Optimization of wideband fiber optic hydrophone probe. for ultrasound sensing applications. A Thesis. Submitted to the Faculty.

Transcription

1 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

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3 iii Dedications to my parents and husband

4 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.

5 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.

6 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 Introduction: Fiber optic acoustic sensors: Intensity Modulated Sensors: Reflection type: Transmission Type: Phase modulated acoustic sensors: Extrinsic interferometric phase modulated sensors: Internal interferometric phase modulated sensors: Frequency/Wavelength Modulated sensors Indirect frequency modulated acoustic sensors with heterodyne detection: Direct wavelength modulated sensors: Acousto-optic Sensor Parameters Noise cancellation in fiber optic hydrophone sensors: Common mode noise rejection by signal processing: Common mode noise rejection by differential amplifier: Common mode noise rejection by anti-parallel photo-diodes: Numerical modeling of optical waveguides: Finite Element Method (FEM): Finite Difference Method (FTD): Beam Propagation Method (BPM): Summary: Chapter 3: Analytical modeling Introduction: Plane wave propagation at two material interface:... 58

7 vii Reflection and Transmission coefficient of plane wave at boundary: Transmission line equivalent theory: Analytical model of uncoated fiber: Extraction of complex refractive index of thin (2nm-35nm) gold films: Need for extraction of complex refractive index: Fabrication: Experimental set-up, results and discussion: Analytical model of coated fiber: Assuming compressible water and incompressible gold: Assuming incompressible water and compressible gold: Combined water and thin gold film compression: Summary Chapter 4: Numerical modeling Introduction Numerical model of standard single mode fiber with step index: Simulation set-up for electromagnetics module: Simulation set-up for coupled acousto-optic analysis: Impact of fiber optic sensor tip geometries: Uncoated Cylindrical etched fiber sensor: Uncoated linear tapered fiber sensor: Uncoated exponential tapered fiber sensor: Numerical model of thin film gold coated fiber sensors: Effect of gold coating on cylindrical etched fiber sensors: Effect of gold coating on linear tapered fiber sensors: Effect of gold coating on exponentially tapered fiber sensors: Summary: Chapter 5: Experimental results Introduction: Measurement Set-up: Acoustic Sub-system: Fiber optic sub-system at 980nm: Fiber optic sub-system at 1550nm: Mechanical holder assembly:

8 viii 5.3 Acoustic measurements using reference PVDF needle hydrophone: Acoustic measurements with fiber optic hydrophone probes: Responsivity improvement measurements: Noise cancellation measurement: Fig 5. 9: Experimental set-up for noise cancellation using balanced detection Frequency domain response to burst acoustic signal at 5 MHz: Summary: Chapter 6: Conclusions and Recommendations for Future Work Introduction: Recommendations for Future work: REFERENCES Appendix A-1: LIST OF EQUIPMENT & COMPONENTS Appendix A-2: HE 11 mode in Single Mode Fiber Appendix A-3: Extracted values of refractive index of thin film gold Appendix A-4: Extraction of photo-elastic constants of thin gold films Appendix A-5: Acoustic to Electrical analogy Appendix A-6: Design of HIFU transducer and verification using PiezoCAD Appendix A-7: Characterization of passive optical link components Appendix A-8: Characterization of optical active link components Appendix A-9: Photo-detector PDB130 C specifications Appendix A-10: Mechanical holder design Appendix A-11: Laser Diode Mount Appendix A-12: Sputter coater holder design Appendix A-13: Ted Pella sputter coater performance specifications

9 ix Appendix A-14: Single stage Single ended inverting amplifier design Appendix A-15: Raman Images of fabricated fiber samples Appendix A-16: Static reflectance in air of coated fiber sensors Appendix A-17: Reflectance from cylindrically etched fiber model Vita

10 x LIST OF TABLES 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 and1550nm Table 4. 1 Responsivity performance comparison of cylindrical etched fiber sensors Table 4. 2 Responsivity performance comparison of linear tapered fiber sensors as function of taper angle Table 4. 3 Responsivity performance comparison of exponential tapered fiber sensors Table 4. 4 Responsivity performance of coated straight cleaved fiber sensor Table 4. 5:Responsivity performance of coated 7 degree linear tapered fiber sensor Table 4. 8 Responsivity performance of 7 degree exponential tapered fiber sensor Table 5. 1: Pressure to voltage responsivity performance of thin film coated fiber samples Table 5. 2: Static reflectance of straight cleaved fiber samples Table 5. 3: Static reflectance of uncoated cylindrically etched fiber samples Table 5. 4: Static reflectance of thin film coated cylindrically etched fiber samples

11 xi Table 5. 5: Static reflectance of uncoated linearly tapered fiber samples: (taper angle 3-5 degrees) Table 5. 6: Static reflectance of thin film coated linearly tapered fiber samples: (taper angle 3-5 degrees) Table 5. 7: Pressure to voltage responsivity performance of fiber optic probes at 980 nm Table 5. 8: Pressure to voltage responsivity performance of fiber optic probes at 1550 nm Table 5. 9: Estimation of coating thickness from coating time based on static reflectance measurement Table Noise cancellation performance of the fiber optic probes at 980nm. Noise power of the photo-detector under no modulation = -112 dbm Table 5. 11: Noise cancellation performance of fiber optic probes at 1550nm. Noise power of the photo-detector under no modulation = -112 dbm Table A-16. 1: Static reflectance performance of thin film coated fiber sensors.. 204

12 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 Fig 2. 4: Transmission type hydrophone using Schlieren technique [13] Fig 2. 5: Principle of intensity modulated total internal reflection pressure sensor [14] Fig 2. 6: Mach Zehnder interferometer using free space optics Fig 2. 7: Michelson interferometer using free space optics 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] Fig 2. 10: Multilayer cylindrical fiber optic phase modulated acoustic sensor [17] 17 Fig 2. 11: Embedded interferometric phase modulated acoustic sensor [19] Fig 2. 13: Concept of Fabry Perot interferometer [23] Fig 2. 14: FP based fiber optic acoustic sensor [25] Fig 2. 15: Schematic of Fabry Perot based phase modulated sensor [25] Fig 2. 16: Concept of multi-layer structure interferometer Fig 2. 17: Fiber optic multilayer hydrophone, i=1.n, L=Low index Layer, H = high index layer, p = Pressure Pulse [27] Fig 2. 18: Phase modulated sensor using heterodyne detection [29]... 28

13 xiii Fig 2. 19: Heterodyne detection using coated fiber optic hydrophone [30] Fig 2. 20: Schematic of Fiber Bragg Grating sensor [31] Fig 2. 21: Implementation of DBR fiber laser structure [35] Fig 2. 22: Schematic of optical hydrophone employing Distributed Bragg Reflector fiber sensor [38] Fig 2. 23: RIN cancellation by signal processing [9] Fig 2. 24: RIN cancellation by differential amplifier [40] Fig 2. 25: RIN cancellation using balanced photo-detector [41] Fig 2. 26: Signal subtraction using anti-parallel photo-diodes Fig 2. 27: Concept of meshing in Finite Element Method Fig 2. 28: Concept of Finite Difference approximation Fig 2. 29: Meshing and using Finite Difference approximation Fig 2. 30: Illustration of the concept of BPM Fig 3. 1: Plane wave reflection and transmission at boundary for normal incidence Fig 3. 2: (a) Plane waves at boundary between different media (b) Transmission line equivalent model of waves at two dielectric interface Fig 3. 3: Transmission line analogue model of uncoated fiber 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 67 Fig 3. 6: Experimental set-up for extraction of complex refractive index of thin (2-35nm) gold films... 72

