylindrically etched geometry

over that of the straight cleaved uncoated fiber sensor. The plot indicates that as

much as 48 dB improvement in p-v responsivity is obtained by using around 5 nm

thin film thickness. This occurs because the rate of change of refractive index of

gold with respect to pressure reaches the maximum at this thickness. For thicker

films (>15nm), the improvement in dynamic responsivity is primarily dominated by

the enhanced reflectance from the thin metallic film. As the film thickness

approaches below 10 nm, the film becomes increasingly dielectric in nature (i.e. the

real part of refractive index exceeds 1) (see chapter 3). In this case, the responsivity

enhancement is dominated by the compressibility of gold by the incident acoustic

pressure amplitude. Below thicknesses of 4-5 nm, the drop is responsivity is seen

due to increased losses in the dielectric film. Thus the numerical model predicted

123

that the cylindrically etched structure with 6 micron tip diameter and around 5nm

gold coating thickness would provide the highest sensitivity (-234 dB re 1 V/µPa)

performance.

4.4 Summary:

Table 4. 8: Performance summary of coated fiber sensors with varying tip geometry

In summary, this chapter gave a detailed account of numerical modeling of

fiber optic hydrophone probe by solving coupled acoustic, electro-magnetic and

stress-strain equations. 4 different fiber tip geometries, namely, straight cleaved,

cylindrically etched, linearly tapered and exponentially tapered fiber sensors were

modeled. The impact of etching diameter was modeled by changing the

cylindrically etched diameter from 6 micron to 12 microns. The impact of variation

of taper angles was also accounted for by considering taper angles of 7 degrees, 15

degrees, 30 degrees and 40 degrees in case of linearly and exponentially tapered

sensors.

Responsivity of different fiber sensor tip geometry, dB re 1V /µPa

Coating

thickness,

nm Cylindrically etched

fiber sensor

Linearly tapered

fiber sensor

Exponentially tapered

fiber sensor

30 nm - 276 - 256 - 277

10 nm - 264 - 240 - 255

7 nm - 250 - 228 - 245

5 nm - 234 - 224 - 233

3 nm - 240 - 227 - 241

2 nm - 252 - 248 -249

124

Further, the impact of thin film gold coating thickness was evaluated on the

above structures in the 2-30nm coating thickness range. Comparison of different tip

geometries as summarized in Table 4.8 revealed that cylindrically etched samples

with around 6 µm tip diameter gave the best performance in terms of providing

spatial averaging free bandwidth of 100 MHz and ease of realization. The

exponentially tapered sensor gave the worst (~30 dB drop) responsivity

performance due to higher leakage of power to the evanescent modes when

compared to the straight cleaved fiber sensor. Coating the cylindrically etched

structure with around 5nm thick gold film provided the highest (i.e. 48 dB)

improvement in p-v responsivity due to higher compressibility of thin film gold by

the incident acoustic pressure. This also established the fact that the acoustic

sensing indeed occurred at the tip of the fiber and the key to increasing the

responsivity improvement is to confine as much of optical power as possible within

the core region. The understanding gained from the numerical analysis in this

chapter was used to develop and test performance improvement of the thin film

coated fiber sensors fabricated in the next chapter.

125

Chapter 5: Experimental results

5.0 Introduction:

This chapter describes the experimental methods and presents the results of the

measurements carried out to verify the findings of the numerical modeling reported

in chapter 4. The chapter is organized as follows: The first section outlines the

measurement set-up to evaluate the responsivity performance of the fiber optic

hydrophone probe at optical wavelengths of 980nm and 1550nm. The next section,

presents the performance results of the fiber optic hydrophone probes using the 1.52

MHz High Intensity Focused Ultrasound (HIFU) acoustic source. Finally, the

simulation and experimental results are compared, and the reasons for the

discrepancies in the results are discussed.

5.1 Measurement Set-up:

The experimental block diagram, as depicted in Fig 5.1, is composed of acoustic

and optic sub-assemblies.

5.1.1 Acoustic Sub-system:

All the acousto-optic pressure to voltage responsivity measurements were

performed in a tank having dimensions 4 ft x 3ft x 1.5 ft containing de-ionized

water at 22 deg C. The acoustic transducer used was a one element High Intensity

Focused Ultrasound (HIFU) transducer (Sonic Concepts H110AS/N 01) with dual

band operation at frequencies of 1.52 MHz and 5.0 MHz. It required a radio

frequency (RF) impedance matching network to match it to 50 ohms over dual

bands of 1.41-1.98 MHz and 5.0-5.7 MHz. The transducer had an active diameter of

20 mm and a focal length of 34.52 mm. RF power amplifier provided a maximum

pulsed power level of 100 W with 10 % duty cycles. The excitation input to the RF

126

power amplifier was provided by the signal generator (Agilent 33251). The position

of the acoustic source and optical hydrophone were controlled by a custom

designed micromanipulator holder assembly (see Appendix A-10 and section

5.2).The PVDF needle hydrophone (Precision Acoustics, UK) served as the

reference hydrophone to evaluate the p-v responsivity (sensitivity) of fiber optic

hydrophone probes using substitution technique. The output of the needle

hydrophone was connected to a 20 dB gain, 100 MHz bandwidth preamplifier with

50 Ohms output impedance.

980nm

quantum well

laser , Lumics

1 W Optical

Isolator,980nm,

Ascentta

InGaAs PIN

photo-detector,

Thorlabs

3 dB coupler,

980nm,

Chiphope

RF Spectrum

Analyzer,

Agilent

Digital

Ocilloscope

Tektronix

Signal

Generator

Agilent

55 dB Power

Amplifier + RF

matching circuit

Water Tank

1.52 MHz HIFU

Transducer,

Sonic Concepts

50% output

50% output

Fabricated

fiber optic

hydrophone

probes

reference

fiber

980nm

quantum well

laser , Lumics

1 W Optical

Isolator,980nm,

Ascentta

InGaAs PIN

photo-detector,

Thorlabs

3 dB coupler,

980nm,

Chiphope

RF Spectrum

Analyzer,

Agilent

Digital

Ocilloscope

Tektronix

Signal

Generator

Agilent

55 dB Power

Amplifier + RF

matching circuit

Water Tank

1.52 MHz HIFU

Transducer,

Sonic Concepts

50% output

50% output

Fabricated

fiber optic

hydrophone

probes

reference

fiber

Fig 5. 1: Experimental set-up at 980nm optical wavelength

5.1.2 Fiber optic sub-system at 980nm:

The optical source at 980 nm was a quantum well pump laser source

(LU0980M200, Lumics Inc) with an output power of 20 dBm at a bias current of

200 mA (see Appendix A-8). The output from the laser was connected to the 980

nm optical isolator (Appendix A-7) in order to avoid unwanted back-reflections into

the laser. The output optical power of the isolator is split into two arms using a 2 x 2

127

3 dB optical coupler at 980 nm (see Appendix A-7). One arm of the optical coupler

is immersed in water as reference while the other arm is connected to the fabricated

fiber optic hydrophone probe sensors. This acousto-optic sensor is immersed in a

water tank and placed in the focal point of the HIFU transducer. All the fibers used

in the system are commercially available 1550nm single mode fibers with FC/APC

connectors. The FC/APC connectors had an optic return loss of 55 dB and were

used to avoid spurious back-reflections from the connectors. The reflected optical

energy is collected in a wideband amplified InGaAs detector (ThorLabs PDB 130C)

with a responsivity of 0.65 A/W at 980 nm and signal bandwidth of 150 MHz. It

has trans-impedance gain of 5 kΩ and noise equivalent power of 12pW/ (Hz) 1/2

.

5.1.3 Fiber optic sub-system at 1550nm:

System block diagram, depicted in Fig 5.2, is composed of optical source, optical

sensor, acoustic source, and optical receiver assemblies. The optical source is the

1550 nm distributed feedback (DFB) laser (Mitsubishi NX8563LB) with an output

power of -2 dBm at a bias current of 35 mA. The laser was held using custom made

laser diode mounts (see Appendix A-11) The source is coupled to a 10 dB optical

coupler and the output from 10 % arm drives the Erbium Doped Fiber Amplifier

(EDFA NuPhotonics NP2000CORSV-303500FCA1) with optical gain of 40 dB and

output power of up to 30 dBm. The output from the EDFA is divided equally using

a 2 x 2 3 dB optical coupler with maximum excess loss of 0.9dB. One of the optical

outputs is immersed in water

128

Fig 5. 2: Experimental set-up at 1550nm optical wavelength.

1550nm DFB

laser diode

Mitsubishi

1550nm isolator,

Ascentta, Inc.

10 dB optical

coupler, 1550nm,

Chiphope

Erbium Doped

Fiber Amplifier

Nuphotonics

1 W Optical

Isolator,1550nm,

Ascentta

InGaAs PIN

photo-detector,

Thorlabs

3 dB coupler,

1550nm,Chip

hope

RF Spectrum

Analyzer,

Agilent

Digital

Ocilloscope

Tektronix

Signal

Generator

Agilent

55 dB Power

Amplifier + RF

matching circuit

Water Tank

1.52 MHz HIFU

Transducer,

Sonic Concepts

10% output

50% output

50% output

Fabricated

fiber optic

hydrophone

probes

reference

fiber

1550nm DFB

laser diode

Mitsubishi

1550nm isolator,

Ascentta, Inc.

