Modeling and Optimization of LCD Optical Performance

Dmitry A. Yakovlev, Saratov State University, RussiaDr Yakovlev is a senior researcher in the Department of Physics at Saratov State University, Russia. He is the head developer of commercial software MOUSE-LCD (MOdeling Universal System of Electrooptics of LCDs), developed in cooperation with HKUST, and the author of a number of efficient methods for computer modeling and optimization of LCDs used within many research projects performed in cooperation with Center Display Research of Hong Kong University of Science and Technology, ROLIC Research Ltd (Switzerland), TechnoDisplay AS (Norway. He has authored 30 refereed journal papers.Vladimir G. Chigrinov, Hong Kong University of Science and Technology, Hong KongProfessor Chigrinov is a member of the department of electrical and electronic engineering at Hong Kong University of Science and Technology. He is the author of 3 books, including Photoalignment of Liquid Crystalline Materials (with Professor Kwok), published by Wiley (2008). He has authored more than 150 refereed journal papers and holds 56 patents in the field of liquid crystals. He is a member of the editorial board of Liquid Crystal Today and Associate Editor of the Journal of SID. Prof. Chigrinov is Vice-President of the Russian SID chapter and a SID Fellow.Hoi Sing Kwok, Hong Kong University of Science and Technology, Hong KongProfessor Kwok is a member of the department of electrical and electronic engineering at Hong Kong University of Science and Technology. He is a fellow of the IEEE, Optical Society of America and the Hong Kong Institution of Engineers. Prof. Kwok is the co-author of Photoalignment of Crystalline Materials (Wiley, 2008) with Prof. Chigrinov and Vladimir M. Kozenkov, and has authored over 300 refereed journal papers.

• Series Editor's Foreword xiiiPreface xvAcknowledgments xixList of Abbreviations xxiAbout the Companion Website xxiii1 Polarization of Monochromatic Waves. Background of the Jones Matrix Methods. The Jones Calculus 11.1 Homogeneous Waves in Isotropic Media 11.1.1 Plane Waves 11.1.2 Polarization. Jones Vectors 31.1.3 Coordinate Transformation Rules for Jones Vectors. Orthogonal Polarizations. Decomposition of a Wave into Two Orthogonally Polarized Waves 91.2 Interface Optics for Isotropic Media 141.2.1 Fresnel's Formulas. Snell's Law 141.2.2 Reflection and Transmission Jones Matrices for a Plane Interface between Isotropic Media 201.3 Wave Propagation in Anisotropic Media 231.3.1 Wave Equations 231.3.2 Waves in a Uniaxial Layer 251.3.3 A Simple Birefringent Layer and Its Principal Axes 301.3.4 Transmission Jones Matrices of a Simple Birefringent Layer at Normal Incidence 321.3.5 Linear Retarders 361.3.6 Jones Matrices of Absorptive Polarizers. Ideal Polarizer 381.4 Jones Calculus 411.4.1 Basic Principles of the Jones Calculus 421.4.2 Three Useful Theorems for Transmissive Systems 461.4.3 Reciprocity Relations. Jones's Reversibility Theorem 501.4.4 Theorem of Polarization Reversibility for Systems Without Diattenuation 531.4.5 Particular Variants of Application of the Jones Calculus. Cartesian Jones Vectors for Wave Fields in Anisotropic Media 55References 572 The Jones Calculus: Solutions for Ideal Twisted Structures and Their Applications in LCD Optics 592.1 Jones Matrix and Eigenmodes of a Liquid Crystal Layer with an Ideal Twisted Structure 592.2 LCD Optics and the Gooch–Tarry Formulas 642.3 Interactive Simulation 672.4 Parameter Space 69References 733 Optical Equivalence Theorem 753.1 General Optical Equivalence Theorem 753.2 Optical Equivalence for the Twisted Nematic Liquid Crystal Cell 773.3 Polarization Conserving Modes 773.3.1 LP1 Modes 783.3.2 LP2 Modes 793.3.3 LP3 Modes 803.3.4 CP Modes 813.4 Application to Nematic Bistable LCDs 823.4.1 2pi Bistable TN Displays 823.4.2 Pi Bistable TN Displays 833.5 Application to Reflective Displays 843.6 Measurement of Characteristic Parameters of an LC Cell 863.6.1 Characteristic Angle Omega 863.6.2 Characteristic Phase Gamma 87References 