14 xiv Fig 3. 7: Reflectance (db) vs coating thickness (nm) of coated fiber sensors at (blue) 980nm, (red) 1480nm and (black) 1550nm wavelength 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) Fig 3. 9: Transmission line analogue of metal coated fiber Fig 3. 10: Improvement in responsivity vs coating thickness considering water compression only Fig 3. 11: Improvement in responsivity vs coating thickness considering thin film gold compression only Fig 3. 12: Improvement in responsivity vs coating thickness considering water and thin film gold compression Fig 4. 1: (a) Geometry of straight cleaved uncoated fiber (b) Geometry of straight cleaved thin film gold coated fiber Fig 4. 2 Mesh structure of uncoated single mode fiber with step index profile Fig 4. 3: Power density profile of uncoated unetched single mode fiber 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 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... 94

15 xv Fig 4. 8: Power density profile of 6 µm etched GRIN single mode fiber model Fig 4. 9: Power density profile of 8 µm etched GRIN single mode fiber model 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 Fig 4. 13: Geometry, mesh structure and boundary conditions of uncoated 7 degree linear tapered fiber sensor 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 Fig 4. 16: Power density profile of 30 degree linear tapered GRIN single mode fiber model Fig 4. 17: Power density profile of 40 degree linear tapered GRIN single mode fiber model Fig 4. 18: Geometry, mesh structure and boundary conditions of exponential tapered GRIN fiber model 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

16 xvi Fig 4. 21: Power density profile of 30 degree exponential tapered GRIN single mode fiber model Fig 4. 22: Power density profile of 40 degree exponential tapered GRIN single mode fiber model Fig Plot of relative responsivity, db of uncoated linearly (red) and exponentially (blue) tapered fiber sensors as function of taper angle. Reference: db re 1 V/µPa 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 Fig 4. 25: Power density profile of a straight cleaved 5 nm gold coated fiber sensor Fig 4. 26: Geometry, mesh structure and boundary conditions of etched 5 nm coated fiber sensor Fig 4. 27: Power density profile of 5nm coated 6 micron etched fiber sensor Fig 4. 28: Power density profile of 5nm coated 8 micron etched fiber sensor Fig 4. 29: Power density profile of 5nm coated 10 micron etched fiber sensor Fig 4. 30: Power density profile of 5nm coated 12 micron etched fiber sensor Fig 4. 31:Geometry, mesh structure and boundary conditions of coated 6 micron etched fiber sensor Fig 4. 32: Power density profile of 5nm coated 7 degree linear tapered fiber sensor

17 xvii Fig 4. 33: Power density profile of 5nm coated 15 degree linear tapered fiber sensor Fig : Power density profile of 5nm coated 30 degree linear tapered fiber sensor Fig 4. 35: Geometry, mesh structure and boundary conditions of 7 degree exponential coated fiber sensor Fig : Power density profile of 5nm 7 degree exponential taper sensor Fig 4. 37: Power density profile of 5nm coated 15 degree exponential taper sensor Fig 4. 38: Power density profile of 5nm coated 30 degree exponential taper sensor 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 5. 1: Experimental set-up at 980nm optical wavelength Fig 5. 2: Experimental set-up at 1550nm optical wavelength 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) 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 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

18 xviii Figure 5. 6: Needle hydrophone 1D and 2D scan data at 1.5 MHz and 5 MHz Fig 5. 7: Responsivity improvement, db vs coating time, sec (ref: -282 db re 1V/µPa) 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. 9: Responsivity improvement, db vs coating thickness, nm (Blue: Simulation, Red: experimental data with errorbar) Fig 5. 10: Experimental set-up for noise cancellation using balanced detection Fig 5. 11: Frequency response of PVDF needle hydrophone Fig 5. 12: Frequency response of straight cleaved uncoated FOHP Fig 5. 13: Frequency response of 4-5nm coated fiber sensor (# 17 T) Fig : Frequency response of 6-7 nm coated fiber sensor (# 12 C) Fig A-2. 1: Propagation constant of the HE 11 mode vs wavelength Fig A-2. 2: Electrical field amplitude profile of HE 11 mode in single mode fiber at 980nm (linear plot) Fig A-2. 3: Electrical field amplitude profile of HE 11 mode in single mode fiber at 980nm (logarithmic scale) 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 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

19 xix 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 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 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] Fig A-9. 3: Responsivity performance of PDB 130C photo-detector [64] Fig A-11. 1: Layout of laser diode mount with bias tee Fig A-11.2: Realization of laser diode mount Fig A-14. 1: Schematic of single ended amplifier Fig A-14. 2: Simulated gain performance of amplifier vs frequency Fig A-14. 3: Layout for single ended amplifier design Fig A-14. 4: Experimental characterization of amplifier gain Fig A-14. 5: Realization of the amplifier Fig A-15. 1: Straight cleaved fiber sample Fig A-15. 2: Linearly tapered fiber sample (5 degree taper angle) Fig A-15. 3: Cylindrically etched fiber sample Fig A-15. 4: Geometry of fiber sample #18 C

20 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 pressuretime 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.

21 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 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.

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23 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 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 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/cm 2 ) 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

24 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).

25 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.

26 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

27 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: E z, t) = E cos( ω t kz + θ ) (2.1) ( o o Where, Eo is electric field amplitude in V/m, ω is angular frequency in rad/s, k is the wavenumber in per meter, andθ o is initial phase in radians.

28 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] 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 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-

29 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 2 ( nc nw ) R = 2 ( n + n ) c w. (2.2) The responsivity or voltage sensitivity is given by R p = R n c n c p R + n w n w p, (2.3) where, n w p = 1.4X10 4 per MPa is the change in refractive index of water with pressure[9]. n c p = 5X10 6 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-

30 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 db re 1 V/µPa. Fig 2. 2: Experimental set-up of single mode intensity modulated fiber optic hydrophone [11] 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,

31 9 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 Acoustic wave Ferrule Light OUT Light IN Optical fiber Optical fiber Moving Acoustic wave fiber 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

32 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

33 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.

34 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. LENS BEAM-SPLITTER LASER SIGNAL PATH Mirror Mirror REFERENCE PATH Detector Detector BEAM-SPLITTER Fig 2. 6: Mach Zehnder interferometer using free space optics Mathematically, let us consider linearly polarized waves with their electric fields as [15]; E 1(r1,t) = E o 1 cos( k. r1 ω t + θ 1 ) (2.4.a) E 2(r2,t) = E o 2 cos( k. r2 ω t + θ 2 ) (2.4.b) Where E o1, E o2 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

35 13 I = I + I + I cosφ (2.5) Where, I 2 φ = k ( r r + ε ε (2.6) 1 2 ) I1 = E1, T 2 I 2 = E2 are the time averaged intensities of the two waves. T ε,ε 1 2 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. Mirror REFERENCE SIGNAL LASER BEAM-SPLITTER SIGNAL PATH Mirror LENS Detector Fig 2. 7: Michelson interferometer using free space optics

36 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]

37 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

38 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. φ = βnl (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 φ = p βn L p + βl n p (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; 1 3 n = n (1 2µ )(2 p12 + p11) (2.9) 2E Where, p, p = Pockel coefficients

39 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 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

40 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 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

