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.

1 INTRODUCTION 1

1.1 Historical Review and Perspective 1

1.2 Classifications of Optical Fiber Sensors 3

1.3 Overview of the Chapters 6

References 8

2 FUNDAMENTALS OF OPTICAL FIBERS 10

2.1 Introduction to Optical Fibers 10

2.1.1 Basic Structure and Fabrication of Optical Fiber 10

2.1.2 Basic Characteristics 12

2.1.3 Classifications of Optical Fibers 17

2.2 Electromagnetic Theory of Step-Index Optical Fibers 18

2.2.1 Maxwell Equations in Cylindrical Coordinates 19

2.2.2 Boundary Conditions and Eigenvalue Equations 23

2.2.3 Weakly Guiding Approximation, Hybrid Modes, and Linear Polarized Modes 26

2.2.4 Field Distribution and Polarization Characteristics 29

2.2.5 Multimode Fiber and Cladding Modes 35

2.2.6 Propagation of Optical Pulses in Optical Fibers 39

2.3 Basic Theory of the Gradient-Index Optical Fiber 42

2.3.1 Ray Equation in Inhomogeneous Media 42

2.3.2 Ray Optics of GRIN Fiber 46

2.3.3 Wave Optics of GRIN Fiber 51

2.3.4 Basic Characteristics of Gradient Index Lens 56

2.4 Special Optical Fibers 57

2.4.1 Rare-Earth-Doped Fibers and Double-Cladding Fibers 57

2.4.2 Polarization Maintaining Fibers 60

2.4.3 Photonic Crystal Fiber and Microstructure Fiber 64

Problems 69

References 71

3 FIBER SENSITIVITIES AND FIBER DEVICES 76

3.1 Fiber Sensitivities to Physical Conditions 76

3.1.1 Sensitivity to Axial Strain 77

3.1.2 Sensitivity to Lateral Pressure 78

3.1.3 Bending-Induced Birefringence 83

3.1.4 Torsion-Induced Polarization Mode Cross-Coupling 87

3.1.5 Bending Loss 91

3.1.6 Vibration and Mechanical Waves in Fiber 95

3.1.7 Sensitivity to Temperature 96

3.2 Fiber Couplers 97

3.2.1 Structures and Fabrications of 2×2 Couplers 98

3.2.2 Basic Characteristics and Theoretical Analyses of the Coupler 99

3.2.3 N×N and 1×N Fiber Star Couplers 110

3.2.4 Coupling in Axial Direction and Tapered Fiber 114

3.3 Fiber Loop Devices Incorporated with Couplers 118

3.3.1 Fiber Sagnac Loops 118

3.3.2 Fiber Rings 126

3.3.3 Fiber Mach–Zehnder Interferometers and Michelson Interferometers 131

3.3.4 Fiber Loops Incorporated with 3×3 Couplers 135

3.4 Polarization Characteristics of Fibers 142

3.4.1 Polarization State Evolution in Fibers 142

3.4.2 Basic Characteristics of Polarization Mode Dispersion 154

3.4.3 Spun Fiber and Circular Birefringence Fiber 157

3.4.4 Faraday Rotation and Optical Activity 159

3.5 Fiber Polarization Devices 162

3.5.1 Fiber Polarizers 162

3.5.2 Fiber Polarization Controller 165

3.5.3 Fiber Depolarizer and Polarization Scrambler 166

3.5.4 Fiber Optical Isolator and Circulator 170

Problems 172

References 174

4 FIBER GRATINGS AND RELATED DEVICES 183

4.1 Introduction to Fiber Gratings 183

4.1.1 Basic Structure and Principle 183

4.1.2 Photosensitivity of Optical Fiber 186

4.1.3 Fabrication and Classifications of Fiber Gratings 190

4.2 Theory of Fiber Grating 194

4.2.1 Theory of Uniform FBG 194

4.2.2 Theory of Long-Period Fiber Grating 202

4.2.3 Basic Theory of Nonuniform Fiber Gratings 208

4.2.4 Inverse Engineering Design 214

4.2.5 Apodization of Fiber Grating 219

4.3 Special Fiber Grating Devices 222

4.3.1 Multisection FBGs 222

4.3.2 Chirped Fiber Bragg Grating 233

4.3.3 Tilted Fiber Bragg Gratings 236

4.3.4 Polarization Maintaining Fiber Gratings 243

4.3.5 In-Fiber Interferometers and Acoustic Optic Tunable Filter 246

4.4 Fiber Grating Sensitivities and Fiber Grating Sensors 249

4.4.1 Sensitivities of Fiber Gratings 250

4.4.2 Tunability of Fiber Gratings 252

4.4.3 Packaging of Fiber Grating Devices 255

