Series Editor''s Foreword xiii Preface xv Acknowledgments xix List of Abbreviations xxi About the Companion Website xxiii 1 Polarization of Monochromatic Waves. Background of the Jones Matrix Methods. The Jones Calculus 1 1.1 Homogeneous Waves in Isotropic Media 1 1.1.1 Plane Waves 1 1.1.2 Polarization.

Jones Vectors 3 1.1.3 Coordinate Transformation Rules for Jones Vectors. Orthogonal Polarizations. Decomposition of a Wave into Two Orthogonally Polarized Waves 9 1.2 Interface Optics for Isotropic Media 14 1.2.1 Fresnel''s Formulas.

Snell''s Law 14 1.2.2 Reflection and Transmission Jones Matrices for a Plane Interface between Isotropic Media 20 1.3 Wave Propagation in Anisotropic Media 23 1.3.1 Wave Equations 23 1.3.2 Waves in a Uniaxial Layer 25 1.

3.3 A Simple Birefringent Layer and Its Principal Axes 30 1.3.4 Transmission Jones Matrices of a Simple Birefringent Layer at Normal Incidence 32 1.3.5 Linear Retarders 36 1.3.6 Jones Matrices of Absorptive Polarizers.

Ideal Polarizer 38 1.4 Jones Calculus 41 1.4.1 Basic Principles of the Jones Calculus 42 1.4.2 Three Useful Theorems for Transmissive Systems 46 1.4.3 Reciprocity Relations.

Jones''s Reversibility Theorem 50 1.4.4 Theorem of Polarization Reversibility for Systems Without Diattenuation 53 1.4.5 Particular Variants of Application of the Jones Calculus. Cartesian Jones Vectors for Wave Fields in Anisotropic Media 55 References 57 2 The Jones Calculus: Solutions for Ideal Twisted Structures and Their Applications in LCD Optics 59 2.1 Jones Matrix and Eigenmodes of a Liquid Crystal Layer with an Ideal Twisted Structure 59 2.2 LCD Optics and the Gooch-Tarry Formulas 64 2.

3 Interactive Simulation 67 2.4 Parameter Space 69 References 73 3 Optical Equivalence Theorem 75 3.1 General Optical Equivalence Theorem 75 3.2 Optical Equivalence for the Twisted Nematic Liquid Crystal Cell 77 3.3 Polarization Conserving Modes 77 3.3.1 LP1 Modes 78 3.3.

2 LP2 Modes 79 3.3.3 LP3 Modes 80 3.3.4 CP Modes 81 3.4 Application to Nematic Bistable LCDs 82 3.4.1 2pi Bistable TN Displays 82 3.

4.2 Pi Bistable TN Displays 83 3.5 Application to Reflective Displays 84 3.6 Measurement of Characteristic Parameters of an LC Cell 86 3.6.1 Characteristic Angle Omega 86 3.6.2 Characteristic Phase Gamma 87 References 87 4 Electro-optical Modes: Practical Examples of LCD Modeling and Optimization 91 4.

1 Optimization of LCD Performance in Various Electro-optical Modes 91 4.1.1 Electrically Controlled Birefringence 91 4.1.2 Twist Effect 101 4.1.3 Supertwist Effect 109 4.1.

4 Optimization of Optical Performance of Reflective LCDs 116 4.2 Transflective LCDs 119 4.2.1 Dual-Mode Single-Cell-Gap Approach 119 4.2.2 Single-Mode Single-Cell-Gap Approach 122 4.3 Total Internal Reflection Mode 124 4.4 Ferroelectric LCDs 131 4.

4.1 Basic Physical Properties 131 4.4.2 Electro-optical Effects in FLC Cells 135 4.5 Birefringent Color Generation in Dichromatic Reflective FLCDs 145 References 149 5 Necessary Mathematics. Radiometric Terms. Conventions. Various Stokes and Jones Vectors 153 5.

1 Some Definitions and Relations from Matrix Algebra 153 5.1.1 General Definitions 153 5.1.2 Some Important Properties of Matrix Products 160 5.1.3 Unitary Matrices. Unimodular Unitary 2 x 2 Matrices.

STU Matrices 160 5.1.4 Norms of Vectors and Matrices 163 5.1.5 Kronecker Product of Matrices 166 5.1.6 Approximations 167 5.2 Some Radiometric Quantities.

Conventions 167 5.3 Stokes Vectors of Plane Waves and Collimated Beams Propagating in Isotropic Nonabsorbing Media 169 5.4 Jones Vectors 171 5.4.1 Fitted-to-Electric-Field Jones Vectors and Fitted-to-Transverse-Component-of-Electric-Field Jones Vectors 171 5.4.2 Fitted-to-Irradiance Jones Vectors 172 5.4.

3 Conventional Jones Vectors 175 References 176 6 Simple Models and Representations for Solving Optimization and Inverse Optical Problems. Real Optics of LC Cells and Useful Approximations 177 6.1 Polarization Transfer Factor of an Optical System 178 6.2 Optics of LC Cells in Terms of Polarization Transport Coefficients 182 6.2.1 Polarization-Dependent Losses and Depolarization. Unpolarized Transmittance 185 6.2.