41 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

42 20 make them unsuitable for ultrasound sensing applications in the range of MHz 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]; 4πnL φ = + 2θ, (2.10) λ where n = refractive index of the Fabry-Perot medium

43 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; Pr P i 2 F sin ( φ / 2) =, (2.11) 2 1+ F sin ( φ / 2) where F = Coefficient of finesse of the interferometer = 2r 1 r 2 2 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 TiO 2.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

44 22 modulus associated with Parylene, enhances the phase sensitivity of this sensor. Detailed construction of the sensor is shown in Figs 2.14 and Pressure 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

45 23 for maximum sensitivity. Based on equation (2.8), the acoustic phase sensitivity in this case is given by φ = p where 4πnL λe F ( k ), (2.12) l E = Young s modulus of Parylene-C F l (k) = 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

46 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. Air n L n H n L n H n L n H Glass substrate 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 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

47 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 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 (Nb 2 O 5 ) and n = 1.48 (SiO 2 ) [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

48 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 = Y m o Y m Y Y o + Y Y o N + 1 N + 1 m m m + m Y + Y N + 1 N + 1 m m (2.13) M = m m m m N = i= 1 M i where M i is the characteristic matrix of the i th layer. M i = cos( knid i) jyi sin( knid i ) j sin( knid i ) / Yi cos( kn d ), (2.14) i i where Yi = optical admittance of the i th layer, n d = optical thickness of the i i ith layer, and d i = physical thickness of the i th layer. The total input reflectance is thus a function of the optical phase shift through each layer and expressed as: R = f kn ) (2.15) ( d i i The responsivity of this sensor is given as: R p = ni di f '( knid i ). + f '( knid i ) (2.16) p p The first term represents the change in refractive index of the i th 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 i th

49 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 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 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.

50 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 f o 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,

51 29 f o + 11MHz 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, o s f + f and frequency shifted signal are combined at the output beamsplitter and detected by the photo-detector. The output of the photo-detector, 11 MHz ± f s, serves as an input to the frequency discriminator, output of which is proportional to the modulation frequency, f s and hence to the incident pressure amplitude. A pressure sensitivity of 26 db re 1 µpa has been obtained over the frequency range of Hz. Fig 2. 19: Heterodyne detection using coated fiber optic hydrophone [30].

52 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 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 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, λ B = 2n eff d (2.17) Where, d = periodicity of the grating. Fig 2. 20: Schematic of Fiber Bragg Grating sensor [31]

53 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 A sensitivity of 81 db re 1 µpa has been obtained in the range of 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]

54 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

55 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 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 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

56 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 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

57 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

58 36 sensor. External control circuit is required to compensate against temperature effects, making the sensing process challenging. Another concern is the nonuniform 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.

59 37 Table 2.1: Performance summary of acousto-optic sensors Sensing technique Detection technique Voltage Responsivity Intensity modulation using multimode fiber [10] Spatial Averaging free BW Sensitivity 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] Intensity detection of 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 Intensity detection - sensor [28] -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] Intensity detection of beat frequencies ---- < 0.22 MHz 164 db re 1 µpa

60 38 follows: The three most important sources of noise in the optical receiver are as (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 < I 2 t >= 4kTGB (2.18) where k = Boltzmann constant = 1.38 X10 23 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 < I 2 >= sh 2 qi DC B, (2.19) where q = charge of an electron I DC = DC photocurrent at the photo-detector. B = measurement bandwidth (iii) Relative Intensity Noise (RIN): This characterizes the random intensity fluctuations of the source caused by the quantum nature of emission of

61 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 RIN 2 R IN 2 DC < I > = (2.20) I The associated RIN noise power spectral density is, 2 RIN 2 DC < I >= RIN. I B, (2.21) where I DC = DC photocurrent at the photo-detector. B = measurement bandwidth 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 Common mode noise rejection by signal processing: Fig 2. 23: RIN cancellation by signal processing [9]

62 40 Staudenraus et al implemented a crude form of RIN cancellation by utilizing the signal processing feature of oscilloscope [9] as illustrated in Fig 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 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 The input optical signal is split and coupled to the sensor and reference arm using the beam splitter. The reference arm

63 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 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 The set-up for RIN cancellation is depicted in Fig 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

64 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

65 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]: Ε = Β t D Η = J + (2.22) t. D. B = = ρ ν 0 Where, E = electric field intensity H = magnetic field intensity D = electric field density B = magnetic field density ρ ν = electric charge density J = current density Solving the above equations for a homogenous, isotropic, source free medium, results in the following,

66 44 Ε = Β t D Η = (2.23) t. D. B = = 0 0 Taking the curl of the first two expressions leads to time harmonic wave equations for electric and magnetic fields expressed below, 2 2 Ε Ε µε = 0 2 t 2 2 Η Η µε = 0 2 t (2.24) Using the phasor notation of electric and magnetic fields, the above expressions are reduced to Helmholtz wave equations given by. 2 E + k 2 2 H + k E = 0 2 H = 0 (2.25) Where, k = ω µε 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

67 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) 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-

68 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, 2 Φ 2 x 2 Φ + 2 y ( k β ) Φ = 0 (2.26) The functional, I = f (Φ) is chosen such that when the functional becomes stationary, it leads to the field solution [43]. That means, solving δ I = 0 (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. 2 Φ 2 x 2 Φ y 2 ( k ) Φ = R 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, W R. da = 0 (2.29) A Where W is the weight associated with the residue. This is called the Galerkin method.

69 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 For 90% and higher accuracy of the results, the size of the element should at least be 1/10 th 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

70 48 boundary conditions are applied to outer boundary of the region under analysis. The final eigenvalue matrix has the form [43, 49], 2 [ ] [ B] ){ Φ} = 0 ( A λ, (2.30) where A and B are matrices which are a function of shaping polynomial N = k is the propagation constant. λ β 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] 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.

71 49 f(-h 2 ) f(0) f(h 1 ) -h 2 0 h 1 x Fig 2. 28: Concept of Finite Difference approximation Consider a 1 dimensional function, continuous and smoothly varying as shown in Fig The Taylor series expansion for the values of the function at h 1 and h 2 can be written as follows: f ( h2 ) = f (0) h2 f '(0) + h2 f "(0) + H ( f (0)) (2.31.a) 1! 2! f ( + h1 ) = f (0) + h`1 f '(0) + h1 f "(0) + H ( f (0)) (2.31.b) 1! 2! 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. f ( h1 ) f ( h2 ) f '(0) = + E( f (0)) (2.32.a) h + h 1 2 2( h2 f ( h1 ) + h1 f ( h2 ) ( h1 + h2 ) f (0)) f "(0) = + E( f (0)) (2.32.b) h h ( h + h ) 1 2 Where, E (f (0)) is the error due to higher order terms. 1 2

72 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. (x p, y q+1 ) (x p-1, y q ) d4 (x p, y q ) d1 d2 d3 (x p+1, y q ) (x p, y q-1 ) Fig 2. 29: Meshing and using Finite Difference approximation The finite difference approximation is used to evaluate the field Ф at a node ( p q x, y ) as below: 2 2 a φ b. φ + c. φ + dφ ( a + b + c + d) φ + ( k β ) φ 0 (2.33). p 1, q + p, q+ 1 p, q 1 p+ 1, q p, q p, q = 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

73 51 conditions on the outermost boundaries, the global matrix is created leading to the eigenmatrix as shown below [43,50]: [ A ]{ φ } = β 2 { φ} (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 Both space and time variables are quantized in this case. Finite difference approximations are used to evaluate the space and time derivatives. Inputs are timesampled 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].