10 dB optical

coupler, 1550nm,

Chiphope

Erbium Doped

Fiber Amplifier

Nuphotonics

1 W Optical

Isolator,1550nm,

Ascentta

InGaAs PIN

photo-detector,

Thorlabs

3 dB coupler,

1550nm,Chip

hope

RF Spectrum

Analyzer,

Agilent

Digital

Ocilloscope

Tektronix

Signal

Generator

Agilent

55 dB Power

Amplifier + RF

matching circuit

Water Tank

1.52 MHz HIFU

Transducer,

Sonic Concepts

10% output

50% output

50% output

Fabricated

fiber optic

hydrophone

probes

reference

fiber

129

as reference while the other arm is connected to the fabricated sensors mentioned

in section 5.4. The optical sensor is immersed in a water tank and placed in the

focal point of a focused acoustic transducer. All the fibers used in the system are

commercially available 1550nm single mode fibers with FC/APC connectors. The

reflected optical energy is collected in a wideband amplified balanced InGaAs

photo-detector (ThorLabs PDB 130C) with a responsivity of 0.95 A/W (see

Appendix A-9) at 1550nm and signal bandwidth of 150 MHz. It has trans-

impedance gain of 5 kΩ and noise equivalent power of 12pW/ (Hz) 1/2

.

5.2 Mechanical holder assembly:

Fig 5. 3: Acoustic holder set up, (Left) 3 D linear translator assembly, (Right) HIFU

transducer and sensor holder assembly depicting needle hydrophone (in center with black

cable) and holes for as many as four optical fiber sensors (two on either side of needle

hydrophone with yellow jackets).

As stated earlier, a custom micro-manipulator holder assembly was designed for

experimental verification of the performance of the fiber optic hydrophone

130

probes. The mechanical drawings of the holder assemblies for the transducer and

acoustic hydrophone probes are shown in Appendix A-10. The transducer holder

Fig 5. 4: Needle hydrophone output at 1.5 MHz and 5 MHz, 60Vpp excitation to transducer,

needle hydrophone tip 1 cm from holder surface.

was kept stationary while the acoustic sensor holder was connected to 3

dimensional linear translational stage (Bislide assemblies, Velmex Inc, New

York). The linear translator had a resolution of 0.1 mm and a travel distance of 5

cm. Fig 5.3 shows the image of the holder assembly. The sensor holder arm was

capable of holding as many as 5 acoustic sensor probes spaced at a distance of 0.5

inch from each other.

5.3 Acoustic measurements using reference PVDF needle hydrophone:

This section briefly describes the reference measurements of the acoustic field

performed using the PVDF needle hydrophone. The acoustic base-line

measurements were carried out at acoustic frequencies of 1.5 MHz and 5 MHz. In

order to account for the differences in the acoustic field profile due to reflections

131

from the holders or any other variables, the measurements were performed at all

the 5 probe locations. The distances of the needle hydrophone probe tip from the

metallic surface of the holder were considered to be 1 mm and 1 cm respectively,

since these were the distances of the fiber sensor tips from the surfaces of the

metallic ferrules considered here.

Fig 5. 5: Needle hydrophone output at 1.5 MHz and 5 MHz, 60Vpp excitation to transducer,

needle hydrophone tip 1 mm from holder surface.

Fig 5.4 shows the response of the needle hydrophone with the tip 1 cm from the

surface of the metallic holder in the time domain. The left hand side data was

recorded at 1.52 MHz frequency and that on the right hand side was recorded at 5

MHz. The evaluated pressure to voltage responsivity of the PVDF needle

hydrophone was evaluated to be around -266 dB re 1 V/µPa to -268 dB re 1

V/µPa. Fig 5.5 shows the response obtained from the needle hydrophone with the

tip 1-2 mm from the surface of the metallic holder. The time domain data is

dispersive in nature. This is possibly due to acoustic reflections from the surface

of the aluminum holder. These reflections are not visible when the tip of the

needle hydrophone is about 1cm from the surface of the holder.he p-v

132

responsivity remained unaffected by the position of the needle hydrophone in the

sensor holder arm so long as the hydrophone was aligned to lie within the focal

region of the transducer.

Figure 5. 6: Needle hydrophone 1D and 2D scan data at 1.5 MHz and 5 MHz.

Figure 5.6 indicates the acoustic field profile of the HIFU transducer at 1.52 MHz

and 5 MHz. The table data indicates that the half pressure beam width is around

3-4 mm at 1.5 MHz and around 1.5-2 mm at 5 MHz. Once the reference

Left / Right scan data at 1.5 MHz

Left/ Right scan data at 5 MHz

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

200

400

600

800

1000

Relative distance from focus, cm

Nee

dle

hyd

roph

on

e o

utp

ut

vo

ltag

e, m

Vp

p

Needle tip 1 cm from surface of holder

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

200

400

600

800

1000


Nee

dle

hy

dro

pho

ne

outp

ut

volt

age,

mV

pp

Needle tip 1cm from surface of holder

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

200

400

600

800

1000


Nee

dle

hy

dro

ph

on

e o

utp

ut

vo

ltag

e, m

Vpp

Needle tip 1 mm from surface of holder

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

200

400

600

800

1000

Relative distance from focus,cm

Nee

dle

hy

dro

ph

one

outp

ut

volt

age,

mV

pp

Needle tip 1mm from surface of holder

133

measurements were done, the fabricated fiber sensors were characterized. The

images of the fabricated fiber sensors and their experimental results are discussed

in the following section.

5.4 Acoustic measurements with fiber optic hydrophone probes:

This section reports the measurement results of the fabricated fiber optic

hydrophone probes. Verification of improvement in responsivity of thin film gold

coated fiber sensors to continuous wave and burst excitation and signal to noise

ratio enhancement using balanced detection technique are presented.

5.4.1 Responsivity improvement measurements:

The geometry of the fabricated fiber probes is shown in appendix A-15. The

initial testing was done with gold coated fiber samples specified in terms of

coating time. Subsequently, in order to have a direct comparison with the

simulation results, a new set of samples were manufactured with a specific

coating thickness.

Table 5. 1: Pressure to voltage responsivity performance of thin film coated fiber samples.

Fiber sample type No of

samples

Coating time Electrical power at 5

MHz, dBm

Uncoated straight

cleaved

6 - -60 dBm(+ 5 dB/-3 dB)

Etched uncoated 3 - -91 dBm(+ 3 dB/-4 dB)

Etched coated 4 5 sec -23 dBm(+10 dB/-4 dB)

Etched coated 2 7 sec -20 dBm(+ 2 dB/-2 dB)

Etched coated 3 15 sec -37 dBm(+ 5 dB/-8 dB)

Etched coated 6 20 sec -50 dBm(+ 1dB/-1 dB)

134

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

Coating time, sec

Imp

rov

emen

t in

res

po

nsi

vit

y ,

dB

Fig 5. 7: Responsivity improvement, dB vs coating time, sec (ref: -282 dB re 1V/µPa).

Table 5.2 summarizes the statistical responsivity values of uncoated and coated

fiber sensors with coating times of 5 sec, 7 sec, 15 sec and 20 sec. Fig 5.6 shows

the improvement in responsivity as function of coating time. The maximum

improvement of about 37-40 dB in responsivity is achieved by using around 5-7

sec coated sample. For such coating times, the increment in static reflectance due

to gold coating is about 1-2 dB. The fact that a 40 dB improvement in

responsivity is observed, points that the compressibility of gold film by the

incident acoustic pressure is indeed the dominant factor for responsivity

performance in such films. As the coating time increases, the responsivity

decreases. The 10 dB improvement in responsivity for a 20 sec coated film is due

to the 10-12 dB improvement in the static reflectance, indicating that for such

films, the water compression by incident acoustic pressure dominates the

responsivity performance.

135

In order to compare the experimental responsivity performance

improvement with those obtained using simulations, it was essential to produce

consistent samples in terms of coating thickness. As mentioned in section 3.3.2,

the coating time was controlled for a particular coating thickness set using a PZT

based thickness sensor. Due to limited availability of samples and their high

(almost 50%) damage rate, only 3 samples each with coating thicknesses of

around 3 nm, 5 nm, 7nm and 10 nm were considered. Additionally each of these

samples belonged to three different geometries (see appendix A-15), namely

straight cleaved, cylindrically etched and linearly tapered structures. The

geometry of the fabricated fiber samples is shown in appendix A-15. In order to

ensure consistency (within 2 % reflectance) of coating thickness, these samples

were placed in a custom designed holder (appendix A-12) in the sputtering

chamber. The static reflectance performance of these sensors is presented in

Tables 5.3 to 5.7.

Table 5. 2: Static reflectance of straight cleaved fiber samples

Static reflectance in air,

dB

Static reflectance in water,

dB

Sample

number

Coating

thickness Experimental Simulation Experimental Simulation

SC uncoated - 16.00 - 15.40 -31.00 -30.50

SC 3 ~ 3 nm -18.85 -17.95 -16.85 -16.65

SC 5 ~ 5 nm -11.65 -10.65 -11.95 -9.75

SC 7 ~ 7 nm - 6.53 -5.06 -6.53 -5.06

SC 10 ~ 10 nm - 4.30 - 4.32 -4.32 -4.32

136

Table 5. 3: Static reflectance of uncoated cylindrically etched fiber samples


dB

Static reflectance in water,

dB

Sample

number

Sample

tip

diameter Experimental Simulation Experimental Simulation

# 11 7.5-8 µm -23.00 -16.50 -38.00 -32.10

# 12 7.5-8 µm -21.60 -16.50 -37.00 -32.10

# 18 7.5-8 µm - 31.40 -16.50 - 38.00 -32.10

Table 5.3 summarizes the static reflectance performance of the straight

cleaved uncoated and thin film gold coated fiber sensors. It is seen that the

simulation results are in agreement with the experimental results. For coating

thicknesses smaller than around 3 nm, the static reflectance of the coated sample

is below that of the static reflectance of the uncoated sample in air. As the coating

thickness increases beyond about 7nm, the static reflectance of the coated fiber

sensor also increases. Around 8-10 dB gain in the static reflectance is seen for

coating thicknesses of about 7 nm.

