Polarization Measurement and Control in Optical Fiber Communication and Sensor Systems

Cover
Title Page
Copyright
Contents
Author Biographies
Preface
Chapter 1 History of Light and Polarization
1.1 Early History of Light
1.2 History of Polarization
1.3 History of Polarization in Optical Fibers and Waveguides
1.3.1 The History of Optical Fiber
1.3.2 History of Polarization in Optical Fibers
1.3.3 Chronicles of Polarization Optics in Optical Fibers from 1959 to 1981
References
Further Reading
Chapter 2 Polarization Basics
2.1 Introduction to Polarization
2.2 The Degenerate Polarization States of Light
2.3 The Polarization Ellipse of Light
2.4 Poincaré Sphere Presentation of Polarization
2.5 Degree of Polarization (DOP)
2.6 Birefringence
2.7 Photoelasticity or Photoelastic Effect
2.8 Dichroism, Diattenuation, and Polarization Dependent Loss
2.9 Polarization Properties of Reflected and Refracted Light
2.9.1 Reflection
2.9.2 Refraction
References
Further Reading
Chapter 3 Polarization Effects Unique to Optical Fiber Systems
3.1 Polarization Variation in Optical Fibers
3.2 Polarization Eigenmodes in a Single Mode Optical Fiber
3.3 Birefringence Contributions in Optical Fibers
3.3.1 Noncircular Core
3.3.2 Internal Lateral Stress
3.3.2.1 Elliptical Cladding
3.3.2.2 Circular Stress Rods
3.3.2.3 Bow‐Tie Shaped Stress Rods
3.3.3 External Lateral Stress
3.3.3.1 Fiber Between Parallel Plates
3.3.3.2 Fiber in an Angled V‐Groove
3.3.4 Fiber Bending
3.3.4.1 Pure‐Bend
3.3.4.2 Bending with Tension
3.3.4.3 Bending with a Kink
3.3.5 Fiber Twist
3.3.6 Electrical and Magnetic Fields
3.3.6.1 Axial Magnetic Field (The Faraday Effect)
3.3.6.2 Transversal Electrical Field
3.4 Polarization Impairments in Optical Fiber Systems
3.4.1 Polarization Mode Dispersion (PMD)
3.4.2 Polarization Dependent Loss (PDL)
3.4.3 Polarization Dependent Gain (PDG)
3.4.4 Polarization Dependent Wavelength (PDW)
3.4.5 Polarization Dependent Modulation (PDM)
3.4.6 Polarization Dependent Responsivity (PDR)
3.5 Polarization Multiplexing
3.6 Polarization Issues Unique to Optic Fiber Sensing System
3.7 Polarization Issues Unique to Microwave Photonics Systems
References
Chapter 4 Mathematics for Polarization Analysis
4.1 Jones Vector Representation of Monochromatic Light
4.1.1 Jones Vector
4.1.2 Orthogonality of Jones Vectors
4.1.3 Linear Independence of Jones Vectors
4.2 Jones Matrix of Optical Devices
4.2.1 Jones Matrix of Optical Elements
4.2.1.1 Linear Retarder and Linear Partial Polarizer in Principal Coordinates
4.2.1.2 Ideal Retarder in Principal Coordinates
4.2.1.3 The Ideal Partial Polarizer in Principal Coordinates
4.2.1.4 Jones Matrix of a Rotator
4.2.1.5 Jones Matrix Transformation Between Two Reference Frames
4.2.2 Jones Matrix of Reflection
4.2.2.1 Law of Reflection
4.2.2.2 Snell's Law
4.2.2.3 Fresnel's Equations
4.2.3 Polarization Compensation of Reflection
4.2.4 Polarization Properties of Corner‐Cube Retroreflector
4.3 Jones Matrix of Multi‐element Optical Systems
4.3.1 Jones Equivalent Theorems
4.3.2 Properties of Optical System Containing Only Retarders and Rotators
4.3.2.1 A Variable Rotator Constructed with Three Retarders
4.3.2.2 A Variable Wave Plate Constructed with a Rotator Between Two Quarter‐Wave Plates
4.3.3 Eigenvector and Eigenvalue of an Optical System