74 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: jβz ( x, y, z) = A( x, y, z e (2.35) Φ ) Substituting the above in equation (2.26) and using the Fresnel approximation that 2 A = 0, we get 2 z 2 2 A A A j β = + + ( k β ) A 2 2 z x y (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 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

75 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]. A (x, y, z) A (x, y, z+ z) A (x,y,z+2 z) z z 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

76 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

77 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

78 56 handles complex geometries (fiber end-face) with greater accuracy when compared to the other techniques.

79 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

80 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

81 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. Incident wave Transmitted wave Reflected wave Medium I η 1 Medium II η 2 Z=0 Fig 3. 1: Plane wave reflection and transmission at boundary for normal incidence 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 (µ 1,ε 1 ) while Medium II is characterized by (µ 2,ε 2 ). Let us assume that the wave is propagating in the +z direction. Thus the propagation unit vector for incident wave is given by k = z.this wave sees a sudden discontinuity at the interface and is i partially reflected. The reflected wave travels in the direction opposite to that of the incident wave and has a propagation unit vector given by k r = - z in the negative z

82 60 direction. The transmitted wave has same direction as that of the incident wave, k = z. t The phasor form of electric and magnetic fields for the three waves can be represented as follows [52]: Incident wave: ~ E i ( z) = x E 1 oi e ~ 1 H i ( z) = z η jkz X E oi e jkz = E y oi η 1 e jkz Where wave number in medium I, k = k1= ω µε. Reflected wave: ~ E r ( z) = x E or e + jkz ~ 1 H r ( z) = ( z) η 1 X E or e + jkz = - y E or + jkz e η 1 Where wave number in medium I, k = k1= ω µε. Transmitted wave: ~ E t ( z) = x E ot e jkz ~ 1 H t ( z) = z η 2 X E ot e jkz = E y ot η 2 e jkz Where wave number in medium II, k = k 2 = ω µε. 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: ~ ~ ~ jkz + jkz E 1( z) = Ei ( z) + E r ( z) = x ( E e + E e ) oi ~ ~ ~ 1 jkz + jkz H 1( z) = H i ( z) + H r ( z) = y ( Eoie Eore ) where k = k1= ω µε. η 1 or

83 61 Field in medium II: ~ ~ = Et ( z = x E 2 ( z) ) E ot e jkz ~ H 2 ~ Eot jkz ( z) = H t ( z) = y e where k = k 2 = ω µε. η 2 Applying boundary conditions for ~ ~ E, H 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, ~ Therefore, ~ E 1( 0) = E 2 (0), H 1( 0) = H 2 (0) ~ ~ E + E = E (3.1) i o r o t o E η E E (3.2) i r t o o o = 1 η1 η 2 Solving (3.1) and (3.2) simultaneously yields, E r o η 2 η1 i = Eo, η 2 + η1 E t o 2η 2 = E η 2 + η1 i o The reflection coefficient ( Γ ) at the boundary is the ratio of reflected electric field to the incident electric field. r Eo η 2 η1 Thus, Γ = = i E. (3.3) o η2 + η1

84 62 Transmission line I Incident wave Transmitted wave Incident wave Transmission line II Transmitted wave Reflected wave Medium I η1 Medium II η2 Z 01 Z 02 Reflected wave Z=0 Z=0 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. t Eo 2η 2 Thus, τ = = i E. (3.4) o η 2 + η 1 For a non- magnetic medium, the intrinsic impedance of the medium is given by η = η o ε r, where ε r = relative permittivity of the medium. The refractive index of a non-magnetic material is given by n ε r. 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 = ε ε r1 r1 + ε ε r 2 r 2 n = 1 n2 n1 + n2 (3.5) 2 ε τ = r1 2n2 = ε r1 + ε r 2 n 1 n + 2 (3.6)

85 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 ( 01 η1 Z, Z 2 ), the electric field is represented in terms of voltage on the line 02 η ~ ~ ( E V ), and the magnetic field is analogous to current on the line ( H I ). Material properties such as µ, ε and refractive index n of the medium are thus r r 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. ~ ~

86 64 Incident wave n core n core n water Incident wave Z 0 = η n 0 core Z L = η n 0 water Γ in Reflected wave Γ in Reflected wave 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, ncore is considered to be 1.41 at incident optical wavelength of 980nm while refractive index of water, nwater is considered to be The fiber core is replaced by a transmission line of characteristic impedance, Z 0 η 0 =.Water is replaced by a load of impedance, n core Z L η 0 =. n water Reflection occurs due to refractive index mismatch at the core-water interface. The reflection coefficient at the fiber core-water interface is given by

87 65 Γ Γ in in Z = Z n n = n L L η n = η water water core core Z + Z η0 n η0 + n n + n core core water water The reflectance (R) for the TEM at normal incidence is given as, R = Γ Γ in in * = Γ in 2 R = n n core core n + n water water 2 (3.8) The return loss is expressed in logarithmic scale of base ten as, R (db) = 20log Γ in = 20log n n core core n + n water water (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 coefficient 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: dr dp * dγin * dγin = Γin. + Γin (3.10) dp dp The responsivity can be also expressed as a function of compression of water and fiber core by the incident acoustic pressure as:

88 66 dr dp dr dnc dr dnw = +. (3.11) dn dp dn dp c w The change in refractive index of water with respect to pressure is a linear relationship given by dn w dp 4 1 = 1.4X10 MPa [11].The compressibility of fiber core is a factor of 100 lower than that of water and given by dn w dp = X MPa Ignoring the refractive index of core change with respect to pressure for a 3% error in the result, equation (3.10) reduces to: dr dp 2nc ( dnw / dp) = (3.12) 2 ( n + n ) c w 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 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 transimpedance 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.

89 Reflectance, db Pressure, MPa Fig 3. 4: Reflectance vs Pressure amplitude of uncoated fiber Fiber Responsivity, db per MPa Pressure, MPa Fig 3. 5: Dynamic Responsivity of uncoated fiber sensor in terms of db per MPa

90 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

91 69 are subsequently used for development of the high sensitivity fiber optic hydrophone probe (FOHP) (See chapter 5) 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-j 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 AuAl 2

92 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

93 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 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 ( 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

94 72 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/m 3 [60]. At least three fiber samples were fabricated for each desired coating thickness in the range of 2.5 nm to 35nm. Laser Source Optical power Meter, EXFO 3 db optical coupler FC/APC connector Sensing Reference Fiber Fiber Air/ water/ 10% Isopropyl alcohol Fig 3. 6: Experimental set-up for extraction of complex refractive index of thin (2-35nm) gold films 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

95 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

96 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 , , and 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).