874 Electro-optical Modes: Practical Examples of LCD Modeling and Optimization 914.1 Optimization of LCD Performance in Various Electro-optical Modes 914.1.1 Electrically Controlled Birefringence 914.1.2 Twist Effect 1014.1.3 Supertwist Effect 1094.1.4 Optimization of Optical Performance of Reflective LCDs 1164.2 Transflective LCDs 1194.2.1 Dual-Mode Single-Cell-Gap Approach 1194.2.2 Single-Mode Single-Cell-Gap Approach 1224.3 Total Internal Reflection Mode 1244.4 Ferroelectric LCDs 1314.4.1 Basic Physical Properties 1314.4.2 Electro-optical Effects in FLC Cells 1354.5 Birefringent Color Generation in Dichromatic Reflective FLCDs 145References 1495 Necessary Mathematics. Radiometric Terms. Conventions. Various Stokes and Jones Vectors 1535.1 Some Definitions and Relations from Matrix Algebra 1535.1.1 General Definitions 1535.1.2 Some Important Properties of Matrix Products 1605.1.3 Unitary Matrices. Unimodular Unitary 2 x 2 Matrices. STU Matrices 1605.1.4 Norms of Vectors and Matrices 1635.1.5 Kronecker Product of Matrices 1665.1.6 Approximations 1675.2 Some Radiometric Quantities. Conventions 1675.3 Stokes Vectors of Plane Waves and Collimated Beams Propagating in Isotropic Nonabsorbing Media 1695.4 Jones Vectors 1715.4.1 Fitted-to-Electric-Field Jones Vectors and Fitted-to-Transverse-Component-of-Electric-Field Jones Vectors 1715.4.2 Fitted-to-Irradiance Jones Vectors 1725.4.3 Conventional Jones Vectors 175References 1766 Simple Models and Representations for Solving Optimization and Inverse Optical Problems. Real Optics of LC Cells and Useful Approximations 1776.1 Polarization Transfer Factor of an Optical System 1786.2 Optics of LC Cells in Terms of Polarization Transport Coefficients 1826.2.1 Polarization-Dependent Losses and Depolarization. Unpolarized Transmittance 1856.2.2 Rotations 1876.2.3 Symmetry of the Sample 1906.3 Retroreflection Geometry 1926.4 Applications of Polarization Transport Coefficients in Optimization of LC Devices 1956.5 Evaluation of Ultimate Characteristics of an LCD that can be Attained by Fitting the Compensation System. Modulation Efficiency of LC Layers 207References 2167 Some Physical Models and Mathematical Algorithms Used in Modeling the Optical Performance of LCDs 2177.1 Physical Models of the Light–Layered System Interaction Used in Modeling the Optical Behavior of LC Devices. Plane-Wave Approximations. Transfer Channel Approach 2177.2 Transfer Matrix Technique and Adding Technique 2377.2.1 Transfer Matrix Technique 2387.2.2 Adding Technique 2427.3 Optical Models of Some Elements of LCDs 246References 2488 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 2518.1 General Properties of the Electromagnetic Field Induced by a Plane Monochromatic Wave in a Linear Stratified Medium 2528.1.1 Maxwell's Equations and Constitutive Relations 2528.1.2 Plane Waves 2568.1.3 Field Geometry 2598.2 Transmission and Reflection Operators of Fragments (TR Units) of a Stratified Medium and Their Calculation 2758.2.1 EW Jones Vector. EW Jones Matrices. Transmission and Reflection Operators 2758.2.2 Calculation of Overall Transmission and Overall Reflection Operators for Layered Systems by Using Transfer Matrices 2818.3 Berreman’s Method 2838.3.1 Transfer Matrices 2838.3.2 Transfer Matrix of a Homogeneous Layer 2858.3.3 Transfer Matrix of a Smoothly Inhomogeneous Layer. Staircase Approximation 2878.3.4 Coordinate Systems 2898.4 Simplifications, Useful Relations, and Advanced Techniques 2918.4.1 Orthogonality Relations and Other Useful Relations for Eigenwave Bases 2918.4.2 Simple General Formulas for Transmission Operators of Interfaces 2978.4.3 Calculation of Transmission and Reflection Operators of Layered Systems by Using the Adding Technique 3038.5 Transmissivities and Reflectivities 3048.6 Mathematical Properties of Transfer Matrices and Transmission and Reflection EW Jones Matrices of Lossless Media and Reciprocal Media 3118.6.1 Properties of Matrix Operators for Nonabsorbing Regions 3118.6.2 Properties of Matrix Operators for Reciprocal Regions 3138.7 