4.3.3.1 The Eigenvalues and Eigenvectors of Retardation Plate
4.3.3.2 The Eigenvalues and Eigenvectors of a Unitary Matrix
4.3.3.3 Obtaining Jones Matrix from Eigenvectors and Eigenvalues
4.3.4 Transmission Properties of an Optical System Including Partial Polarizers
4.3.5 Experimental Measurement of Jones Matrix
4.3.6 Jones Calculus in Retracing Optical Path
4.3.6.1 Jones Matrix of a Double‐Pass Optical System with a Mirror
4.3.7 N‐Matrix and Polarization Evolution
4.3.7.1 Expression of M in Terms of N
4.3.7.2 Circular Retardation Plate
4.3.7.3 Linear Retardation Plate
4.3.7.4 Elliptical Retardation Plate
4.3.8 Jones Matrix of Twisted Fiber
4.4 Mueller Matrix Representation of Optical Devices
4.4.1 Definition of Mueller Matrix
4.4.2 Mueller Matrix of Optical Elements
4.4.2.1 Mueller Matrix of a Retarder with a Horizontal Fast‐Axis
4.4.2.2 Mueller Matrix of Rotator
4.4.2.3 Mueller Matrix of a Partial Polarizer
4.4.2.4 Mueller Matrix of Retardation Plate with Fast Axis at θ from the x‐Axis
4.4.2.5 Mueller Matrix of the Partial Polarizer with Fast Axis at θ from the x‐Axis
4.5 Polarization Evolution in Optical Fiber
4.5.1 Rotation Matrix Representation of the Unitary Optical System
4.5.2 Infinitesimal Rotation and Rotation Vector in Fiber
4.5.2.1 Infinitesimal Rotation and Rotation Vector
4.5.3 Birefringence Vector and Polarization Evolution Along with Fiber
4.5.3.1 Linear Birefringence
4.5.3.2 Circular Birefringence (Optical Activity)
4.5.3.3 Elliptical Birefringence (Optical Activity)
4.5.3.4 Elliptical Birefringence with Twist
4.5.4 PMD Vector and Polarization Evolution with Optical Frequency
4.5.4.1 Principal States of Polarization and PMD Vector
4.5.4.2 PMD Vector Concatenation Rules
4.6 Polarimetric Measurement of PMD
4.6.1 Poincaré Sphere Arc Method
4.6.2 Poincaré Sphere Analysis
4.6.3 Mueller Matrix Method
4.6.4 Jones Matrix Eigenanalysis
4.7 Polarization Properties of Quasi‐monochromatic Light
4.7.1 Analytic Signal Representation of Polychromatic Light
4.7.1.1 Quasi‐monochromatic Light
4.7.2 Coherency Matrix
4.7.2.1 Completely Unpolarized Light
4.7.2.2 Completely Polarized Light
4.7.2.3 Partially Polarized Light and Degree of Polarization
4.7.2.4 Coherency Matrix of the Superposition of Individual Waves
4.7.2.5 Superposition of Two Individual Waves with Mutually Orthogonal Polarizations
4.7.3 The Stokes Parameters of Quasi‐monochromatic Plane Wave
4.7.3.1 Completely Unpolarized Light
4.7.3.2 Completely Polarized Light
4.7.3.3 Partially Polarized Light
4.7.4 Depolarization of Polychromatic Plane Wave by Birefringence Media
4.7.4.1 Power Spectral Density
4.7.4.2 Polarization State of a Polychromatic Light After Passing Through a Birefringence Medium
4.7.4.3 Polychromatic Light with Rectangular Spectrum
4.7.4.4 Polychromatic Light with Gaussian or Lorentzian Spectrum
References
Further Reading
Chapter 5 Polarization Properties of Common Anisotropic Media
5.1 Plane Waves in Anisotropic Media
5.1.1 Dielectric Tensor and Its Symmetry
5.1.2 Plane Wave Propagation in Anisotropic Media
5.1.2.1 Fresnel's Equation of Wave Normals
5.1.3 The Index Ellipsoid
5.2 Optical Properties of Anisotropic Crystals
5.2.1 Light Propagation in Uniaxial Crystals
5.2.1.1 Ordinary Ray
5.2.1.2 Extraordinary Ray
5.2.1.3 Optical Axis