97 75 Real part of complex refractive index of gold. Imaginary part of complex refractive index of gold a Coating thickness,nm Coating thickness, nm 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

98 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 Coating thickness [54] Evaporated films n-jk at 980 nm [57] [59] Evaporated films Current work % deviation (n, k) Sputtered films 35 nm 0.22-j j %,34% 20 nm j j j %,28% 20 nm (mesomorphic) j ~ 15 nm j j %,22% ~ 5 nm j j6.15 2%,11% ~ 3 nm j j %,19% ~ 2 nm j j %,25% Table 3. 2: Refractive index data of 20nm and 35nm thick gold films at 1480nm and 1550nm Coating thickness 35 nm n-jk at 1480 nm [54] [57] Current work j nm j nm (Mesomorphic) j j j7.55 n-jk at 1550 nm [54] [57] [55] Current work j j j j j j j

99 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 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. Incident wave n c d n d n w Incident wave η Zc = n o c Reflected wave Z d d η o = n d η o Z w = n w Reflected wave Γ in Γ in Fig 3. 9: Transmission line analogue of metal coated fiber

100 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, Z c η 0 =.Water is n c replaced by a load of impedance, Z w η 0 =.The gold coating of thickness d is n w represented by a transmission line of characteristic impedance, Z d η 0 = and length n d 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, n c is considered to be 1.41 while refractive index of water, nw is taken as 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, Z in Z w + Z d tanh γd = Z d (3.11) Z + Z tanh γd d w where γ = 2π ( n j. k) j is the complex propagation constant. λ The complex reflection co-efficient in this case is given by, Γ in = Z Z in in Z + Z c c (3.12) Equation (3.11) can be re-written in terms of refractive indices of the material as, Z in = η 0 η0 nw n η d 0 n d η0 + nd η0 + n w 2π ( k + tanh λ 2π ( k + tanh λ jn) d. (3.13) jn) d

101 79 Substituting equation (3.13) in equation (3.11), a simplified form of reflection coefficient in terms of refractive index of the materials is obtained and given by the equation, nd ( nc nw ) + ( nwnc nd ) tanhγd Γ in = (3.14) 2 n ( n + n ) + ( n n + n ) tanhγd d c w The effective reflectance (R) is given by, R = Γ Γ in in * The return loss is expressed as, w c d 2 R.L = 10 log(r) = 10 log ( Γ Γ in in * ) (3.15) The dependence of reflectance on pressure can be found by differentiating equation (3.15) with respect to pressure as follows, dr dp dγin * dγin = Γin. + Γin *. (3.16) dp dp 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, dγ in dp Γ = n in c n c P Γ + n in w n w P Γin + d d P (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, Γ d in Γ = n in g n g d + Γ j k in g k g d (3.18)

102 80 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. 30 Responsivity improvement of gold coated FOHP using peicewise TL model Impact of water compression Improvement in responsivity, db Coating thickness,nm Fig 3. 10: Improvement in responsivity vs coating thickness considering water compression only Assuming compressible water and incompressible gold: In this case, modified as, d nw <<, where P P n w = 1.4 X 10-4 per MPa. Equation (3.16) can be P dr * R Γin nw R Γin nw = Γin... + Γin... * dp Γ n P Γ n P in w in w * (3.19) Where, Γ n in w 2n = d [ n w tanhγd + n [ n d ( n c d (tanhγd) + n ) + ( n n w c w 2 n n + n c 2 d d n n c w 2 ) tanhγd] tanhγd] (3.20)

103 81 Improvement in responsivity, db Responsivity improvement of gold coated FOHP using peicewise TL model Impact of gold compression Coating thickness,nm 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 Assuming incompressible water and compressible gold: In this case, d P nw >> P d. Assuming = 10 pm per MPa, the equation (3.17) P reduces to, dγ in dp Γin = d d p (3.21) The improvement in responsivity for this case is shown in Fig. 3.11

104 82 Improvement in responsivity, db Responsivity improvement of gold coated FOHP using peicew ise TL model Impact of gold compression Impact of water compression Total improvement in responsivity Coating thickness,nm Fig 3. 12: Improvement in responsivity vs coating thickness considering water and thin film gold compression 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 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

105 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 fullwave numerical modeling results and for further optimization of the fiber sensor design to be discussed in the next chapter.

106 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 multiphysics 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

107 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: 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 1/10 th 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.

108 86 Impedance boundary Impedance boundary r Matched boundary Port Matched boundary cladding core cladding Water 50 µm Impedance boundary cladding core Water Thin film gold coating cladding Impedance boundary Impedance boundary Matched boundary 10 µm 10 µm 25 µm 15 µm 25 µm 15 µm Port Matched boundary 50 µm Impedance boundary Z 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 fiberoptic 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, E + ni k E = 0 (4.1.a)

109 H + ni k H = 0 (4.1.b) 100 nm 300 nm 80 nm 80 nm 100 nm Fig 4. 2 Mesh structure of uncoated single mode fiber with step index profile Where, n i 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, 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 1/10 th of the incident wavelength was employed, where for shortest wavelength of interest (here, 980 nm) the resolution

110 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 (HE 11 ) 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, Γ = (E E1 ).E E 1.E 1 1.Where, (4.2) E = Total electric field. E 1 = Incident electric field. The impedance boundary condition was given by, n Eφ ( H ) + = 0 η i Where, (4.3) η i = 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

111 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, n ( E) = jβ Eφ i (4.4) Where, β i = propagation constant of the wave in the cladding. This sets the condition that the field propagates along z direction with the propagation constant, β i. Finally, continuity condition was imposed at all interior boundaries given by, r r nˆ ( H1 H 2 ) = 0 (4.5) Where, H 1 and H 2 are the magnetic fields in the media at interface 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, 2 s 2.( (1/ ρ ) p ( ω /( ρ c ) p) = 0 (4.6) Where, p = Pressure field. o ρ o = Density of water = 1000 Kg/ m 3. c s = Acoustic velocity in water = 1500 m/s. 0 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.

112 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 (n w ) as a variable dependent on the pressure distribution, given by, n n = no + p. Where, (4.7) p w. p = pressure amplitude distribution (in MPa) n = static index of refraction of water = 1.33 o n p = 1.4X10 4 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 db while the dynamic responsivity was -55 db per MPa.

113 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 %.

114 92 Impedance boundary Matched boundary Port Impedance boundary Matched boundary Impedance boundary 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.

115 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 db while the dynamic responsivity was 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 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 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

116 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. Radiation boundary 200 nm Radiation boundary 200 nm Pressure boundary 120 nm 80 nm Radiation boundary 200 nm 6 µm 200 nm Radiation boundary Matched Boundary Impedance Boundary 6 µm Impedance Boundary Port Boundary Matched Boundary Fig 4. 6: Geometry, mesh structure and acoustic boundary conditions of etched GRIN single mode fiber model. Impedance Boundary Fig 4. 7 RF boundary conditions of etched GRIN single mode fiber model.

117 95 Fig 4. 8: Power density profile of 6 µm etched GRIN single mode fiber model. Fig 4. 9: Power density profile of 8 µm etched GRIN single mode fiber model.

118 96 Fig 4. 10: Power density profile of 10 µm etched GRIN single mode fiber model. Fig 4. 11: Power density profile of 12 µm etched GRIN single mode fiber model.

119 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 Fiber Sensor Geometry Static Reflectance, db Dynamic responsivity in db per MPa Unetched Uncoated fiber db db per MPa Uncoated 12um etched fiber db db per MPa Uncoated 10um etched fiber db db per MPa Uncoated 8um etched fiber db db per MPa Uncoated 6um etched fiber db db per MPa 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 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.

