Application Improvements of Slab-Coupled Optical Fiber Sensors

Transcription

1 Brigham Young University BYU ScholarsArchive All Theses and Dissertations Application Improvements of Slab-Coupled Optical Fiber Sensors Spencer L. Chadderdon Brigham Young University - Provo Follow this and additional works at: Part of the Electrical and Computer Engineering Commons BYU ScholarsArchive Citation Chadderdon, Spencer L., "Application Improvements of Slab-Coupled Optical Fiber Sensors" (2014). All Theses and Dissertations This Dissertation is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu.

2 Application Improvements of Slab-Coupled Optical Fiber Sensors Spencer Lee Chadderdon A dissertation submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Stephen M. Schultz, Chair Richard H. Selfridge Aaron R. Hawkins Gregory P. Nordin Daniel E. Smalley Department of Electrical and Computer Engineering Brigham Young University March 2014 Copyright 2014 Spencer Lee Chadderdon All Rights Reserved

3 ABSTRACT Application Improvements of Slab-Coupled Optical Fiber Sensors Spencer Lee Chadderdon Department of Electrical and Computer Engineering Doctor of Philosophy This dissertation explores techniques for improving slab-coupled optical fiber sensor (SCOS) technology for use in specific applications and sensing configurations. SCOS are advantageous for their small size and all-dielectric composition which permit non-intrusive measurement of electric fields within compact environments; however, their small size also limits their sensitivity. This work performs a thorough analysis of the factors contributing to the performance of SCOS and demonstrates methods which improve SCOS, while maintaining its small dimensions and high level of directional sensitivity. These improvements include increasing the sensitivity by 9x, improving the frequency response to include sub 300 khz frequencies, and developing a method to tune the resonances. The analysis shows that the best material for the slab waveguide is an electro-optic polymer because of its low RF permittivity combined with high electro-optic coefficient. Additional improvements are based on changing the crystal orientation to a transverse configuration, which enhances the sensitivity due to a combined increase in the effective electrooptic coefficient and electric field penetration into the slab. The transverse SCOS configuration not only improves the overall sensitivity but increases the directional sensitivity of the SCOS. Lithium niobate and electro-optic polymer are both experimentally shown to exhibit minimal frequency dependent sensitivity making them suitable for broad frequency applications. Simultaneous interrogation of multiple SCOS with a single tunable laser is achieved by tuning the resonant wavelengths of KTP SCOS so their resonances overlap. Keywords: optics, fiber optics, D-fiber, electric field sensors, electro-optic materials

4 ACKNOWLEDGEMENTS First, I would like to thank my wife for her unending support and encouragement throughout the course of my studies. She was the one who encouraged me to pursue a graduate degree. I would also like to thank my parents and parents-in-law who have all been a great support to me and who have shown continued interest in my progress and in this work. I would especially like to thank my graduate committee whose advice and encouragement have been fundamental to the progress in my research. In particular, my advisers Dr. Stephen Schultz and Dr. Richard Selfridge, whose direction and countless hours of collaboration have helped me to become a better student and researcher. I have had the privilege to work with many people throughout my research and am grateful for their associations and help with my research. In particular, Richard Gibson, as much of his work formed the basis of my own research, and Josh Kvavle, who was a great mentor. My research would not have been possible without the support of our funders. I want to thank the Test Resource Management Center and the Test and Evaluation/Science Technology Program for their financial support along with KVH Industries, Inc. who donated the D-fiber. Finally, I would like to thank Brigham Young University and the Department of Electrical and Computer Engineering for their resources and academic support.

5 TABLE OF CONTENTS LIST OF TABLES... viii LIST OF FIGURES... ix 1 Introduction Sensor Selection Contributions and Dissertation Outline Background Waveguide Coupling of SCOS SCOS Operation as an Electric Field Sensor SCOS Fabrication Packaging and Connectorization SCOS Sensitivity to Other Physical Phenomena Electro-Optic Polymer SCOS SCOS Sensitivity Resonance Slope Resonance Shift SCOS Design Polymer SCOS Fabrication Freestanding EO Polymer Films Waveguide Attaching Polymer SCOS Characterization Summary Improvements in SCOS Sensitivity by Exploiting a Tangential Field Condition Directional Sensitivity of SCOS iv

6 4.1.1 Index Ellipsoid Refractive Index Calculations SCOS Sensitivity Optimization Effective Electro-Optic Coefficient Electric Field Penetration SCOS Optimization Results Summary Frequency Dependent Electric Field Penetration Experimental Setup Frequency Response Results Summary Resonance Tuning for Selective Laser Wavelength Interrogation Resonance Tuning Multi-Sensor Interrogation Resonance Tuned Multi-Axis SCOS Summary Ion Trap Electric Field Characterization Paul Trap Electric Field Characterization Coaxial Ion Trap Electric Field Characterization Summary Other Contributions SCOS Calibration System Description Calibration Results v

7 8.1.3 Summary Multi-axis Sensing Design and Fabrication Mapping SCOS Signal to Electric Field Multi-Axis Accuracy Summary High Speed Full Spectrum Interrogation of Fiber Bragg Gratings System Description Experimental Results Summary Conclusion Contributions Electro-Optic Polymer SCOS Transverse SCOS for Improved Sensitivity by Utilizing a Tangential Field Condition Frequency Dependent Sensitivity of SCOS Tuning the Resonant Wavelengths of SCOS Ion Trap Electric Field Profile Measurements Calibration of SCOS Multi-Axis Electric Field Sensors Using SCOS High-Speed Full-Spectrum Interrogation of FBG Sensors Future Work Three-Axis Sensor Using Transverse and Longitudinal SCOS Configurations Push-Pull SCOS Side Polished Panda Fiber SCOS vi

8 9.2.4 Interrogation of SCOS using Phase Modulated Optical Source Non-Intrusive, High Voltage Sensor REFERENCES vii

9 LIST OF TABLES Table 3-1. EO material parameters [50, 62-74] Table 3-2. Pertinent SCOS parameters for 100 μm thick slab waveguides with primary sensing direction of crystal aligned normal to flat surface of D-fiber...36 Table 4-1. Index Parameters for 1 MV/m field applied across x, y, z axes of the materials Table 4-2. Pertinent SCOS parameters for 100 µm thick and 1 mm wide slab waveguides for detection of 1 MV/m fields [61, 76, 77] Table 4-3. SCOS measurements...61 Table 8-1. Measured spectral response of the filter viii

10 LIST OF FIGURES Figure 1-1. D-dot electric field sensor [19]....3 Figure 1-2. Fiber coupled electro-optic sensor....4 Figure 1-3. SCOS compared in size with a penny....6 Figure 2-1. Cross sectional diagram of a SCOS Figure 2-2. SCOS showing optical input into the D-fiber and the coupled slab waveguide where modes are scattered (Top). Sample transmission spectrum of a SCOS (Bottom). The FSR is the spacing between adjacent modes Figure 2-3. Ray diagram showing polarization of light as it couples between the D-fiber and slab waveguide for (a) TE and (b) TM polarized modes Figure 2-4. SCOS transmission spectra corresponding to TM (solid) and TE (dash) operating polarizations Figure 2-5. Diagram of typical setup for SCOS interrogation Figure 2-6. An incident electric field causes a shift of λ resulting in a change in the transmitted power of P if a laser is used with a fixed wavelength Figure 2-7. Scanning electron microscope (SEM) image of a D-fiber Figure 2-8. Diagram of setup used for SCOS fabrication Figure 2-9. SCOS transmission spectra showing variation in resonance depth during fabrication Figure Measured optical slope as a function of resonance depth Figure Optical image of LiNbO 3 slab waveguide attached to D-fiber Figure 2-12: A cross section of a SCOS device in packaging...26 Figure 2-13: A photograph of a SCOS packaged in an FR4 trough Figure Transmission spectrum of EO polymer SCOS for varying levels of input power Figure Transmission spectrum for LiNbO 3 SCOS for different amounts tension applied to the fiber ix

11 Figure 3-1. Mode dispersion versus slab thickness for slab waveguide with various bulk indices Figure 3-2. Mode dispersion for a 100 μm thick slab waveguide as a function of slab refractive index Figure 3-3. Hot embossing process...38 Figure 3-4. Poled polymer between two glass slides Figure 3-5. Attached polymer slab to D-fiber...39 Figure 3-6. SEM of a polymer SCOS Figure 3-7. Picture of polymer SCOS used for characterization (top) and transmission spectra of ASE source and SCOS showing off-resonance loss (bottom). The SCOS is packaged in a FR4 tough and low index epoxy Figure 3-8. Testing setup for SCOS sensor characterization. PD, photodetector; TIA, transimpedance amplifier; HV, high-voltage amplifier; ESA, electrical spectrum analyzer; OSC, oscilloscope Figure 3-9. AC component of the field measured using an electrical spectrum analyzer with 100 point averaging Figure Measured transmitted power of SCOS for select laser wavelengths (red dots) fitted to transmission spectrum from OSA Figure 4-1: The index ellipsoid. The values for n x, n y, and n z are determined by the direction the electric field is penetrating the ellipsoid Figure 4-2. Two possible SCOS configurations for electric-field detection occurring orthogonal to the direction of the optical fiber Figure 4-3. Model used for Maxwell 2D simulation to determine strength of E-field within normal and transverse slab waveguides Figure 4-4. Electric field strength relative to position for transverse and normal slab waveguides Figure 4-5. E slab /E inc ratio as function RF permittivity, ε slab Figure 4-6. SCOS electric field test setup consisting of tunable laser, photo detector (PD), transimpedance amplifier (TIA) and electrical spectrum analyzer (ESA). A signal generator and electrodes were used to produce an electric field across the SCOS x

12 Figure 4-7. Transmission spectra for SCOSs fabricated using x-cut and z-cut KTP slab waveguides Figure 4-8. AC component of electric field measurement using electrical spectrum analyzer with 100 point averaging Figure 5-1. SCOS interrogation system Figure 5-2. Transmission spectra of SCOS used for frequency response characterization Figure 5-3. Frequency dependence of wavelength shift for KTP, LiNbO 3 and Polymer SCOS Figure 5-4. Frequency dependence of relative permittivity for KTP and LiNbO 3 crystals Figure 6-1. Rotation of biaxial crystal on the optical fiber Figure 6-2. Resonant mode shift as a function of KTP crystal rotation for TE (dashed) and TM (solid) polarization with three measured values shown with dots Figure 6-3. Resonant mode wavelengths of a z-cut KTP SCOS for three different crystal rotations. The top portion of the figure shows pictures of the SCOS that were used to determine the crystal rotations Figure 6-4. Interrogation of multiple SCOS using a single tunable laser Figure 6-5. SCOS configuration for a two-axis electric field sensor Figure 6-6. X-cut (dash) and z-cut (dash dot) KTP SCOS transmission spectra when the principal refractive indices of the crystals are aligned to the optical fiber and the spectrum of the z-cut SCOS (solid) after its resonant mode is tuned to overlap the x-cut SCOS Figure 6-7. Testing setup used to interrogate the two-axis SCOS, where PD is the photodetector, TIA is the transimpedance amplifier, HV is the high-voltage amplifier, and OSC is the oscilloscope Figure 6-8. Measured electric field signals as a function of incident field angle for two orthogonally placed SCOS Figure 7-1. Paul Trap structure with simulated electric field Figure 7-2. Setup and SCOS configuration for measuring axial field in Paul Trap Figure 7-3. SCOS signal as function of axial position through Paul Trap Figure 7-4. Electric field error between simulated and measured values xi

13 Figure 7-5. Deviation from ideal electric field for simulated profiles for SCOS with 0.5 mm, 1 mm, and 3 mm long sensing areas. (b) Error between simulated field irrespective of the size of the sensing region and for longer coupling regions Figure 7-6. Maximum electric field error as function of length of the sensing region Figure 7-7. Coaxial ion trap components (left) and setup for SCOS measurements (right) Figure 7-8. SCOS configurations for measuring axial (a-direction) and radial (r-direction) electric fields in ion trap Figure 7-9. SCOS electric field measurements along radial directions at 0º (dash dot), 35º (dash dash), and 110º (solid)...88 Figure SCOS measurements of axial field along axial direction at center of ion trap (r = 0) Figure SCOS measurements showing axial field along axial and radial directions at 0 deg Figure 8-1. Laser calibration setup block diagram Figure 8-2. The waveform produced by the calibration program. The program was set up to test each wavelength of the tunable laser (0.2 nm step size), and took approximately 30 minutes to complete Figure 8-3: Setup of a three-axis SCOS using x-cut KTP in a longitudinal SCOS configuration Figure 8-4: A photograph of a 3-axis SCOS sensor Figure 8-5: Four coordinate systems for the multi-axis SCOS Figure 8-6: Unit vectors for the three optic axes relative to the global axes Figure 8-7. Illustration of the measurement configuration with the unit vector of the third SCOS aligned to be parallel to the rotation axis of the test set-up. The thick black lines correspond to the parallel plate electrodes Figure 8-8: The normalized voltage as a function of angle for (solid) SCOS 1 and (dashed) SCOS 2. The difference between the maximum of sensor 1 and the minimun of sensor 2 is the angle offset Figure 8-9. (a) Angle error with the electric field applied in the tf-plane. (b) Angle error with the electric field applied in the tn-plane Figure Block diagram of interrogator xii

14 Figure MEMS filter static response Figure (a) The voltage applied to the tunable filter. The time-varying optical power with the tunable laser adjusted to (b) nm, (c) nm, (d) and nm. (e) The time-varying wavelength response of the tunable filter Figure The generation of the time-varying wavelength spectrum. (a) The measured time-varying optical power is combined with (b) the wavelength-time mapping to construct (c) individual wavelength spectrum Figure (a) The time-varying optical power transmitted through the tunable filter. (b) The time-varying signal with the periodic noise eliminated Figure False-color mapping of the time-varying wavelength spectrum Figure The progression of the full spectral response for various strike numbers Figure Normalized FBG reflected intensity during impact 8. The black line shows the location of the point of highest intensity in FBG reflection for each scan Figure Down-sampled images from 100 khz to 0.5 khz Figure FBG placement on positive rail Figure Spectral response of two FBGs on positive rail xiii

15 1 INTRODUCTION Many electric field sensing applications require a sensor capable of characterizing fields in compact environments with minimal electromagnetic interference. Several such applications include (1) safeguarding of sensitive electronics from high powered microwave (HPM) and electromagnetic pulse (EMP) attacks, (2) measuring current densities in the rails of railguns and (3) mapping of electric fields within ion trap structures. HPM and EMP weapons emit short, high-powered, high-frequency pulses that couple with conductive lines in electronics, inducing large currents that destroy the electronics. The weapons have the ability to quickly disable all electronics in an area removing an area of all modern machinery and electronics [1-5]. To safeguard electronic systems from these attacks, the electronic device is shielded by encasing it within a metal box or mesh to block the external field [6]. The efficacy of the shielding is determined by characterizing the electric fields in the vicinity of the electronics without altering the target field or affecting the electronics and shielding. In order to meet these requirements, the sensor must be non-perturbing, small in sensing area for high spatial localization of fields, and directionally sensitive to measure the full three-axis field direction and amplitude [7]. A railgun is an electromagnetic projectile launcher that has undergone significant research for applications as a weapon and to launch spacecraft [8-10]. The gun consists of two parallel conducting rails bridged by a conducing armature which supports the projectile. A 1

16 massive current discharge on the rails creates a current loop which induces a magnetic field that pushes the armature and attached projectile up and out of the rails at extremely high speeds [11, 12]. Some of the primary limitations of current railgun technology are associated with a phenomenon called velocity skin effect (VSE). As the armature moves down the rails, high current density concentrations form in the rear section of the armature connecting the rails. This current causes non-uniform pressure on the armature due to magnetic forces associated with the current flow. The main problems associated with this effect are (1) reduction in the peak velocity of the launcher and (2) reduction in the reusability of the launcher due to pre-mature failure of the rails and other components. In order to develop better rail and armature configurations, an understanding of current density distributions along the conducting rails is needed. The current density J can be determined by measuring electric field E and applying Ohm s Law given as J = σe, (1-1) where σ is the conductivity of the rail. In order to measure this field, the electric field sensor needs to be capable of measuring mixed frequency near-fields exclusively in the direction along rail [13-16]. The field measurement also needs to be nonmetallic to eliminate the possibility of induced currents. Radio-frequency ion traps have been increasing in popularity for use as mass analyzers due to their high sensitivity, compact size and relatively low cost. Ion traps use large electric fields to selectively isolate or trap ionized particles which can be mass-selectively ejected and analyzed [17, 18]. Characterizing the electric fields within the ion traps gives insight into their effectiveness in trapping and manipulating ions. It is especially useful in more complex and compact traps where misalignment of the structure results in suboptimal trapping regions. To 2

17 properly characterize the fields, the sensor needs to be non-perturbing, small and direction sensitive. The development and testing of all of these applications require the measurement of electric fields. Furthermore, the electric field sensing element needs to be nonintrusive requiring it to have a small cross-sectional area and nonmetallic. 1.1 Sensor Selection Figure 1-1 shows a commercially available D-dot electric field sensor [19]. D-dot sensors measure the time-derivative of the electric flux density across their sensor head [20]. Although these sensors are highly sensitive, their large physical dimensions and metallic composition results in disruption of the fields and difficulty of placement in space-restrictive environments [7]. In addition, the wire connecting the sensor to the instrumentation creates an electrical path through the shielding reducing the ability of the shielding to stop the electric field. Figure 1-1. D-dot electric field sensor [19]. 3

