Focusing on polarization matrix optics in many forms, this book includes coverage of a wide range of methods which have been applied to LCD modeling, ranging from the simple Jones matrix method to elaborate and high accuracy algorithms suitable for off-axis optics. Researchers and scientists are constantly striving for improved performance, faster response times, wide viewing angles, improved colour in liquid crystal display development, and with this comes the need to model LCD devices effectively. The authors have significant experience in dealing with the problems related to the practical application of liquid crystals, in particular their optical performance.
Key features:
- Explores analytical solutions and approximations to important cases in the matrix treatment of different LC layer configurations, and the application of these results to improve the computational method
- Provides the analysis of accuracies of the different approaches discussed in the book
- Explains the development of the Eigenwave Jones matrix method which offers a path to improved accuracy compared to Jones matrix and extended Jones matrix formalisms, while achieving significant improvement in computational speed and versatility compared to full 4x4 matrix methods
- Includes a companion website hosting the authors' program library LMOPTICS (FORTRAN 90), a collection of routines for calculating the optical characteristics of stratified media, the use of which allows for the easy implementation of the methods described in this book. The website also contains a set of sample programs (source codes) using LMOPTICS, which exemplify the application of these methods in different situations
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 Inhomogeneous Nonabsorbing Anisotropic Layer with Negligible
Bulk Reflection at Normal Incidence. Simple Representations of Polarization
Matrices of LC Layers at Normal Incidence 463 12.4 Immersion Model of the
Polarization-Converting System of an LCD 466 12.5 Determining
Configurational and Optical Parameters of LC Layers With a Twisted Structure:
Spectral Fitting Method 474 12.5.1 How to Bring Together the Experiment and
Unitary Approximation 476 12.5.2 Parameterization and Solving the Inverse
Problem 480 12.5.3 Appendix to Section 12.5 489 12.6 Optimization of
Compensation Systems for Enhancement of Viewing Angle Performance of LCDs 490
References 504 13 A FewWords About Modeling of Fine-Structure LCDs and the
Direct Ray Approximation 507 13.1 Virtual Microscope 508 13.2 Directional
Illumination and Diffuse Illumination 513 References 516 A LCD Modeling
Software MOUSE-LCD Used for the HKUST Students Final Year Projects (FYP) from
2003 to 2011 517 A.1 Introductory Remarks 517 A.2 Fast LCD 517 A.2.1 TN
Cell 517 A.2.2 Effect of d/p Ratio 519 A.2.3 Effect of K22/K11 520 A.2.4
Effect of K33/K11 520 A.2.5 Effect of delta 521 A.2.6 Effect of gamma 521
A.2.7 Effect of Anchoring Strength W 523 A.2.8 Optimized TN Cell With Fast
Response Time 523 A.2.9 Other LC Modes 524 A.3 Color LCD 524 A.3.1 The
Super-Twisted Nematic Cell 524 A.3.2 STN Birefringent Colors in Transmissive
and Reflective Modes 525 A.4 Transflective LCD 525 A.4.1 Vertical Aligned
Nematic Cell 525 A.5 Switchable Viewing Angle LCD 535 A.6 Optimal e-paper
Configurations 535 A.7 Color Filter Optimization 536 References 536 B Some
Derivations and Examples 537 B.1 Conservation Law for Energy Flux 537 B.2
Lorentz s Lemma 538 B.3 Nonexponential Waves 538 B.4 To the Power Series
Method (Section 11.3.3) 540 B.5 One of the Ways to Obtain the Explicit
Expressions for Transmission Jones Matrices of an Ideal Twisted LC Layer 541
Reference 543 Index 545