4.4.4 Fiber Grating Sensor Systems and Their Applications 259

Problems 263

References 266

5 DISTRIBUTED OPTICAL FIBER SENSORS 278

5.1 Optical Scattering in Fiber 278

5.1.1 Elastic Optical Scattering 279

5.1.2 Inelastic Optical Scattering 281

5.1.3 Stimulated Raman Scattering and Stimulated Brillouin Scattering 285

5.2 Distributed Sensors Based on Rayleigh Scattering 286

5.2.1 Optical Time Domain Reflectometer 286

5.2.2 Polarization OTDR 292

5.2.3 Coherent OTDR and Phase Sensitive OTDR 294

5.2.4 Optical Frequency Domain Reflectometry 298

5.3 Distributed Sensors Based on Raman Scattering 300

5.3.1 Raman Scattering in Fiber 301

5.3.2 Distributed Anti-Stokes Raman Thermometry 304

5.3.3 Frequency Domain DART 307

5.4 Distributed Sensors Based on Brillouin Scattering 308

5.4.1 Brillouin Scattering in Fiber 308

5.4.2 Brillouin Optical Time Domain Reflectrometer 312

5.4.3 Brillouin Optical Time Domain Analyzer 316

5.5 Distributed Sensors Based on Fiber Interferometers 322

5.5.1 Configuration and Characteristics of Interferometric Fiber Sensors 323

5.5.2 Low Coherence Technology in a Distributed Sensor System 327

5.5.3 Sensors Based on Speckle Effect and Mode Coupling in Multimode Fiber 331

Problems 335

References 337

6 FIBER SENSORS WITH SPECIAL APPLICATIONS 351

6.1 Fiber Optic Gyroscope 351

6.1.1 Interferometric FOG 352

6.1.2 Brillouin Laser Gyro and Resonance Fiber Optic Gyroscope 362

6.2 Fiber Optic Hydrophone 364

6.2.1 Basic Structures 365

6.2.2 Sensor Arrays and Multiplexing 370

6.2.3 Low Noise Laser Source 372

6.3 Fiber Faraday Sensor 373

6.3.1 Faraday Effect in Fiber 374

6.3.2 Electric Current Sensor Based on Faraday Rotation 376

6.4 Fiber Sensors Based on Surface Plasmon Effect 379

6.4.1 Surface Plasmon Effect 379

6.4.2 Sensors Based on SPW 383

Problems 386

References 387

7 EXTRINSIC FIBER FABRY–PEROT INTERFEROMETER SENSOR 395

7.1 Basic Principles and Structures of Extrinsic Fiber F-P Sensors 395

7.1.1 Structures of EFFP Devices 396

7.1.2 Basic Characteristics of a Fabry–Perot Interferometer 398

7.2 Theory of a Gaussian Beam Fabry–Perot Interferometer 401

7.2.1 Basic Model and Theoretical Analysis 401

7.2.2 Approximation as a Fizeau Interferometer 404

7.3 Basic Characteristics and Performances of EFFPI Sensors 406

7.3.1 Sensitivity of an EFFPI Sensor 406

7.3.2 Linear Range and Dynamic Range of Measurement 408

7.3.3 Interrogation and Stability 410

7.3.4 Frequency Response 413

7.4 Applications of the EFFPI Sensor and Related Techniques 417

7.4.1 Localization of the Sound Source 417

7.4.2 Applications in an Atomic Force Microscope 418

7.4.3 More Application Examples 419

Problems 421

References 422

APPENDICES 427

Appendix 1 Mathematical Formulas 427

A1.1 Bessel Equations and Bessel Functions 427

A1.2 Runge–Kutta Method 432

A1.3 The First-Order Linear Differential Equation 433

A1.4 Riccati Equation 433

A1.5 Airy Equation and Airy Functions 434

Appendix 2 Fundamentals of Elasticity 435

A2.1 Strain, Stress, and Hooke’s Law 435

A2.2 Conversions Between Coordinates 438

A2.3 Plane Deformation 440

A2.4 Equilibrium of Plates and Rods 443

A2.5 Photoelastic Effect 446

Appendix 3 Fundamentals of Polarization Optics 446

A3.1 Polarized Light and Jones Vector 446

A3.2 Stokes Vector and Poincar´e Sphere 447

A3.3 Optics of Anisotropic Media 449

A3.4 Jones Matrix and Mueller Matrix 450

A3.5 Measurement of Jones Vector and Stokes Vector 453

Appendix 4 Specifications of Related Materials and Devices 454

A4.1 Fiber Connectors 456

INDEX 459

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