Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems

Chapter 1 History of Light and Polarization 2 1.1 Early history of light 2 1.2 History of polarization 4 1.3 History of polarization in optical fibers and waveguides 8 1.3.1 The history of optical fiber 8 1.3.2 History of polarization in optical fibers 11 1.3.3 Chronicles of polarization optics in optical fibers from 1959 to 1981 15 Reference 17 Bibliography 18 Chapter 2 Polarization Basics 19 2.1 Introduction to Polarization 19 2.2 The degenerate polarization states of light 20 2.3 The polarization ellipse of light 23 2.4 Poincaré Sphere presentation of polarization 27 2.5 Degree of polarization (DOP) 29 2.6 Birefringence 32 2.7 Photoelasticity or photo-elastic effect 34 2.8 Dichroism, diattenuation, and polarization dependent loss 34 2.9 Polarization properties of reflected and refracted light 35 Appendix 2A 36 Bibliography 37 Chapter 3 Polarization effects unique to optical fiber systems 39 3.1 Polarization variation in optical fibers 39 3.2 Polarization eigenmodes in a single mode optical fiber 40 3.3 Birefringence contributions in optical fibers 42 3.3.1 Noncircular Core 42 3.3.2 Internal lateral stress 44 3.3.3 External lateral stress 46 3.3.4 Fiber Bending 47 3.3.5 Fiber Twist 48 3.3.6 Electrical and Magnetic Fields 50 3.4 Polarization impairments in optical fiber systems 51 3.5 Polarization multiplexing 59 3.6 Polarization issues unique to optic fiber sensing system 60 3.7 Polarization issues unique to microwave photonics systems 61 References 62 Chapter 4 Mathematics for polarization analysis 66 4.1 Jones vector representation of monochramtic light 66 4.1.1 Jones vector 66 4.1.2 Mutual orthogonality of Jones vectors 69 4.1.3 Linear independence of Jones vectors 70 4.2 Jones matrix of optical devices 71 4.2.1 Jones Matrix of optical elements 72 4.2.2 Jones matrix of reflection 78 4.2.3 Polarization compensation of reflection 83 4.2.4 Polarization properties of corner-cube retroreflector 85 4.3 Jones matrix of multi-element optical systems 86 4.3.1 Jones equivalent theorems 86 4.3.2 Properties of the optical system containing only retarders and rotators 87 4.3.3 Eigenvector and eigenvalue of an optical system 90 4.3.3 Transmission properties of an optical system including partial polarizers 93 4.3.5 Experimental measurement of Jones matrix 97 4.4.6 Jones calculus in retracing optical path 99 4.3.7 N-matrix and polarization evolution 105 4.3.8 Jones matrix of twisted optical fiber 112 4.4 Mueller matrix representation of optical devices 117 4.4.1 Definition of Mueller matrix 117 4.4.2 Mueller matrix of optical elements 120 4.5 Polarization evolution in optical fiber 125 4.5.1 Rotation matrix representation of unitary optical systems 125 4.5.2 Infinitesimal rotation and rotation vector in optical fiber 128 4.5.3 Birefringence vector and polarization evolution along an optical fiber 132 4.5.4 PMD vector and polarization evolution with optical frequency 138 4.6 PMD measurement 143 4.6.1 Poincare sphere analysis 144 4.6.2 Mueller matrix method 147 4.6.4 Jones Matrix Eigenanalysis 149 4.7 Polarization properties of quasi-monochromatic Light 151 4.7.1 Coherency matrix 151 4.7.2 The Stokes parameters of quasi-monochromatic plane wave 156 4.7.3 Depolarization of quasi-monochromatic plane wave with birefringence media 159 References 164 Chapter 5 Polarization properties of common anisotropic media 166 5.1 Plane wave in anisotropic media 166 5.1.1 Dielectric tensor and its symmetry 166 5.1.2 Plane-wave propagation in anisotropic media 169 5.2 The index ellipsoid 172 5..2.1 Optical axis 173 5.2.2 ordinary and extraordinary wave 174 5.2.3 Light propagation in uniaxial crystals 175 5.2.4 Double refraction and applicaitons 178 5.3 