120 98 5 Improvement in sensitivity, db Cylindrically etched tip diameter, µm 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, P in 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 The responsivity of the uncoated unetched straight cleaved

121 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 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. Matched Boundary Port Boundary Matched Boundary 200 nm 80 nm 200 nm α Impedance Boundary 200 nm 200 nm Impedance Boundary 120 nm 6 µm Fig 4. 13: Geometry, mesh structure and boundary conditions of uncoated 7 degree linear tapered fiber sensor. Impedance Boundary

122 100. 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

123 101 Fig 4. 16: Power density profile of 30 degree linear tapered GRIN single mode fiber model Fig 4. 17: Power density profile of 40 degree linear tapered GRIN single mode fiber model

124 102 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 Fiber Sensor Geometry Uncoated 7 degree linear tapered fiber sensor Uncoated 15 degree linear tapered fiber sensor Uncoated 30 degree linear tapered fiber sensor Uncoated 40 degree linear tapered fiber sensor Static Reflectance, db Dynamic responsivity in db per MPa db db per MPa db db per MPa db db per MPa db db per MPa 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

125 103 contained in the core region, the responsivity increases behavior approaches that of the straight cleaved fiber sensor (i.e. taper angle of 90 degrees) 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 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 Matched Boundary Port Boundary Matched Boundary 200 nm 80 nm 200 nm Impedance Boundary 200 nm 120 nm 6 µm 200 nm Impedance Boundary Impedance Boundary Fig 4. 18: Geometry, mesh structure and boundary conditions of exponential tapered GRIN fiber model

126 104 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.

127 105 Fig 4. 21: Power density profile of 30 degree exponential tapered GRIN single mode fiber model. Fig 4. 22: Power density profile of 40 degree exponential tapered GRIN single mode fiber model.

128 106 Table 4. 3 Responsivity performance comparison of exponential tapered fiber sensors Fiber Sensor Geometry Uncoated 7 degree exp tapered fiber Uncoated 15 degree exp tapered fiber Uncoated 30 degree exp tapered fiber Uncoated 40 degree exp tapered fiber Static Reflectance, db Dynamic responsivity in db per MPa db db per MPa db db per MPa db db per MPa db db per MPa The power density profile of the 7 degree, 15 degree, 30 degree and 40 degree exponentially tapered fiber sensor are shown in Figs 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 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.

129 107 0 Relative responsivity, db Taper angle, degrees Fig Plot of relative responsivity, db of uncoated linearly (red) and exponentially (blue) tapered fiber sensors as function of taper angle. Reference: 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.

130 Numerical model of thin film gold coated fiber sensors: Impedance boundary Radiation boundary Port Matched boundary Matched Boundary 200 nm 80 nm 200 nm n cladding n core n cladding 300 nm n water 100 nm n gold Pressure boundary Impedance boundary Radiation boundary ~ 2-20nm Fixed boundary Free boundary Pressure 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.

131 109 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 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 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 kg/m 3 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].

132 110 Assuming that the gold film is isotropic, this change in the refractive index produced by applied strain is given by [61], 3 n0 n g = ps. Where, (4.7) 2 n = Refractive index of thin film gold under zero stress (pressure) condition. o 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 Coating thickness, nm Dynamic responsivity with water compression only 30nm - 52 db/mpa -51 db/mpa 20nm -50 db/mpa -46 db/mpa Dynamic responsivity with water and gold compression 15nm -51 db/mpa -43 db/mpa 10nm -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 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

133 111 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

134 112 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 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. Matched Boundary Port Matched boundary 200 nm 200 nm Radiation boundary 200 nm 80 nm 6 µm 200 nm Radiation boundary 120 nm Pressure boundary Fig 4. 26: Geometry, mesh structure and boundary conditions of etched 5 nm coated fiber sensor.

135 113 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

136 114 Fig 4. 28: Power density profile of 5nm coated 8 micron etched fiber sensor Fig 4. 29: Power density profile of 5nm coated 10 micron etched fiber sensor

137 115 Fig 4. 30: Power density profile of 5nm coated 12 micron etched fiber sensor Matched boundary Port Matched boundary 200 nm 200 nm 80 nm Radiation boundary 200 nm 6 µm 200 nm 120 nm Pressure boundary Radiation boundary Fig 4. 31:Geometry, mesh structure and boundary conditions of coated 6 micron etched fiber sensor

138 116 Table 4. 6:Responsivity performance of coated 7 degree linear tapered fiber sensor. 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 Effect of gold coating on linear tapered fiber sensors: Fig 4. 32: Power density profile of 5nm coated 7 degree linear tapered fiber sensor

139 117 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 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. Fig 4. 33: Power density profile of 5nm coated 15 degree linear tapered fiber sensor

140 118 Fig : 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 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 Taper angles of 7 degrees, 15 degrees, and 30 degrees were considered for coating

141 119 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 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 Radiation boundary Matched boundary Port Matched boundary 200 nm 200 nm 200 nm 80 nm 200 nm 120 nm 6 µm Pressure boundary Radiation boundary Fig 4. 35: Geometry, mesh structure and boundary conditions of 7 degree exponential coated fiber sensor

142 120 Fig : Power density profile of 5nm 7 degree exponential taper sensor Fig 4. 37: Power density profile of 5nm coated 15 degree exponential taper sensor

143 121 Fig 4. 38: Power density profile of 5nm coated 30 degree exponential taper sensor 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.

144 122 Improvement in Sensitvity, db Coating thickness,nm 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

145 123 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 Coating thickness, nm Responsivity of different fiber sensor tip geometry, db re 1V /µpa Cylindrically etched fiber sensor Linearly tapered fiber sensor 30 nm nm Exponentially tapered fiber sensor 7 nm nm nm nm 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.

146 124 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.

147 125 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 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 MHz and MHz. The transducer had an active diameter of 20 mm and a focal length of mm. RF power amplifier provided a maximum pulsed power level of 100 W with 10 % duty cycles. The excitation input to the RF

148 126 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 50% output reference fiber 50% output Fabricated fiber optic hydrophone probes Signal Generator Agilent 55 db Power Amplifier + RF matching circuit 1.52 MHz HIFU Transducer, RF Spectrum Analyzer, Agilent Digital Ocilloscope Tektronix Water Tank Sonic Concepts Fig 5. 1: Experimental set-up at 980nm optical wavelength 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

149 127 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/ 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 FCA1) 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

150 128 Erbium Doped Fiber Amplifier Nuphotonics 10 db optical coupler, 1550nm, Chiphope 10% output 1 W Optical 3 db coupler, Isolator,1550nm, 1550nm,Chip Ascentta hope 50% output reference InGaAs PIN fiber photo-detector, Thorlabs 50% output Fabricated fiber optic hydrophone probes Signal Generator Agilent 55 db Power Amplifier + RF matching circuit 1550nm isolator, Ascentta, Inc MHz HIFU Transducer, Water Tank Sonic Concepts 1550nm DFB laser diode Mitsubishi RF Spectrum Analyzer, Agilent Digital Ocilloscope Tektronix Fig 5. 2: Experimental set-up at 1550nm optical wavelength.

151 129 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 transimpedance gain of 5 kω and noise equivalent power of 12pW/ (Hz) 1/ 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

152 130 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

153 131 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

154 132 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. Left / Right scan data at 1.5 MHz Left/ Right scan data at 5 MHz Needle hydrophone output voltage, mvpp Relative distance from focus, cm Needle tip 1 cm from surface of holder Needle hydrophone output voltage, mvpp Relative distance from focus, cm Needle tip 1cm from surface of holder Needle hydrophone output voltage, mvpp Relative distance from focus, cm Needle tip 1 mm from surface of holder Needle hydrophone output voltage, mvpp Relative distance from focus,cm Needle tip 1mm from surface of holder 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 mm at 5 MHz. Once the reference

155 133 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 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 dbm(+ 5 db/-3 db) cleaved Etched uncoated 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)

156 Improvement in responsivity, db Coating time, sec 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 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 db improvement in the static reflectance, indicating that for such films, the water compression by incident acoustic pressure dominates the responsivity performance.