Table 5. 4: Static reflectance of thin film coated cylindrically etched fiber samples


dB

Static reflectance in

water, dB

Sample

number

Coating

thickness

Experimental Simulation Experimental Simulation

# 11 C 4-5 nm - 22.30 -15.90 -20.50 -14.82

# 12 C 6-7 nm -18.04 -6.66 -25.00 -20.66

# 18 C ~ 12 nm -27.00 -2.92 - 28.50 -12.92

137

Table 5.4 presents the static reflectance values of uncoated cylindrically

etched fiber samples. As expected, the static reflectance of the etched fiber sample

is lower than that of an un-etched one. The 4-6 dB difference between the

simulation results and experimental results could arise from the fact that the

simulation considered an etching length of 25 µm at most. The etched section

introduces attenuation in the medium which is dependent on the length of etched

region. The actual etch length in the fabricated samples varied from sample to

sample from around 600 µm to 1 mm. The static reflectance of the coated fiber

sensors is shown in table 5.4. A 1 dB improvement in static reflectance is

obtained for thickness of 4-5 nm. About 3.5 dB improvement is observed for

coating thickness of around 6-7 nm.

Table 5. 5: Static reflectance of uncoated linearly tapered fiber samples: (taper angle 3-5

degrees)


dB


water, dB

Sample

number

Sample tip

diameter


# 1 ~ 6 µm - 26.40 -18.30 -38.00 -33.30

# 5 ~ 5 µm -28.80 -20.30 -37.00 -35.30

# 17 ~ 6.5 µm -23.30 -18.30 -34.00 -33.30

The static reflectance performance of the linearly tapered uncoated and coated

fiber samples is presented in tables 5.6 and 5.7. The tapered fibers with coating

thicknesses of around 4-5 nm, 6-7 nm and 2-3 nm were considered. About 1 dB

138

drop in static reflectance is obtained for about 4-5nm thick film while around 2

dB improvement is obtained for around 6-7 nm.

Table 5. 6: Static reflectance of thin film coated linearly tapered fiber samples: (taper angle

3-5 degrees)


dB


water, dB

Sample

number

Coating

thickness


# 17 T 4-5 nm -25.00 -17.70 -23.50 -16.80

# 1 T 6-7 nm -25.00 -7.96 -35.00 -22.00

# 5 T 2-3 nm -28.00 -23.35 - 40.00 -20.50

Table 5. 7: Pressure to voltage responsivity performance of fiber optic probes at 980 nm

Sample

number

Electrical

power at

1.5 MHz,

dBm

Electrical

power at 5

MHz, dBm

Improvement

in responsivity,

simulation

Ref = -282 dB

re 1 V/µPa

Improvement

in responsivity,

experimental

Ref = -282 dB

re 1 V/µPa

SC uncoated - 60 dBm - 58 dBm 0 0

SC 3 - 47 dBm - 46 dBm 50 dB 13 dB

SC 5 - 8 dBm - 5 dBm 68 dB 52 dB

SC 7 - 33 dBm - 34 dBm 46 dB 27 dB

SC 10 - 84 dBm X 18 dB X

# 11 C(4-5nm) - 22 dBm - 47 dBm 52 dB 38 dB

# 12 C(6-7nm) - 35 dBm - 37 dBm 36 dB 25 dB

# 18 C(~12nm) - 28 dBm - 30 dBm 21 dB 30 dB

# 27 C(4-5nm) -29 dBm - 28 dBm 48 dB 31 dB

# 29 C(1-2nm) - 45 dBm - 43 dBm 15 dB 17 dB

# 17 T(4-5 nm) -24 dBm - 22 dBm 50 dB 36 dB

# 1 T (6-7nm) - 32 dBm - 33 dBm 34 dB 28 dB

# 5 T (2-3 nm) -95 dBm X 40 dB X

139

These fiber samples were placed simultaneously with the needle

hydrophone in acoustic sensor holder and positioned in the water tank as shown in

Fig 5.3. The HIFU transducer was using a continuous wave source at 1.5 MHz

and 5 MHz with 18 Vpp signal amplitude. The needle hydrophone output with 20

dB amplifier was measured to be – 18 dBm at frequencies of 1.5 MHz and 5

MHz. The responsivity performances of the above listed fiber optic hydrophone

probes at 980nm are presented in Table 5.8. The responsivity performance of the

fiber samples at 1550nm optical wavelength is summarized in Table 5.9

Table 5. 8: Pressure to voltage responsivity performance of fiber optic probes at 1550 nm

Sample

number

Electrical

power at 1.5

MHz, dBm

Electrical

power at 5

MHz, dBm

Improvement in

responsivity, dB

(ref: -282 dB re 1V/µPa)

SC uncoated - 60 dBm - 61 dBm 0

SC 3 - 43 dBm - 44 dBm 17 dB

SC 5 - 6 dBm - 5 dBm 55 dB

SC 7 - 33 dBm - 34 dBm 27 dB

SC 10 X X X

# 11 C - 50 dBm - 47 dBm 10 dB

# 12 C - 33 dBm - 32 dBm 27 dB

# 18 C - 30 dBm - 30 dBm 30 dB

# 27 C -29 dBm - 28 dBm 31 dB

# 29 C - 45 dBm - 43 dBm 17 dB

# 17 T -24 dBm - 22 dBm 38 dB

# 1 T - 31 dBm - 30 dBm 30 dB

# 5 T X X X

140

0 5 10 15 20 25 300

10

20

30

40

50


Impro

vem

ent

in r

esponsi

vit

y,d

B

Fig 5. 8: Improvement in responsivity, dB vs coating thickness. Data indicated by blue line:

simulation, red square: Experiment. Ref = -282 dB re 1V/µPa.

Fig 5.7 shows the comparison of the experimental and simulation results

of improvement in responsivity with reference to an uncoated straight cleaved

fiber sensor. Though the trend in improvement of responsivitiy matched with the

numerical prediction, some deviations from the ideal values exist due to practical

limitations. Samples SC 10 and # 5 T exhibited a very poor responsivity. The

fibers were possibly damaged while testing. The fiber samples with around 4-5

nm coating thickness exhibited the highest responsivity improvement of 50 dB.

This matches with the thickness value predicted numerically. The 14-16 dB

difference between the numerical prediction and the experimentally measured

values arises from the 4-6 dB difference in the static reflectance due to etching of

the fiber samples as seen in Table 5.4. The other reason for the difference between

the expected and experimental results could be due to the error in the assumption

of the Youngs’ modulus of thin films as shown in Appendix A-4. The difference

141

of 37 dB between the predicted responsivity of the 2-3 nm coated sample

indicates that the fiber exhibited a more loss than predicted. This is also seen from

the 20 dB loss in static reflectance data of the 2-3 nm coated fiber sample in Table

5.7. This loss could have arisen either due to impurities deposited at the sensing

tip while coating or due to scattering of light at the tip. Sample # 18 C with 12 nm

coating thickness exhibits anomalous behavior. Around 15 dB higher responsivity

performance is observed when compared to the numerical prediction. This could

result from the fact the coating thickness value was actually lower than the

indicated value of around 12 nm. From the static reflectance data in Table 5.5, a

25 dB lower static reflectance performance of this sample in comparison to the

simulation result indicates that the coating thickness was below 3nm. The other

important factor contributing to the responsivity performance is the shape of the

fiber sensor as seen in Chapter 4. Sample # 18 C has the shape as indicated in Fig

A-15.4 (appendix A-15) which is different from the three cases considered in this

work.

Statistical verification of simulation predictions:

As already discussed, in order to verify the numerical simulation results, it was

necessary to consider coated fiber samples fabricated in terms of coating

thickness. In absence of sufficient samples for obtaining statistical information, it

was necessary to express coating time in terms of coating thickness. As seen from

Appendix A-13, for a fixed current rate, sample to target distance and sputter

chamber pressure, as the coating time increases, the coating thickness also

increases. For instrument settings of 0.04 mbar pressure, 20 mm distance sample

142

0 5 10 15 20 25 300

10

20

30

40

50

Coating thickness, nm

Impro

vem

ent

in r

esponsi

vit

y,

dB

to target distance, and current of 20 mA, the coating times from 5 sec- 20 sec

roughly corresponded to coating thicknesses in the range from 2nm – 20nm.

Further, a better estimation of coating thickness from coating time was obtained

by considering static reflectance in air data. Appendix A-16 summarizes the static

performance of coated fiber samples in the range from 2-35 nm in air.

Table 5. 9: Estimation of coating thickness from coating time based on static reflectance

measurement

T

Fig 5. 9: Responsivity improvement, dB vs coating thickness, nm (Blue: Simulation, Red:

experimental data with errorbar)

Coating

time

No of

samples

Improvement in static reflectance

over uncoated fiber , dB

Coating thickness

5 sec 4 1-2 dB 3.5 – 5 nm

7 sec 2 1-2 dB 3.5 – 5 nm

15 sec 3 8-10 dB 8 – 10 nm

20 sec 6 10-14 dB 15 – 20 nm

143

As seen from Table 5.10, a 5-7 sec coating time results in 1-2 dB improvement in

static reflectance in comparison to that of the uncoated fiber sensor. Such a static

reflectance value corresponds to coating thickness in the range of 3.5 -5nm.