Optical activity 181 5.4 Linear electro-optic effect 185 5.4.1 Electro-optic effect 185 5.4.2 Pockels electro-optic effect and electro-optic coefficient 186 5.4.3 Pockels effect of Lithium Niobate and applicaitons 188 5.5 Stress-induced birefringence 192 5.5.1 Stress-induced birefringence in glass 192 5.5.2 Stress-induced birefringence in optical fiber 195 References 195 Chapter 6 Polarization management components and devices 200 6.1 Polarization management fibers 200 6.2 Polarizers 202 6.2.1 Birefringence Crystal Polarizers 202 6.2.2 Sheet Polarizers 204 6.3 Polarization Beam Splitters/Combiners 206 6.3.1 Birefringence Crystal PBS 207 6.3.2 Thin film coating PBS 211 6.3.3 Fiber pigtailed polarizers and PBS 212 6.3.3 Waveguide PBS 214 6.4 Linear birefringence based polarization management components 214 6.4.1 Wave plates 214 6.4.2 Polarization manipulation with a quarter-wave plate 215 6.4.3 Polarization manipulation with a half-wave plate 216 6.5 Polarization control with linear birefringence 217 6.5.1 Polarization control with multiple waveplates of fixed retardation but variable orientation 218 6.5.2 Polarization controller with a single wave plate of variable retardation orientation 220 6.5.3 Polarization control with multiple wave-plates of variable retardation but fixed orientation 224 6.5.4 Polarization controller with LiNbO3 based integrated optical circuit (IOC) 226 6.5.5 Minimum-element polarization controllers 228 6.6 Polarization control with circular birefringence 229 6.6.1 Magneto-optic or Faraday materials 229 6.6.2 Magneto-optic properties of rear-earth iron garnet films 232 6.6.3 Faraday rotator based simple polarization management devices 239 6.6.4 Variable Faraday rotator based polarization controllers 242 6.6.5 Non-reciprocal fiber optic devices made with MO garnets 243 6.7 PMD and PDL artifacts 247 6.7.1 Differential group delay (DGD) artifacts 247 6.7.2 Second order polarization mode dispersion (SOPMD) artifacts 248 6.7.3 Polarization dependent loss (PDL) artifacts 249 6.8 Depolarizer 250 6.8.1 Space domain depolarizer 250 6.8.2 Time domain depolarizer 254 References 261 Bibliography 265 Chapter 7 Active polarization management modules and instruments 267 7.1 Polarization stabilization and tracking 267 7.1.1 Reset-free polarization control 267 7.1.2 Polarization monitoring for active polarization control 269 7.1.3 Polarization Synthesizer 269 7.1.4 General purpose polarization tracker 271 7.1.5 PMD compensation with a polarization tracker 272 7.1.6 Polarization demultiplexing with a polarization tracker 273 7.1.7 Polarization tracking for coherent detection 277 7.2 Polarization scrambling and emulation 278 7.2.1 Polarization scrambling basics 279 7.2.2 Polarization scrambling simulation 279 7.2.3 Variable rate polarization scrambling and emulation 280 7.2.4 Quasi-uniform rate polarization scrambling 282 7.2.5 Factors degrading the performance of the polarization scramblers 287 7.2.6 Polarization scrambler applications 287 7.3 PDL emulator 289 7.4 PMD generation and emulation 290 7.4.1 PMD generator and emulator based on polarization splitting and combining 291 7.4.2 PMD generator and emulator based on polarization switching 292 7.4.3 Polarization optimized PMD source 297 7.5 Polarization related tests in coherent systems 303 References 307 Chapter 8 Polarization related measurements for optical fiber systems 371 8.1 Stokes polarimeters for SOP and DOP measurements 371 8.1.1 Time division Stokes polarimetry 372 8.1.2 Amplitude division polarimeters 380 8.1.3 Advantages and disadvantages of different configurations 387 8.1.4 Polarimeter calibration with DOP 388 8.2 Analog Mueller matrix polarimetry 391 8.2.1 Rotating element Mueller matrix polarimeters 392 8.2.3 