Calculation of EW 4 x 4 Transfer Matrices for LC Layers 3198.8 Transformation of the Elements of EW Jones Vectors and EW Jones Matrices Under Changes of Eigenwave Bases 3228.8.1 Coordinates of the EW Jones Vector of a Wave Field in Different Eigenwave Bases 3228.8.2 EW Jones Operators in Different Eigenwave Bases 326References 3289 Choice of Eigenwave Bases for Isotropic, Uniaxial, and Biaxial Media 3319.1 General Aspects of EWB Specification. EWB-generating routines 3319.2 Isotropic Media 3389.3 Uniaxial Media 3429.4 Biaxial Media 352References 36510 Efficient Methods for Calculating Optical Characteristics of Layered Systems for Quasimonochromatic Incident Light. Main Routines of LMOPTICS Library 36710.1 EW Stokes Vectors and EW Mueller Matrices 36810.2 Calculation of the EW Mueller Matrices of the Overall Transmission and Reflection of a System Consisting of "Thin" and "Thick" Layers 37510.3 Main Routines of LMOPTICS 38410.3.1 Routines for Computing 4 x 4 Transfer Matrices and EW Jones Matrices 38410.3.2 Routines for Computing EW Mueller Matrices 38810.3.3 Other Useful Routines 391References 39211 Calculation of Transmission Characteristics of Inhomogeneous Liquid Crystal Layers with Negligible Bulk Reflection 39311.1 Application of Jones Matrix Methods to Inhomogeneous LC Layers 39411.1.1 Calculation of Transmission Jones Matrices of LC Layers Using the Classical Jones Calculus 39411.1.2 Extended Jones Matrix Methods 40411.2 NBRA. Basic Differential Equations 40911.3 NBRA. Numerical Methods 42011.3.1 Approximating Multilayer Method 42111.3.2 Discretization Method 42711.3.3 Power Series Method 42811.4 NBRA. Analytical Solutions 43011.4.1 Twisted Structures 43011.4.2 Nontwisted Structures 43211.4.3 NBRA and GOA. Adiabatic and Quasiadiabatic Approximations 43411.5 Effect of Errors in Values of the Transmission Matrix of the LC Layer on the Accuracy of Modeling the Transmittance of the LCD Panel 437References 43812 Some Approximate Representations in EWJones Matrix Method and Their Application in Solving Optimization and Inverse Problems for LCDs 44112.1 Theory of STUM Approximation 44212.2 Exact and Approximate Expressions for Transmission Operators of Interfaces at Normal Incidence 44712.3 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 46312.4 Immersion Model of the Polarization-Converting System of an LCD 46612.5 Determining Configurational and Optical Parameters of LC Layers With a Twisted Structure: Spectral Fitting Method 47412.5.1 How to Bring Together the Experiment and Unitary Approximation 47612.5.2 Parameterization and Solving the Inverse Problem 48012.5.3 Appendix to Section 12.5 48912.6 Optimization of Compensation Systems for Enhancement of Viewing Angle Performance of LCDs 490References 50413 A FewWords About Modeling of Fine-Structure LCDs and the Direct Ray Approximation 50713.1 Virtual Microscope 50813.2 Directional Illumination and Diffuse Illumination 513References 516A LCD Modeling Software MOUSE-LCD Used for the HKUST Students Final Year Projects (FYP) from 2003 to 2011 517A.1 Introductory Remarks 517A.2 Fast LCD 517A.2.1 TN Cell 517A.2.2 Effect of d/p Ratio 519A.2.3 Effect of K22/K11 520A.2.4 Effect of K33/K11 520A.2.5 Effect of delta 521A.2.6 Effect of gamma 521A.2.7 Effect of Anchoring Strength W 523A.2.8 Optimized TN Cell With Fast Response Time 523A.2.9 Other LC Modes 524A.3 Color LCD 524A.3.1 The Super-Twisted Nematic Cell 524A.3.2 STN Birefringent Colors in Transmissive and Reflective Modes 525A.4 Transflective LCD 525A.4.1 Vertical Aligned Nematic Cell 525A.5 Switchable Viewing Angle LCD 535A.6 Optimal e-paper Configurations 535A.7 Color Filter Optimization 536References 536B Some Derivations and Examples 537B.1 Conservation Law for Energy Flux 537B.2 Lorentz’s Lemma 538B.3 Nonexponential Waves 538B.4 To the Power Series Method (Section 11.3.3) 540B.5 One of the Ways to Obtain the Explicit Expressions for Transmission Jones Matrices of an Ideal Twisted LC Layer 541Reference 543Index 545

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