Fundamentals of Optical Fiber Sensors

ZUJIE FANG is a Professor at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. KEN K. CHIN is a Professor of Physics at the New Jersey Institute of Technology. His research interests include infrared imaging sensing and device physics. RONGHUI QU is a Professor at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. HAIWEN CAI is a Professor at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences.

• Preface xi1 Introduction 11.1 Historical Review and Perspective 11.2 Classifications of Optical Fiber Sensors 31.3 Overview of the Chapters 6References 82 Fundamentals of Optical Fibers 102.1 Introduction to Optical Fibers 102.1.1 Basic Structure and Fabrication of Optical Fiber 102.1.2 Basic Characteristics 122.1.3 Classifications of Optical Fibers 17 2.2 Electromagnetic Theory of Step-Index Optical Fibers 182.2.1 Maxwell Equations in Cylindrical Coordinates 192.2.2 Boundary Conditions and Eigenvalue Equations 232.2.3 Weakly Guiding Approximation, Hybrid Modes, and Linear Polarized Modes 262.2.4 Field Distribution and Polarization Characteristics 292.2.5 Multimode Fiber and Cladding Modes 352.2.6 Propagation of Optical Pulses in Optical Fibers 392.3 Basic Theory of the Gradient-Index Optical Fiber 422.3.1 Ray Equation in Inhomogeneous Media 422.3.2 Ray Optics of GRIN Fiber 462.3.3 Wave Optics of GRIN Fiber 512.3.4 Basic Characteristics of Gradient Index Lens 562.4 Special Optical Fibers 572.4.1 Rare-Earth-Doped Fibers and Double-Cladding Fibers 572.4.2 Polarization Maintaining Fibers 602.4.3 Photonic Crystal Fiber and Microstructure Fiber 64Problems 69References 713 Fiber Sensitivities and Fiber Devices 763.1 Fiber Sensitivities to Physical Conditions 763.1.1 Sensitivity to Axial Strain 773.1.2 Sensitivity to Lateral Pressure 783.1.3 Bending-Induced Birefringence 833.1.4 Torsion-Induced Polarization Mode Cross-Coupling 873.1.5 Bending Loss 913.1.6 Vibration and Mechanical Waves in Fiber 953.1.7 Sensitivity to Temperature 963.2 Fiber Couplers 973.2.1 Structures and Fabrications of 2×2 Couplers 983.2.2 Basic Characteristics and Theoretical Analyses of the Coupler 993.2.3 N×N and 1×N Fiber Star Couplers 1103.2.4 Coupling in Axial Direction and Tapered Fiber 1143.3 Fiber Loop Devices Incorporated with Couplers 1183.3.1 Fiber Sagnac Loops 1183.3.2 Fiber Rings 1263.3.3 Fiber Mach–Zehnder Interferometers and Michelson Interferometers 1313.3.4 Fiber Loops Incorporated with 3×3 Couplers 1353.4 Polarization Characteristics of Fibers 1423.4.1 Polarization State Evolution in Fibers 1423.4.2 Basic Characteristics of Polarization Mode Dispersion 1543.4.3 Spun Fiber and Circular Birefringence Fiber 1573.4.4 Faraday Rotation and Optical Activity 1593.5 Fiber Polarization Devices 1623.5.1 Fiber Polarizers 1623.5.2 Fiber Polarization Controller 1653.5.3 Fiber Depolarizer and Polarization Scrambler 1663.5.4 Fiber Optical Isolator and Circulator 170Problems 172References 1744 Fiber Gratings and Related Devices 1834.1 Introduction to Fiber Gratings 1834.1.1 Basic Structure and Principle 1834.1.2 Photosensitivity of Optical Fiber 1864.1.3 Fabrication and Classifications of Fiber Gratings 1904.2 Theory of Fiber Grating 1944.2.1 Theory of Uniform FBG 1944.2.2 Theory of Long-Period Fiber Grating 2024.2.3 Basic Theory of Nonuniform Fiber Gratings 2084.2.4 Inverse Engineering Design 2144.2.5 Apodization of Fiber Grating 2194.3 Special Fiber Grating Devices 2224.3.1 Multisection FBGs 2224.3.2 Chirped Fiber Bragg Grating 2334.3.3 Tilted Fiber Bragg Gratings 2364.3.4 Polarization Maintaining Fiber Gratings 2434.3.5 In-Fiber Interferometers and Acoustic Optic Tunable Filter 2464.4 Fiber Grating Sensitivities and Fiber Grating Sensors 2494.4.1 Sensitivities of