Similarly, the 8-10 dB improvement in static reflectance for 15 sec coating time

corresponds to coating thickness of 8-10 nm while a 20 sec coating time

corresponds to coating thickness of 15-20 nm. Using this data, the experimental

improvement in responsivity is plotted as a function of coating thickness in Fig

5.8 along with the associated error-bar for each set of samples.

In summary, this section presented the acoustic measurement results of the

fiber optic hydrophone probes as a function of coating time as well as coating

thickness. Initial testing results indicated a maximum responsivity improvement

of around 40 dB for fiber samples with 5-7 sec coating. Responsivity performance

measurement in terms of coating thickness indicated that maximum (38 dB)

improvement is obtained at around 4-5 nm. The static reflectance improvement

due to thin film coating for such films was around 1-2 dB. This indicated that, for

such thicknesses, the dominant factor contributing to the responsivity

improvement was the compressibility of the gold films by incident acoustic

pressure. As the coating thickness increases, the improvement in responsivity is

dominated by the enhancement in static reflectance due to thin metal film. A

drastic drop (around 20-30 dB) in responsivity is observed for coating thickness

of below 3nm. This indicates the presence of scattering of light from the

discontinuous films or other phenomenon not accounted for in the numerical

model.

144

5.4.2 Noise cancellation measurement:

Fig 5. 10: Experimental set-up for noise cancellation using balanced detection

Fig 5.8 shows the implementation of optical technique of noise cancellation using

balanced photo-detector PDB 130C. The optical signal which contains intensity

noise is split into two halves using a 3 dB optical coupler. As discussed earlier,

one of the arms is connected to the fiber sensor, while the other arm is used as

reference. This reference arm is now connected to one of the inputs of the

balanced detector. An optical attenuator is connected through this reference arm

to adjust for amplitude imbalance. The reflected signal which contains both the

signal and noise component is fed as an input to the other arm of the photo-

detector and is then displayed on the spectrum analyzer.

Optical laser

source or

EDFA

3 dB coupler

Sensor arm

reference arm

(noise)

attenuator

+_

Display circuit

Balanced

Photo-detector

Reflected power

(Signal + noise)

Optical laser

source or

EDFA

3 dB coupler

Sensor arm

reference arm

(noise)

attenuator

+_

Display circuit

Balanced

Photo-detector

Optical laser

source or

EDFA

3 dB coupler

Sensor arm

reference arm

(noise)

attenuator

+_

Display circuit

Balanced

Photo-detector

Reflected power

(Signal + noise)

145

Table 5. 10 Noise cancellation performance of the fiber optic probes at 980nm. Noise power

of the photo-detector under no modulation = -112 dBm.

.

Sample

number

RIN noise

power

predicted

Noise power

without

balanced

detection

Noise power

with

balanced

detection

Experimental

noise

cancellation

SC

uncoated

- 125 dBm -112 dBm -112 dBm 0 dB

SC 3 -95 dBm -95 dBm -105 dBm 10 dB

SC 5 -88 dBm -88 dBm -98 dBm 10 dB

SC 7 -74 dBm -80 dBm -88 dBm 8 dB

SC 10 -70 dBm -112 dBm -112 dBm X

# 11 C -102 dBm -104 dBm -112 dBm 8 dB

# 12 C -111 dBm -112 dBm -112 dBm Not RIN

dominated

# 18 C

-118 dBm -112 dBm -112 dBm Not RIN

dominated

# 27 C

-127 dBm -112 dBm -112 dBm Not RIN

dominated

# 29 C

- 132 dBm -112 dBm -112 dBm Not RIN

dominated

# 17 T -108 dBm -108 dBm -112 dBm 7 dB

# 1 T -131 dBm -112 dBm -112 dBm Not RIN

dominated

# 5 T -141 dBm -112 dBm -112 dBm X

The analysis in [66] reports that for an ideal receiver, with perfect matching

between the two anti-parallel photo-diodes, complete common mode noise

cancellation is achieved. Practically, the achievable RIN cancellation depends on

the CMRR (Common Mode Rejection Ratio) of the receiver. Appendix A-9 lists

the specifications of the balanced photo-detector PDB 130C. The CMRR and

hence the maximum achievable noise cancellation with this receiver is 35 dB,

assuming that the two inputs to the balanced photo-detector have perfect

amplitude and phase balance.

146

Table 5. 11: Noise cancellation performance of fiber optic probes at 1550nm. Noise power of

the photo-detector under no modulation = -112 dBm .

Sample

number

RIN noise

power

predicted

Noise power

without

balanced

detection

Noise power

with

balanced

detection

Experimental

noise

cancellation

SC

uncoated

- 108 dBm -104 dBm -112 dBm 8 dB

SC 3 -81.6 dBm -82 dBm -92 dBm 10 dB

SC 5 -77.68 dBm -75 dBm -85 dBm 10 dB

SC 7 -60.74 dBm -69 dBm -80 dBm 10 dB

SC 10 -56.28 dBm -112 dBm -112 dBm X

# 11 C -88.68 dBm -89 dBm -98 dBm 9 dB

# 12 C -97.68 dBm -100 dBm -106 dBm 6 dB

# 18 C -105 dBm -112 dBm -112 dBm Not RIN

dominated

# 17 T -95 dBm -95 dBm -106 dBm 11 dB

# 1 T -117 dBm -118 dBm -112 dBm Not RIN

dominated

# 5 T -127 dBm -106 dBm -112 dBm X

Tables 5.10 and 5.11 summarize the noise performance of the various fiber

sensors at optical wavelengths of 980nm and 1550nm respectively. All the values

were obtained for 20 dBm of incident optical power. It can be seen that as the

coating thickness increases, the RIN dominated noise power at the receiver also

increases. A maximum noise cancellation of 10 dB was achieved using the

balanced photo-detector. From Appendix A-9, it is seen that common mode

rejection ratio of 35 dB is achievable using this balanced receiver. However,

analysis presented in [66] indicated that the amount of common mode noise

cancellation depends on the amplitude as well as phase balance and on the RIN

correlation co-efficient. The analysis predicted that an amplitude mismatch of 15-

147

0 10 20 30 40 50 60 70 80 90 100-120

-110

-100

-90

-80

-70

-60

-50

-40

X: 4.999

Y: -45.48

Frequency, MHz

Ele

ctri

cal

pow

er,d

Bm

20 % between the two noise inputs of the photo-detector could reduce the amount

of noise cancellation by around 25-30 dB. It also pointed out that the RIN noise

power is dependent on the extent of RIN correlation and that the achievable RIN

cancellation decreases with decrease in the correlation co-efficient. The minimum

detectable pressure for the fiber samples with 4-5 nm coating was evaluated to be

0.1 KPa for a reference bandwidth of 1 Hz.

5.4.3 Frequency domain response to burst acoustic signal at 5 MHz:

This section presents the response of the fabricated fiber optic hydrophone probes

to an acoustic burst signal of 10% duty cycle at 5 MHz and 6 MPa pressure

amplitude.

Fig 5. 11: Frequency response of PVDF needle hydrophone

148

0 10 20 30 40 50 60 70 80 90 100-120

-110

-100

-90

-80

-70

-60

-50

-40

X: 4.999

Y: -72.84

Frequency, MHz

Ele

ctri

cal

po

wer

, d

Bm

0 10 20 30 40 50 60 70 80 90 100-120

-100

-80

-60

-40

-20

0

X: 4.999

Y: -35.58

Frequency, MHz

Ele

ctri

cal

pow

er,

dB

m

Fig 5. 12: Frequency response of straight cleaved uncoated FOHP

Fig 5. 13: Frequency response of 4-5nm coated fiber sensor (# 17 T)

149

0 10 20 30 40 50 60 70 80 90 100-120

-100

-80

-60

-40

-20

0

X: 4.847

Y: -59.23

Frequency, MHz

Ele

ctri

cal

Pow

er,

dB

m

Fig 5. 14 : Frequency response of 6-7 nm coated fiber sensor (# 12 C)

The frequency domain performance of the needle hydrophone and the

uncoated straight cleaved sample is shown Figs 5.9 and 5.10 respectively. The

performance of the fiber sensor with 4-5 nm of coating thickness and the 6-7nm

coating thickness is shown in Figs 5.11 and 5.12 respectively. The amplitude of

the fundamental and the harmonics increases as the responsivity increases. An

improvement of 37 dB and 12 dB in the fundamental signal is seen the case of the

4-5nm and 6-7 nm coated fiber sample, respectively in comparison to that

obtained from an uncoated fiber sample. Also, as the responsivity increases, the

signal to noise ratio of the harmonics also increases.

Beyond 35 MHz, the signal to noise ratio of the harmonics is insufficient and

the harmonics are indiscernible from the noise. Subsequent testing of the laser

revealed that this could be a result of amplification of noise by the resonant cavity

formed between the external Bragg grating and the laser end-face. These gratings

150

were located at 200 (+/- 20) cm distance from the end-face, creating resonances at

around 50-56 MHz and its multiples [71] in accordance with the relationship f =

c/2nL, where c is the speed of light in air, n is the refractive index of the fiber, L

is the length of the resonant cavity. Once again, the balanced detection technique

did not provide the necessary 35 dB noise cancellation due to its dependence on

the amplitude and phase balance as well as on the RIN correlation co-efficient.

The noise correlation co-efficient depends on degree of matching of the photo-

detectors and the coherence of the optical signal entering the two arms of the

photo-detector. Analysis in [66] indicates that only 10% mismatch in the RIN

correlation reduces the achievable signal to noise ratio improvement by 35 dB. A

higher noise correlation can be achieved by ensuring that the optical path length

difference between the signals between the two arms of the balanced photo-

detector is limited to the coherence length of the laser.

