Modeling and Optimization of LCD Optical Performance.

Intro -- Modeling and Optimization of LCD Optical Performance -- Contents -- Series Editor's Foreword -- Preface -- Acknowledgments -- List of Abbreviations -- About the Companion Website -- 1 Polarization of Monochromatic Waves. Background of the Jones Matrix Methods. The Jones Calculus -- 1.1 Homogeneous Waves in Isotropic Media -- 1.1.1 Plane Waves -- 1.1.2 Polarization. Jones Vectors -- 1.1.3 Coordinate Transformation Rules for Jones Vectors. Orthogonal Polarizations. Decomposition of a Wave into Two Orthogonally Polarized Waves -- 1.2 Interface Optics for Isotropic Media -- 1.2.1 Fresnels Formulas. Snells Law -- 1.2.2 Reflection and Transmission Jones Matrices for a Plane Interface between Isotropic Media -- 1.3 Wave Propagation in Anisotropic Media -- 1.3.1 Wave Equations -- 1.3.2 Waves in a Uniaxial Layer -- 1.3.3 A Simple Birefringent Layer and Its Principal Axes -- 1.3.4 Transmission Jones Matrices of a Simple Birefringent Layer at Normal Incidence -- 1.3.5 Linear Retarders -- 1.3.6 Jones Matrices of Absorptive Polarizers. Ideal Polarizer -- 1.4 Jones Calculus -- 1.4.1 Basic Principles of the Jones Calculus -- 1.4.2 Three Useful Theorems for Transmissive Systems -- 1.4.3 Reciprocity Relations. Joness Reversibility Theorem -- 1.4.4 Theorem of Polarization Reversibility for Systems Without Diattenuation -- 1.4.5 Particular Variants of Application of the Jones Calculus. Cartesian Jones Vectors for Wave Fields in Anisotropic Media -- References -- 2 The Jones Calculus: Solutions for Ideal Twisted Structures and Their Applications in LCD Optics -- 2.1 Jones Matrix and Eigenmodes of a Liquid Crystal Layer with an Ideal Twisted Structure -- 2.2 LCD Optics and the Gooch-Tarry Formulas -- 2.3 Interactive Simulation -- 2.4 Parameter Space -- References -- 3 Optical Equivalence Theorem -- 3.1 General Optical Equivalence Theorem.

3.2 Optical Equivalence for the Twisted Nematic Liquid Crystal Cell -- 3.3 Polarization Conserving Modes -- 3.3.1 LP1 Modes -- 3.3.2 LP2 Modes -- 3.3.3 LP3 Modes -- 3.3.4 CP Modes -- 3.4 Application to Nematic Bistable LCDs -- 3.4.1 2 Bistable TN Displays -- 3.4.2 Bistable TN Displays -- 3.5 Application to Reflective Displays -- 3.6 Measurement of Characteristic Parameters of an LC Cell -- 3.6.1 Characteristic Angle Ω -- 3.6.2 Characteristic Phase Γ -- References -- 4 Electro-optical Modes: Practical Examples of LCD Modeling and Optimization -- 4.1 Optimization of LCD Performance in Various Electro-optical Modes -- 4.1.1 Electrically Controlled Birefringence -- 4.1.2 Twist Effect -- 4.1.3 Supertwist Effect -- 4.1.4 Optimization of Optical Performance of Reflective LCDs -- 4.2 Transflective LCDs -- 4.2.1 Dual-Mode Single-Cell-Gap Approach -- 4.2.2 Single-Mode Single-Cell-Gap Approach -- 4.3 Total Internal Reflection Mode -- 4.4 Ferroelectric LCDs -- 4.4.1 Basic Physical Properties -- 4.4.2 Electro-optical Effects in FLC Cells -- 4.5 Birefringent Color Generation in Dichromatic Reflective FLCDs -- References -- 5 Necessary Mathematics. Radiometric Terms. Conventions. Various Stokes and Jones Vectors -- 5.1 Some Definitions and Relations from Matrix Algebra -- 5.1.1 General Definitions -- 5.1.2 Some Important Properties of Matrix Products -- 5.1.3 Unitary Matrices. Unimodular Unitary 2 × 2 Matrices. STU Matrices -- 5.1.4 Norms of Vectors and Matrices -- 5.1.5 Kronecker Product of Matrices -- 5.1.6 Approximations -- 5.2 Some Radiometric Quantities. Conventions -- 5.3 Stokes Vectors of Plane Waves and Collimated Beams Propagating in Isotropic Nonabsorbing Media -- 5.4 Jones Vectors -- 5.4.1 Fitted-to-Electric-Field Jones Vectors and Fitted-to-Transverse-Component-of-Electric-Field Jones Vectors -- 5.4.2 Fitted-to-Irradiance Jones Vectors.