157 135 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. Sample number Table 5. 2: Static reflectance of straight cleaved fiber samples Coating Static reflectance in air, db Static reflectance in water, db thickness Experimental Simulation Experimental Simulation SC uncoated SC 3 ~ 3 nm SC 5 ~ 5 nm SC 7 ~ 7 nm SC 10 ~ 10 nm

158 136 Table 5. 3: Static reflectance of uncoated cylindrically etched fiber samples Sample number Sample tip Static reflectance in air, db Static reflectance in water, db diameter Experimental Simulation Experimental Simulation # µm # µm # µm 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 Sample number Coating thickness Static reflectance in air, db Static reflectance in water, db Experimental Simulation Experimental Simulation # 11 C 4-5 nm # 12 C 6-7 nm # 18 C ~ 12 nm

159 137 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) Sample number Sample tip diameter Static reflectance in air, db Static reflectance in water, db Experimental Simulation Experimental Simulation # 1 ~ 6 µm # 5 ~ 5 µm # 17 ~ 6.5 µm 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

160 138 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) Sample number Coating thickness Static reflectance in air, db Static reflectance in water, db Experimental Simulation Experimental Simulation # 17 T 4-5 nm # 1 T 6-7 nm # 5 T 2-3 nm 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 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

161 139 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

162 Improvement in responsivity,db Coating thickness,nm 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 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

163 141 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

164 142 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 Coating No of Improvement in static reflectance Coating thickness time samples over uncoated fiber, db 5 sec db nm 7 sec db nm 15 sec T db 8 10 nm 20 sec db nm 50 Improvement in responsivity, db Coating thickness, nm Fig 5. 9: Responsivity improvement, db vs coating thickness, nm (Blue: Simulation, Red: experimental data with errorbar)

165 143 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 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 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.

166 Noise cancellation measurement: Optical laser source or EDFA Reflected power (Signal + noise) 3 db coupler Sensor arm reference arm (noise) attenuator + _ Balanced Photo-detector Display circuit 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 photodetector and is then displayed on the spectrum analyzer.

167 145. Table 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 dbm -112 dbm -112 dbm 0 db uncoated 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 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 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.

168 146 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 dbm -104 dbm -112 dbm 8 db uncoated SC dbm -82 dbm -92 dbm 10 db SC dbm -75 dbm -85 dbm 10 db SC dbm -69 dbm -80 dbm 10 db SC dbm -112 dbm -112 dbm X # 11 C dbm -89 dbm -98 dbm 9 db # 12 C 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-

169 % between the two noise inputs of the photo-detector could reduce the amount of noise cancellation by around 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 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 X: Y: Electrical power,dbm Frequency, MHz Fig 5. 11: Frequency response of PVDF needle hydrophone

170 E lectrical pow er, d B m X: Y: Frequency, MHz Fig 5. 12: Frequency response of straight cleaved uncoated FOHP 0-20 X: Y: Electrical power, dbm Frequency, MHz Fig 5. 13: Frequency response of 4-5nm coated fiber sensor (# 17 T)

171 Electrical Power, dbm X: Y: Frequency, MHz Fig : 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

172 150 were located at 200 (+/- 20) cm distance from the end-face, creating resonances at around 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 photodetectors 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 photodetector 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

173 151 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 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 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.

174 152 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 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 semiempirical 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.

175 153 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 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

176 154 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 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 db of common mode rejection, which led to relative intensity noise cancellation.

177 155 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

178 156 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 photoelastic 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 TiO 3 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

179 157 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 MHz and its multiples [71]. Use of alternative laser source without external Bragg gratings could be explored.

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186 Appendices 164

187 165 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 TDS MHz Bandwidths, 2 GS/s Sample Rates In line filter MFJ 1164B AC line RFI filter. 120V/25A/3000W max. RF Spectrum Agilent E408A (Mainframe) 20 Hz 2.4 GHz Analyzer RF Network Agilent 8712ET 300 khz 1.3 GHz Analyzer EDFA at 1550nm Nuphoton Technologies NP2000CORSV FCA1 Optical gain of 40 db, Maximum output 10 db optical coupler at 1550nm 3 db optical coupler at 1550nm Balanced Photo- Detector Low power optical isolator at 1550nm High power optical isolator at 1550nm Optical isolator at 980nm 3 db optical coupler at 980nm ChipHope Ascentta SMSCA223RPF1005 FA CP-S XX- S-L-10-FA power:30 dbm 2x2 coupler with 10/90 coupling ratio 2x2 coupler with 50/50 coupling ratio Thor Labs PDB130C Sensor InGaAs, Bandwidth 150MHz, Peak Responsivity: nm Ascentta ISILPD55SS9 Single mode, 1550 nm isolator, Maximum power handling of 400 Ascentta Ascentta Chip Hope IS-IL-P-D-55-S-S9- FA-1W VIS-S-980-HI-L-10- NE-09 SMSCC223RP5005F A mw. Single mode, 1550 nm isolator, Maximum power handling of 1W. Single mode, 980 nm isolator, Maximum power handling of 400 mw. Single mode 2X2 coupler with 50/50 coupling ratio

188 166 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 HE 11 mode. The power in the cladding region is almost 50 db lower than the power in the cladding region. β, rad/m 12 x Beta Vs wavelength of HE 11 mode of single mode optical fiber 980nm 1550nm wavelength, nm Fig A-2. 1: Propagation constant of the HE 11 mode vs wavelength.

189 X: 3.79e-005 Y: 1.01e+004 Electrical field amplitude, V/m X: Y: 5633 X: Y: Radial distance,µm Fig A-2. 2: Electrical field amplitude profile of HE 11 mode in single mode fiber at 980nm (linear plot) X: 3.79e-005 Y: Electrical field, db V/m X: Y: X: Y: radial distance, µm Fig A-2. 3: Electrical field amplitude profile of HE 11 mode in single mode fiber at 980nm (logarithmic scale).

190 X: Y: X: Y: X: Y: Power density, db W/cm Radial distance,µm Fig A-2. 4: Power density profile of HE 11 mode in single mode fiber at 980nm

191 169 Appendix A-3: Extracted values of refractive index of thin film gold Thickness, d nm No of samples Extracted 980nm Extracted 1480nm Extracted 1550nm 2.5nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j nm j j j5.052

192 170 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], n n p d n g = ps = (A-4.1) 2 2d 0 Where, n g = Change in refractive index of thin gold film n 0 = Refractive index of thin film gold under zero pressure. d 0 = 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 photoelastic 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 The refractive index change was differentiated with respect to change in n g coating thickness. This gave the ratio d. 3. The photo-elastic constant was calculated using the relationship,

193 171 2d 0 ng p =. d. n 3 0 The extracted values of photo-elastic constants at 980 nm optical wavelength and elastic constants are summarized in the table below. Thin Film Photo-elastic constant Young s Modulus Thickness 2 nm -0.2-j GPa 3 nm -0.5-j GPa 5 nm -0.1-j GPa 7 nm 0.2-j GPa 10 nm 0.55-j GPa 15 nm 0.2-j0.2 4 GPa 20 nm 0.6-j GPa 30 nm 1.5-j GPa