18 Integrating the electro-optic effect within an optical fiber system provides an alternate electric field sensing mechanism with considerably less electric field perturbation. The significantly lower intrusiveness of the fiber sensor originates from its all-dielectric structure. In addition, the flexible fiber allows the device to be threaded within electronic components allowing easier placement and no external electrical path [21, 22]. One common technique for incorporating the electro-optic effect with an optical fiber system is to couple light from a fiber into an electro-optic material [23-28]. Figure 1-2 shows a commercially available fiber coupled electric field sensor based on the electro-optic effect, with physical dimensions of 6 mm 6 mm 40 mm [29]. Fiber coupled sensors are typically phase based sensors that utilize either interferometry or polarimetry [30, 31]. Figure 1-2. Fiber coupled electro-optic sensor. An interferometry based sensor such as the Mach-Zehnder interferometer detects electric fields by splitting a single optical beam into two paths and then recombining the beams after they pass through an electro-optic medium causing a phase difference. An applied electric field causes a phase change between the paths resulting in destructive interference and a change in output power when the beams are recombined [21, 24, 32, 33]. Polarimetric sensors are also phase sensors; however, the phase shift occurs between the two polarization components of a single light beam as it passes through a birefringent material, thus altering the polarization state of the light [34]. Since the birefringence of an electro-optic material changes with an electric field, the 4

19 change in the polarization state of output light is dependent on the field strength. By placing a polarizer at the output, the change in polarization results in a change in the output power [28, 29, 35, 36]. Although these phase based sensors exhibit high levels of sensitivity and bandwidth, their minimum size is limited by (1) the length of the sensing element required to achieve an appreciable phase shift and (2) the components and support structure required for coupling between the fiber and electro-optic material. Another group of fiber sensors based on the electro-optic effect utilize evanescent coupling from a fiber core into an electro-optic slab waveguide [37-40]. One such sensor is the slab-coupled optical fiber sensor (SCOS) which consists of an electro-optic slab waveguide attached to a D-shaped fiber [41, 42]. A SCOS is used to detect electric fields by monitoring the transmission power though the fiber. The amount of light in the fiber that couples into the slab that is lost is dependent on the applied electric field. This sensor exhibits many of the same benefits of phase based electro-optic sensors including minimized electromagnetic interference and high bandwidth; however, the dimensions can be much smaller since no additional components or packaging are required for functionality. The smaller size further decreases the sensor intrusiveness and allows for even greater spatial resolution and measurement of nearfields. Figure 1-3 illustrates the small nature of a SCOS by comparing it in size to a penny. The small crystal on the optical fiber above the R in the picture is the actual sensing element of the device. 5

20 Figure 1-3. SCOS compared in size with a penny. Even though the SCOS is advantageous because of its small size, the small size results in lower sensitivity. The SCOS reported in [41] demonstrates a minimal detectable field of 200 V/m. Although this is sufficient for some applications, it is insufficient if the source has a wide frequency band. In addition, the sensitivity of a SCOS is determined in part by the dielectric properties of the electro-optic slab waveguide. Some of the electro-optic materials used in SCOS exhibit frequency dependent dielectric phenomena which results in SCOS with frequency dependent sensitivity. This prevents the use of SCOS in applications which have electric fields with mixed frequency content. This work primarily demonstrates techniques for improving SCOS, while maintaining its small dimensions and high level of directional sensitivity. These improvements include increasing the sensitivity, improving the frequency response, and developing a method to tune the resonances. This work also demonstrates mapping of electric fields within ion traps. 6

21 1.2 Contributions and Dissertation Outline This dissertation consists of three main parts. The first part discusses background information on SCOS technology, including the operation and fabrication of SCOS devices. This information is presented in Chapter 2. The second part focuses on my major contributions towards SCOS technology and is presented in Chapters 3 7. My major contributions generally deal with improving the sensitivity of SCOS and developing SCOS configurations for use in specific applications. These contributions have been published in four peer reviewed journals and three technical conferences. Additionally, one paper is currently under preparation for submission to a peer reviewed journal. My major contributions are presented as follows: I developed an electro-optic polymer SCOS. o S. Chadderdon, R. Gibson, R. Selfridge, S. Schultz, W. Wang, R. Forber, J. Luo, and A. Jen, "Electric-field sensors utilizing coupling between a D-fiber and an electro-optic polymer slab," Appl. Opt. 50, (2011) o D. Perry, S. Chadderdon, R. Gibson, B. Shreeve, R. H. Selfridge, S. M. Schultz, W. C. Wang, R. Forber, J. Luo, "Electro-optic polymer electric field sensor," Proceedings of SPIE Vol. 7982, 79820Q (2011) I pioneered the use of transverse SCOS for improved sensitivity by utilizing a tangential field condition. o S. Chadderdon, L. Woodard, D. Perry, R. H. Selfridge, and S. M. Schultz, "Improvements in electric field sensor sensitivity by exploiting a tangential field condition," Appl. Opt. 52, (2013) 7

22 o S. Chadderdon, L. Woodard, D. Perry, R. Selfridge, S. Schultz, "Improvements in electric field sensor sensitivity by exploiting a tangential field configuration," Proceedings of SPIE Vol. 8693, 86930V (2013) I characterized the frequency dependent sensitivity of SCOS. o S. Chadderdon, B. M. Whitaker, E. Whiting, D. Perry, R. H. Selfridge, and S. M Schultz, "Frequency dependence of slab coupled optical sensor sensitivity," Appl. Opt. 52, (2013) I developed a technique for tuning the resonant wavelength locations of SCOS for single wavelength interrogation. o S. Chadderdon, L. Woodard, D. Perry, R. Selfridge, and S. Schultz, "Single tunable laser interrogation of slab-coupled optical sensors through resonance tuning," Appl. Opt. 52, (2013) o S. Chadderdon, D. Perry, J. Van Wagoner, R. Selfridge, S. Schultz, "Multi-axis, all-dielectric electric field sensors," Proceedings of SPIE Vol. 8376, (2012) I have demonstrated the feasibility of SCOS for characterizing electric fields within ion traps. o S. Chadderdon, L. Shumway, A. Powell, A. Li, D. Austin, A. Hawkins, R. Selfridge, S. Schultz, Ion trap electric field measurements using slab coupled optical sensors. (In Preparation) Chapter 3 provides a detailed analysis of electric field sensing using SCOS. The analysis explains that the best material for the slab waveguide is an inorganic electro-optic polymer material because it exhibits low RF permittivity combined with a high electro-optic coefficient. 8

23 This chapter also describes the development of polymer SCOS including the development of free-standing electro-optic polymer films, the fabrication of SCOS using these films, and experimental testing. Chapter 4 presents sensitivity improvements to SCOS using crystalline slab waveguides. The improvements are based on changing the crystal orientation, which enhances sensitivity due to a combined increase in the effective electro-optic coefficient and electric field penetration into the slab waveguide. This chapter provides a detailed comparison of the different crystal orientations and their respective sensitivities and sensing directions. Chapter 5 presents the frequency dependent sensitivity of SCOS. The dependence is caused by the frequency characteristics of the relative permittivity. The frequency dependence of SCOS sensitivity is demonstrated for SCOS fabricated from several different electro-optic materials. Chapter 6 describes a method for tuning the resonant wavelengths of SCOS. This method allows multiple sensors to be interrogated simultaneously with a single tunable laser. The tuning range is dependent on the operating polarization. In this chapter the resonance tuning is described and demonstrated by rotating a slab waveguide. In the final section the concept is demonstrated by using a single laser to interrogate a two-axis electric field SCOS sensor. In Chapter 7, SCOS are used to map the electric fields within two ion trap structures. The measurements are compared with simulations to demonstrate the feasibility of SCOS for performing non-perturbing measurement of fields within ion traps and other compact environments. The third part of the dissertation is contained in Chapter 8 and includes minor contributions to SCOS technology and contributions to topics unrelated to SCOS. These 9

24 contributions have been published in eight peer reviewed journals with another submitted and eight technical conference presentations. The contributions are as follows: I have contributed to the development of multi-axis electric field sensors using SCOS. o D. Perry, S. Chadderdon, R. Forber, W. Wang, R. Selfridge, and S. Schultz, "Multiaxis electric field sensing using slab coupled optical sensors," Appl. Opt. 52, (2013) I have contributed to the development of a calibration technique for SCOS. o B. Whitaker, J. Noren, S. Chadderdon, W. Wang, R. Forber, R. Selfridge, and S. Schultz, "Slab coupled optical fiber sensor calibration, " Rev. Sci. Instrum. 84, (2013) I have contributed to the development of a high-speed full-spectrum fiber Bragg grating interrogation system. o T. Vella, S. Chadderdon, R. Selfridge, S. Schultz, S. Webb, C. Park, K. Peters and M. Zikry, "Full-spectrum interrogation of fiber Bragg gratings at 100 khz for detection of impact loading," Meas. Sci. Technol (2010) o S. Webb, K. Peters, M. A. Zikry, S. Chadderdon, S. Nikola, R. Selfridge, S. Schultz, "Full-spectral interrogation of fiber Bragg grating sensors exposed to steady-state vibration," Experimental Mechanics, 53 (4), (2013) o S. Webb, P. Shin, K. Peters, M. A. Zikry, N. Stan, S. Chadderdon, R. Selfridge and S. Schultz, "Characterization of fatigue damage in adhesively bonded lap joints through dynamic, full-spectral interrogation of fiber Bragg grating sensors part 2. simulations," Smart Mater. Struct. 23 (2014)

25 o S. Webb, P. Shin, K. Peters, M. A. Zikry, N. Stan, S. Chadderdon, R. Selfridge and S. Schultz, "Characterization of fatigue damage in adhesively bonded lap joints through dynamic, full-spectral interrogation of fiber Bragg grating sensors part 1. experiments," Smart Mater. Struct. 23 (2013) o S. Webb, K. Peters, M. Zikry, T. Vella, S. Chadderdon, R. Selfridge and S. Schultz, "Wavelength hopping due to spectral distortion in dynamic fiber Bragg grating sensor measurements," Meas. Sci. Technol (2011) o Sean C. Webb, Peter Shin, Kara J. Peters, M. A. Zikry, S. Chadderdon, N. Stan, R. Selfridge, S. Schultz, "Characterization of fatigue damage in adhesively bonded lap joints through dynamic, full-spectral interrogation of fiber Bragg grating sensors," Proceedings of SPIE Vol. 8693, 86930H (2013) o N. Stan, D. C. Bailey, S. Chadderdon, S. Webb, M Zikry, K. Peters, R Selfridge, S. Shultz, Increasing dynamic range of fiber Bragg grating edge filtering interrogation with a proportional control loop. Meas. Sci. Technol. (accepted for publication 2014) o D. Bailey, N. Stan, S. Chadderdon, D. T. Perry, S. Schultz, R. Selfridge, "Dynamic shape sensing using a fiber Bragg grating mesh," Proceedings of SPIE Vol. 8693, (2013) o N. Stan, D. Bailey, S. Chadderdon, R., S. Schultz, Sean C. Webb, Kara J. Peters, Mohammed Zikry, "High dynamic range high sensitivity FBG interrogation," Proceedings of SPIE Vol. 8694, 86940N (2013) 11

26 o S. Webb, A. Noevere, K. Peters, M. A. Zikry, T. Vella, S. Chadderdon, R. Selfridge, S. Schultz, "Full-spectral interrogation of fiber Bragg grating sensors for damage identification," Proceedings of SPIE Vol. 7982, 79820C (2011) o S. Chadderdon, T. Vella, R. Selfridge, S. Schultz, S. Webb, C. Park, K. Peters, M. Zikry, "High-speed full-spectrum interrogation of fiber Bragg gratings for composite impact sensing," Proceedings of SPIE Vol. 7648, (2010) o S. Webb, K. Peters, M. A. Zikry, T. Vella, S. Chadderdon, R. Selfridge, S. Schultz, "Impact induced damage assessment in composite laminates through embedded fiber Bragg gratings," Proceedings of SPIE Vol. 7648, (2010) o N. Stan, S. Chadderdon, R. Selfridge, S. Schultz, S. Webb, K. Peters, M. Zikry, "High-speed full-spectrum interrogation of fiber Bragg grating sensor application in reducing sensor strain sensitivity," Proceedings of SPIE Vol. 8347, 83471N (2012) o S. Webb, K. Peters, M. A. Zikry, S. Chadderdon, R. Selfridge, S. Schultz, "Full spectral interrogation of fiber Bragg grating sensors for measurements of damage during steady-state vibration," Proceedings of SPIE Vol. 8346, 83460C (2012) o S. Chadderdon, R. Selfridge, S. Schultz, S. Webb, C. Park, K. Peters, M. Zikry, "High-speed full-spectrum fiber Bragg gratings interrogator system and testing," Proceedings of SPIE Vol. 7753, 77537Q (2011) Section 8.1 deals with the development and interrogation of a three-axis SCOS device for 3-dimensional mapping of electric fields. Section 8.2 discusses an automated SCOS calibration system for simplifying electric-field measurements. Section 8.3 presents a high-speed fullspectrum fiber Bragg grating interrogation system. 12

27 2 BACKGROUND SCOS utilize the principles of evanescent waveguide coupling and the linear electro-optic effect (Pockel s effect) to detect electric fields. They consist of a small electro-optic slab mounted to a D-shaped optical fiber with an elliptical shaped core. Optical power transmitted though the fiber will fluctuate with an applied electric field. This chapter explains waveguide coupling, SCOS operation as an electric field sensor and SCOS fabrication. 2.1 Waveguide Coupling of SCOS Figure 2-1 shows a diagram of a SCOS device. The slab and fiber core are two optical waveguides that when placed close enough together have overlapping evanescent fields. This allows light from one waveguide to couple into the other waveguide. n s t N f Figure 2-1. Cross sectional diagram of a SCOS. 13

28 Coupling only occurs when the mode indices of the fiber and slab waveguide match. Since the slab waveguide has a large number of modes, the mode indices only match at specific wavelengths, λ m, as given by [43-45] 2t 2 2 λ m = ns N f, (2-1) m where N f is the effective index of the fiber mode (N f =1.451 for D-fiber when λ = 1550 nm), n s is the bulk refractive index of the slab waveguide, t is the thickness of the slab waveguide, and m is the mode number. This equation neglects the phase shifts associated with the evanescent field boundary conditions because the slab waveguide is thick. Figure 2-2 shows the resulting SCOS transmission spectrum consisting of periodic resonance dips where optical coupling occurs and power is wavelength selectively transferred from the fiber to the slab. The spacing between adjacent modes is given by the free spectral range (FSR). With a thick slab there are a large number of modes, and the FSR can be approximated to be FSR = 2t 2 λ 2 n s N f 2. (2-2) In general, the slab waveguide is chosen to be thick enough so that the FSR is less than the operable range of the laser source. Since most electro-optic materials are anisotropic, the slab waveguide index n s actually depends on the direction of the optical electric field within the EO slab. The elliptical shaped core of the D-fiber is polarization maintaining and supports two quasi-orthogonal modes [46]. The transverse magnetic (TM) mode has an electric field that is primarily perpendicular to the flat surface of the D-fiber and the transverse electric (TE) mode has an electric field that is primarily parallel to the flat surface of the D-fiber. 14

29 optical input coupled modes SCOS transmission normalized transmission (a. u.) FSR wavelength (nm) Figure 2-2. SCOS showing optical input into the D-fiber and the coupled slab waveguide where modes are scattered (Top). Sample transmission spectrum of a SCOS (Bottom). The FSR is the spacing between adjacent modes. Figure 2-3 shows the optical electric field direction when the light is coupled into the slab waveguide for both TE and TM modes. In this illustration the f direction is the propagation direction of the optical fiber, the n direction is normal to the flat surface of the D-fiber, and t is perpendicular to the other two directions. The t direction is called the transverse direction. Figure 2-3 (a) shows that the direction of the electric field for the TE mode is the same within the optical fiber core and the slab waveguide. The slab index is thus determined entirely by the slab waveguide orientation and is given by n s =n t, where n t is the refractive index of the slab in the direction transverse to the flat surface of the fiber. 15

30 Figure 2-3 (b) shows that the direction of the electric field for the TM mode within the slab waveguide depends on the characteristic propagation angle within the slab waveguide. The propagation angle within the slab θ s is determined by Snell s law as given by N sin 1 f θ = s (2-3) ns. The slab index n s depends on the characteristic propagation angle θ s of the electric field component as given by [47, 48] n s n f nn =, 2 (2-4) n sin + 2 f 2 2 ( θ ) n cos ( θ ) s n s where n f and n n are respectively the refractive indices of the slab in the direction of the fiber and normal to the flat surface of the fiber. The slab index n s is thus determined by simultaneously solving Eqs. 2-3 and 2-4. n (a) θ θ s Ε f t f Ε n (b) Ε θ θ s Ε f t f Figure 2-3. Ray diagram showing polarization of light as it couples between the D-fiber and slab waveguide for (a) TE and (b) TM polarized modes. 16