2 Rotations 187 6.2.3 Symmetry of the Sample 190 6.3 Retroreflection Geometry 192 6.4 Applications of Polarization Transport Coefficients in Optimization of LC Devices 195 6.5 Evaluation of Ultimate Characteristics of an LCD that can be Attained by Fitting the Compensation System. Modulation Efficiency of LC Layers 207 References 216 7 Some Physical Models and Mathematical Algorithms Used in Modeling the Optical Performance of LCDs 217 7.1 Physical Models of the Light-Layered System Interaction Used in Modeling the Optical Behavior of LC Devices.

Plane-Wave Approximations. Transfer Channel Approach 217 7.2 Transfer Matrix Technique and Adding Technique 237 7.2.1 Transfer Matrix Technique 238 7.2.2 Adding Technique 242 7.3 Optical Models of Some Elements of LCDs 246 References 248 8 Modeling Methods Based on the Rigorous Theory of the Interaction of a Plane Monochromatic Wave with an Ideal Stratified Medium.

Eigenwave (EW) Methods. EW Jones Matrix Method 251 8.1 General Properties of the Electromagnetic Field Induced by a Plane Monochromatic Wave in a Linear Stratified Medium 252 8.1.1 Maxwell''s Equations and Constitutive Relations 252 8.1.2 Plane Waves 256 8.1.

3 Field Geometry 259 8.2 Transmission and Reflection Operators of Fragments (TR Units) of a Stratified Medium and Their Calculation 275 8.2.1 EW Jones Vector. EW Jones Matrices. Transmission and Reflection Operators 275 8.2.2 Calculation of Overall Transmission and Overall Reflection Operators for Layered Systems by Using Transfer Matrices 281 8.

3 Berreman''s Method 283 8.3.1 Transfer Matrices 283 8.3.2 Transfer Matrix of a Homogeneous Layer 285 8.3.3 Transfer Matrix of a Smoothly Inhomogeneous Layer. Staircase Approximation 287 8.

3.4 Coordinate Systems 289 8.4 Simplifications, Useful Relations, and Advanced Techniques 291 8.4.1 Orthogonality Relations and Other Useful Relations for Eigenwave Bases 291 8.4.2 Simple General Formulas for Transmission Operators of Interfaces 297 8.4.

3 Calculation of Transmission and Reflection Operators of Layered Systems by Using the Adding Technique 303 8.5 Transmissivities and Reflectivities 304 8.6 Mathematical Properties of Transfer Matrices and Transmission and Reflection EW Jones Matrices of Lossless Media and Reciprocal Media 311 8.6.1 Properties of Matrix Operators for Nonabsorbing Regions 311 8.6.2 Properties of Matrix Operators for Reciprocal Regions 313 8.7 Calculation of EW 4 x 4 Transfer Matrices for LC Layers 319 8.

8 Transformation of the Elements of EW Jones Vectors and EW Jones Matrices Under Changes of Eigenwave Bases 322 8.8.1 Coordinates of the EW Jones Vector of a Wave Field in Different Eigenwave Bases 322 8.8.2 EW Jones Operators in Different Eigenwave Bases 326 References 328 9 Choice of Eigenwave Bases for Isotropic, Uniaxial, and Biaxial Media 331 9.1 General Aspects of EWB Specification. EWB-generating routines 331 9.2 Isotropic Media 338 9.

3 Uniaxial Media 342 9.4 Biaxial Media 352 References 365 10 Efficient Methods for Calculating Optical Characteristics of Layered Systems for Quasimonochromatic Incident Light. Main Routines of LMOPTICS Library 367 10.1 EW Stokes Vectors and EW Mueller Matrices 368 10.2 Calculation of the EW Mueller Matrices of the Overall Transmission and Reflection of a System Consisting of "Thin" and "Thick" Layers 375 10.3 Main Routines of LMOPTICS 384 10.3.1 Routines for Computing 4 x 4 Transfer Matrices and EW Jones Matrices 384 10.

3.2 Routines for Computing EW Mueller Matrices 388 10.3.3 Other Useful Routines 391 References 392 11 Calculation of Transmission Characteristics of Inhomogeneous Liquid Crystal Layers with Negligible Bulk Reflection 393 11.1 Application of Jones Matrix Methods to Inhomogeneous LC Layers 394 11.1.1 Calculation of Transmission Jones Matrices of LC Layers Using the Classical Jones Calculus 394 11.1.

2 Extended Jones Matrix Methods 404 11.2 NBRA. Basic Differential Equations 409 11.3 NBRA. Numerical Methods 420 11.3.1 Approximating Multilayer Method 421 11.3.

2 Discretization Method 427 11.3.3 Power Series Method 428 11.4 NBRA. Analytical Solutions 430 11.4.1 Twisted Structures 430 11.4.

2 Nontwisted Structures 432 11.4.3 NBRA and GOA. Adiabatic and Quasiadiabatic Approximations 434 11.5 Effect of Errors in Values of the Transmission Matrix of the LC Layer on the Accuracy of Modeling the Transmittance of the LCD Panel 437 References 438 12 Some Approximate Representations in EWJones Matrix Method and Their Application in Solving Optimization and Inverse Problems for LCDs 441 12.1 Theory of STUM Approximation 442 12.2 Exact and Approximate Expressions for Transmission Operators of Interfaces at Normal Incidence 447 12.3 Polarization Jones Matrix of an Inhomo.