5.2.2 Light Propagation in Biaxial Crystals
5.2.3 Double Refraction
5.2.4 Spatial Walk‐Off
5.2.5 Optical Activity
5.3 Electro‐optic Effect
5.3.1 General Description
5.3.2 Linear Electro‐optic Effect
5.3.2.1 Example: The Electro‐optic Effect in LiNbO3
5.3.2.2 Case 1: Electric Field is Applied Along the z‐Axis
5.3.2.3 Case 2: Electric Field is Applied Along the x‐Axis
5.3.2.4 Case 3: Electric Field is Along the y‐Axis
5.4 The Photoelastic Effect in Isotropic Media
5.4.1 Birefringence and Strain‐Optical Tensor in Isotropic Material
5.4.2 Relationship Between Birefringence and Stress Tensor
Reference
Further Reading
Chapter 6 Polarization Management Components and Devices
6.1 Polarization Management Fibers
6.1.1 Low Birefringence Fiber
6.1.2 Polarization Maintaining Fiber
6.1.3 Polarizing Fiber
6.1.4 Spun Fiber
6.2 Polarizers
6.2.1 Birefringence Crystal Polarizers
6.2.2 Sheet Polarizers
6.2.2.1 Film Polarizers
6.2.2.2 Glass Polarizers
6.2.3 Waveguide Polarizers
6.2.4 Other Types of Polarizers
6.3 Polarization Beam Splitters/Combiners
6.3.1 Birefringence Crystal PBS
6.3.1.1 PBS with Angular Separation
6.3.1.2 PBS with Lateral Separation
6.3.2 Thin Film Coating PBS
6.3.3 Fiber Pigtailed Polarizers and PBS
6.3.4 Waveguide PBS
6.4 Linear Birefringence Based Polarization Management Components
6.4.1 Wave Plates
6.4.2 Polarization Manipulation with a Quarter‐Wave Plate
6.4.2.1 Circular and Elliptical Polarizer
6.4.2.2 Anti‐reflection or Anti‐glare Film
6.4.3 Polarization Manipulation with a Half‐Wave Plate
6.5 Polarization Control with Linear Birefringence
6.5.1 Polarization Control with Multiple Wave Plates of Fixed Retardation but Variable Orientation
6.5.2 Polarization Controller with a Single Wave Plate of Variable Retardation and Orientation
6.5.3 Polarization Control with Multiple Wave Plates of Variable Retardation but Fixed Orientation
6.5.4 Polarization Controller with LiNbO3‐Based Integrated Optical Circuit (IOC)
6.5.5 Minimum‐Element Polarization Controllers
6.6 Polarization Control with Circular Birefringence
6.6.1 Magneto‐optic or Faraday Materials
6.6.2 Magneto‐optic Properties of Rare‐Earth Iron Garnet Films
6.6.2.1 Perpendicular Anisotropy Thick Films
6.6.2.2 Planar Anisotropy Thick Films
6.6.3 Faraday Rotator Based Simple Polarization Management Devices
6.6.3.1 Faraday Mirror
6.6.3.2 Polarization Switch
6.6.3.3 Variable and Fixed Polarization Rotators
6.6.4 Variable Faraday Rotator Based Polarization Controllers
6.6.5 Non‐reciprocal Fiber Optic Devices Made with MO Garnets
6.6.5.1 Polarization Sensitive Isolator
6.6.5.2 Polarization Sensitive 3‐Port Circulator
6.6.5.3 Polarization Independent Isolator
6.6.5.4 Polarization Independent Circulator
6.7 PMD and PDL Artifacts
6.7.1 Differential Group Delay (DGD) Artifacts
6.7.2 Second Order Polarization Mode Dispersion (SOPMD) Artifacts
6.7.3 Polarization Dependent Loss (PDL) Artifacts
6.8 Depolarizer
6.8.1 Space Domain Depolarizer
6.8.1.1 Polarization Sensitive Space Domain Depolarizer
6.8.1.2 Polarization Insensitive Space Domain Depolarizer
6.8.2 Time Domain Depolarizer
6.8.2.1 Polarization Sensitive Time Domain Depolarizer
6.8.2.2 Polarization Insensitive Time Domain Depolarizer – Lyot Depolarizers
6.8.2.3 Polarization Insensitive Time Domain Depolarizer – Parallel Configurations