31 Figure 2-4 shows the transmission spectra of a SCOS fabricated using a z-cut potassium titanyl phosphate (KTP) crystal as the slab waveguide. The KTP slab is oriented such that the z- axis of the crystal is normal to the flat of the fiber, the x-axis is in the direction of the fiber and y- axis is transverse to the flat of the fiber. The two spectra correspond to the two operating polarizations (TM and TE) of the SCOS. The difference in the appearance of the spectra is partially due to the difference in the effective index of the two modes. The principal refractive indices of KTP at λ = 1550 nm are n x = , n y = and n z = [49-51]. For the TM mode, the light propagates at an angle θ s = 54º resulting in a slab index of n s = 1.79, where the slab index has contributions from both n z and n x indices. For the TE modes, the light propagates at an angle θ s = 57º; however, the direction of the optical electric field component stays transverse to the fiber resulting in a slab index of n s = n y. Due to the difference in slab index for each mode, the resonance dips occur at different wavelengths. 1.2 transmission power (mw) TM TE wavelength (nm) Figure 2-4. SCOS transmission spectra corresponding to TM (solid) and TE (dash) operating polarizations. 17

32 2.2 SCOS Operation as an Electric Field Sensor SCOS detect electric fields by monitoring the coupling of light between the core of the D-fiber and the attached electro-optic (EO) slab waveguide. The refractive indices of the EO slab change with an applied field as given by 1 n n 3 r E s s eff, (2-5) 2 where E is applied field within the EO slab, and r eff the electro-optic coefficient of the EO slab [52, 53]. The change in the refractive index of the slab creates a shift in the transmission spectrum, λ. The shift in the spectrum for practical electric fields is typically very small, on E the order of λ 5 pm ~ 10 [54]. Therefore, the detection is accomplished using an edge E V / m detection method. Figure 2-5 shows the setup for edge detection interrogation. In this method a laser with linewidth << resonance width is transmitted through the SCOS with its wavelength tuned to the edge of a resonant mode. A photodiode converts the optical transmission power through the fiber into an electric signal which is then amplified and captured using an oscilloscope. Figure 2-6 illustrates that a shift in the resonance results in a change in the transmitted power. The resulting power transmitted through the SCOS is given by P trans P λ = Po + E(t), λ E (2-6) where P o is the power transmitted through the SCOS with no applied electric field, P is the λ slope of the resonance. The transmitted power increases or decreases as the spectrum shifts, 18

33 resulting in a conversion between spectral shift and power. The electric field is determined by monitoring the output power of the SCOS. tunable laser E SCOS oscilloscope TIA PD electrical connection Figure 2-5. Diagram of typical setup for SCOS interrogation. 1.2 transmission power, P trans (mw) λ P 1534 λlaser 1544 wavelength, λ (nm) Figure 2-6. An incident electric field causes a shift of λ resulting in a change in the transmitted power of P if a laser is used with a fixed wavelength. 19

34 In order to determine the magnitude of an arbitrary electric field from a SCOS signal, the SCOS signal is first calibrated with a known electric field. The SCOS votage signal received by the oscilloscope V s is given by V s = Po + P λ E G, λ E (2-7) where G is the combined gain and responsivety of the photo detector and transimpedance amplifer in units of V/W. Rather than calculating each parameter individually to determine the field E, a calibration factor C is used instead to relate the SCOS voltage signal to a know electric field E k. The calibration factor is given by P λ Vs V C = G = λ E E k o, (2-8) where V o = P o G and the calibration factor has units of mv/(kv/m). A known field is applied to the SCOS by inserting the sensor between parallel plate electrodes with separation distance d and then applying known voltage V to result in electric field E=V/d. From Eq. 2-6, the sensitivity of a SCOS is dependent on both the slope of the resonance ( P/ λ) and the shift in the resonance ( λ/e inc ). Both these parameters depend on the material selection and orientation of the slab waveguide; however, the slope is also heavily dependent on the SCOS fabrication process. 2.3 SCOS Fabrication In order for coupling to occur between the core of an optical fiber and the slab waveguide, the two waveguides must first be in close proximity. Figure 2-7 shows that the D- fiber has a D-shaped cladding with an elliptical shaped core that is already close to the flat 20

35 surface of the fiber. Only a small portion of the cladding needs to be removed to expose the evanescent field, leaving most of the fiber cladding intact so that the structural integrity of the fiber is not significantly compromised [55]. The cladding is removed by using a hydrofluoric acid etch. The amount of cladding removed is accurately controlled by monitoring the birefringence change in the fiber as the acid removes the cladding layer [56, 57]. Figure 2-7. Scanning electron microscope (SEM) image of a D-fiber. After completing the etch process, the electro-optic slab is coupled to the etched portion of the fiber using MY-145 optical adhesive (MY Polymers Ltd.), which is a UV cure epoxy that has a refractive index of n=1.45. Figure 2-8 shows the setup for coupling the slab. The light from an amplified spontaneous emission source is polarized and coupled into the D-fiber. To ensure optimal coupling, the transmission is monitored using an optical spectrum analyzer (OSA) while the slab is positioned on the fiber. Once good coupling is attained as identified by the shape of the resonances, the epoxy is cured with a UV lamp, which secures the slab to the fiber. 21

36 ASE Source linear polarizer EO slab placement optical spectrum analyzer Figure 2-8. Diagram of setup used for SCOS fabrication. The coupling strength κ between the fiber guided mode and the slab waveguide mode is one of the key parameters in obtaining a narrow resonance [58]. For parallel waveguide directional couplers, the transmission coefficient is given by [59] T = 1 2 κ π + λ 2 κ 2 ( N ) N f 2, (2-9) where the coupling coefficient, κ, is assumed to be identical between both waveguides and N and N f are respectively the effective mode indices of the EO slab waveguide and the D-fiber. The slope is found by taking the derivative of Eq. 2-9 with respect to N, resulting in T N 2 π 2 κ λ = 2 2 π κ + λ ( N N ) ( N N ) f f 2 2. (2-10) The coupling coefficient κ is primarily affected by the separation distance between fiber core and slab waveguide. The slope can be increased by increasing the separation distance between the waveguides which reduces the coupling coefficient. However, weaker coupling requires a longer interaction length and is more sensitive to loss and EO slab uniformity. Therefore, there is a limit to the effectiveness of decreasing the coupling coefficient κ. 22

37 The waveguide separation distance is affected by both the amount of fiber cladding removed during the etch and the thickness of the epoxy layer. To compensate for possible thickness variations, the slab is slid along the transition region of the etched portion of the fiber until the optimal separation distance is located resulting in resonances with steeper slopes. Light is coupled into the D-fiber by first focusing it with a microscope objective and then using a three-axis micro positioning stage to align the fiber core to the focused beam. The amount of light focused into the fiber often varies by as much as 15 dbm due to variations in the quality of the cleave or placement of the fiber. Since the slope of the resonance is a function of optical transmission power, it is often difficult to identify steep slopes by viewing the transmission in linear units. An alternate method is to view transmission spectrum in logarithmic units, where the slope is identified in terms of resonance depth and off-resonance loss. Figure 2-9 shows the change in the transmission spectrum as the slab is slid along the transition region. Figure 2-10 shows the measured optical slope as a function of the resonance depth. Deeper resonances general equate to resonances with steeper slope; however, the increase in slope is minimal once resonance depth reaches approximately db. 23

38 0 optical transmission (db) wavelength (nm) Figure 2-9. SCOS transmission spectra showing variation in resonance depth during fabrication. 10 (W/m x 10 ) 8 optical slope resonance depth (db) Figure Measured optical slope as a function of resonance depth Packaging and Connectorization After attaching the slab to the fiber, the SCOS is packaged and connectorized to protect the sensor and allow easier operation. Figure 2-11 shows a SCOS after the slab has been cured to the fiber. The slab is 1 mm long while the etched region is about 15 mm long. The etched D-fiber 24

39 is fragile and susceptible to contamination. Packaging not only protects the fiber during handling and operation but also prevents exposure to contamination which can lead to high optical loss. Figure Optical image of LiNbO 3 slab waveguide attached to D-fiber. The requirements for the packaging depend on the application. For applications in which the physical size of the sensor is the primary concern, the stripped fiber and slab are simply recoated multiple times with the index matching epoxy. Although, this helps protect the SCOS from contamination, extra care must be taken during handling to prevent the fiber from breaking or the slab from decoupling from the fiber. For applications requiring robust packaging, the SCOS is inserted into a trough structure and then covered with low index epoxy. Figure 2-12 shows a cross section of this packaging. The slab and etched fiber is surrounded on all sides to reinforce the structure and protect the weaker etched region of the fiber. Since the packaging size and material affect the intrusiveness of the sensor, all dielectric materials are used in the packaging to minimize electric field perturbation. Also, materials exhibiting any frequency dependent dielectric phenomena should be avoided. Figure 2-13 shows a photograph of a SCOS packing in a trough made of FR4 board. FR4 board 25

40 packaging is easy to fabricate and exhibits high mechanical strength. This allows the packaging to be small while maintaining a flat rigid structure. low index epoxy SCOS Trough Figure 2-12: A cross section of a SCOS device in packaging Figure 2-13: A photograph of a SCOS packaged in an FR4 trough. Since the SCOS is a polarization sensitive device, it is crucial that the correct polarization of light is launched into the D-fiber. Launching into the wrong axis or both axes results in incorrect operation and decreased performance due to optical losses and/or cross-talk between polarizations. To maintain the correct linear polarization through the SCOS, the D-fiber connector is aligned to the polarization axis of the laser used for interrogation. 26

41 2.4 SCOS Sensitivity to Other Physical Phenomena Electric field measurements with SCOS technology takes advantage of the highly sensitive nature of mode coupling in order to monitor small index changes in the slab material from the electro-optic effect. However, the slab index and other coupling parameters vary with other factors including temperature, pressure and strain [49, 60-62]. Figure 2-14 show three transmission spectra of a polymer SCOS for different input powers. In addition to the expected increase in the power, there is also a shift in the resonant wavelength due to the polymer slab heating up as optical power is coupled into it from the fiber. Figure 2-15 shows three transmission spectra of lithium niobate SCOS for different levels of tension (strain) applied to the fiber. Similar to the change in temperature, the resonance locations have shifted. As appropriate, these environmental variables should be taken into consideration wherever a SCOS is used. The rate-of-change of environmental effects depends on the application. In some instances there will be a fixed change in temperature or strain as may be the case when installing the sensor inside a compact electronic device. The tension on the sensor from placement or heat produced by the electronics may shift the resonance and the interrogation wavelength will need to be adjusted prior to use. For other applications, the electric fields of interest may be isolated from other physical phenomena that affect material or fiber index by a large margin in the frequency domain. 27

42 transmission power (dbm) wavelength (nm) Figure Transmission spectrum of EO polymer SCOS for varying levels of input power. 0 transmission power (dbm) wavelength (nm) Figure Transmission spectrum for LiNbO 3 SCOS for different amounts tension applied to the fiber. 28

43 3 ELECTRO-OPTIC POLYMER SCOS The small size of the SCOS is advantageous for many electric field sensing applications because it minimizes field perturbation, results in precise field localization and enables the sensor to be placed in virtually any environment suitable for an optical fiber. However, the small sensing region also results in lower sensitivity [41] compared with other fiber based electric-field sensing techniques [28]. Therefore, there is a need to understand the details of SCOS sensitivity and how it may be improved without causing a significant change in the physical size of the sensor. The sensitivity is improved by either reducing electronic noise or increasing the optical signal. This chapter provides a detailed analysis of the SCOS signal strength. One of the results of this analysis is the benefit of using electro-optic materials with a low RF electrical permittivity. The low RF permittivity of electro-optic polymers makes them potentially more sensitive than other inorganic materials. However, the SCOS requires a fairly thick layer with uniform thickness. This chapter also describes the development of polymer SCOS including the development of freestanding electro-optic polymer films, the fabrication of SCOS using these films by attaching them to D-fiber, and experimental testing. 29

44 3.1 SCOS Sensitivity The key components for SCOS operation are resonant coupling between the fiber and slab waveguides and the linear electro-optic effect. These components translate to slope of the resonance ( P/ λ), and the shift in the resonant wavelength with applied electric field ( λ/e) Resonance Slope From Section 2.3 the transmission slope of a parallel waveguide directional coupler is T N 2 π 2 κ λ = 2 2 π κ + λ ( N N ) ( N N ) f f 2 2, (3-1) where, κ is the coupling coefficient and is assumed to be identical between both waveguides, and N and N f are respectively the effective mode indices of the slab and fiber. The factors that affect the slope are coupling coefficient κ, and the dispersion in the electro-optic slab waveguide. The coupling coefficient is largely dependent on the fabrication process and weaker coupling generally results in steeper slope. Because the mode indices of the waveguides need to be matched for resonant coupling, the mismatch in waveguide dispersion causes the resonance to be wavelength-sensitive. A larger difference in the dispersion between the two waveguides causes the resonance to be steeper and thus the SCOS to be more sensitive. The dispersion of the electro-optic slab waveguide depends on both its refractive index contrast and thickness. Figure 3-1 shows the dispersion as a function of slab waveguide thickness for a LiNbO 3 slab at 1550 nm. A large change in dispersion exists for waveguides between 0.5 μm and 20 μm thick; however, the rate at which the dispersion increases levels off around 20 μm. The shape of this dispersion curve with 30

45 respect to waveguide thickness does not change with the refractive index contrast of the slab waveguide, but the peak value will scale with the refractive index of the electro-optic slab. In addition to increasing the waveguide dispersion, the insertion loss of the SCOS also increases with slab thickness. Figure 3-2 shows the dispersion of the slab waveguide at λ=1550 nm as a function of the bulk slab index of the electro-optic material. This calculation is performed using a waveguide with a thickness of t=100 μm. N/ λ (nm 1 x 10 5 ) n s =2.18 n s =1.90 n s = n s = slab waveguide thickness, t (µm) Figure 3-1. Mode dispersion versus slab thickness for slab waveguide with various bulk indices. 31

46 N/ λ (nm 1 x 10 5 ) slab index, n s Figure 3-2. Mode dispersion for a 100 μm thick slab waveguide as a function of slab refractive index Resonance Shift The shift in the resonance wavelength locations is due to a combination of resonant coupling and linear electro-optic effect. The wavelength locations where resonant coupling occurs is given as 2t 2 2 λ m = ns N f, (3-2) m where N f is the effective index of the fiber mode, n s is the bulk refractive index of the slab waveguide, t is the thickness of the slab waveguide, and m is the mode number. The change in the bulk refractive index of the electro-optic slab due to an electric field is given by the linear electro-optic effect as 1 3 slab ns ns reff E, (3-3) 2 32

47 where E slab is the electric field within the EO slab, and r eff is the effective electro-optic coefficient of the EO slab. The SCOS wavelength shift is determined by first taking the derivative of Eq. 3-4 with respect to the slab index resulting in λ = n and then substituting in Eq. 3-3 to get the result s 1 2 λ n n 2 s s 2 N f, (3-4) 4 1 λ ns λ = r, 2 2 eff Eslab (3-5) 2 n N s where λ is the operating wavelength of the SCOS. When using the electro-optic crystal in a sensing application there is often a difference between the incident electric field and the electric field within the crystal resulting in f λ = E inc λ ns n N 2 s 2 f r eff f E ( ε ), slab (3-6) where f E is the electric field penetration ratio that relates an electric field within the crystal E slab to the incident electric field E inc. The bulk slab index n s and the effective electro-optic coefficient r eff depend on the polarization of light propagating through the slab and the orientation of the slab indices relative to the fiber. In this chapter, SCOS are configured to measure the electric field normal to the flat surface of the D-fiber with either TM or TE polarized light launched into the D-fiber. The slab index n s is determined using the procedure described in Section 2.1. The effective electro-optic coefficient is determined by first solving for the new refractive indices of the slab due to an electric field applied in the direction parallel to the z-axis of the slab E z. The new refractive indices are given as 33

48 n n 1 3 = nx nx r Ez, (3-7) 2 x ' = n y n y r E z, (3-8) 2 y ' 23 and n 1 3 = nz nz r Ez. (3-9) 2 z ' 33 The effective linear electro-optic coefficient is then found from Eq. 3-3 resulting in r eff n s, 1 3 ns Ez 2 (3-10) where n s is the change in slab index with an applied field, which is the difference between the slab index with and without an applied field. Since n s and E z are proportional, r eff remains the same for different values of E z. From Eq. 3-6, the primary components affecting the resonant wavelength shift are the slab index, effective electro-optic coefficient and the electric field penetration ratio into the slab waveguide. These parameters are strongly dependent on the material selection of the electrooptic slab waveguide. Generally materials that exhibit larger electro-optic coefficients and lower permittivity will be more sensitive. The parameters are also dependent on the operating polarization, the orientation of the slab in relation to the fiber, and dimensions of the slab in relation to the applied field. The effects of orientation and dimensions of the slab waveguide on SCOS sensitivity are discussed in Chapter 4. 34