5.5 Summary:

This chapter described the measurement set-up for determination of

pressure to voltage responsivity and noise cancellation of the fiber optic

hydrophone probes at 980nm and 1550nm respectively. The base-line

characterization of acoustic transducer was performed using a PVDF needle

hydrophone as reference. P-v responsivity of the fiber optic hydrophone probes

fabricated as a function of coating time as well as coating thickness was

evaluated. Testing results indicated a maximum responsivity improvement of

around 40 dB for fiber samples with 5-7 sec coating time and about 38 dB

improvement at around 4-5 nm thickness. This was in agreement with the

151

numerical simulation results. The static reflectance improvement due to thin film

coating for such films was around 1-2 dB. This indicated that, for such films, the

dominant factor contributing to the responsivity improvement was the

compressibility of the gold films by incident acoustic pressure. As the coating

thickness increases, the improvement in responsivity was dominated by the

enhancement in static reflectance due to thin metal film. A drastic drop (around

20-30 dB) in responsivity was observed for coating thickness of below 3 nm. This

indicates the presence of scattering of light from the discontinuous films or other

impurities not accounted for in the numerical model. A noise cancellation (or

SNR improvement) of around 10-11 dB was achieved using balanced detection

technique. The improvement in responsivity was also demonstrated by the

frequency response of the fiber optic hydrophone probe to burst acoustic pressure.

The amplitude (or SNR) of the fundamental as well as the harmonic signals

increased with increase in responsivity till 35 MHz. The improvement in

responsivity beyond 35 MHz could not be verified due to the presence of

resonance feedback induced RIN from the laser source. Thus, the maximum

responsivity of around – 245 dB re 1 V/µPa and sensitivity of the 0.1 kPa

(referenced to 1 Hz bandwidth) was achieved by using 4-5nm thin film coated

etched fiber optic hydrophone probe with balanced detection.

152

Chapter 6: Conclusions and Recommendations for Future Work

6.0 Introduction:

This thesis has focused on DEVELOPMENT AND REALIZATION OF

OPTIMUM FIBER OPTIC HYDROPHONE PROBE for calibration of

transducers up to 100 MHz without spatial averaging of acoustic field. The

improvements in performance are achieved through efficient fiber sensor design

and system architecture developed based on high power optical source at

wavelengths of 1550nm and 980nm. Both wavelengths are matured for long haul

optical communication applications, hence technologically suitable for cost

effective products. In this chapter, first summary of work in this thesis is

presented followed by the recommendations for future improvements.

6.1. Conclusions:

The analytical modeling of uncoated fiber sensor and thin (2-35 nm) film

gold coated fiber optic sensors based on transmission line analogy was presented.

The work also provided a detailed account of the development of a novel semi-

empirical technique for extraction of complex refractive index of thin film gold

for thickness ranging from 2nm-35nm at optical wavelengths of 980nm, 1480nm

and 1550nm. Another innovative aspect of the work was the extraction of stress

strain relationship of thin film gold in the thickness range of 2 nm-35 nm. The

complex index of refraction and Young modulus data were indispensable in

modeling and optimization of 100 MHz FOHP in calculation of optimized

pressure responsivity.

153

The initial transmission line based analytical model of thin (2-35 nm) film

gold coated fiber optic sensors predicted as much as 30 dB improvement in

responsivity over that of an uncoated fiber sensor for coating thicknesses of

around 4-5 nm. An in depth account of the optimization procedure based on finite

element analysis of thin film coated straight cleaved, cylindrically etched, linearly

tapered and exponentially tapered fiber sensor geometries was provided.

Simulation results indicated that the responsivity performance of cylindrically

etched fiber sensor with around 6-7µm tip diameter was comparable to that of the

linearly tapered structure with about 7 degree of taper angle. Both the structures

provided 15 -20 dB drop in responsivity over that of the straight cleaved unetched

fiber sensor. The exponentially tapered sensor gave the worst loss (~30 dB) in

responsivity performance due to higher power leakage from propagating core

mode to the cladding modes when compared to the straight cleaved fiber sensor.

Thus, it was concluded that the cylindrically etched structure with around 6-7 µm

tip diameter coated with 4-5nm thick gold film provided the highest (i.e. 48 dB)

improvement in p-v responsivity. Experimental results of the fabricated samples

corroborated with the simulated results, indicating that a maximum responsivity

improvement is indeed exhibited by samples with around 4-5 nm of gold coating

thickness. An unprecedented pressure to voltage responsivity of around -244 dB

re 1 V/µPa is achieved by using gold coated etched fiber sensors with around 4-

5nm of gold coating thickness. This is more than the required 20 dB improvement

in the responsvity over that of the PVDF needle hydrophone. This improvement

in responsivity was observed only by considering that the compression of thin

154

gold films in the thickness range of 4-5nm was comparable to that of the

compression of water. This was done by considering Young’s modulus of around

0.1 GPa, which is a factor of 500 smaller than that of bulk gold. A 10 dB

improvement in sensitivity (minimum detectable pressure) of the fiber optic

hydrophone probe was also achieved by balanced detection at the receiver,

resulting in minimum detectable pressure of 0.1 kPa. Based on the above

simulation and experimental results, it is evidenced that the goals of the thesis are

achieved.

6.2. Recommendations for Future work:

To further improve performance of fiber sensor, further research topics are

recommended.

Adhesion of thin film gold coating:

While testing the coated fiber sensors, it was observed that some of the samples

exhibited a sudden drop in responsivity. Examination of the fiber tips under the

microscope revealed that of the gold coating was partly removed from the tip.

Thus, the issue of adhesion of the gold layer to the fiber tip requires to be

examined. The adhesion of gold to the fiber tip could be improved by using a few

angstroms thick layer of metal (chromium) or polymer (3-mercaptopropyl

trimethoxysilane) as an under-layer [67]. The effect of the under layer on the

responsivity performance will have to be determined.

Responsivity improvement along with noise cancellation:

The balanced detection scheme implemented in the work, provided about 10-11

dB of common mode rejection, which led to relative intensity noise cancellation.

155

Even though the balanced receiver was capable of providing as much as 35 dB of

common mode rejection, but due to amplitude mismatch between the two inputs

to the detector the full potential was not achieved. Higher noise cancellation can

be achieved by using high precision optical attenuators to provide a finer control

over the amplitude balance. Higher noise cancellation at frequencies beyond 35

MHz, can be obtained by ensuring that the optical path length difference between

the two arms to the photo-detector is within the coherence length of the laser. This

ensures a higher degree of noise correlation and better noise cancellation.

Analysis indicates that by making the correlation co-efficient closer to unity, as

much as 35 dB improvement in SNR can be achieved. Simultaneous 3 dB

improvement in the signal can be achieved along with noise cancellation by

combining the signals in phase and noise out of phase. This requires the use of an

element which provides optical phase control in addition to amplitude control.

Optical hybrid with 180 degrees phase imbalance from Optoplex or Celight can

be used for this purpose [68].

Survivability of fiber sensors:

As stated already, the fabricated fiber samples were extremely fragile and

had a 50% survival rate. In order to avoid any fluctuations in the back-reflected

signal, the fiber samples were glued to ferrules which had a diameter of 2 mm and

a length of about 1 cm. While testing in the tank, the fibers were subjected to high

stress at the end of the ferrule, developing micro-cracks and subsequently

breaking. It is important to improve the survivability of the fiber samples in order

to avoid the need to calibrate the fiber optic hydrophone probe repeatedly after

156

replacement. Survivability of the samples could be improved by placing fibers in

metal chucks [69] as opposed to ferrules. Also, use of a protective jacket/ sleeve

at the fiber to ferrule transition can improve the survivability of samples.

Material study of ultra-thin gold films:

During the course of this work, it was observed that many properties of

ultrathin (< 10nm) gold films were not available in literature. Also, at such film

thicknesses, the properties of the material showed a drastic change from their bulk

behavior. The refractive index extraction as well the determination of photo-

elastic and Young’s modulus of thin film gold was performed based on numerical

models which assumed uniform coating of gold layer. This simplification was

made in order to gain an understanding of the complex acousto-optic interactions

involved in responsivity improvement. A more accurate model can be created by

taking into account the discontinuous nature or morphology of films at coating

thicknesses of below 10nm [70].

Impact of various coating materials:

This work focused on the use of gold as the coating material for obtaining the

improvement in responsivity. Ultrathin films of metals such as silver, platinum

and copper exhibit properties similar to that of gold and are frequently used in

biosensing applications. The impact of these metals and dielectrics such as TiO3

on the responsivity performance can also be explored.

Resonance feedback induced RIN at 55 MHz and its harmonics:

As discussed in the results of chapter 5, resonance feedback induced RIN from the

optical system masked the information content at frequencies higher than 35

157

MHz. Further testing revealed that these harmonics originated from the laser

source. This could be due to amplification of noise by the resonant cavity formed

between the external Bragg grating and the laser end-face. These gratings were

located at 200 (+/- 20) cm distance from the end-face, creating resonances at

around 50-56 MHz and its multiples [71]. Use of alternative laser source without

external Bragg gratings could be explored.

158

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Appendices

165

Appendix A-1: LIST OF EQUIPMENT & COMPONENTS

Equipment Manufacturer Model Specifications

Function

Generator

Agilent 33250A 80 MHz

Function/Arbitrary

Waveform Generator

Power

Amplifier

ENI 3100LA 250 kHz – 150 MHz

,Gain 55 dB

Digital

Oscilloscope

Tektronix TDS2022 200 MHz Bandwidths, 2

GS/s Sample Rates

In line filter MFJ 1164B AC line RFI filter.

120V/25A/3000W max.