References
Further Reading
Chapter 7 Active Polarization Management Modules and Instruments
7.1 Polarization Stabilization and Tracking
7.1.1 Reset‐Free Polarization Control
7.1.2 Polarization Monitoring for Active Polarization Control
7.1.3 Polarization Synthesizer
7.1.4 General Purpose Polarization Tracker
7.1.5 PMD Compensation with a Polarization Tracker
7.1.6 Polarization Demultiplexing with a Polarization Tracker
7.1.7 Polarization Tracking for Coherent Detection
7.2 Polarization Scrambling and Emulation
7.2.1 Polarization Scrambling Basics
7.2.2 Polarization Scrambling Simulation
7.2.3 Variable Rate Polarization Scrambling and Emulation
7.2.4 Quasi‐uniform Rate Polarization Scrambling
7.2.4.1 Device Construction
7.2.4.2 SOP Variation Rates Induced by Fiber Squeezers
7.2.4.3 Random Polarization Scrambling
7.2.4.4 Uniform Rate Scrambling
7.2.4.5 Quasi‐uniform Rate Scrambling
7.2.4.6 Rate Multiplication Method for Overcoming Fiber Squeezer Speed Limitations
7.2.5 Factors Degrading the Performance of the Polarization Scramblers
7.2.6 Polarization Scrambler Applications
7.3 PDL Emulator
7.4 PMD Generation and Emulation
7.4.1 PMD Generator and Emulator Based on Polarization Splitting and Combining
7.4.1.1 First‐Order PMD Generator and Emulator
7.4.1.2 All‐Order PMD Generator and Emulator
7.4.2 PMD Generator and Emulator Based on Polarization Switching
7.4.2.1 Binary DGD Generator Using MO Polarization Switching
7.4.2.2 PMD Emulation with the Binary Programmable DGD Generator
7.4.3 Polarization Optimized PMD Source
7.4.3.1 PMD Emulator vs. PMD Source
7.4.3.2 Polarization Optimization
7.4.3.3 Ternary Polarization Rotation Switch
7.4.3.4 Continuous Polarization Rotator
7.4.3.5 Polarization Optimized PMD Source Based on Ternary Polarization Switches
7.4.3.6 PMD Monitoring by PMD Compensation
7.5 Polarization Related Tests in Coherent Systems
7.5.1 Verifying System Performance
7.5.2 Polarization Test Instrumentation
References
Chapter 8 Polarization Related Measurements for Optical Fiber Systems
8.1 Stokes Polarimeters for SOP and DOP Measurements
8.1.1 Time Division Stokes Polarimetry
8.1.1.1 Rotating Element Polarimetry
8.1.1.2 Oscillating Element Stokes Polarimetry
8.1.1.3 Retardation Modulation polarimetry
8.1.2 Amplitude Division Polarimeters
8.1.2.1 Beam Splitter Based Amplitude Division Polarimeters
8.1.2.2 In‐Line Polarimeter
8.1.2.3 Wave‐Front Division Polarimeters
8.1.3 Advantages and Disadvantages of Different Configurations
8.1.4 Polarimeter Calibration with DOP
8.2 Analog Mueller Matrix Polarimetry
8.2.1 Rotating Element Mueller Matrix Polarimeters
8.2.2 Retardation Modulating Mueller Matrix Polarimeters
8.2.3 Oscillating Element Mueller Matrix Polarimeters
8.2.4 Imperfections in Mueller Matrix Polarimeters and Instrument Calibration
8.3 Polarization Extinction Ratio Measurements
8.3.1 Rotating Polarizer PER Measurement
8.3.2 PER Degradation at Fiber Connection
8.3.3 Polarization Maximization for Fast PER Measurement
8.3.4 PER Measurement with a Stokes Polarimeter
8.3.4.1 PM Fiber PER Measurements
8.3.4.2 PM Fiber Connector Key Orientation Measurements
8.3.4.3 PM Fiber Connector Stress Measurements
8.3.5 Distributed Polarization Crosstalk Measurement Method