49 3.2 SCOS Design The SCOS sensitivity depends on the coupling coefficient κ, slab thickness t, bulk slab index n s, effective EO coefficient r eff, and slab RF permittivity ε slab. These design parameters can be divided into fabrication related parameters (κ and t) and the selection of the EO slab material. The slab thickness t should be chosen above the knee in the curve shown in to get the maximum benefit to sensitivity but should not be too thick, because the insertion loss will increase. The coupling coefficient κ is adjusted during SCOS fabrication to produce the steepest slope (see Section 2.3). The other design parameters are related to the selection of the slab waveguide. Material selection affects both the slope and the shift in the resonance with applied field. Materials with a larger bulk index have a greater maximum threshold for steeper resonance slope as seen in Figure 3-2; however, since the slope is largely dependent on SCOS fabrication, the figure-of-merit for sensitivity is chosen to be the shift in the resonance (Δλ/E). Table 3-1 lists properties of several EO materials. Notice that the inorganic materials (LiNbO3, LiTaO3, KTP, KDP, KD*P, and SBN) have significantly larger RF permittivity (ε slab ) than the organic materials (DAST and EO polymer). Table 3-2 provides the various parameters that contribute to the resonant shift. KDP and KD*P have the largest shift of the inorganic materials because they have a refractive index that is close to the effective index of the optical fiber mode, N f. However, the small refractive index difference causes the dispersion in the slab waveguide to be too low; resulting in a resonance slope that would be too shallow. The materials with the best shift and slope are the organic materials (DAST and EO polymer) because these materials have the lowest RF permittivity combined with strong EO effect. 35

50 Table 3-1. EO material parameters [50, 62-74]. Crystal n x n y n z r 13 (pm/v) r 23 (pm/v) r 33 (pm/v) εslab LiNbO LiTaO KTP a KD*P (r 41 ) 25 (r 63 ) 48 KDP (r 41 ) 10.3 (r 63 ) 20 SBN DAST (r 11 ) 21 (r 21 ) 5 (r 13 ) 5.2 EO Polymer (AJL/APC) a Relative permittivity value of KTP is the average of two reported values. Table 3-2. Pertinent SCOS parameters for 100 μm thick slab waveguides with primary sensing direction of crystal aligned normal to flat surface of D-fiber Crystal Angle slab index, n s r eff (pm/v) E slab /E inc shift (m 2 /V) LiNbO3 (TM) LiNbO3 (TE) LiTaO3 (TM) LiTaO3 (TE) KTP (TM) KTP (TE) KDP (TM) KDP (TE) KD*P (TM) KD*P (TE) SBN (TM) SBN (TE) DAST (TM) DAST (TE) EO Polymer (TM) EO Polymer (TE) Polymer SCOS Fabrication The material with one of the best shift parameters (Δλ/E) is EO polymer because it has a large EO coefficient and a low RF permittivity. In order to produce a SCOS with steep resonance slope, the slab waveguide needs to be very uniform and thicker than around 20 μm. In practice, the FSR of the SCOS needs to be small enough to fit within the tuning range of the laser. If a FSR of less than 30 nm is required, then the thickness of the polymer needs to be larger than 43 μm (see Eq. 2-2). 36

51 A common method used to create polymer waveguides is spin coating. However, it is difficult to create highly uniform layers when the thickness is larger than around 10 μm, and the problems with non-uniformity become even worse when the substrate is not planar, such as when coating onto a D-fiber. Therefore, a new fabrication method has been developed to enable the fabrication of a thick uniform polymer layer using a hot embossing process Freestanding EO Polymer Films Figure 3-3 illustrates the main steps of the hot embossing process used to fabricate the freestanding polymer film. First of all, a polymer film is created by drop-casting the EO polymer onto an indium-tin-oxide-coated glass slide. Figure 3-3 (b) illustrates how two of the drop-casted slides are cofacially stacked together with polyimide sheets from Dupont placed between the slides to control the thickness. Figure 3-3 (c) shows that the stack is pressed together with high force while the film is heated above its softening temperature (170 C for the EO polymer). This process can produce freestanding and thick (30 75 μm) films of EO polymers with high film quality and parallelism. The polymer-glass slide stack is then removed from the press and poled by applying high voltage to the ITO layers while the sample temperature is held at a temperature around the glass transition temperature of the polymer. Figure 3-4 shows the poled thick film sandwiched between two ITO-coated glass slides. In this particular case, the hot embossing process was used to fabricate a 50 μm thick layer of AJL/APC polymer [72-74]. The polymer was then poled by heating it up to 115 C and applying a poling voltage of 4 kv. The EO polymer was then measured to have a linear electro-optic coefficient of r 33 = 70 pm/v at 1550 nm. Figure 3-4 shows the poled thick film sandwiched between two ITO coated glass slides. 37

52 (a) polymer ITO film glass (b) polyimide spacer (c) Figure 3-3. Hot embossing process Figure 3-4. Poled polymer between two glass slides Waveguide Attaching The top ITO coated glass slide is removed and a small piece of the EO polymer is cut off to create the desired free-standing EO polymer film. The technique for attaching the polymer film to the D-fiber is similar to the method described in (see Section 2.3); however, the thin polymer slab is flexible and tends to bend slightly making it hard to get uniform coupling along 38

53 the slab. If coupling is difficult to achieve, a glass or fused silica slide is glued to the polymer to increase its rigidity. Figure 3-5 shows that the EO polymer SCOS has a physical size that is close to the width of the optical fiber and a length typically under a few millimeters. Figure 3-5. Attached polymer slab to D-fiber Figure 3-6 shows a cross-sectional scanning electron microscope (SEM) image of the polymer SCOS. Notice how flat the resulting freestanding polymer film is, as well as how close the polymer film is to the D-fiber. Figure 3-6. SEM of a polymer SCOS. 39

54 3.3.3 Polymer SCOS Characterization The objective of the characterization is to determine the basic SCOS parameters, which are the insertion loss, the resonance slope (ΔP/Δλ), and the shift per unit of electric field (Δλ/E). Figure 3-7 shows a picture and transmission spectrum of the polymer SCOS used for characterization. The insertion loss is approximately 8.9 db and is determined by measuring the difference in power between the ASE source and the SCOS at an off-resonance location. Figure 3-7. Picture of polymer SCOS used for characterization (top) and transmission spectra of ASE source and SCOS showing off-resonance loss (bottom). The SCOS is packaged in a FR4 tough and low index epoxy. Figure 3-8 provides a block diagram of the test setup used for characterizing the slope and shift. In this test a voltage was created by using a high-voltage amplifier to amplify a sinusoidal voltage signal. The resulting voltage had a peak amplitude of 500 V and frequency of 40

55 20 khz. This voltage was applied to planar electrodes with a separation of 6 mm to produce an electric field of E(t) = sin( t) kv/m. (3-11) The optical signal is transmitted through the SCOS and converted into a current with the photodetector (PD). The current is then converted into a voltage with the transimpedance amplifier. The resulting voltage signal is given by V = P o G + ΔP Δλ Δλ E G sin( t), (3-12) where P o is the average optical power incident onto the photodetector, G is the combined gain of the transimpedance amplifier and responsivity of the photodetector (950 V/W). The resulting quasi-dc and AC components of the signal are given respectively by and V DC = P o G, (3-13) V AC = ΔP Δλ Δλ E G sin( t). (3-14) function generator tunable laser HV SCOS PD TIA ESA oscilloscope Figure 3-8. Testing setup for SCOS sensor characterization. PD, photodetector; TIA, transimpedance amplifier; HV, high-voltage amplifier; ESA, electrical spectrum analyzer; OSC, oscilloscope. 41

56 The electrical spectrum analyzer is used to record the AC portion of the signal because it can easily pull the signal out of the noise. Figure 3-9 shows that the AC portion of the field has an amplitude of 8.2 mv. In order to estimate the material-dependent shift in the resonance, the slope of the resonance and electrical gain need to be measured. The resonance slope increases when more optical power is input into the SCOS. Therefore, the slope needs to be measured under the same operating conditions as the AC test. To achieve a good estimate of the slope, the wavelength of the tunable laser was scanned around the operating wavelength used during the test while the transmission power was captured with the oscilloscope. Figure 3-10 shows the transmission spectrum of the SCOS normalized to the voltages corresponding to the wavelengths of the tunable laser. The slope around the operating wavelength was then averaged, resulting in a resonance slope of ΔV = ΔP Δλ Δλ G = (9.8 ± 0.1) V 108 m. (3-15) 10 8 SCOS signal (mv) frequency (khz) Figure 3-9. AC component of the field measured using an electrical spectrum analyzer with 100 point averaging. 42

57 4 transmission voltage (V) λ laser wavelength (nm) Figure Measured transmitted power of SCOS for select laser wavelengths (red dots) fitted to transmission spectrum from OSA. This slope parameter takes into account the power transmitted through the SCOS and the electrical gain. The actual slope of the optical power is attained by dividing the voltage slope by the electrical gain. The power input in the SCOS was 10 mw, by factoring in the insertion loss, the resulting electrical gain was calculated as 3025 V/W. The resulting optical slope is ΔP Δλ = (3.28 ± 0.3) 105 W m. (3-16) The measured shift in the resonance is then determined by dividing the measured AC voltage signal by the slope and known electric field, resulting in Δλ E = V AC ΔV = Δλ E o ( )( ) m2 18 = (100.4 ± 0.2) 10 V, (3-17) 43

58 which is within the measurement error of the predicted value of m 2 /V. The resulting SCOS signal is thus given by V = E(t). (3-18) The AC portion of the voltage signal can be increase by filtering out the DC voltage and then amplifying the signal using a low noise voltage amplifier. 3.4 Summary The detailed analysis of the SCOS quantifies the sensitivity dependence of the slab waveguide material parameters such as the index of refraction, the linear electro-optic coefficient, and the RF permittivity. In addition to a large electro-optic coefficient, a low RF permittivity is very important for high sensor sensitivity. A method for fabricating a SCOS with electro-optic polymer was also demonstrated. This method involved creating a freestanding electro-optic film, which was then attached to the D-fiber. The resulting polymer SCOS was tested to have a resonance slope of P/ λ = W/m, a shift parameter of λ/ Ε = m 2 /V, and a signal of V s = E(t). The resulting SCOS matches the theoretical derivation for the SCOS response. 44

59 4 IMPROVEMENTS IN SCOS SENSITIVITY BY EXPLOITING A TANGENTIAL FIELD CONDITION The previous chapter demonstrated improvements in sensor sensitivity through material selection, in which the use of electro-optic polymer increased sensitivity due to its low RF permittivity and high electro-optic coefficient. Although the polymer SCOS exhibits higher sensitivity, it also has several disadvantages related to fabrication, availability, cost, and temperature stability (see Section 2.4). This chapter presents an alternate method for improving the sensitivity of SCOS without increasing its size by changing the orientation and sensing direction of SCOS relative to the fiber. One of the side effects of changing the orientation of the slab is that it affects the directional sensitivity of the SCOS. For many applications, a high level of directional sensitivity is required. Therefore, an analysis of the directional sensitivity of SCOS is first performed in order to optimize the sensitivity of the SCOS while maintaining high level of single-axis sensitivity. 4.1 Directional Sensitivity of SCOS The directional sensitivity of SCOS is determined by first analyzing the change in the principal refractive indices of the EO slab due to applied electric fields in the x, y, z directions of the crystal axes and then applying the polarization and slab geometry effects. The change in the principal refractive indices due to an electric field is most easily shown using the index ellipsoid. 45

60 4.1.1 Index Ellipsoid The index ellipsoid is a geometric representation used to depict the orientation and magnitude of the refractive indices of a crystal. Figure 4-1 shows a diagram of an index ellipsoid with applied electric field E o. For a birefringent crystal, the index ellipsoid can be expressed in Cartesian coordinates as x 2 n2 + y2 x n2 + z2 = 1, (4-1) y n2 z where n x, n y, and n z are the axes of the index ellipsoid and correspond to the principal refractive indices of the crystal [52]. The materials considered for SCOS are either uniaxial (n x = n y n z ) or biaxial (n x n y n z ). z E o n z y n x n y x Figure 4-1: The index ellipsoid. The values for n x, n y, and n z are determined by the direction the electric field is penetrating the ellipsoid. 46

61 An electric field applied in an arbitrary direction to an electro-optic crystal causes a linear change in the indices of refraction due to the linear electro-optic effect as given by or in matrix form as Δ 1 n 2 = r ij E j, (4-2) i j Δ 1 n 2 1 Δ 1 n 2 2 Δ 1 r 11 r 12 r 13 n 2 r 21 r 22 r 23 3 r Δ 1 = 31 r 32 r E x 33 n 2 r 41 r 42 r E y, (4-3) 43 4 Δ 1 r 51 r 52 r E 53 z n 2 r 61 r 62 r 63 5 Δ 1 n 2 6 where the r-terms are the linear electro-optic coefficients, which are elements of the electro-optic tensor of the material, and the E is an applied electric field parallel to the crystal axes in x, y, and z-directions. An electric field applied to the crystal results in a new index ellipsoid given as 1 n2 + Δ 1 x n 2 x n2 + Δ 1 y n 2 y n2 + Δ 1 z n 2 z Δ 1 n 2 yz 4 + 2Δ 1 n 2 xz + 2Δ 1 5 n 2 xy = 1, 6 (4-4) where x, y, and z-directions are determined by the symmetry axes of the crystal. In addition, the presence of cross terms (i.e. yz, xz, xy) causes the ellipsoid to rotate and the lengths of the principal axes to change. From Section 3.2 the materials of most interest for SCOS are KTP, EO polymer and LiNbO 3. The electro-optic behavior of these materials is analyzed for fields directed in the x, y, 47

62 and z directions of the principal crystal axes. The procedure for calculating the change in the refractive indices of a material when under the influence of an applied field is based on [75] Potassium Titanyl Phosphate (KTP) KTP is a biaxial crystal with principal refractive indices n x = , n y = and n z = The crystal has orthorhombic 2mm symmetry with electro-optic tensor 0 0 r r 23 r = 0 0 r 33, (4-5) 0 r 42 0 r where r 13 = 8.8 pm/v, r 23 = 13.8 pm/v, r 33 = 35, r 42 = 8.8 pm/v and r 51 = 6.99 pm/v. When an electric field is applied, the index ellipsoid equation becomes 1 n x 2 + r 13E z x n y 2 + r 23E z y n z 2 + r 33E z z 2 +2r 42 E y yz + 2r 51 E x xz = 1. (4-6) In the case of a z-directed field, there are no cross terms and consequently no rotation of the index ellipsoid. The principal refractive indices are respectively perturbed by the r 11, r 23, and r 33 coefficients. Fields directed in x and y-directions will result in rotation of the index ellipsoid due to the presence of cross term coefficients r 42 and r 51 [52]. The r 42 term causes a rotation of θ x = 1 2 tan 1 2r 42E y 1 n2 1 (4-7) y n2 z about the x-axis for a y-directed field. The r 51 term causes a rotation of 48

63 θ y = 1 2 tan 1 2r 51E x 1 n2 1 (4-8) x n2 z about the y-axis for an x-directed field. Due to the high birefringence of the crystal, this rotation is very small resulting in a very small sensitivity to E x and E y Electro-optic Polymer (AJL8/APC) Electro-optic polymer has a uniaxial structure with principal refractive indices n x n y 1.66 and n z = The electro-optic tensor for polymer is 0 0 r r 13 r = 0 0 r 33. (4-9) 0 r 13 0 r where r 13 = 23 pm/v and r 33 = 70 pm/v. When an electric field is applied, the index ellipsoid equation becomes 1 n x 2 + r 13E z x n y 2 + r 13E z y n z 2 + r 33E z z 2 + 2r 13 E y yz + 2r 13 E x xz = 1. (4-10) The index ellipsoid for polymer is very similar to that of KTP. Fields applied in each respective direction will yield rotations about the same axes except the value of rotation and resulting refractive index perturbations will be different due to differing values of electro-optic coefficients. 49

64 Lithium Niobate (LiNbO 3 ) LiNbO 3 is a uniaxial crystal with principal refractive indices n x = n y = and n z = The crystal has Trigonal 3m symmetry with electro-optic tensor, 0 r 22 r 13 0 r 22 r 13 r = 0 0 r 33, (4-11) 0 r 51 0 r r where r 13 = 8.6 pm/v, r 33 = 31 pm/v, r 22 = 3.4 pm/v and r 51 = 28 pm/v. When an arbitrary electric field is applied, the index ellipsoid equation becomes 1 n x 2 r 22E y + r 13 E z x n y 2 + r 22E y + +r 23 E z y n z 2 + r 33E z z 2 + 2r 51 E y yz + 2r 51 E x xz 2r 22 E x xy = 1. (4-12) LiNbO 3 behaves similarly to KTP and polymer for a z-directed field in which all three principal indices are perturbed respective to the coefficients in the third column of the tensor. In the case of a field applied in the y-direction, the presence of the r 22 coefficients in second column of the tensor result in non-negligible perturbation of the n x and n y indices. This is also similar to KTP, the r 51 coefficient in the second column causes a rotation of the index ellipsoid that is negligibly small due to large index contract between n y and n z. θ x = 1 2r 51 E x 2 tan 1 1 n2 + r 22E y 1. (4-13) y n2 z Finally, for an x-directed field, the combined presence of r 51 and r 22 coefficients causes multiple orthogonal rotations of the index ellipsoid about the principal axes. The first rotation is about the y-axis and is given as 50