RF Spectrum

Analyzer

Agilent E408A (Mainframe) 20 Hz – 2.4 GHz

RF Network

Analyzer

Agilent 8712ET 300 kHz – 1.3 GHz

EDFA at

1550nm

Nuphoton

Technologies

NP2000CORSV3035

00FCA1

Optical gain of 40 dB,

Maximum output

power:30 dBm

10 dB optical

coupler at

1550nm

ChipHope SMSCA223RPF1005

FA

2x2 coupler with 10/90

coupling ratio

3 dB optical

coupler at

1550nm

Ascentta CP-S-15-50-22-XX-

S-L-10-FA

2x2 coupler with 50/50

coupling ratio

Balanced

Photo-

Detector

Thor Labs PDB130C Sensor InGaAs,

Bandwidth 150MHz,

Peak Responsivity: 0.95

A/W @ 1550nm

Low power

optical

isolator at

1550nm

Ascentta ISILPD55SS9 Single mode, 1550 nm

isolator, Maximum

power handling of 400

mW.

High power

optical

isolator at

1550nm

Ascentta IS-IL-P-D-55-S-S9-

FA-1W

Single mode, 1550 nm

isolator, Maximum

power handling of 1W.

Optical

isolator at

980nm

Ascentta VIS-S-980-HI-L-10-

NE-09

Single mode, 980 nm

isolator, Maximum

power handling of 400

mW.

3 dB optical

coupler at

980nm

Chip Hope SMSCC223RP5005F

A

Single mode 2X2

coupler with 50/50

coupling ratio

166

Appendix A-2: HE 11 mode in Single Mode Fiber

This appendix shows the mode profile of the dominant mode in the graded index

single mode fiber obtained using COMSOL. It can be seen from Figs A-2.2 to A-

2.4, that almost all the energy is contained within the core for the HE11 mode. The

power in the cladding region is almost 50 dB lower than the power in the cladding

region.

Fig A-2. 1: Propagation constant of the HE11 mode vs wavelength.

800 1000 1200 1400 1600 1800 20004

5

6

7

8

9

10

11

12x 10

6

wavelength, nm

β,

rad

/m

Beta Vs wavelength of HE11

mode of single mode optical fiber

980nm

1550nm

800 1000 1200 1400 1600 1800 20004

5

6

7

8

9

10

11

12x 10

6

wavelength, nm

β,

rad

/m

Beta Vs wavelength of HE11

mode of single mode optical fiber

980nm

1550nm

167

-10 -5 0 5 100

2000

4000

6000

8000

10000

12000

X: 3.79e-005

Y: 1.01e+004

X: -3.166

Y: 5633

Radial distance,µm

Ele

ctri

cal

fiel

d a

mp

litu

de,

V/m

X: 3.166

Y: 5479

-15 -10 -5 0 5 10 155

10

15

20

25

30

35

40

45X: 3.79e-005

Y: 40.04

X: -3.317

Y: 37.16

X: 3.317

Y: 37.02

radial distance, µm

Ele

ctri

cal

fiel

d,

dB

V/m

Fig A-2. 2: Electrical field amplitude profile of HE11 mode in single mode fiber at 980nm

(linear plot).

Fig A-2. 3: Electrical field amplitude profile of HE11 mode in single mode fiber at 980nm

(logarithmic scale).

168

-10 -5 0 5 100

10

20

30

40

50

60X: 0.1508

Y: 53.13

Radial distance,µm

Po

wer

den

sity

, d

B W

/cm

2X: -2.412

Y: 50.23

X: 2.412

Y: 50.23

Fig A-2. 4: Power density profile of HE11 mode in single mode fiber at 980nm

169

Appendix A-3: Extracted values of refractive index of thin film gold

Thickness, d nm No of

samples

Extracted RI @ 980nm Extracted RI @

1480nm

Extracted RI @

1550nm

2.5nm 3 3.16-j5.02 3.66-j5.72 4.16-j6.12

3.5nm 5 3.056-j5.69 2.67-j6.20 4.15-j5.10

5 nm 3 2.15-j6.75 2.76-j6.15 3.56-j5.76

6.5 nm 3 1.21-j6.86 1.46-j11.2 1.82-j11.62

8 nm 3 1.15-j5.647 1.25-j8.95 1.74-j6.95

9 nm 1 0.98-j6.67 1.04-j8.52 1.34-j6.54

10 nm 3 0.95-j6.26 1.05-j8.72 1.13-j7.82

15nm 3 0.85-j5.88 0.86-j7.85 0.91-j7.12

16.5nm 2 0.72-j5.10 0.965-j9.02 0.88-j5.725

20nm 3 0.65-j4.365 0.61-j7.55 0.71-j5.82

23.5nm 2 0.47-j5.58 0.55-j8.99 0.67-j5.91

25nm 3 0.39-j4.86 0.48-j7.65 0.68-j6.09

27nm 3 0.42-j3.5 0.45-j6.65 0.59-j7.04

30nm 3 0.35-j4.20 0.42-j6.55 0.585-j6.52

35 nm 3 0.23-j4.15 0.4-j7.25 0.54-j5.052

170

Appendix A-4: Extraction of photo-elastic constants of thin gold films

The change in refractive index of an isotropic medium due to incident stress is

given by the following relationship [61],

0

3

0

3

0

22 d

dpnpS

nng

∆−=−=∆ (A-4.1)

Where,

gn∆ = Change in refractive index of thin gold film

0n = Refractive index of thin film gold under zero pressure.

0d = Original thickness of gold film in absence of deformation.

d∆ = Change in thickness due to deformation by incident pressure.

p = Strain-optical co-efficient of thin gold film

As in the case of refractive index of thin films, the values of stress-optical

constants of thin films were different from their bulk values. The values of photo-

elastic constants at such thicknesses were unknown. Hence, these values were

extracted from experimental results. The extraction procedure is described as

follows:

1. The extracted refractive indices were curve fitted using the best fitting

function in MATLAB as shown in Fig 3.8 of chapter 3.

2. The refractive index change was differentiated with respect to change in

coating thickness. This gave the ratiod

ng

∆

∆.

3. The photo-elastic constant was calculated using the relationship,

171

3

0

0

.

2

nd

ndp

g

∆

∆−= .

The extracted values of photo-elastic constants at 980 nm optical wavelength and

elastic constants are summarized in the table below.

Thin Film

Thickness

Photo-elastic constant

Young’s Modulus

2 nm -0.2-j0.43 0.1 GPa

3 nm -0.5-j0.46 0.1 GPa

5 nm -0.1-j0.77 0.3 GPa

7 nm 0.2-j0.273 0.4 GPa

10 nm 0.55-j0.07 0.9 GPa

15 nm 0.2-j0.2 4 GPa

20 nm 0.6-j0.2 10 GPa

30 nm 1.5-j0.1 70 GPa

172

Appendix A-5: Acoustic to Electrical analogy

Acoustical to Electrical quantities lumped analogy:

Acoustical quantities Equivalent electrical quantities

Pressure = Force/ Area (1Pa = 1N/sq.m) Voltage (Volts)

Volume velocity = dx/dt (cu.m/s) Current (Amperes)

Volume displacement = x (cu.m) Charge (Coulomb)

Inertance = Pressure / rate of volume

velocity = Mass/(Area)2 (Kg/m

4)

Inductance = Voltage /rate of change

of current (Henry)

Acoustic resistance, Ra = Pressure/

Volume velocity (Pa.s/cu.m)

Resistance =Voltage/ Current (Ohms)

Acoustic Compliance, = Volume

Displacement /Pressure (cu.m/Pa)

Capacitance =Charge/ Voltage (Farad)

Acoustical to Electrical quantities Wave analogy:

Acoustic wave equation Electro-magnetic wave equation

Where,

p = pressure (N/m2)

c = acoustic wave velocity (m/s)

2

2

22

2 1

t

E

cx

E

∂

∂=

∂

∂ or

2

2

22

2 1

t

H

cx

H

∂

∂=

∂

∂

Where,

E or H = Electric or Magnetic field

c = speed of EM wave (m/s)

Characteristic Acoustic impedance of

medium,

cZ .ρ= = Density X acoustic wave velocity

(Rayls)

Intrinsic impedance of medium, ε

µη =

(Ohms)

Amplitude reflection co-efficient,

12

12

ZZ

ZZr

+

−=

Reflection co-efficient,

12

12

ηη

ηη

+

−=r

Intensity reflection co-efficient,

R =

2

12

122

ZZ

ZZr

+

−=

Power reflection co-efficient or Reflectance

R =

2

12

122

ηη

ηη

+

−=r

Acoustic intensity,

Z

PI

2

= (W/sq.m) where,

P = Pressure amplitude (N/sq.m)

Z = Acoustic impedance of medium (Rayls)

Power density,

η

2E

S = (W/sq.m) where,

E = Electric field amplitude (V/m)

η = Intrinsic impedance of medium (Ohms)

Acoustic power ,

Pac = I X Area (Watts) where,

I = Acoustic intensity

Power delivered,

P = S X Area (Watts) where,

S = Power density

173

Appendix A-6: Design of HIFU transducer and verification using PiezoCAD

The Piezo-electric stress strain equations from the Structural mechanics module

and the linear acoustic wave equations from the Acoustics module are coupled

together to simulate the performance of the HIFU transducer in COMSOL. The in

detail modeling procedure is described below:

Geometry and Meshing:

Fig A-6. 1: Geometry and mesh structure of focused transducer model.