8.3.6 PER of Free‐Space Optical Polarization Components
8.4 PDL, PDG, and PDR Measurements
8.4.1 Polarization Scrambling Method for PDL and PDG Measurements
8.4.2 Jones and Mueller Matrix Analysis Methods
8.4.2.1 Mueller Matrix Method (MMM)
8.4.2.2 Jones Matrix Eigenanalysis (JME) Method
8.4.3 Maximum–Minimum Search Method for Accurate PDL and PDG Measurements
8.4.4 PDL Measurement Guidelines
8.4.4.1 Comparison of Different Methods
8.4.4.2 Error Caused by Light Source Fluctuation
8.4.4.3 Error Caused by Double Reflections
8.4.4.4 Error from Connector and Cable Contributions
8.4.4.5 Variation Caused by System PDL
8.4.5 PDR Measurement
8.4.5.1 The Polarization Scrambling Method
8.4.5.2 The Maximum and Minimum Search Method
8.4.5.3 The Mueller Matrix Method
8.4.6 DOP Measurements
8.5 Real‐Time Performance Monitoring of a Communication System with DOP Measurement
8.5.1 SNR and Channel Power Monitoring via DOP Measurement
8.5.2 Optical Amplifier Noise Figure Measurement
8.5.3 SNR, PMD Depolarization, and Channel Power Monitoring via DOP Measurement
8.6 PMD Measurements of Optical Components and Optical Fibers
8.6.1 Pulse‐Delay Method
8.6.2 Modulation Phase‐Shift Method
8.6.3 Interferometric Method
8.6.4 PMD Measurement by PMD Compensation
8.6.5 Fixed‐Analyzer Method
8.6.6 SOP Trace Analysis Method
8.6.7 Poincaré Sphere Arc Method with Two Arbitrary Input SOPs
8.6.8 Poincaré Sphere Analysis (PSA) Method with Three Mutually Orthogonal Output SOPs
8.6.9 Mueller Matrix Method (MMM)
8.6.10 Jones Matrix Eigenanalysis (JME) Method
References
Further Reading
Chapter 9 Binary Polarization Generation and Analysis
9.1 Highly Repeatable Magneto‐optic Binary PSG
9.1.1 Binary PSG Descriptions
9.1.1.1 2‐Bit PSG
9.1.1.2 4‐Bit PSG
9.1.1.3 6‐Bit PSG
9.1.2 Experimental Demonstration
9.1.3 Imperfections of the Binary PSG
9.1.3.1 General Expression of the Stokes Vector of Generated PSG
9.1.3.2 Stokes Vectors of Some Specific SOPs Generated by PSG
9.1.3.3 Experimental Verification
9.1.3.4 Applications
9.2 Highly Accurate Binary Magneto‐optic Polarization State Analyzer (PSA)
9.2.1 Device Description
9.2.1.1 Device Structure
9.2.1.2 Operation Theory
9.2.1.3 Degeneracy
9.2.1.4 Distinctive Logic States (DLS)
9.2.1.5 Mueller Matrix Method
9.2.1.6 Selection of Logic States
9.2.2 Self‐Calibrating Binary PSA
9.2.2.1 Self‐Calibration Method
9.2.2.2 Perfect QWP and Polarizer Alignment
9.2.2.3 Experiments
9.3 Binary Mueller Matrix Polarimetry
9.3.1 System Description of Binary Mueller Matrix Polarimetry
9.3.2 Theoretical Background
9.3.2.1 Jones Matrix Eigenanalysis (JME)
9.3.2.2 Mueller Matrix Measurement (MMM)
9.3.3 Experimental Results
9.3.3.1 PMD Measurement Resolution
9.3.3.2 DGD and SOPMD Measurements
9.3.3.3 PDL Measurement
9.3.3.4 Repeatability Measurements and Accuracy Determination
9.3.3.5 Differences Between Mueller Matrix and Jones Matrix Methods
9.3.3.6 Summary
9.4 Application Examples of Binary Mueller Matrix Polarization Analyzers
9.4.1 PM Fiber Beat Length Measurement
9.4.2 Characterization of Sensing Coils for Fiber Optic Gyroscopes
9.4.3 Circular Birefringence Measurement and Spun Fiber Characterization
9.4.3.1 Measurement Principle
9.4.3.2 Experimental Setup
9.4.3.3 Verification of Birefringence Measurements
9.4.3.4 Thermal Coefficient of Circular Birefringence in Spun Fiber