65 θ y = 1 2 tan 1 2r 51E x 1 n2 1. (4-14) x n2 z This rotation results in slight perturbation to the n x and n z indices. The next rotation occurs about the z-axis and is given by θ z = 1 2 tan 1 2r 22E x 1 (n x ) 2 1, (4-15) n2 y where n x is the perturbed index n x which was a result of the previous rotation. Since n x n y, the resulting rotation angle is large θ z 45º which results in non-negligible perturbation of the n x and n y indices. An additional 4 rotations are required; however, further perturbation of the principal indices is insignificant since the remaining rotation angles are so small Refractive Index Calculations Changes in the principal refractive indices of KTP, LiNbO 3, and EO polymer were calculated for a 1 MV/m electric field applied with orientation across the principal axes x, y and z of the crystals. To quantify the cross-axis sensitivity of the materials, the change in the refractive indices corresponding to a field aligned to the primary sensing direction (field direction which causes the greatest change in the refractive indices) are divided by the change in the refractive indices from fields of equal amplitude applied in off-axis orientations. The primary sensing direction for the materials considered in this work is along the z-axis of the crystals. The resulting cross-axis sensitivities of the crystal indices are given by 51

66 Δn 2 2 ix + Δn iy Cc i = Δn iz, (4-16) with Δn ij = n i E j = E 0 n i, (4-17) where i signifies the three possible refractive index components (i=x,y,z) and j signifies the electric field component (j=x,y,z). Table 4-1 summarizes the cross-sensitivity results. The table confirms that the primary sensing direction for all three materials is along the z-axis of the crystal as the indices experience the most change for a field applied in this direction. Both KTP and electro-optic polymer exhibit minimal cross-axis sensitivity for all three principal indices, while LiNbO 3 does not. In order to use LiNbO 3 in applications where single axis sensitivity is required, the SCOS must be configured such that n x and n y indices are not utilized. Of the materials, KTP exhibits the highest level of single-axis sensitivity. Table 4-1. Index Parameters for 1 MV/m field applied across x, y, z axes of the materials. index change ( 10-5 ) crystal cross-axis sensitivity (db) Crystal (E j =E o ) Δn xj Δn yj Δn zj Cc x Cc y Cc z LiNbO3 (E x ) LiNbO3 (E y ) LiNbO3 (E z ) KTP (E x ) E-4 <1E E-4 KTP (E y ) <1E E E-4 KTP (E z ) EO Polymer (E x ) <1E EO Polymer (E y ) EO Polymer (E z ) SCOS Sensitivity Optimization One of the key components in the sensitivity of a SCOS is the resonant wavelength shift to an applied field. As previously derived in Chapter 3, the wavelength shift is given as 52

67 λ = E inc λ ns n N 2 s 2 f r eff f E ( ε ). slab (4-18) The two primary components affecting the wavelength shift are the (1) effective electro-optic coefficient r eff and (2) the electric field penetration ratio into the slab waveguide f E (ε slab ). The result of this work is that both of these factors are increased by changing the orientation of the EO slab waveguide relative to the D-fiber. Figure 4-2 shows the two possible SCOS configurations which allow electric field detection perpendicular to the direction of the optical fiber. The first is referred to as normal SCOS configuration because it uses a z-cut slab with the sensing direction (z-axis) normal to the flat surface of the D-fiber. The SCOS demonstrated so far use this configuration. The second orientation is the transverse SCOS configuration because it uses an x-cut slab with its sensing direction transverse to the flat surface of the fiber. n s normal SCOS z transverse SCOS z z, sensing direction n s (a) (b) Figure 4-2. Two possible SCOS configurations for electric-field detection occurring orthogonal to the direction of the optical fiber. 53

68 4.2.1 Effective Electro-Optic Coefficient The procedure for determining the effective electro-optic coefficient of a SCOS is outlined in Section The coefficient is dependent on the operating polarization of light and the orientation of the crystal axes relative to the fiber. For a z-cut SCOS the largest electro-optic coefficient is obtained by operating the SCOS with TM polarized light (see Section 2.1). From Eq. 2-4 the bulk slab index n s is a combination of n z index and the index corresponding to the crystal axis in the direction of the fiber. For KTP, aligning the y-axis of the crystal to the fiber utilizes the r 23 coefficient, which is the next largest linear electro-optic coefficient after the r 33. Since polymer and LiNbO 3 are uniaxial materials, alignment of the remaining crystal axis is not necessary. Since a refractive index apart from n z is utilized for the normal configuration, a LiNbO 3 SCOS with this configuration will have poor single-axis sensitivity (see Table 4-1). The effective EO coefficients for normal KTP, polymer and LiNbO 3 SCOS are respectively 26.4 pm/v, 53 pm/v, and 19 pm/v. For the transverse slab configuration, the use of TE polarized light results in the largest EO coefficient. The optical electric field is in the z-axis of the crystal, resulting in a slab index of n s = n z and an effective electro-optic coefficient of r eff = r 33. Since only the n z index is utilized, a LiNbO 3 SCOS with transverse configuration will exhibit single-axis sensitivity. The EO coefficients for transverse KTP and LiNbO 3 SCOS are respectively 35 pm/v and 31 pm/v. Limitations in the fabrication and poling of EO polymer limit it to only z-cut, meaning a polymer SCOS with transverse orientation is not currently feasible; however for completeness, the EO coefficient of a transverse polymer SCOS would be 70 pm/v. The resulting increase in the wavelength shift due to the increase EO coefficients from the transverse configuration for KTP, polymer and LiNbO 3 SCOS are respectively 1.33x, 1.32x and 1.68x. 54

69 4.2.2 Electric Field Penetration The electromagnetic boundary conditions state that the normal component of the electric flux density and the tangential component of the electric field are equal on both sides of the boundary resulting in D slab nˆ = D inc nˆ, (4-19) and E slab tˆ = E inc tˆ. (4-20) With the z-cut EO slab the electric field being measured is normal to the boundary resulting in the electric flux density being equal across the boundary. This boundary condition causes the ratio between the electric field in the slab and the incident field, which is in air, to be given by E E slab inc 1 =, (4-21) ε slab where ε slab is the relative RF permittivity of the slab. This drop in electric field results in a decrease in the SCOS sensitivity. With the x-cut EO crystal the electric field being measured is tangential to the surface eliminating the drop in electric field (see Eq. 4-20). However, the extent of the EO crystal is small resulting in this simplistic description being inaccurate. Therefore, a two-dimensional numerical electromagnetic simulation program called Maxwell 2D from Ansoft (Canonsburg, PA) is used to attain more accurate results. Figure 4-3 shows that the electric field is created using two electrodes with 10 mm spacing and applied voltage of 100V 0-p resulting in a 10 kv/m electric field. The two slabs were oriented between the electrodes so their respective optic axes were parallel to the direction of the electric field. Both 55

70 slabs are 0.1 mm thick and 1 mm long. The analysis is two-dimensional meaning that the slabs are extruded or infinite into the plane of the paper. E slab waveguides 1 mm electrodes z z 100 µm normal slab transverse slab Figure 4-3. Model used for Maxwell 2D simulation to determine strength of E-field within normal and transverse slab waveguides. Figure 4-4 shows the results of the simulation for slab waveguides having an RF permittivity of 21 which are surrounded by air. The transverse slab configuration exhibits significantly higher field strength within the slab compared to the normal slab. Since the larger dimension of the transverse slab is oriented along the electric field, it exploits more of a tangential boundary condition allowing the electric field to penetrate further into the slab. 56

71 Figure 4-4. Electric field strength relative to position for transverse and normal slab waveguides. The simulation was repeated using different slab permittivity values to determine the electric field ratio, E slab /E inc. The electric field value used for E slab is the average of the field located at the center region of the slab, which is aligned to the core of the D-fiber (see Figure 4-2). Figure 4-5 shows the resulting ratio as a function of relative permittivity for ε r = 10 to ε r = 40. The results of the simulations are fit to functions for normal and transverse SCOS slab configurations given respectively by and f E E ε slab (4-22) E ε slab ( ) = =, inc slab f E E ε slab (4-23) E ε slab ( ) = =. inc Both of these configurations exhibit a decrease in refractive index change with an increase in permittivity. However, in all cases the transverse slab produces a larger refractive index change. slab 57

72 0.6 electric field penetration, f E (ε slab ) transverse normal slab permittivity, ε slab Figure 4-5. E slab /E inc ratio as function RF permittivity, ε slab. The electric field penetration ratios for the KTP, LiNbO 3 and EO polymer slabs were found by inserting the relative permittivity of a material in into Eqs and The increase in electric field penetration of the transverse slab configuration results in an electric field penetration improvement of 7.2x, 8.3x, and 3.1x respectively for KTP, LiNbO 3, and EO polymer SCOS Optimization Results Since the operating polarization, orientation of the slab relative to fiber, and dimensions of the slab relative to the incident field all affect the sensitivity of the SCOS, the directional sensitivity in addition to the wavelength shift of transverse and normal configurations is compared. The directional sensitivity is quantitatively determined by computing the cross-axis sensitivity of the SCOS configurations. The cross-axis sensitivity of a SCOS configuration 58

73 compares the resonant wavelength shift due to an electric field applied in the sensing direction of the crystal to the shifts for off-axis field components. The resulting sensor cross-axis sensitivity is given by Cs = λ 2 E + λ 2 x E y. λ E z (4-24) Table 4-2 compares the resonant shift for a 1 MV/m field directed in the sensing direction of the transverse and normal SCOS configurations and their respective cross-axis sensitivity. The transverse SCOS configuration improves not only the shift parameter but also the directional sensitivity of the devices, even permitting SCOS fabricated with LiNbO 3 to be used in applications requiring a high degree of directional sensitivity. Table 4-2. Pertinent SCOS parameters for 100 µm thick and 1 mm wide slab waveguides for detection of 1 MV/m fields [61, 76, 77]. EO Material sensing direction polarization n s r eff (pm/v) ε slab f ( ε ) E slab shift (m 2/ V) sensor cross-axis sensitivity (db) KTP (z-cut) normal TM KTP (x-cut) transverse TE LN (z-cut) normal TM LN (x-cut) transverse TE EO Polymer (z-cut) EO Polymer (x-cut) normal TM transverse TE Experimental Verification: KTP SCOS Configuration To verify the increase in electric field sensitivity of the transverse SCOS configuration, x- cut and z-cut KTP SCOS were fabricated and their respective optical signals were compared when subjected to an identically applied electric field. Figure 4-6 provides a block diagram of the 59

74 test setup. A signal generator with electrodes was used to produce a 3.33 kv/m, 1.05 MHz electric field parallel to the z-axes of the x-cut and z-cut KTP SCOS. function generator tunable laser PD TIA ESA electrodes z transverse SCOS z normal SCOS z, sensing direction Figure 4-6. SCOS electric field test setup consisting of tunable laser, photo detector (PD), transimpedance amplifier (TIA) and electrical spectrum analyzer (ESA). A signal generator and electrodes were used to produce an electric field across the SCOS. Since the steepness of the resonant slope also affects the SCOS signal, the input optical powers of the two SCOSs were adjusted until their resonance slopes were approximately the same. Figure 4-7 shows the corresponding transmission spectrum for the x-cut and z-cut SCOSs. The slope was calculated by stepping through tunable laser wavelengths and measuring the corresponding voltage [78]. The voltage slope ( V/ λ) was then divided by the gain G to convert it to a resonant slope as given by P 1 V =. λ G λ (4-25) Using this approach the laser was tuned to a wavelength of λ z = nm and λ x = nm for interrogation of the z-cut and x-cut SCOSs respectively. 60

75 1.2 transmission power (mw) x-cut z-cut λ z λ x wavelength, λ (nm) Figure 4-7. Transmission spectra for SCOSs fabricated using x-cut and z-cut KTP slab waveguides. Figure 4-8 shows the measured output of the ESA for both the z-cut (normal) and x-cut (transverse) SCOS with a TIA gain of 10 6 V/A and Table 4-3 contains the numeric measurements. The variation in the SCOS signals is the result of instabilities in the optical power caused by laser fluctuations. The transverse SCOS showed an increase in signal resulting in an 8.6x improvement in electric field sensitivity when compared to the normal SCOS. The improvement in signal matches the theoretical improvement in sensitivity. Table 4-3. SCOS measurements KTP crystal operating slab configuration cut polarization slope (W/m) SCOS signal (mv) normal z-cut TM 6.53E ± transverse x-cut TE 6.58E ± ratio (transverse/normal) ±

76 150 transverse SCOS signal (mv) normal frequency (MHz) Figure 4-8. AC component of electric field measurement using electrical spectrum analyzer with 100 point averaging. 4.3 Summary Several factors affect the sensitivity of SCOS, including the operating polarization, orientation of the slab relative to the fiber, and dimensions of the slab relative to the incident field. The optimal design involves using an x-cut slab with sensing direction transverse to the flat surface of the fiber. The transverse SCOS configuration not only improves the overall sensitivity but increases the directional sensitivity for SCOS fabricated with KTP, LiNbO 3, and EO polymer. In the case of LiNbO 3, a high level of directional sensitivity is only achieved with the transverse configuration. 62

77 5 FREQUENCY DEPENDENT ELECTRIC FIELD PENETRATION The sensitivity of SCOS is determined in part by the RF permittivity of the electro-optic slab. Many electro-optic materials exhibit a different permittivity value depending on the frequency of the applied electric field. This results in frequency dependent sensitivity. When using a SCOS to characterize single-frequency electric fields, the measured SCOS signal and actual electric field relationship is easily determined by calibrating the SCOS to a known field prior to testing (see Section 2.2); however, for pulsed electric fields containing mixed frequency content, the relationship between frequency and electric field sensitivity may be too complex to accurately determine the actual electric field being measured. There is need to determine the effect of frequency on the permittivity of the slab waveguide. In this chapter, the frequency response of KTP, LN, and EO polymer SCOS are tested. 5.1 Experimental Setup Figure 5-1 shows the equipment used to test the frequency response. The electric field is created using a function generator to apply a sinusoidal voltage with a peak of 10 V across electrodes spaced 2 mm apart. The frequency characteristics of the electronics limited the experiment to a frequency range of approximately 1 khz to 1 MHz. 63

78 Figure 5-1. SCOS interrogation system. Four SCOS were fabricated and tested. The first two were fabricated with t=100 µm thick KTP crystal. One used a z-cut crystal orientation and is referred to as zktp while the other one used an x-cut crystal and is referred to as xktp. The third sensor was fabricated with a t=100 µm thick x-cut LiNbO 3 crystal and is referred to as xln. The final sensor consists of a t=50 µm thick EO polymer slab and is referred to zp. In order to make an equal comparison between the four sensors only the wavelength shift was compared (see Eq. 3-6). The measured signal was divided by the photodiode responsivity (R=0.95 A/W), the gain of the TIA (G=1000 V/V), and the slope of the resonance. The slope of the resonance is measured from Figure 5-2 resulting in P/ λ zktp =0.88 mw/nm, P/ λ xktp =0.83 mw/nm, P/ λ xln =2.5 mw/nm and P/ λ xp =0.35 mw/nm. 64

79 Figure 5-2. Transmission spectra of SCOS used for frequency response characterization. 5.2 Frequency Response Results Figure 5-3 shows the measured SCOS wavelength shift as a function of frequency. Both of the KTP SCOSs exhibit a decrease in sensitivity at low frequencies because KTP exhibits high ionic conductivity along the optical crystal axis [49], resulting in the relative permittivity being frequency dependent [76, 77]. The increase in the relative permittivity causes a decrease in the index change (see Eqs. 3-3, 4-22, 4-23) resulting in a decrease in SCOS wavelength shift. Although the two KTP SCOS display a similar frequency dependence, the transverse KTP SCOS 65

80 (xktp) has a higher shift because it is less sensitive to large relative permittivity (see Figure 4-4). Unlike the two KTP SCOS the transverse LiNbO 3 SCOS (xln) and normal Polymer SCOS (zp) display negligible frequency dependent wavelength shift because in this range their relative permittivity s are fairly constant [61, 62]. Figure 5-3. Frequency dependence of wavelength shift for KTP, LiNbO 3 and Polymer SCOS. Figure 5-4 shows the frequency dependence of the relative permittivity for KTP, LiNbO 3 and Polymer. The permittivity is calculated from the measured shift (Figure 5-3) and the numerical permittivity functions (Eqs and 4-23). The two KTP slabs exhibit similar permittivity curves with values in the range of 17.4<ε slab <1001. This range of permittivity lies between the two published values [76, 77]. The discrepancies in the two KTP curves are attributed to the fact that the effects of the optical fiber and packaging, which protects the SCOS, are not considered in the simulation of the numerical permittivity functions. The relative 66

81 permittivity of LiNbO 3 and EO polymer are both fairly constant having respective permittivity values of approximately 29 and 3.96, which are consistent with the literature [67, 74]. Figure 5-4. Frequency dependence of relative permittivity for KTP and LiNbO 3 crystals. Based on the experimental results, the EO polymer SCOS has the highest wavelength shift, followed by transverse KTP SCOS; however, the KTP SCOS exhibit significant reduction in sensitivity below 300 khz. While the transverse KTP SCOS has approximately 1.6x larger wavelength shift than transverse LiNbO 3 SCOS above 300 khz, it has 3.43x less wavelength shift at 10 khz. For this reason, KTP SCOS should be reserved for measuring high frequency electric fields. If used to detect a single, low single frequency field, the sensitivity calibration must be performed at the same frequency to ensure accurate results. Since both LiNbO 3 and EO polymer have a flat sensitivity response, they are suitable for measuring mixed frequency content electric fields and neither need frequency specific calibration. 67