194 172 Appendix A-5: Acoustic to Electrical analogy Acoustical to Electrical quantities lumped analogy: Acoustical quantities Pressure = Force/ Area (1Pa = 1N/sq.m) Volume velocity = dx/dt (cu.m/s) Volume displacement = x (cu.m) Inertance = Pressure / rate of volume velocity = Mass/(Area) 2 (Kg/m 4 ) Acoustic resistance, Ra = Pressure/ Volume velocity (Pa.s/cu.m) Acoustic Compliance, = Volume Displacement /Pressure (cu.m/pa) Equivalent electrical quantities Voltage (Volts) Current (Amperes) Charge (Coulomb) Inductance = Voltage /rate of change of current (Henry) Resistance =Voltage/ Current (Ohms) Capacitance =Charge/ Voltage (Farad) Acoustical to Electrical quantities Wave analogy: Acoustic wave equation Where, p = pressure (N/m 2 ) c = acoustic wave velocity (m/s) Characteristic Acoustic impedance of medium, Z = ρ.c = Density X acoustic wave velocity (Rayls) Amplitude reflection co-efficient, Z 2 Z1 r = Z 2 + Z1 Intensity reflection co-efficient, R = r 2 = Z Z 2 2 Z + Z Acoustic intensity, 2 P I = (W/sq.m) where, Z P = Pressure amplitude (N/sq.m) Z = Acoustic impedance of medium (Rayls) Acoustic power, Pac = I X Area (Watts) where, I = Acoustic intensity Electro-magnetic wave equation E 1 E H 1 H = or = x c t x c t Where, E or H = Electric or Magnetic field c = speed of EM wave (m/s) Intrinsic impedance of medium, η = (Ohms) µ ε Reflection co-efficient, η 2 η1 r = η 2 + η1 Power reflection co-efficient or Reflectance R = r 2 η 2 η1 = η + η Power density, E S = (W/sq.m) where, η E = Electric field amplitude (V/m) η = Intrinsic impedance of medium (Ohms) Power delivered, P = S X Area (Watts) where, S = Power density

195 173 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: Radiation boundary 1.2 cm Acceleration boundary Water ( 0.15 mm) Water Focal region (0.1 mm ) Radiation boundary PZT Transducer Radiation boundary 4.5 cm 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

196 174 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 1/10 th 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, S E = * 10 m / N. (A-6.1) Relative permittivity matrix, ε r = (A-6.2)

197 175 In the acoustics domain, the density of water is considered to be 1000 Kg/m 3 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 backreflections 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.

198 176 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.

199 177 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

200 178 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)

201 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

202 180 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 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 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.

203 181 Appendix A-7: Characterization of passive optical link components Low power isolator at 1550nm (IS-IL-P-D-55-S-S9-FA): Parameters Manufacturer Measurement Insertion Loss 0.86 db 0.89 db Isolation 60 db 63 db 10 db coupler at 1550nm (SMSCA223RP1005FA): Parameters Manufacturer Measurement Coupling factor db db Insertion loss through port 0.85 db 0.89 db Isolation NA 51 db 3 db coupler at 1550nm (CP-S XX-S-L-10-FA): Parameters Manufacturer Measurement Coupling factor 3.36 db 3.59 db Insertion loss through port 3.52 db 3.94 db Isolation NA 48 db High power isolator at 1550nm (IS-IL-P-D-55-S-S9-FA-1W): Parameters Manufacturer Measurement Insertion loss 0.5 db 0.73 db Isolation 70 db 70 db High power isolator at 980 nm (VIS-S-980-HI-L-10-NE-09): Parameters Manufacturer Measurement Insertion loss 1 db 3 db Isolation 35 db 35 db 3 db coupler at 980 nm (SMSCC223RP5005FA): Parameters Manufacturer Measurement Coupling factor 3.48 db 3.74 db Insertion loss through port 3.45 db 3.99 db Isolation NA 60 db

204 182 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 dbm dbm dbm dbm dbm dbm EDFA output optical power, dbm Characterization of optical laser diode at 1550 nm FU-68PDF-V520MB (Mistubishi Inc, Japan): 10 Laser output power, dbm Bias current, ma

205 183 Characterization of 980nm laser LU098M450 (Lumics Inc., Germany): 400 Plot of Optical power Vs Bias 980nm Optical power, mw Threshold=62 ma Bias current, ma

206 184 Appendix A-9: Photo-detector PDB130 C specifications Specifications of PDB 130C balanced photodetector [64].

207 185 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]

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

209 187 Appendix A-10: Mechanical holder design Top view Holder section K1 Tolerance on all pieces = unless specified Material: Aluminium 5 X Ф = ¼ Front view RHS view

210 188 Holder section D2 Top view X Φ = ¼ To E To TH -1 To TH -1 Front view RHS view

211 189 Holder section E Top View Φ = ¼ To D1 Front View To D2 RHS view

212 190 Holder section TH-1 Holder section TH X Φ = ¼ X Φ = ¼ Top View 0.3 To D Top View To TH-1 To TH Φ = Φ = To TH-2 Front View 1.25 To TH-2 RHS view 2.5 Front View RHS view

213 191 Main rod R2 Scale: 2.5 : 1 Top View X Φ = ¼ To FH Front View RHS view

214 192 Top View FH-1 and FH X Φ = ¼ 0.5 From rod R RHS View To arm FA Front View

215 193 Holder section FA Top View To FH-1 To FH-2 Φ = ¼ 0.5 Front View RHS View

216 194 Fiber Holder FH 2 X Φ = ¼ Tolerance for holes= X Φ =

217 195 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

218 196 Appendix A-12: Sputter coater holder design Centers of all small holes 0.1 from inner circle Material: Plexiglas Ф = X Ф = 2.5mm (± 0.001) X Ф = 1/8 nylon screws 0.2 Top view thick Front view RHS view

219 197 4 pieces required Material : Teflon Ф = 1/8 threaded hole for nylon screws Ф = 0.25 If not available, use plexiglas 0.25 X0.25 square bar with 1 height. Threaded ¼ hole at center Top View 1 Front View RHS View

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

221 199 Appendix A-14: Single stage Single ended inverting amplifier design Ideal simulation with OPAMP model in ADS: S-PARAMETERS C C1 C=0.01 uf R R1 R=95.3 Ohm S_Param SP1 Start=100 khz Stop=2 GHz Step=1 MHz OpAmp AMP1 R R4 R=50 Ohm Term Term2 Num=2 Z=50 Ohm Term Term1 R Num=1 R2 Z=50 Ohm R=50 Ohm R R3 R=2 kohm Fig A-14. 1: Schematic of single ended amplifier 40 m1 freq= 1.100MHz db(s(2,1))= m6 freq= 239.1MHz db(s(2,1))= db(s(2,1)) m1 m E5 1E6 1E7 1E8 1E9 freq, Hz 2E9 Fig A-14. 2: Simulated gain performance of amplifier vs frequency

222 200 Layout for Single Ended Amplifier: Fig A-14. 3: Layout for single ended amplifier design. Gain,dB Gain performance of Single ended amplifier. X: 100 Y: Frequency, MHz Gain phase, degrees Frequency, MHz Fig A-14. 4: Experimental characterization of amplifier gain.

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

224 202 Appendix A-15: Raman Images of fabricated fiber samples 100µ m Fig A-15. 1: Straight cleaved fiber sample 6-7 µm α Fig A-15. 2: Linearly tapered fiber sample (5 degree taper angle)

225 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.