5.4.3 Conventional Jones Vectors -- References -- 6 Simple Models and Representations for Solving Optimization and Inverse Optical Problems. Real Optics of LC Cells and Useful Approximations -- 6.1 Polarization Transfer Factor of an Optical System -- 6.2 Optics of LC Cells in Terms of Polarization Transport Coefficients -- 6.2.1 Polarization-Dependent Losses and Depolarization. Unpolarized Transmittance -- 6.2.2 Rotations -- 6.2.3 Symmetry of the Sample -- 6.3 Retroreflection Geometry -- 6.4 Applications of Polarization Transport Coefficients in Optimization of LC Devices -- 6.5 Evaluation of Ultimate Characteristics of an LCD that can be Attained by Fitting the Compensation System. Modulation Efficiency of LC Layers -- References -- 7 Some Physical Models and Mathematical Algorithms Used in Modeling the Optical Performance of LCDs -- 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 -- 7.2 Transfer Matrix Technique and Adding Technique -- 7.2.1 Transfer Matrix Technique -- 7.2.2 Adding Technique -- 7.3 Optical Models of Some Elements of LCDs -- References -- 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 -- 8.1 General Properties of the Electromagnetic Field Induced by a Plane Monochromatic Wave in a Linear Stratified Medium -- 8.1.1 Maxwells Equations and Constitutive Relations -- 8.1.2 Plane Waves -- 8.1.3 Field Geometry -- 8.2 Transmission and Reflection Operators of Fragments (TR Units) of a Stratified Medium and Their Calculation -- 8.2.1 EW Jones Vector. EW Jones Matrices. Transmission and Reflection Operators.

8.2.2 Calculation of Overall Transmission and Overall Reflection Operators for Layered Systems by Using Transfer Matrices -- 8.3 Berremans Method -- 8.3.1 Transfer Matrices -- 8.3.2 Transfer Matrix of a Homogeneous Layer -- 8.3.3 Transfer Matrix of a Smoothly Inhomogeneous Layer. Staircase Approximation -- 8.3.4 Coordinate Systems -- 8.4 Simplifications, Useful Relations, and Advanced Techniques -- 8.4.1 Orthogonality Relations and Other Useful Relations for Eigenwave Bases -- 8.4.2 Simple General Formulas for Transmission Operators of Interfaces -- 8.4.3 Calculation of Transmission and Reflection Operators of Layered Systems by Using the Adding Technique -- 8.5 Transmissivities and Reflectivities -- 8.6 Mathematical Properties of Transfer Matrices and Transmission and Reflection EW Jones Matrices of Lossless Media and Reciprocal Media -- 8.6.1 Properties of Matrix Operators for Nonabsorbing Regions -- 8.6.2 Properties of Matrix Operators for Reciprocal Regions -- 8.7 Calculation of EW 4 × 4 Transfer Matrices for LC Layers -- 8.8 Transformation of the Elements of EW Jones Vectors and EW Jones Matrices Under Changes of Eigenwave Bases -- 8.8.1 Coordinates of the EW Jones Vector of a Wave Field in Different Eigenwave Bases -- 8.8.2 EW Jones Operators in Different Eigenwave Bases -- References -- 9 Choice of Eigenwave Bases for Isotropic, Uniaxial, and Biaxial Media -- 9.1 General Aspects of EWB Specification. EWB-generating routines -- 9.2 Isotropic Media -- 9.3 Uniaxial Media -- 9.4 Biaxial Media -- References -- 10 Efficient Methods for Calculating Optical Characteristics of Layered Systems for Quasimonochromatic Incident Light. Main Routines of LMOPTICS Library -- 10.1 EW Stokes Vectors and EW Mueller Matrices -- 10.2 Calculation of the EW Mueller Matrices of the Overall Transmission and Reflection of a System Consisting of "Thin" and "Thick" Layers.

10.3 Main Routines of LMOPTICS -- 10.3.1 Routines for Computing 4 × 4 Transfer Matrices and EW Jones Matrices -- 10.3.2 Routines for Computing EW Mueller Matrices -- 10.3.3 Other Useful Routines -- References -- 11 Calculation of Transmission Characteristics of Inhomogeneous Liquid Crystal Layers with Negligible Bulk Reflection -- 11.1 Application of Jones Matrix Methods to Inhomogeneous LC Layers -- 11.1.1 Calculation of Transmission Jones Matrices of LC Layers Using the Classical Jones Calculus -- 11.1.2 Extended Jones Matrix Methods -- 11.2 NBRA. Basic Differential Equations -- 11.3 NBRA. Numerical Methods -- 11.3.1 Approximating Multilayer Method -- 11.3.2 Discretization Method -- 11.3.3 Power Series Method -- 11.4 NBRA. Analytical Solutions -- 11.4.1 Twisted Structures -- 11.4.2 Nontwisted Structures -- 11.4.3 NBRA and GOA. Adiabatic and Quasiadiabatic Approximations -- 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 -- References -- 12 Some Approximate Representations in EW Jones Matrix Method and Their Application in Solving Optimization and Inverse Problems for LCDs -- 12.1 Theory of STUM Approximation -- 12.2 Exact and Approximate Expressions for Transmission Operators of Interfaces at Normal Incidence -- 12.3 Polarization Jones Matrix of an Inhomogeneous Nonabsorbing Anisotropic Layer with Negligible Bulk Reflection at Normal Incidence. Simple Representations of Polarization Matrices of LC Layers at Normal Incidence -- 12.4 Immersion Model of the Polarization-Converting System of an LCD -- 12.5 Determining Configurational and Optical Parameters of LC Layers With a Twisted Structure: Spectral Fitting Method -- 12.5.1 How to Bring Together the Experiment and Unitary Approximation -- 12.5.2 Parameterization and Solving the Inverse Problem.

12.5.3 Appendix to Section 12.5.

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