82 5.3 Summary The SCOS sensitivity is affected by the relative permittivity of the electro-optic slab which affects the electric field penetration into the slab. Many EO materials exhibit frequency dependent dielectric phenomena which results in frequency dependent sensitivity. Characterizing the frequency dependent sensitivity of SCOS reveals conditions in which electric field sensing measurements are accurate, especially if the frequency of the electric field being measured is different than that used to calibrate the SCOS. 68

83 6 RESONANCE TUNING FOR SELECTIVE LASER WAVELENGTH INTERROGATION The resonant wavelengths of SCOS are dependent on the thickness of the slab and the effective index of refraction of the slab waveguide. Since SCOS interrogation requires a laser with a wavelength that coincides with the edge of a resonant wavelength, differences in the thickness or orientation of the slab affect the interrogation wavelength. Commercially available electro-optic crystals have dimension tolerances on the order of 10 µm [67]. A slight change in thickness will drastically affect the interrogation wavelength. To effectively manage the wide range in potential interrogation wavelengths, a tunable laser is used for interrogation. For applications requiring simultaneous measurements of an electric field at multiple points and in multiple directions, a tunable laser for each sensor is required. This greatly increases the complexity and cost of the interrogation system. To overcome this complexity there is a need to tune the wavelength resonances of the SCOS to align all the resonances. Once tuned, multiple sensors can be interrogated with a single tunable laser. In addition, this technique allows fixed wavelength lasers to be used for SCOS interrogation. This chapter presents a method that allows precise wavelength tuning of the resonances of a SCOS by using a biaxial crystal and rotating it with respect to the optical fiber. First resonance tuning is described and demonstrated by rotating a z-cut KTP crystal relative to an 69

84 optical fiber. Then simultaneous interrogation of SCOS is demonstrated by using a single tunable laser to interrogate a two-axis electric field SCOS sensor. 6.1 Resonance Tuning The objective is to tune the SCOS resonance without changing the sensing direction of the SCOS. The tuning is attained by using a biaxial electro-optic crystal such as KTP. With KTP there are only significant changes in the indices of refraction when there is an electric field in the direction of the z-axis of the crystal (see Section 4.1). By orienting the z-axis of the crystal perpendicular to the flat surface of the D-fiber the KTP slab can be rotated about the z-axis of the crystal without affecting the sensing direction. In order to understand the effect of KTP crystal rotation, Figure 6-1 illustrates that there are two different coordinate systems. The first system is related to the EO crystal symmetry and it has axes of x, y, and z, where the corresponding EO crystal indices are n x, n y, and n z. The second coordinate system is related to the D-fiber orientation and it has directions f, t, and n, where f points in the fiber propagation direction, n is normal to the flat surface of the D-fiber, and t is transverse to the flat surface of the fiber and orthogonal to both f and n. With these coordinate systems n is parallel to z, and there is an angle φ between f and y. 70

85 Figure 6-1. Rotation of biaxial crystal on the optical fiber. For the TE mode the slab index is the refractive index corresponding to an electric field in the t direction and is given by n s n n = nt = 2 2 (6-1) n sin x x y ( ) cos ( ). 2 2 φ + n φ y The slab index for the TM mode is given by n s nnn f = 2 2 (6-2) n sin n ( ) cos ( ), 2 2 θ + n θ f where n f nxny = 2 2 (6-3) n cos x ( ) sin ( ), 2 2 φ + n φ y n n = n z, (6-4) and θ is the propagation angle of the light coupling from the fiber into the slab (see Eq. 2-3). The refractive indices for KTP are n x = 1.73, n y = and n z = [76]. Figure 6-2 show the calculated shift in the resonance λ for both TE and TM fiber modes around λ=1560 nm with a KTP slab thickness of t=112.4 µm. The resulting tuning range for the TE mode is 71

86 22.24 nm and for the TM mode it is 6.67 nm. These calculations demonstrate that the tuning behavior differs for the two modes. First, the shift in resonance wavelength for the TM mode has significantly less tuning range due to the oblique angle at which the light propagates through the slab waveguide. This results in a smaller change in the slab index and ultimately a smaller shift in the resonance wavelength as the crystal is rotated on the fiber. Despite the smaller tuning range, the TM mode is more sensitive and is thus the mode that is often used (see Section 3.2). shift, λ (nm) TM crystal rotation,φ (deg) Figure 6-2. Resonant mode shift as a function of KTP crystal rotation for TE (dashed) and TM (solid) polarization with three measured values shown with dots. TE In order to demonstrate tuning, a 100 ± 20 µm thick z-cut KTP slab was coupled to an etched D-fiber. The slab was first rotated and then shifted along the fiber until a deep resonant mode occurred. This process was repeated for several other crystal orientations. Figure 6-3 shows that pictures were taken of three different KTP crystal orientations and the corresponding transmission spectrum was measured using a broadband optical source and an optical spectrum analyzer. These three measurements are also shown as points on Figure

87 Figure 6-3. Resonant mode wavelengths of a z-cut KTP SCOS for three different crystal rotations. The top portion of the figure shows pictures of the SCOS that were used to determine the crystal rotations. 6.2 Multi-Sensor Interrogation Figure 6-4 shows the system used to interrogate n SCOS using a single tunable laser. The resonances of n-1 SCOS are tuned to match a specific SCOS, typically one that cannot be tuned without changing the sensing direction. A 1xn optical splitter couples light from the tunable laser into each sensor. Each SCOS signal is individually received by a separate photo detector. The quality of the SCOS signals are largely dependent on the power and stability of the light transmitted through each SCOS. As the optical power transmitted through each SCOS decreases, the SCOS signal-to-noise ratio also decreases. Since photo detectors are relatively inexpensive, a high performance tunable laser is the primary cost of the interrogation system. Alternatively, if all n SCOS can be tuned, the tunable laser can be replaced with a fixed wavelength laser. Instead 73

88 of tuning the resonance to match another SCOS, the resonances are tuned to match the wavelength of the laser. tunable laser 1 2 SCOS SCOS 1 2 detector detector n SCOS n detector Figure 6-4. Interrogation of multiple SCOS using a single tunable laser. 6.3 Resonance Tuned Multi-Axis SCOS To demonstrate SCOS resonance tuning a two-axis electric field sensor (nf-plane) was fabricated. Figure 6-5 shows that the two-axis sensor consists of an x-cut and z-cut KTP SCOS. The z-axis, which is the sensing direction, of the x-cut KTP slab is aligned to be parallel to the fiber, while the z-axis of the z-cut SCOS is aligned to be normal to fiber direction. The resonance of the x-cut KTP SCOS cannot be tuned because any rotation of the crystal would change the sensing direction. Therefore, the resonance of the z-cut SCOS was shifted by rotating the z-cut KTP crystal until its resonance overlaps with that of the x-cut SCOS. 74

89 longitudinal SCOS z n t f normal SCOS z z, sensing direction Figure 6-5. SCOS configuration for a two-axis electric field sensor. Figure 6-6 shows the transmission spectra for the fabricated x-cut SCOS and the z-cut SCOS before and after tuning the resonances. A resonant mode of the x-cut SCOS is located at 1559 nm, an off-resonance wavelength for the initially placed z-cut SCOS. In order to achieve overlapping resonant modes, the z-cut crystal was rotated by approximately 89 degrees, shifting the resonant mode by 6.6 nm and allowing the use of a single tunable-laser at nm for both SCOS. Figure 6-6. X-cut (dash) and z-cut (dash dot) KTP SCOS transmission spectra when the principal refractive indices of the crystals are aligned to the optical fiber and the spectrum of the z-cut SCOS (solid) after its resonant mode is tuned to overlap the x-cut SCOS. 75

90 Figure 6-7 shows the setup used to test the two-axes of the multi-axis SCOS device. The two SCOS are interrogated simultaneously using a single tunable laser and a 1x2 optical splitter to couple light into both SCOS. A function generator and high voltage amplifier connected to two planar electrodes produced an electric field with amplitude of 30 kv/m and frequency of 68 khz. The electrodes were attached to a rotating stage that allows the direction of the electric field incident on the two SCOS to continuously change. Since the optic axes of the two SCOS are not aligned, each SCOS detects a different component of the incident electric field. The power transmitted through each SCOS is received separately using two photodetectors and then amplified and converted to voltage with transimpedance amplifiers. Using two channels of the oscilloscope, the electric field components were determined by measuring the change in the voltage signal V s of each SCOS as given by V s = C E(t), (6-5) where C is the calibration factor of the SCOS that relates the received power to the electric field. Figure 6-8 shows the corresponding SCOS signals in which the data was collected at every half degree increment for 270 degrees of electrode rotation. The data is displayed in dbv to accentuate the response of the SCOS signals as the electric field direction changes. The angles at which the amplitudes of the two SCOS signals are at a maximum and minimum correspond to when the incident electric field is parallel and perpendicular to the optic axes of the slab waveguides. The measurement reveals that the z-axes of the two SCOS are not precisely orthogonal and the x-cut SCOS measuring fields in the f-axis of the sensor is marginally more sensitive to electric fields than the z-cut SCOS measuring fields in the n-axis of the sensor. Using 76

91 this information, the electric field orientation is determined for any arbitrary electric field incident on the sensors in the nf-plane. function generator HV tunable laser SCOS PD PD TIA TIA oscilloscope Figure 6-7. Testing setup used to interrogate the two-axis SCOS, where PD is the photodetector, TIA is the transimpedance amplifier, HV is the high-voltage amplifier, and OSC is the oscilloscope. If a resonance of the z-cut SCOS had not been tuned to overlap that of the x-cut SCOS, each SCOS would have to be interrogated individually, requiring two tunable lasers to acquire measurements simultaneously. Although this solution may be acceptable for some applications, it quickly becomes impractical as more sensors are added to the system. Each sensor would require an additional tunable laser, greatly increasing the complexity and cost of the system. 6.4 Summary This chapter outlines a method for tuning the resonant wavelengths of SCOS. The resonant modes are tuned by rotating the biaxial slab waveguide relative to the optical D-fiber. This allows the operating wavelength of SCOS to be adjusted to match that of another SCOS. Resonance tuning is demonstrated with a SCOS consisting of a z-cut KTP crystal as the slab waveguide. The resonances were tuned to match an x-cut SCOS in order to make a two-axis electric field sensor capable of being interrogated with a single tunable laser. 77

92 SCOS signal (dbm) fn plane nt plane electric field orientation angle (deg) Figure 6-8. Measured electric field signals as a function of incident field angle for two orthogonally placed SCOS. 78

93 7 ION TRAP ELECTRIC FIELD CHARACTERIZATION This chapter demonstrates the capabilities of SCOS for characterizing electric field profiles within radio-frequency ion traps. Ion traps use large electric fields to selectively isolate or trap ions which can be mass-selectively ejected and analyzed [79]. Recently, there has been significant effort in miniaturization of ion traps as their size reduction is often seen as the key to developing portable mass spectrometry systems [80-94]. The electric fields in conventional ion traps are generated with 3-diemensional electrode structures with complex geometries. Effective mass analysis relies on precisely-shaped electric fields. As traps are miniaturized it becomes increasingly difficult to maintain the relative accuracy of electrode geometry and alignment needed to produce these fields due to limitations in machining technology used for fabrication of the devices. Surface roughness and geometrical defects can be quite large relative to the size of the miniature traps and ultimately reduce performance [95]. One example of an alternate approach toward miniaturization of ion traps involves generating trapping fields between two planar ceramic plates [96]. Based on microfabrication technology, a series of electrode rings are lithographically patterned on the facing surfaces of each ceramic plate. The potential applied to each ring is independently-adjustable, allowing the trapping field to be modified or fine-tuned simply by changing the RF potential applied to each electrode ring. The electric field is independent of electrode geometry and can be optimized electronically. The simple geometry of planar ion traps addresses many obstacles related to 79

94 miniaturization such as geometrical defects and machining tolerances; however, the devices are still susceptible to fabrication and assembly defects which can cause suboptimal trapping fields. Problems associated with the performance of an ion trap can only be seen during operation and the cause of which are unknown without knowledge of the trapping field profiles. Therefore, there is a need to characterize the electric fields in order to verify and troubleshoot ion trap operation. This can be achieved by using an electric field sensor; however, in order to properly characterize the fields, the sensor needs to be non-perturbing, small and directionally sensitive. SCOS are suitable for characterizing fields within ion traps due to their small physical dimensions, high level of directional sensitivity and spatial localization. In this chapter, the feasibility of SCOS for measuring fields within ion traps is established by characterizing the fields within a commercially available quadrupole ion trap or Paul Trap [97]. The Paul Trap has a well-defined and documented trapping field profile. Simulated fields are compared to the fields measured with a SCOS. Then a SCOS is used to characterized more complex fields within a planar plate ion trap called a coaxial ion trap [98]. The coaxial ion trap includes both toroidal and quadrupolar trapping fields in a single mass analyzer. 7.1 Paul Trap Electric Field Characterization The Paul Trap used is a 3-dimensional quadrupole ion trap consisting of two hyperbolic metal electrodes with their foci facing each other and a hyperbolic ring electrode centered between the other two electrodes. The quadrupole ion trap assembly was taken out of a Varian Saturn GC-MS. As with other commercial ion traps, the endcap electrodes are separated 10.6% farther apart than the ideal QIT design would dictate. Figure 7-1 shows a photo of the trap with a 80

95 simulated 2-dimensional cross section of electric field profile on one side. The simulation was performed using Maxwell 2D (ANSYS, Inc.) and illustrates the operation of the trap. The structure generates a saddle-shaped field to form a central trapping region for charged ions. Ions enter and exit the trap through 1.2 mm holes located in the top and bottom electrodes. a Figure 7-1. Paul Trap structure with simulated electric field. Figure 7-2 shows a longitudinal KTP SCOS ready to characterize the axial field between top and bottom electrodes of a Paul Trap. The longitudinal SCOS is sensitive to fields in the direction of the fiber. The optical fiber of the SCOS is inserted though the holes in the top and bottom electrodes. Since the holes are 1.2 mm in diameter, a small crystal is needed in order to fit within the structure. A crystal with 0.3 mm width and 1 mm length was selected as the slab waveguide. The field within the trap was generated by grounding the top and bottom electrodes and then driving the center electrode with a function generator and high voltage amplifier. The 81

96 trap was placed on a motorized stage so that the axial field profile could be characterized by changing the spatial position of the trap relative to sensing region of the SCOS. The SCOS output was received by a photodiode, amplified and then captured using an electric spectrum analyzer. Prior to measuring the electric field within the ion trap, the SCOS was first calibrated with a known electric field generated using parallel plate electrodes. An electric field of kv/m was produced by applying a voltage of 500 V with frequency 20 khz to electrodes with a spacing of 5.65 mm. This resulted in a SCOS signal of V s =11.9 mv and a calibration factor of C=0.134 mv/(kv/m). The electric field within the ion trap is then determined by dividing the SCOS signal by the calibration factor. Figure 7-2. Setup and SCOS configuration for measuring axial field in Paul Trap. Figure 7-3 shows the SCOS signal (points) corresponding to incremental measurements of the axial field along a 20 mm section in the Paul Trap for a 500 V 0-p, 20 khz signal driving the trap. The frequency of the driving signal was selected based on the frequency response of the high voltage amplifier, which has an upper corner frequency around 60 khz. Although the 82

97 selected frequency is much lower than typically used for ion trap operation, the generated electric field profile should be the same. The measurements were taken every 0.16 mm and reveal a clearly defined trapping region at the center of the ion trap. 60 electric field (kv/m) position (mm) Figure 7-3. SCOS signal as function of axial position through Paul Trap. To verify the accuracy of the SCOS measurements, a simulation of the axial fields inside the Paul Trap was performed using SIMION (Scientific Instrument Services, Inc.). In Figure 7-3 the simulated fields for the Paul Trap (solid line) closely resemble the measured fields. Figure 7-4 shows the error between the simulated and measured fields. The error was calculated by subtracting the measured field from the simulated field. Factors believed to contribute to the error include (1) random noise, like laser power fluctuations, thermal noise in the photodetector, etc., (2) misalignment of the sensing direction of the SCOS relative to the target field, and (3) the size of the sensing region of the SCOS which deals with field localization. 83

98 5 error (kv/m) axial position, a (mm) Figure 7-4. Electric field error between simulated and measured values. Laser power fluctuations are typically small but cause the received SCOS signal to oscillate around the actual field level. In Figure 7-4, the laser fluctuations are most noticeable between -6 mm and 6 mm positions. The electric fields produced in the Paul Trap have components in multiple directions. Although the SCOS is supposed to only detect fields in a single direction, any misalignment of the crystal or fiber relative to the target field may cause the measured field to be larger or smaller than the actual field. In Figure 7-4, the average measured field is slightly larger than the simulated field which is indicative of misalignment of the sensing direction of the SCOS relative to the target field. The sensing region of a SCOS is the area of coupling between the fiber core and slab waveguide. The fiber core is only a few microns wide but coupling length may be as long as the slab waveguide. The SCOS signal produced by an external field is the average field within this region. To demonstrate how the size of the sensing region affects the accuracy of the ion trap 84