Oscillating element Mueller matrix polarimeters 394 8.2.4 Imperfections in Mueller matrix polarimeters and instrument calibration 395 8.3 Polarization extinction ratio measurements 395 8.3.1 Rotating polarizer PER measurement 397 8.3.2 PER degradation at fiber connection 398 8.3.3 Polarization maximization for fast PER measurement 399 8.3.4 PER measurement with a Stokes polarimter 400 8.3.5 Distributed Polarization Crosstalk Measurement Method 403 8.3.6 PER of free-space optical polarization components 404 8.4 PDL , PDG, and PDR measurements 404 8.4.1 Polarization scrambling method for PDL and PDG measurements 404 8.4.2 Jones and Mueller matrix analysis method 406 8.4.3 Maximum-minimum search method for accurate PDL and PDG measurements 406 8.4.4 PDL measurement guidelines 410 8.4.5 PDR measurement 413 References 415 Chapter 9 Binary polarization generation and analysis 425 9.1 Highly repeatable magneto-optic binary PSG 425 9.1.1 Binary PSG descriptions 426 9.1.2 Experimental demonstration 428 9.1.3 Imperfections of the binary PSG 431 9.2 Highly accurate binary magneto-optic polarization state analyzer (PSA) 439 9.2.1 Device description 439 9.2.2 Self-calibrating binary PSA 442 9.3 Binary Mueller matrix polarimetry 446 9.3.1 System description of binary Mueller matrix polarimetery 447 9.3.2 Theoretical background 448 9.3.3 Experimental results 451 9.4 Some applications of binary Mueller matrix polarization analyzers 458 9.4.1 PM fiber beat length measurement 458 9.4.2 Characterization of sensing coils for fiber optic gyroscopes 459 9.4.3 Circular birefringence measurement and spun fiber characterization 460 9.4.4 Effective Verdet constant measurement of spun optical fibers 467 9.4.5 Wave plate analyzer using binary magneto-optic rotators 478 9.4.6 PDL measurement of a Multi-port component using a binary PSG 483 9.5 Multi-channel binary PSA 485 9.6 WDM system performance monitoring using a multi-channel binary PSA 485 Appendix 9.A1 488 Appendix 9.A2 489 Referencences 489 Chapter 10 Distributed polarization analysis and its applications 497 10.1 Distributed polarization crosstalk analysis and its applications (CD-PDA) 498 10.1.1 Polarization crosstalk in PM fibers 498 10.1.2 Description of distributed polarization crosstalk analyzer (DPXA) 500 10.1.3 Identification of causes for polarization cross-talks from measurement results 503 10.1.4 Capabilities and limitations of DPXA 507 10.1.5 Applications of distributed polarization analysis 508 10.2 Distributed Mueller matrix polarimetery and its applications 526 10.2.1 System description 526 10.2.2 Expression of bending-induced birefringence in SMF 529 10.2.3 Measurement setup and results 530 10.2.4 Validations with a non-distributed Mueller matrix polarimetery system 533 10.2.5 Distributed transversal force sensing 536 10.2.6 Investigation clamping-force induced birefringence of SM fibers in V-grooves 549 10.3 Polarization scrambled OFDR for distributed birefringence measurement and stress sensing 559 10.4 P-OTDR based DPA system 564 References 566 Chapter 11 Polarization for optical frequency analysis and optical sensing applications 573 11.1 Optical frequency analysis techniques 573 11.1.1 Polarimeter based optical frequency analyzer 574 11.1.2 Sine-cosine optical frequency detection with polarization manipulation 583 11.2 Polarimetry fiber optic gyroscope 590 11.2.1 Introduction 590 11.2.2 Operation Principle 591 11.3 Polarimetric magnetic field and electrical current sensors 599 11.3.1 Transmissive magnetic and current sensors using MO garnet films 600 11.3.2 Reflective magnetic and current sensors using MO thick film as the sensing medium 604 11.3.3 Reflective current sensor using optical fiber as the sensing medium 607 References 610