The PZT transducer has a thickness of half wavelength at the acoustic frequency

of 1.56 MHz. Based on the results of the PiezoCAD model discussed later in the

appendix, the transducer material is chosen to be PZT-4. The speed of sound in

PZT-4 medium is 4000 m/s [62]. At the acoustic frequency of 1.5 MHz, the half

wavelength thickness corresponds to 1.34 mm. This is chosen to be the thickness

of the transducer in the COMSOL model. The diameter of the transducer is

measured to be 2.4 cm and is used in the model. The crystal is shaped in the form

of a concave lens structure to focus the acoustic waves at a focal distance of 3.5

4.5 cm

1.2

cm Water ( 0.15 mm)

Water

Focal

region

(0.1 mm )

PZT Transducer

Radiation boundary

Radiation boundary

Rad

iation

bo

un

dary

Acceleratio

n b

ou

nd

ary

4.5 cm

1.2

cm Water ( 0.15 mm)

Water

Focal

region

(0.1 mm )

PZT Transducer

Radiation boundary

Radiation boundary

Rad

iation

bo

un

dary

Acceleratio

n b

ou

nd

ary

174

cm in front of the transducer. The focal distance is obtained from the HIFU

characterization data reported in [39]. In order to have 90% accuracy in the

simulation results, the mesh dimensions must be at least 1/10th

of the acoustic

wavelength in the regions [47]. At the frequency of 1.5 MHz, the acoustic

wavelength in water region is around 1 mm, while that in PZT-4 material is

around 2.6 mm. Thus, the mesh dimension in the water region is considered to be

0.15 mm while mesh size in the PZT material as well as the focal region is set at 1

mm.

Subdomain Settings:

Piezo-electric stress strain module: Based on the design in PiezoCAD, PZT-4

material is chosen as the crystal material. The strain-charge format is chosen with

the crystal orientation in z-x direction. The thickness was considered to be 1.2 cm.

The compliance and stiffness matrix are available from the data provided at

Piezoelectric Technology Data for Designers, Morgan Matroc Inc [62].

Compliance matrix,

−−

−−

−−

=

7.3200000

0390000

0039000

0005.1531.531.5

00031.53.1205.4

00031.505.43.12

ES * Nm /10 212− . (A-6.1)

Relative permittivity matrix,

=

130000

014750

001475

rε . (A-6.2)

175

In the acoustics domain, the density of water is considered to be 1000 Kg/m3 and

the speed of acoustic wave through water is set to be 1500 m/s.

Boundary Settings:

For Piezo stress strain analysis, all the boundaries are set to be free. For the top

and bottom boundaries, the displacement along x direction is restricted. The right

hand boundary of the transducer is excited with an electric potential of 60 V. The

left hand boundary is grounded. Zero charge is considered on remaining

boundaries.

For the acoustics module, the outer boundaries of the water region are set to

matched boundary/ radiation boundary in order to prevent spurious back-

reflections from these artificial boundaries. The right hand side boundary of the

transducer is assigned an acceleration boundary, where acceleration computed as

a part of the piezo stress strain analysis solution is used. The acceleration

boundary conditions are also used at the top and bottom surfaces of the

transducer. The left hand boundary is forced to zero acceleration, since we are

considering only waves propagating in the positive z direction. In reality, the

vibrations originating from the left hand boundary are damped using epoxy or

quarter wave back-plates.

176

Results:

Fig A-6. 2: Z displacement profile of focused transducer at resonant frequency of 1.59 MHz

Fig A-6. 3: Electrical impedance of focused transducer at fundamental resonance.

177

Fig A-6. 4: Pressure distribution of focused transducer at 1.5 MHz

Fig A-6. 5: 2D linear plot of pressure field at the focus of transducer, focal length = 35 mm

178

The results in Figs A-6.2 and A-6.3 indicate that the displacement of the PZT

transducer and hence the impedance of the transducer is the highest the

fundamental resonance. The focal length is around 35 mm. The 2 D pressure field

plot in Fig A-6.5 indicates that at the focus, the half power beam width of the

transducer is around 3.5mm. 60V of potential across the transducer produces 1.1

MPa pressure at the focus. The resultant voltage to pressure conversion efficiency

is calculated to be 18 KPa per Volt. The focusing gain due to the lens at the front

end of the transducer is calculated to be a factor of 3, and is obtained by taking the

ratio of pressure at the focus to the pressure at the surface of the transducer in Fig

A6.4.

Verification of results using PiezoCAD:

In order to verify the performance of the model created in COMSOL,

PiezoCAD was used. Modeling in PiezoCAD (Sonic Concepts, Woodenville,

WA) is based on transmission line analogue model. The model however does not

account for the gain associated with the lens at the front end of the transducer.

The model predicts the pressure at the surface of the transducer. The input

parameters to the model are as follows:

1. Design frequency = 1.52 MHz

2. Thickness of the piezo material = 0.5 * lambda

3. Material : PZT-4

4. Size and shape: Circular 10 mm diameter

5. Faceplates – Magnesium (9.9MRayls, quarter wave layer)

- Polycarbonate AS (3.8 MRayls, quarter wave layer)

179

6. Backplates - Filled Epoxy – 15 mm

7. Acoustic load: Front: 1.5 MRayls (water).

8. Electrical impedance: 50 ohms (Tx and Rcr).

9. Electrical matching network: L_sh= 8.3 uH, C_ser=1.657 nF.

Fig A-6. 6: Electrical input impedance of the transducer at fundamental and 3

rd harmonics.

Fig A-6. 7: Voltage to pressure transfer function of transducer at fundamental and 3

rd

harmonic

180

From Fig A-6.6, the input impedance shows a resonance behavior at the

fundamental frequency of 1.5 MHz. A similar behavior is seen from the result in

Fig A-6.3 obtained using COMSOL. Fig A-6.7 shows that voltage to pressure

transfer function at the tip of the transducer is 5.736 KPa per volt at the

fundamental resonance. As seen earlier, there is a factor of 3 gain due to focusing.

Taking this multiplication factor into account, the voltage to pressure transfer

ratio changes to 17.21 KPa per volt which closely matches with the value of 18

KPa per volt, obtained using COMSOL. Thus the result from COMSOL acoustic

model is verified.

181

Appendix A-7: Characterization of passive optical link components

Low power isolator at 1550nm (IS-IL-P-D-55-S-S9-FA):

10 dB coupler at 1550nm (SMSCA223RP1005FA):

3 dB coupler at 1550nm (CP-S-15-50-22-XX-S-L-10-FA):

High power isolator at 1550nm (IS-IL-P-D-55-S-S9-FA-1W):

High power isolator at 980 nm (VIS-S-980-HI-L-10-NE-09):

3 dB coupler at 980 nm (SMSCC223RP5005FA):

Parameters Manufacturer Measurement

Insertion Loss 0.86 dB 0.89 dB

Isolation 60 dB 63 dB


Coupling factor 10.23 dB 10.14 dB

Insertion loss through port 0.85 dB 0.89 dB

Isolation NA 51 dB




Isolation NA 48 dB


Insertion loss 0.5 dB 0.73 dB



Insertion Loss 0.86 dB 0.89 dB



Insertion loss 1 dB 3 dB





Isolation NA 60 dB

182

Appendix A-8: Characterization of optical active link components

Characterization of 1550nm Erbium Doped Final Amplifier

NP2000CORSV303500FCA1 (Nuphoton Technologies, California):

Input

current, mA

Pump laser

current, mA

Booster

current, mA

EDFA output optical

power, dBm

792 201 297 15 dBm

906 201 405 18 dBm

1030 201 532 20 dBm

1350 201 840 23 dBm

2350 201 1812 27 dBm

3920 201 3342 30 dBm

Characterization of optical laser diode at 1550 nm FU-68PDF-V520MB

(Mistubishi Inc, Japan):

0 50 100 1500

2

4

6

8

10

Bias current, mA

La

ser

ou

tpu

t p

ow

er,

dB

m

183

Characterization of 980nm laser LU098M450 (Lumics Inc., Germany):

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

Bias current, mA

Op

tica

l po

wer

, m

WPlot of Optical power Vs Bias current @ 980nm

Threshold=62 mA

184

Appendix A-9: Photo-detector PDB130 C specifications

Specifications of PDB 130C balanced photodetector [64].

185

Fig A-9. 1: Common mode noise rejection performance of PDB 130-C photodetector [64]

Fig A-9. 2: Noise vs frequency performance of PDB 130C photo-detector [64]

186

Fig A-9. 3: Responsivity performance of PDB 130C photo-detector [64].