99 measurement shown in Figure 7-3, electric field profiles for SCOS with different size sensing regions are simulated by applying moving averages (with the number of averages corresponding to length of the sensing region) to the simulated field data. Figure 7-5 shows the deviation from the ideal electric field profile for simulated field profiles with 0.5 mm, 1 mm and 3 mm long sensing regions. For comparison, the field profile measured from the SCOS is also included. In all cases the deviation in the electric field dominates at the edges of the trapping region. The amount of deviation for the 1 mm long sensing region closely resembles the deviation in the SCOS measurement. This points toward the dominate source of error being due to the size of the sensing region, which for the actual SCOS is also around 1 mm. Figure 7-5. Deviation from ideal electric field for simulated profiles for SCOS with 0.5 mm, 1 mm, and 3 mm long sensing areas. (b) Error between simulated field irrespective of the size of the sensing region and for longer coupling regions. Figure 7-6 shows the maximum error as a function of the length of the sensing region. As expected, the maximum error increases as the coupling length increases. This illustrates the necessity of a small sensing region in order to have minimal measurement error. 85

100 40 maximum error (kv/m) coupling length (mm) Figure 7-6. Maximum electric field error as function of length of the sensing region. 7.2 Coaxial Ion Trap Electric Field Characterization Figure 7-7 shows the structure of a coaxial ion trap. The device is comprised of two parallel ceramic plates separated by 5.74 mm with identical concentric metal rings on their facing surfaces. RF potentials applied to the metal rings generate an electric field profile with components in both axial (between plates) and radial (extending out from the center) directions which form multiple, linked trapping regions. Figure 7-7. Coaxial ion trap components (left) and setup for SCOS measurements (right). 86

101 The potential applied to each electrode ring is controlled by a connected printed circuit board (PCB) containing capacitive voltage dividers. The value of the capacitors determine the potential of each ring. Any defects in the PCB capacitors or metal electrode rings can result in suboptimal field generation. In addition, misalignment of the ceramic plates will also affect the fields generated. The fields within this trap are measured similar to the Paul Trap; however, due to the open structure, a variety of different field profiles can be measured. To distinguish between axial (a-direction) and radial (r-direction) fields within the ion trap, two different SCOS configurations which have different sensing directions are used. Figure 7-8 shows the two configurations relative to the ion trap plates. The transverse SCOS measures axial fields and the longitudinal SCOS is used to measure radial fields. ion trap plates z transverse SCOS a r z longitudinal SCOS z, sensing direction Figure 7-8. SCOS configurations for measuring axial (a-direction) and radial (r-direction) electric fields in ion trap. The ion trap is placed on a rotation mount fixed to a motorized two axis linear stage. This enables the plates of the ion trap to be rotated and spatially adjusted in both vertical (a-direction) and horizontal (r-direction) directions relative to the SCOS. Figure 7-9 shows electric field measurement profiles captured along three different radial directions of a coaxial ion trap for a 30 khz, 500 V 0-p sinusoidal signal applied to the ion trap. 87

102 The electric field was measured using a longitudinal SCOS positioned such that it was equally spaced between the plates (a=0) and then spatially adjusted by 0.16 mm increments in the r- direction. Figure 7-9. SCOS electric field measurements along radial directions at 0º (dash dot), 35º (dash dash), and 110º (solid). 88

103 The fields in the center region of the trap are approximately the same for the three angles; however, as the fields extend out radially, the field profiles digress in both shape and amplitude. Although experimental data in [98] showed successful operation of this device, the measurements show that the radial electric fields of this ion trap are not rotationally symmetric towards the edges of the device. Reported difficulties in the mass-selective transfer of ions form the toroidal to the quadrupolar trapping region, or the limited mass resolution reported, may be due to these measured deviations. Figure 7-10 shows an axial electric field profile measured using a transverse SCOS positioned at the center of the plates (r=0) which is spatially adjusted by 0.01 mm increments in the a-direction. This measurement matches the expected axial field profile of the trap at this position based on earlier simulations [98]. 80 axial electric field (kv/m) axial position, a (mm) Figure SCOS measurements of axial field along axial direction at center of ion trap (r = 0). Figure 7-11 shows a measured 2D electric field profile of the axial field along both the axial and radial directions. Measurements were taken at 0.01 mm increments in the a-direction 89

104 and mm increments in the r-direction. The measurements shows the presence of several trapping regions, or regions where the field is at a minimum; however there are some deviations in axial symmetry of fields, further indicating potential problems the trap my exhibit while trapping ions. These deviations are indicative of errors in the lithographic patterning and microfabrication used to make the device. Figure SCOS measurements showing axial field along axial and radial directions at 0 deg. 7.3 Summary The measurements show that SCOS offer a feasible method for characterizing the electric field profiles within ion traps. Measurement of the fields offers insight into the functionality of traps which is not obtainable solely by performing simulations. SCOS are suited for making these measurements due to their small physical dimensions, high level of directional sensitivity and minimal perturbation of the target fields. Although it is beyond the scope of this work to make correlations between measured electric field profile anomalies and problems associated with the operation of ion traps, it is clear that SCOS provide a valuable new tool for obtaining new information about the fields within ion traps. 90

105 8 OTHER CONTRIBUTIONS This chapter focuses on minor contributions toward SCOS technology and work unrelated to SCOS. Section 8.1 deals with SCOS interrogation and calibration and discusses an automated technique for determining the optimal interrogation wavelength of a SCOS. Section 8.2 presents an analysis of multi-axis sensing with SCOS and a method for determining electric field orientation using a sensitivity matrix. Section 8.3 presents a system for high-speed fullspectrum interrogation of fiber Bragg gratings. 8.1 SCOS Calibration. Since the resonant wavelength locations of a SCOS are sensitive to changing environmental effects (see Section 2.4), the SCOS may need to be calibrated prior to each use. The calibration involves identifying the interrogation wavelength with the best sensitivity and the relationship between the SCOS signal and an electric field. There are several possible techniques which can be used to calibrate the SCOS. One such method involves viewing the SCOS signal at different laser wavelengths while an electric field is applied to the SCOS. A function generator is used to produce a single-frequency electric field applied across the SCOS while an electric spectrum analyzer captures the SCOS signal. The ESA allows a smaller field to be used for calibration as it can easily distinguish the field from noise as 91

106 it analyzes the frequency content of the signal. However, the use of a function generator and ESA is burdensome for field testing. This section demonstrates an automated method for SCOS calibration which is optimized for field testing. The equipment necessary for calibration is reduced by utilizing the sound card from a laptop computer to act as both function generator and electrical spectrum analyzer System Description The basic process for laser calibration is straightforward and involves (1) applying a single frequency sinusoidal electric field to the SCOS, (2) tuning the laser to a particular wavelength, (3) measuring the SCOS signal, and (4) determining the amplitude of the sinusoidal SCOS voltage signal. This process is repeated across the desired wavelength band and the optimum wavelength is the one that has the largest signal. In order to automate the laser calibration the tuning of the laser wavelength and the measurement of the SCOS amplitude needs to be controlled by a computer. In addition, it is advantageous to reduce the size of the required equipment to facilitate field testing. The additional equipment must perform the following functions: create the electric field, extract the SCOS amplitude, and control and record the data Calibration Setup In order to simplify the calibration electronics, both the electric field generation and the SCOS detection are performed using a standard laptop. Figure 8-1 shows a block diagram of the calibration setup. 92

107 electrical connection laser COM Port electrodes tunable laser SCOS CPU (LabVIEW) speaker out HV computer mic in 1 kω PD Figure 8-1. Laser calibration setup block diagram. A discretely tunable laser with a minimum wavelength of nm, a maximum wavelength of nm, and a step size of 0.2 nm is interfaced with the laptop using COM port. The computer produces a pure sinusoidal tone in the audible frequency range using the speaker output port of the computer. The sinusoidal voltage signal is then amplified using a fixed gain voltage amplifier. The sinusoidal voltage is connected to electrodes on both sides of the SCOS to create a known electric field around the SCOS. This field is detected by monitoring the power transmitted through the SCOS using the photo-detector with a resistor to convert the signal from a current to a voltage. The voltage is then recorded using the microphone input port of the computer. Rather than use the built-in audio capabilities of the laptop, an external sound card was used for improved performance. The Soundblaster X-Fi Surround 5.1 Pro USB that was used has a 24-bit resolution and a 96 khz sampling rate, as opposed to the 16-bit/48 khz specifications of standard computer audio cards. The higher amplitude-resolution is recommended in order to more accurately analyze the calibration data. 93

108 Calibration Program After setting up the equipment, the laptop controls the laser calibration using a LabVIEW program. The program plays a sinusoidal tone to create an electric field of a specific frequency using the sound card, amplifier, and electrodes. The program then records the SCOS measurement and determines the amplitude of the signal at the peak frequency by performing an FFT. The procedure is then repeated for all desired wavelengths of the laser to identify the laser wavelength which results in the SCOS signal with the highest amplitude. Once the optimal interrogation wavelength is determined, the relationship between the SCOS signal amplitude and the electric field is determined by using a calibration factor. The calibration factor is simply the ratio of the SCOS signal and the known electric field Calibration Results Figure 8-2 shows the SCOS signal spectrum compared to the transmission spectrum of a KTP SCOS. The calibration was performed for the entire laser spectrum from nm to nm with a step size of 0.2 nm. In this calibration test the sound card and amplifier created a voltage signal of V = sin(2π 10 4 t) V. This voltage was then applied to electrodes with a separation of 3 mm resulting in an applied electric field of E = V d = sin(2π 104 t) kv m. (8-1) The program reported that the optimal wavelength was nm. It took approximately 30 minutes to perform a complete calibration involving every possible wavelength of the laser. 94

109 SCOS transmission (V) SCOS Signal (mv) wavelength (nm) Figure 8-2. The waveform produced by the calibration program. The program was set up to test each wavelength of the tunable laser (0.2 nm step size), and took approximately 30 minutes to complete. The time can be reduced by limiting the range of wavelengths or increasing the wavelength step size. If the wavelength step size is increased, the program may step over the optimal wavelength in the calibration process, especially for SCOS with narrow resonance width. Since the optimal wavelength for interrogation of the SCOS is found, the calibration factor for that wavelength is then calculated as C = mv/(kv/m) Summary There are several benefits to using this laser calibration technique. It requires less equipment for field testing and since it is automated, the measurements can be made with less 95

110 user interaction. The key concept behind the laser calibration is using a standard computer sound card for both the creation of the electric field and detection of the SCOS voltage signal. 8.2 Multi-axis Sensing This section presents the development of a three-axis SCOS device used for mapping the direction and strength of electric fields. First, the design and fabrication of a three-axis sensor is demonstrated. This is followed by a mapping technique which uses a sensitivity matrix to extract orthogonal field components of an arbitrarily directed field from the three-axis sensor. Last, the accuracy of the mapping technique is analyzed Design and Fabrication Three SCOS configured to have orthogonal sensing directions can be used to determine the direction and amplitude of an arbitrary electric field by having each sensor detect one of the three electric field components (see Section 4.1). Figure 8-3 shows one configuration using three SCOS devices. In this configuration, a longitudinal SCOS with an x-cut crystal having sensing direction parallel to the fiber is used in conjunction with two normal SCOS with z-cut crystals in order reduce the physical dimensions of the sensor. 96

111 longitudinal SCOS n z t f normal SCOS z normal SCOS z z, sensing direction Figure 8-3: Setup of a three-axis SCOS using x-cut KTP in a longitudinal SCOS configuration. Figure 8-4 shows a photograph of an actual three-axis sensor. The three-axis sensor consists of an x-cut KTP SCOS, a z-cut KTP SCOS, and an electro-optic polymer. The electrooptic polymer was used to demonstrate the ability to mix different sensing materials. The three sensors are packaged separately in FR4 board. The separate packaging allows sensors to be easily replaced if one sensor breaks or if a different sensor type is required. Figure 8-4: A photograph of a 3-axis SCOS sensor. 97

112 8.2.2 Mapping SCOS Signal to Electric Field The technique for determining the electric field magnitude and direction from the three SCOS signals involves generating a sensitivity matrix. The sensitivity matrix contains the calibration factors for each of the three SCOS and their sensitivity to orthogonal electric field components E t, E f, E n. The matrix is found by first determining the individual coordinate system of each SCOS, dictated by the orientation of the crystal axes, in relation to a global coordinate system which defines the electric field. Figure 8-5 shows the four coordinate systems. Figure 8-5: Four coordinate systems for the multi-axis SCOS. If each individual SCOS coordinate system is perfectly aligned to one of the global coordinate system axes then the mapping is simple. As an example, the sensitivity matrix for the orthogonal configuration in Figure 8-5 would be C C C 3 E t E f V 1 V 2 =, (8-2) E n V 3 resulting in an electric field mapping of E t = V 1 C 1, E f = V 2 C 2, and E n = V 3 C 3, where V i is the measured voltage and C i is the calibration factor for the i th SCOS. 98

113 In practice the sensing direction of each SCOS will not totally be orthogonal to each other. In order to accommodate this discrepancy, each of the three sensing directions (z 1, z 2, and z 3 ) is defined by a unit vector using the global coordinate system. Figure 8-6: Unit vectors for the three optic axes relative to the global axes. When the t global axis is used as the reference vector then the unit vector for the first SCOS is defined as s 1 = 1t + 0f + 0n, (8-3) where t, f, and n, are the unit vectors in the global coordinate directions. Figure 8-6 shows that the global coordinate system can be configured such that the unit vector for both the first and second SCOS both lie within the tf-plane resulting in 99

114 s 2 = s 2t t + s 2f f + 0n, (8-4) where s 2 2t + s 2 2f = 1. Figure 8-6 also shows that the final unit vector can have components in all three direction and is given by s 3 = s 3t t + s 3f f + s 3n n. (8-5) The unit vectors in combination with the calibration factors are used to create a sensitivity matrix that is used to solve the vector representing the electric field as given by C E t V 1 C 2 s 2t C 2 s 2f 0 E f = V 2, (8-6) C 3 s 3t C 3 s 3f C 3 s 3n E n V 3 where V 1, V 2, and V 3 are measured signals, C 1, C 2, and C 3 are the calibration factors, and E t, E f, and E n are the estimated electric field components. The unit vectors that correspond to the optic axis for the three electro-optic crystals (s 1, s 2, s 3 ) are determined by making three different angle measurements. Figure 8-7 shows the configurations used to make each of the angle measurements. In each of the measurements the multi-axis SCOS is aligned such that the rotation axis of the test set-up is parallel to one of the SCOS axes. The SCOS produces a maximum voltage when the electric field is aligned with the SCOS unit vector and a minimum when it is perpendicular. Therefore, by simultaneously measuring the normalized voltage for the first and second SCOS, the angular difference between their unit vectors (labeled as α in Figure 8-7) was determined by simply finding the angular difference between the two maxima or finding the angle offset between the maximum of one and the 100

115 minimum of the other. This process is repeated for the other SCOS configuration until all the unit vectors are determined. s 1 α t s 2 f s 3 β n t s 3 γ s 2 n f s 3 s 2 s 1 s 1 (a) (b) (c) Figure 8-7. Illustration of the measurement configuration with the unit vector of the third SCOS aligned to be parallel to the rotation axis of the test set-up. The thick black lines correspond to the parallel plate electrodes. The unit vectors are determined from the three angular measurements by using dot products between the unit vectors resulting in and s 1 s 2 = cos α, (8-7) s 1 s 3 = cos β, (8-8) Equations 8-7 to 8-9 can be combined with Eq. 8-5 to yield s 2 s 3 = cos γ. (8-9) s 2t = cos α, (8-10) s 2f = 1 s 2 2t, (8-11) s 3t = cos β, (8-12) 101

116 s 3f = cos γ s 2ts 3t s 2f, (8-13) and s 3n = 1 s 2 3t s 2 3f. (8-14) Figure 8-8 shows the normalized voltage measurements for SCOS 1 and 2 as a function of field angle. In this measurement the angle offset (the distance between a maximum and a minimum) is used because it requires a smaller range of measurement angle. In the sensor used the measured unit vector separation angles are α=87º and β=81º. The packaging method used resulted in γ being smaller than the resolution this test is able to detect so it is approximated with γ =90 o. The resulting calibration factors of the three SCOS are C 1 = 2.5 mv kv/m, C 2 = 0.12 mv kv/m, and C 3 = 0.84 mv kv/m. 1 maximum signal at 51º normalized SCOS signal offset angle = 3º minimum signal at 54º electric field orientation angle (deg) Figure 8-8: The normalized voltage as a function of angle for (solid) SCOS 1 and (dashed) SCOS 2. The difference between the maximum of sensor 1 and the minimun of sensor 2 is the angle offset. 102

117 The unit vectors for the three optic axes are obtained from α, β, and γ resulting in s 1 = 1t + 0f + 0n, (8-15) s 2 = f + 0n, and (8-16) s 3 = 0.156t + 0f n. (8-17) The unit vectors in combination with the calibration factors are used to form the sensitivity matrix, which becomes E t E f = E n V 1 V 2 V 3, (8-18) where the measured voltages are in units of mv and the electric fields are in units of kv/m Multi-Axis Accuracy The error for each of the two rotations was determined to know how accurately the multiaxis sensor predicts the direction of a three dimensional electric field. In each test the field was detected by two of the sensors and only noise was detected on the output of the third sensor. The tangent of the two vectors was taken to determine estimated field direction and compared to the angle of the actual field direction to determine the error in the angle. Figure 8-9(a) shows the error in the predicted angle for the tf-plane field test and Figure 8-9(b) shows the error for the tnplane test. 103