9.4.3.5 Linear Birefringence Measurement in Spun Fiber with Different Temperatures
9.4.4 Effective Verdet Constant Measurement of Spun Optical Fibers
9.4.4.1 Introduction of the Effective Verdet Constant
9.4.4.2 Experiment
9.4.5 Wave‐Plate Analyzer Using Binary Magneto‐optic Rotators
9.5 PDL Measurement of a Multi‐port Component Using a Binary PSG
9.6 Multi‐channel Binary PSA
9.7 WDM System Performance Monitoring Using a Multi‐channel Binary PSA
References
Chapter 10 Distributed Polarization Analysis and Its Applications
10.1 Distributed Polarization Crosstalk Analysis and Its Applications
10.1.1 Polarization Crosstalk in PM Fibers
10.1.2 Description of Distributed Polarization Crosstalk Analyzer (DPXA)
10.1.3 Identification of Causes for Polarization Crosstalks from Measurement Results
10.1.3.1 Crosstalk Caused by Discrete Polarization Coupling Points
10.1.3.2 Crosstalk Caused by Continuous Polarization Coupling
10.1.3.3 Crosstalk Caused by Quasi‐Continuous Coupling
10.1.4 Capabilities and Limitations of DPXA
10.1.5 Applications of Distributed Polarization Crosstalk Analysis
10.1.5.1 Complete Characterization of PM Fibers
10.1.5.2 Transversal Force Sensing Using Distributed Polarization Crosstalk Analysis
10.1.5.3 Temperature Sensing Using Distributed Polarization Crosstalk Analysis
10.1.5.4 Simultaneously Transversal Stress and Temperature Sensing with DPXA
10.2 Distributed Mueller Matrix Polarimetry and Its Applications
10.2.1 System Description
10.2.2 Expression of Bending‐Induced Birefringence in SMF
10.2.3 Measurement Setup and Results
10.2.4 Validations with a Non‐distributed Mueller Matrix Polarimetry System
10.2.4.1 Residual Birefringence (RB) Validation
10.2.4.2 Bending‐Induced Birefringence Validation
10.2.5 Distributed Transversal Force Sensing
10.2.5.1 Sensing Principles
10.2.5.2 Calibration of TF Measurement Sensitivity
10.2.5.3 Validation of Distributed TF Fiber Sensing
10.2.6 Investigation Clamping‐Force Induced Birefringence of SM Fibers in V‐Grooves
10.2.6.1 Theoretical Expressions
10.2.6.2 V‐Grooves and Measurement Setup
10.2.6.3 Experimental Results and Discussions
10.3 Polarization Scrambled OFDR for Distributed Polarization Analysis
10.3.1 System and Algorithm Descriptions
10.3.2 Experimental Results
10.4 P‐OTDR Based Distributed Polarization Analysis Systems
References
Chapter 11 Polarization for Optical Frequency Analysis and Optical Sensing Applications
11.1 Optical Frequency Analysis Techniques
11.1.1 Polarimeter‐Based Optical Frequency Analyzer
11.1.1.1 Swept‐Frequency (Wavelength) Measurement
11.1.1.2 Spectral Shape Analysis
11.1.2 Sine–Cosine Optical Frequency Detection with Polarization Manipulation
11.1.2.1 Concept Description of Sine–Cosine Optical Frequency Detection
11.1.2.2 Experimental Results of Sine–Cosine Optical Frequency Detection
11.2 Polarimetry Fiber Optic Gyroscope
11.2.1 Introduction
11.2.2 Operation Principle
11.2.3 Experimental Validation
11.3 Polarimetric Magnetic Field and Electrical Current Sensors
11.3.1 Transmissive Magnetic and Current Sensors Using MO Garnet Films
11.3.2 Reflective Magnetic and Current Sensors Using MO Thick Film as the Sensing Medium
11.3.3 Reflective Current Sensor Using Optical Fiber as the Sensing Medium
References
Index
EULA