Fiber Gratings 2504.4.2 Tunability of Fiber Gratings 2524.4.3 Packaging of Fiber Grating Devices 2554.4.4 Fiber Grating Sensor Systems and Their Applications 259Problems 263References 2665 Distributed Optical Fiber Sensors 2785.1 Optical Scattering in Fiber 2785.1.1 Elastic Optical Scattering 2795.1.2 Inelastic Optical Scattering 2815.1.3 Stimulated Raman Scattering and Stimulated Brillouin Scattering 2855.2 Distributed Sensors Based on Rayleigh Scattering 2865.2.1 Optical Time Domain Reflectometer 2865.2.2 Polarization OTDR 2925.2.3 Coherent OTDR and Phase Sensitive OTDR 2945.2.4 Optical Frequency Domain Reflectometry 2985.3 Distributed Sensors Based on Raman Scattering 3005.3.1 Raman Scattering in Fiber 3015.3.2 Distributed Anti-Stokes Raman Thermometry 3045.3.3 Frequency Domain DART 3075.4 Distributed Sensors Based on Brillouin Scattering 3085.4.1 Brillouin Scattering in Fiber 3085.4.2 Brillouin Optical Time Domain Reflectrometer 3125.4.3 Brillouin Optical Time Domain Analyzer 3165.5 Distributed Sensors Based on Fiber Interferometers 3225.5.1 Configuration and Characteristics of Interferometric Fiber Sensors 3235.5.2 Low Coherence Technology in a Distributed Sensor System 3275.5.3 Sensors Based on Speckle Effect and Mode Coupling in Multimode Fiber 331Problems 335References 3376 Fiber Sensors With Special Applications 3516.1 Fiber Optic Gyroscope 3516.1.1 Interferometric FOG 3526.1.2 Brillouin Laser Gyro and Resonance Fiber Optic Gyroscope 3626.2 Fiber Optic Hydrophone 3646.2.1 Basic Structures 3656.2.2 Sensor Arrays and Multiplexing 3706.2.3 Low Noise Laser Source 3726.3 Fiber Faraday Sensor 3736.3.1 Faraday Effect in Fiber 3746.3.2 Electric Current Sensor Based on Faraday Rotation 3766.4 Fiber Sensors Based on Surface Plasmon Effect 3796.4.1 Surface Plasmon Effect 3796.4.2 Sensors Based on SPW 383Problems 386References 3877 Extrinsic Fiber Fabry–Perot Interferometer Sensor 3957.1 Basic Principles and Structures of Extrinsic Fiber F-P Sensors 3957.1.1 Structures of EFFP Devices 3967.1.2 Basic Characteristics of a Fabry–Perot Interferometer 3987.2 Theory of a Gaussian Beam Fabry–Perot Interferometer 4017.2.1 Basic Model and Theoretical Analysis 4017.2.2 Approximation as a Fizeau Interferometer 4047.3 Basic Characteristics and Performances of EFFPI Sensors 4067.3.1 Sensitivity of an EFFPI Sensor 4067.3.2 Linear Range and Dynamic Range of Measurement 4087.3.3 Interrogation and Stability 4107.3.4 Frequency Response 4137.4 Applications of the EFFPI Sensor and Related Techniques 4177.4.1 Localization of the Sound Source 4177.4.2 Applications in an Atomic Force Microscope 4187.4.3 More Application Examples 419Problems 421References 422Appendices 427Appendix 1 Mathematical Formulas 427A1.1 Bessel Equations and Bessel Functions 427A1.2 Runge–Kutta Method 432A1.3 The First-Order Linear Differential Equation 433A1.4 Riccati Equation 433A1.5 Airy Equation and Airy Functions 434Appendix 2 Fundamentals of Elasticity 435A2.1 Strain, Stress, and Hooke’s Law 435A2.2 Conversions Between Coordinates 438A2.3 Plane Deformation 440A2.4 Equilibrium of Plates and Rods 443A2.5 Photoelastic Effect 446Appendix 3 Fundamentals of Polarization Optics 446A3.1 Polarized Light and Jones Vector 446A3.2 Stokes Vector and Poincar´e Sphere 447A3.3 Optics of Anisotropic Media 449A3.4 Jones Matrix and Mueller Matrix 450A3.5 Measurement of Jones Vector and Stokes Vector 453Appendix 4 Specifications of Related Materials and Devices 454A4.1 Fiber Connectors 456Index 459

“The book provides a well-organized and in-depth treatment of optical fiber sensors for students and can also serve as a convenient reference for engineers and scientists working in the field.”  (IEEE Electrical Insulation Magazine, 1 March 2014)