118 angle error (deg) angle error (deg) electric field orientation angle (deg) electric field orientation angle (deg) (a) (b) Figure 8-9. (a) Angle error with the electric field applied in the tf-plane. (b) Angle error with the electric field applied in the tn-plane. For the tf-plane test the average absolute error is 1.26º with a standard deviation of 1.82º. For the tn-plane test the average absolute error was 1.11º with a standard deviation of 1.51º. The sensors are more accurate over the areas where multiple sensors detect the electric field. When the electric field is in a direction where one sensor is close to the measurement noise floor the error increases. This can be seen in Figure 8-9 where the error increases at the extremes. If the detection band is limited to 20 o <θ<70 o then the average error becomes 0.89 o for the tf-plane measurement and 0.41 o for the tn measurement Summary A multi-axis electric field sensor is created using three SCOS sensors with respective sensing directions at orthogonal orientations. A sensitivity matrix is calculated in order to map the three SCOS measurements from an arbitrarily oriented electric field into three orthogonal field components. A fabricated three-axis sensor was able to detect electric field direction with 104

119 an average error of less than 1.5º. The size of the sensor was kept compact by using x-cut KTP which has a sensing direction parallel to the direction of the fiber. 8.3 High Speed Full Spectrum Interrogation of Fiber Bragg Gratings Fiber Bragg gratings (FBG) sensors are useful for static and dynamic event monitoring which make then suitable for a wide variety of applications [99-103]. Dynamic interrogation of FBG sensors has primarily been performed using peak-tracking methods that have repetition rates approaching the megahertz range [104]. However, tracking the variations in the peak response of a FBG sensor reflection spectrum can result in inaccurate measurements. For example, when under the influence of vibrations, acoustical noise, and transverse strains FBG sensor spectra associated with impact and vibrations not only have peak shifts, but the reflection spectrum can exhibit dramatic spreading or even peak splitting [ ]. This section describes the development and testing of an FBG interrogator that measures the FBG reflection spectrum at a high repetition rate. After a description of the system and a discussion of the limitations on the repetition rate, experimental results from two dynamic strain events are shown. These tests are of a woven carbon fiber composite and an electromagnetic railgun System Description Figure 8-10 shows a block diagram of the interrogation system. A broadband spectrum is produced using an erbium amplified spontaneous emission (ASE) source and amplified with an erbium-doped fiber amplifier (EDFA). The amplified broadband signal passes through a 50/50 splitter to a FBG sensor. The portion of the spectrum that is reflected by the FBG returns through 105

120 the splitter to a MEMS optical filter/photodiode package. The electrical current produced by the filter/photodiode package is amplified using a transimpedance amplifier (TIA). The time-varying amplified electrical signal is then captured using a high-speed analog-to-digital converter (ADC). interrogator ASE source EDFA ADC TIA MEMS filter/ photodetector FBG function generator Figure Block diagram of interrogator. The basic operation of the interrogator can be divided into three main parts. (1) An optical filter with a time-varying transmission wavelength. (2) Electronics to amplify and save the time-varying optical power transmitted through the filter. (3) Post-processing to convert the time-varying optical power into a time-varying wavelength spectrum Electronic Components The MEMS filter/photodiode component used in the system is made by Nortel Networks. The filter is a Fabry-Pérot (FP) cavity composed of two thin film reflective membranes separated by a small air gap. The cavity reflects all wavelengths except for a narrow band with a width of approximately 60 pm [108]. The specific wavelength associated with the transmission band depends on the distance separating the two membranes. This distance is controlled by applying a 106

121 voltage in the range of 0 32 V. Figure 8-11 shows the measured transmission wavelength of a filter as a function of applied static voltage over a portion of its range MEMS transmitted wavelength (nm) applied voltage (V) Figure MEMS filter static response. In the current system the transmission wavelength of the tunable filter is swept by applying a sinusoidal voltage. At each instance in time a particular voltage is applied to the tunable filter resulting in the transmission of a narrow wavelength spectrum. Since the filter only transmits a narrow spectrum, the filter performs a sampling of the reflection spectrum of the FBG sensor system as the voltage is swept. The time-varying optical signal is converted into a current by the photodetector that is integrated with the tunable filter package. The current signal is amplified with a TIA that has a gain of 1000 V/A. The voltage is then digitized and saved using a Compuscope ADC card produced by Gage (Lockport, IL). The ADC card has 14-bit sampling and an acquisition rate of 107

122 100 Msamples/s. The ADC attains a high acquisition rate by storing the data in the 64 Msamples of memory on the ADC card and then downloading the data after the testing is complete Post-Processing The objective of the post-processing is to convert the time-varying optical power transmitted through the optical filter into a time-varying wavelength spectrum. The postprocessing can be divided into three primary areas that include (1) tunable filter characterization, (2) data processing, and (3) data filtering and visualization Filter Characterization In order to convert the time-varying optical power into a time-varying wavelength spectrum, the system needs to be characterized to determine the time-varying transmission wavelength of the tunable filter. The inertia of the thin film membranes within the tunable filter causes the wavelength range shown in Figure 8-11 to change with the frequency of the applied driving voltage. The total wavelength-sweep of the tunable filter decreases with an increase in the frequency of the driving voltage. In addition, there is also a delay between the driving voltage and the corresponding transmission wavelength of the filter. This delay is more significant at high frequency. Rather than characterize the filter response (transmission wavelength versus voltage) a calibration routine is used to determine the wavelength of light that is transmitted by the filter at any point in the sampled data. In steady state this allows us to make a direct correlation between time and wavelength. In order to calibrate the high-speed interrogator, a tunable laser is substituted for the broadband source/fbg setup. The laser power only reaches the photodetector when the transmission peak of the filter corresponds to the wavelength of the incident laser. 108

123 Therefore, wavelength response can be directly correlated with time relative to the sinusoidal driving voltage. The first step is to determine the desired wavelength range of the interrogator. The wavelength range is adjusted by changing the DC value and AC amplitude of the driving voltage. This range is typically determined by the particular FBG used and the total strain anticipated during the test. The minimum wavelength is set by increasing the wavelength of the tunable laser until a peak appears in the signal for each period of the driving voltage. The maximum wavelength is fixed by increasing the wavelength of the tunable laser until the peaks disappear. Once the wavelength boundaries are determined, the tunable laser wavelength is varied in 0.1 nm increments. Figure 8-12 shows driving voltage and three data sets that are captured with the laser tuned to different wavelengths. There are two peaks for each period of the driving voltage. Each peak represents an instance when the filter transmits the wavelength used by the tunable laser. For each pair of peaks in these images, the left-most peak occurs in response to the rise of the function generator voltage, while the right-most peak is in response to the voltage falling. As the wavelength increases the first peak in the pair shifts toward the left, and the second peak in the pair shifts to the right. The first image in figure 3 shows the driving voltage as a function of time. The next three images show how the various peaks are integrated together to create a mapping between the wavelength and the ADC sample number and Figure 8-12(e) shows the resulting mapping. It should be noted that if there were no delay between changes in the function generator voltage and changes in plate separation in the FP MEMS filter then each pair of peaks would be centered at the local maximum of the function-generator signal. Because there is a delay the peaks are centered at a point about 350 samples later, a time delay of 3.5 microseconds. The 109

124 frequency-dependent filter response and the delay reinforce why a steady-state driving voltage works better than an approach that requires the filter to settle. (a) (b) power voltage λ=1544.6nm (c) (d) power power λ=1547.8nm λ=1551.1nm (e) wavelength samples Figure (a) The voltage applied to the tunable filter. The time-varying optical power with the tunable laser adjusted to (b) nm, (c) nm, (d) and nm. (e) The time-varying wavelength response of the tunable filter Data Processing The objective of the data processing is to convert the time-varying optical power into a time-varying wavelength spectrum. Figure 8-13(a) shows a representative graph of the measured 110

125 time-varying optical power. The time-varying optical power is combined with the timewavelength mapping shown in Figure 8-12(e). Each decreasing portion of the wavelength (shown as a solid line in Figure 8-13(b)) is combined with the corresponding time-varying power to produce a wavelength spectrum shown in Figure 8-13(c). Each of these wavelength spectra are associated with the average time over which the data is collected. This process assumes that the FBG spectrum is essentially constant over the small time interval. wavelength power t 1 t 2 t 3 wavelength Figure The generation of the time-varying wavelength spectrum. (a) The measured time-varying optical power is combined with (b) the wavelength-time mapping to construct (c) individual wavelength spectrum. The repetition rate of the measurement is essentially the frequency of the applied driving voltage. The number of wavelength points within each spectrum is given by ADC sampling rate points =η, voltage frequency (8-19) where η is around 0.4 and comes from the fact that only the decreasing portion of the wavelength mapping is used and a certain portion of the region is not used near the top and bottom of the 111

126 sine wave where it is flat. Therefore, there is a trade-off between the number of wavelength points and the repetition rate of the measurement. Furthermore, the wavelength points are not equally spread over the entire spectrum because of the nonlinear shape of the sine wave. The limited number of wavelength points in a spectrum limits either the total wavelength span of the measurement or the wavelength resolution. Table 8-1 shows the measured response of the tuned filter used in this work with a driving voltage of 5 V. As expected, both the maximum wavelength range and the number of data points per spectra depend on the frequency of the function generator used to drive the tunable filter. If the interrogator is used to cover the maximum wavelength span then there will be a decrease in the wavelength resolution as indicated in Table 8-1. Frequency (khz) Table 8-1. Measured spectral response of the filter. Wavelength Range (nm) Data Points Mid-spectrum Wavelength Resolution(pm) Midspectrum Strain(µε) The objective of this interrogation system is to be able to measure FBG that have nonuniform strain resulting in the need to measure the entire reflection spectrum. However, for reference, if the FBG experiences uniform strain the relationship between strain and wavelength resolution is 1.2pm/µε [109]. Table 8-1 shows the corresponding strain resolution if the filter is made to cover its maximum wavelength range. If a high resolution is desired then the wavelength range can be decreased by simply lowering the driving voltage. 112

127 Data Filtering and Visualization Figure 8-14(a) shows that the measured time-varying signal has periodic noise. The source of this noise is not known; however, it is likely due to the close proximity of the function generator to the MEMS filter. At any rate, because of its periodic nature the noise appears to be artificial and it can be reduced dramatically by using simple digital filtering algorithms. Figure 8-14(b) shows the same data after using a second-order Chebyshev stop-band filter. The numerical filter was applied to each data set prior to processing the time-varying data described in the previous subsection. It preserves the essential features of the spectrum, but eliminates the artificial noise. (a) (b) sample number Figure (a) The time-varying optical power transmitted through the tunable filter. (b) The time-varying signal with the periodic noise eliminated. The processed data is organized into a matrix in order to visualize the time progression of the spectrum during the impact event. Each column of the matrix corresponds to a specific point in time relative to the beginning of the spectral sweep, and the rows of the matrix each represent one spectral sweep. Figure 8-15 shows the combined individual wavelength spectra after they are converted into false-color representations and cascaded together to produce a time-varying response of the event. The horizontal axis shows time and the vertical axis denotes the 113

128 wavelength. The spectral peaks are shown in red and dark blue corresponds to wavelengths at which little or no reflected light occurs. Figure False-color mapping of the time-varying wavelength spectrum Experimental Results Two tests were conducted to demonstrate the capabilities of the FBG interrogator system. For both tests data was recorded with interrogator driving frequencies of around 100 khz and the driving voltage was adjusted to cover the desired wavelength range. In the first test a FBG was embedded into a 24-layer woven graphite fiber epoxy laminate specimen. The FBG was placed 16 mm from the point of impact and embedded at midplane. The specimen received multiple strikes from the impact head in a drop tower facility described in [110, 111]. The sample was impacted with an energy of 11.6 J. Data was recorded for each successive strike until the composite specimen was perforated by the impact head. Fullspectral interrogation of the embedded FBG was performed for each strike using the newlydeveloped high-speed full-spectrum system. In this test the driving voltage was set to have a frequency of 100 khz, the DC value and AC amplitude were adjusted to cover the wavelength range of 1544 nm to 1552 nm, the ADC had a sampling rate of 100 Msamples per second, and 114

129 the measurement consisted of 431 points per wavelength spectrum giving a wavelength resolution from 28 pm near the center of the spectrum (λ=1548 nm) to 5 pm near the edges. For reference, if the strain is uniform this wavelength resolution corresponds to a strain resolution of 23 µε near the center of the spectrum and 4 µε near the edges. Figure 8-16 shows a progression of false-color images depicting the spectral response of the embedded FBG as it experiences strikes throughout the test. The top image shown corresponds to strike 4 and the bottom image corresponds to strike 86, just before failure of the composite. Figure The progression of the full spectral response for various strike numbers. 115

130 The high-speed full spectral interrogation makes clear several important features in this particular sample. (1) The relaxation time of the response increases dramatically as the material approaches failure. (2) The initial strikes show that the strike causes a compression of the fiber (shifts to shorter wavelengths), while later spectra indicate that the strikes create tension in the grating. (3) The spectrum becomes wider as the number of strikes increases; this is true in the transient case and in steady state. (4) A multiple-peak complex spectrum is evident on every strike, but becomes more pronounced as the strike number increases. Figure 8-17 shows the spectrum for strike 8, which compares peak detection with fullspectrum imaging. The false-color image is the full-spectrum display while the black line tracks the peak of the reflection spectrum wavelength (nm) time (ms) Figure Normalized FBG reflected intensity during impact 8. The black line shows the location of the point of highest intensity in FBG reflection for each scan. In the false-color image the reflection band of the FBG can be clearly seen to broaden and split into multiple peaks, a phenomenon that is only detectable using full-spectrum interrogation. In contrast, peak-tracking shows the progression of only the most prominent 116

131 reflected wavelength. The peak location marked in black shifts less than 1 nm away from the steady-state Bragg wavelength, but the full-spectrum image shows that some portion of the sensor shifts by 2 nm or more, indicating nearly twice as much compressive strain. In this situation full-spectrum interrogation is necessary in order to fully characterize the stresses on the sensor, and peak-tracking methods provide only an incomplete picture. Figure 8-18 demonstrates advantages of high-rate sampling of the FBG spectrum. The top image shows the spectral response of 100 khz. The remaining images are down-sampled to simulate the spectral plots that would have appeared if the driving speed were 10, 5, 2, 1, and 0.5 khz, respectively. This figure shows clearly for this particular arrangement that a full spectrum sampling rate of 500 Hz would show rough changes in relaxation time, but would be wholly inadequate for determining peak splitting and details in the transient response. Similarly, as the interrogation rate increases more spectral and temporal details emerge. However, the figure also indicates for this particular material system that a 10 khz repetition rate might be adequate to observe the important features of the response. This means for any particular system one may choose a lower repetition rate to increase the spectral resolution or conserve on memory or processing time. 117

132 Figure Down-sampled images from 100 khz to 0.5 khz. The other test used a railgun as a demonstration platform because it has high speed events with large amounts of strain. Figure 8-19 illustrates how the two FBG sensors were attached side by side on the positive rail of an electromagnetic railgun located at NRL. The railgun tests were performed with rectangular bore geometry, 1 MA of current supplied to the rails and the armature moving at 1.5 km/s along the rail. 118

133 armature conducting rail travel direction to interrogator FBG sensors conducting rail Figure FBG placement on positive rail. Figure 8-20 shows the spectral response of the two FBGs as the railgun fires. The driving voltage was set to a frequency of 101 khz and wavelength range of 1540 nm to 1546 nm which resulted in an average wavelength resolution of 18 pm and a strain resolution of 15µε. The spectral response of the FBGs is stable until the armament is near the point on the rail where the FBGs are located. As expected, the FBG near the bore experiences compression while the FBG away from the bore experiences tension indicating a bending wave. Even though the strain should be fairly uniform, Figure 4c shows that the reflection peak exhibits a split. Thus, a peak tracking FBG interrogation system could potentially produce erroneous results. Further investigation would be needed to determine the cause of the peak splitting. An electromagnetic railgun measurement was also done at a repetition rate of 300 khz. The basic shape of the collected data was essentially the same, resulting in a reduction in the strain resolution. The trade-off between wavelength resolution and repetition rate results in the need to vary the repetition rate around the specific test. 119

134 Figure Spectral response of two FBGs on positive rail Summary The test data shows that high-speed full spectral interrogation of FBG sensors offers a wide range of data that is not available using standard high-speed peak tracking of FBG spectra. Strain applied to an FBG may result in spectral features much more complicated than simply a shift in the peak wavelength. In fact, merely tracking peaks in wavelength can give ambiguous results when the spectral response has multiple peaks of similar height. The interrogation system is made possible by using a high-speed MEMS tunable filter driven by a sinusoidal steady state signal. This is in contrast to other interrogation systems that perform dynamic real-time peak tracking. The combination of these two innovations is required to take reliable data at over 100 khz. Although it is beyond the scope of this work to identify particular failure modes or to make correlations between spectral evolution and end of life predictions, it is clear that the richness of high-speed full-spectral measurement provides a valuable new source of data about structures as they respond to transient events. 120