187

Appendix A-10: Mechanical holder design

Holder section K1

0.827 ”

0.827 ”

1.535 ”

1.535 ”1.535 ”

5 X Ф

= ¼ ”

2.36 ”

0.5 ”

3.07 ”

0.5 ”

Top view

Front view RHS view

Holder section K1

0.827 ”

0.827 ”

1.535 ”

1.535 ”1.535 ”

5 X Ф

= ¼ ”

2.36 ”

0.5 ”

3.07 ”

0.5 ”

Top view

Front view RHS view

Tolerance on all

pieces = 0.005” unless

specified

Material: Aluminium

188

Holder section D2

Top view

Front viewRHS view

0.5”

0.25”0.25”

0.75”

3 X Φ = ¼”

1.5” 1”

0.5”

To E

To TH -1 To TH -1

Holder section D2

Top view

Front viewRHS view

0.5”

0.25”0.25”

0.75”

3 X Φ = ¼”

1.5” 1”

0.5”

To E

To TH -1 To TH -1

189

Holder section E

Φ = ¼”0.5”

0.4”6 ”

Top View

Front ViewRHS view

0.2”

0.2”

To D1 To D2

Holder section E

Φ = ¼”0.5”

0.4”6 ”

Top View

Front ViewRHS view

0.2”

0.2”

To D1 To D2

190

0.3” 0.3”

2”

Holder section TH-1

Front ViewRHS view

Holder section TH-2

Top View

1”

2.5”

Front View

Φ =

0.5375”

1.5”

RHS view

0.3” 0.3”

0.5”0.5”

1.25”

2 X Φ = ¼”

1”

To TH-2To TH-2

To D-2

To TH-1To TH-1

2.5”

1”

Top View

4 X Φ = ¼”

0.75” 0.75”

1.25”

Φ =

0.5475”

0.5”0.5”

0.3” 0.3”

2”

Holder section TH-1

Front ViewRHS view

Holder section TH-2

Top View

1”

2.5”

Front View

Φ =

0.5375”

1.5”

RHS view

0.3” 0.3”

0.5”0.5”

1.25”

2 X Φ = ¼”

1”

To TH-2To TH-2

To D-2

To TH-1To TH-1

2.5”

1”

Top View

4 X Φ = ¼”

0.75” 0.75”

1.25”

Φ =

0.5475”

0.5”0.5”

191

Main rod R2 Scale: 2.5 : 1

1 ”16.5 ”

Front ViewRHS view

Top View

1.7 ”

0.3 ”

1.7 ”

6 X Φ = ¼”

0.3 ”

7.25 ” 2 ”

0.5 ”

To FH-1

Main rod R2 Scale: 2.5 : 1

1 ”16.5 ”

Front ViewRHS view

Top View

1.7 ”

0.3 ”

1.7 ”

6 X Φ = ¼”

0.3 ”

7.25 ” 2 ”

0.5 ”

To FH-1

192

3 X Φ = ¼”

3 ”

1 ”

1.5 ” 0.5 ”

0.5 ”

0.5 ”

FH-1 and FH-2

From rod R2

To arm FA

Top View

Front View

RHS View

3 X Φ = ¼”

3 ”

1 ”

1.5 ” 0.5 ”

0.5 ”

0.5 ”

FH-1 and FH-2

From rod R2

To arm FA

Top View

Front View

RHS View

193

Holder section FA

8 ”

0.5 ”

0.5 ”Φ = ¼”

To FH-2To FH-1

0.25 ”

Top View

Front View RHS View

Holder section FA

8 ”

0.5 ”

0.5 ”Φ = ¼”

To FH-2To FH-1

0.25 ”

Top View

Front View RHS View

194

0.2”3”

2 X Φ = ¼”

0.5”

1 ”

3 ”

Fiber Holder FH

0.5” 0.5”

0.25”

5 X Φ = 0.1”1 ”

0.5”0.5”

1 ”1 ”

1.5 ”

0.2”3”

2 X Φ = ¼”

0.5”

1 ”

3 ”

Fiber Holder FH

0.5” 0.5”

0.25”

5 X Φ = 0.1”1 ”

0.5”0.5”

1 ”1 ”

1.5 ”

2 X Φ = ¼”

0.5”

1 ”

3 ”

Fiber Holder FH

0.5” 0.5”

0.25”

5 X Φ = 0.1”1 ”

0.5”0.5”

1 ”1 ”

1.5 ”

Tolerance for

holes= 0.001”

195

Appendix A-11: Laser Diode Mount

Fig A-11. 1: Layout of laser diode mount with bias tee

Fig A-11.1 shows the design of laser diode mount developed for butterfly package

using Zero Insertion Force (ZIF) sockets. Bias tee is provided for external

modulation.

Fig A-11.2: Realization of laser diode mount

196

Appendix A-12: Sputter coater holder design

Material: Plexiglas

Top view

Front view RHS view

Centers of all small holes – 0.1” from inner circle

Ф = 0.82 ”

4 X Ф = 1/8 ”

nylon screws

8 X Ф =

2.5mm (±

0.001)

0.2 ”

0.2 ”

0.125 ”

thick

Material: Plexiglas

Top view

Front view RHS view

Centers of all small holes – 0.1” from inner circle

Ф = 0.82 ”

4 X Ф = 1/8 ”

nylon screws

8 X Ф =

2.5mm (±

0.001)

0.2 ”

0.2 ”

0.125 ”

thick

197

Ф = 0.25 ”Ф = 1/8”

threaded

hole for

nylon screws

4 pieces required Material : Teflon

Top View

1 ”

Front View RHS View

If not available, use plexiglas

0.25”X0.25” square bar with 1” height.

Threaded ¼” hole at center

Ф = 0.25 ”Ф = 1/8”

threaded

hole for

nylon screws

4 pieces required Material : Teflon

Top View

1 ”

Front View RHS View

If not available, use plexiglas

0.25”X0.25” square bar with 1” height.

Threaded ¼” hole at center

198

Appendix A-13: Ted Pella sputter coater performance specifications

199

Appendix A-14: Single stage Single ended inverting amplifier design

Ideal simulation with OPAMP model in ADS:

S_Param

SP1

Step=1 MHz

Stop=2 GHz

Start=100 kHz

S-PARAMETERS

Term

Term2

Z=50 Ohm

Num=2

Term

Term1

Z=50 Ohm

Num=1

R

R2

R=50 Ohm

R

R3

R=2 kOhm

R

R1

R=95.3 Ohm

C

C1

C=0.01 uF R

R4

R=50 OhmOpAmp

AMP1

Fig A-14. 1: Schematic of single ended amplifier

1E6 1E7 1E8 1E91E5 2E9

10

20

30

0

40

freq, Hz

dB(S(2,1))

m1m6

m1freq=dB(S(2,1))=26.018

1.100MHzm6freq=dB(S(2,1))=22.997

239.1MHz

Fig A-14. 2: Simulated gain performance of amplifier vs frequency

200

Layout for Single Ended Amplifier:

Fig A-14. 3: Layout for single ended amplifier design.

0 50 100 1500

10

20

30

40Gain performance of Single ended amplifier.

Gai

n,d

B

Frequency, MHz

X: 100Y: 21.11

0 50 100 150

-100

0

100

Frequency, MHz

Gai

n p

has

e, d

egre

es

Fig A-14. 4: Experimental characterization of amplifier gain.

201

Fig A-14. 5: Realization of the amplifier.

202

100µ m100µ m

Appendix A-15: Raman Images of fabricated fiber samples

Fig A-15. 1: Straight cleaved fiber sample

Fig A-15. 2: Linearly tapered fiber sample (5 degree taper angle)

α

6 -7

µm

α

6 -7

µm

203

6-7

µm

6-7

µm

Fig A-15. 3: Cylindrically etched fiber sample.

Fig A-15. 4: Geometry of fiber sample #18 C.

Fig A-15. 5: Geometry of damaged fiber sample.

204

Appendix A-16: Static reflectance in air of coated fiber sensors

Table A-16. 1: Static reflectance performance of thin film coated fiber sensors

Coating

thickness, nm

Static reflectance at

980 nm, dB

Static reflectance improvement,

dB (Ref: -16 dB)

2.5 nm -20.45 - 4.45

3.5 nm -17.95 - 1.95

5.0 nm -10.65 +5.35

6.7 nm -5.06 +10.94

10.0 nm -4.32 +11.68

15.0 nm -3.75 +12.25

20.0 nm -2.92 +13.08

25.0 nm -1.90 +14.10

30.0 nm -2.18 +13.82

35.0 nm -1.45 +14.55

205

Appendix A-17: Reflectance from cylindrically etched fiber model

Fig A-17. 1: Assignment of ports for cylindrically etched fiber sensor.

The reflection co-efficient in this case is the combination of contribution from the

boundaries at port 2 and port 3 as follows:

The numerical analysis in COMSOL yielded, S12 = 0.316, S13= 0.94

Using the above values, the reflection co-efficient at port 1 = 321 89.01.0 Γ+Γ=Γ

Thus it is seen that contribution of port 3 (almost 90 %) to the total reflectance at

input is dominant. This is expected because the half power beam width of the

single mode fiber shown in Appendix A-2 is around 6.6 µm. Since the fiber

considered here, is etched till a maximum diameter of 6 µm, the contribution from

the etched faces is less significant.

1

2

31

2

3

3

2

132

2

1211

313132121211

Γ+Γ=

Γ+Γ=

SSS

SSSSS

206

Vita

Rupa Gopinath Minasamudram was born in Pune, India on the 30th

of

October 1982.After completion of high school, she enrolled for the undergraduate

program in Electronics and Telecommunication Engineering at Vishwakarma

Institute of Technology, Pune, India where she received the degree of Bachelor of

Engineering degree in 2004. In Fall 2004, she was admitted into the graduate

program of College of Engineering at Drexel University. In 2008, she received

her Master of Science degree in Telecommunication Engineering. Rupa’s research

interests include fiber optic communication, fiber optic sensing, thin film acousto-

optic interactions, and radio over fiber.

3 journal papers and 6 conference papers were published during Rupa’s

graduate career at Drexel University, including:

R. Gopinath, P. Arora, G. Gandhi, A. S. Daryoush, M. El-Sherif, and P. A.

Lewin, "Thin film metal coated fiber optic hydrophone probe," Applied. Optics.

48, pp 77-82, 2009.

S. Umchid, R. Gopinath, K. Srinivasan, P. A. Lewin, A. S. Daryoush, L. Bansal,

and M. El-Sherif, “Development of calibration techniques for ultrasound probes

in the frequency range from 1 to 100 MHz,” Ultrasonics 49, 306–311, 2009

and 3 other journal papers and a patent application in progress.

Rupa also received the SPIE best student paper award at the International

Photonics Conference at IIT Delhi , India 2008.

optimization of wideband fiber optic hydrophone probe for ... · manseta, adil mudassir, gaurav...

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