Optics of Liquid Crystal Displays

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1 Optics of Liquid Crystal Displays Second Edition POCHIYEH CLAIRE GU WILEY A John Wiley & Sons, Inc., Publication

Contents Preface Preface to the First Edition xiii xv Chapter 1. Preliminaries 1 1.1. Basic Components of LCDs 2 1.1.1. Polarizers 2 1.1.2. Transparent Electrodes 4

2 Contents Preface Preface to the First Edition xiii xv Chapter 1. Preliminaries Basic Components of LCDs Polarizers Transparent Electrodes Liquid Crystal Cell Birefringent Thin Film Compensators Color Filters Brightness Enhancement Films (BEFs) AM and TFTs (Active Matrix and Thin Film Transistors) Diffusers Backlights Properties of Liquid Crystals Orientational Order Parameter Dielectric Constants Refractive Index Elastic Constants Viscosity Rotational Viscosity Surface Alignment and Rubbing Field-Induced Distortion Electro-Optical Effect Dynamics of Molecular Rotation Rise Time and Decay Time 39 References 47 Suggested Readings 48 Problems 48 Chapter 2. Polarization of Optical Waves Monochromatic Plane Waves and Their Polarization States Linear Polarization States Circular Polarization States Elliptical Polarization States Complex Number Representation Jones Vector Representation Partially Polarized and Unpolarized Light 64

VI CONTENTS 2.5. Poincare Sphere 67 2.5.1. Phase Retarders 70 2.5.2. Polarization Transformation Using Retarders and the Graphical Representation on the Poincare Sphere 71 2.5.3.

3 VI CONTENTS 2.5. Poincare Sphere Phase Retarders Polarization Transformation Using Retarders and the Graphical Representation on the Poincare Sphere Pancharatnam Phase 77 References 78 Problems 78 Chapter 3. Electromagnetic Propagation in Anisotropic Media Maxwell Equations and Dielectric Tensor Lorentz Reciprocity Theorem Plane Waves in Homogeneous Media and Normal Surface к in the xy-plane к in the yz-plane к in the z*-plane Classification of Media Power Flow in Anisotropic Media (I) Power Flow in Anisotropic Media (II) Light Propagation in Uniaxial Media Propagation Perpendicular to the c-axis Propagation in the *г-р1апе Propagation along the c-axis Double Refraction at a Boundary Anisotropic Absorption and Polarizers Extinction Ratio and Real Sheet Polarizers Field of View of Crossed Polarizers Polarization States D O1 and D o Reflective Polarizers Optical Activity and Faraday Rotation Faraday Rotation Light Propagation in Biaxial Media Method of Index Ellipsoid Perturbation Approach Classification of Biaxial Crystals 160 References 162 Problems 163 Chapter 4. Jones Matrix Method Jones Matrix Formulation Example: A Half-Wave Retardation Plate Example: A Quarter-Wave Plate General Properties of the Jones Matrix Eignvectors of Jones Matrix 186

CONTENTS 4.1.5. Linearly Polarized Inputs with Linearly Polarized Outputs 188 4.1.6. Equivalent Circuit of a General Birefringent Network 190 4.1.7. Tunable Wave Plates 192 4.1.8. Circular and Quasi-Circular Polarizers 194 4.

4 CONTENTS Linearly Polarized Inputs with Linearly Polarized Outputs Equivalent Circuit of a General Birefringent Network Tunable Wave Plates Circular and Quasi-Circular Polarizers Intensity Transmission Spectrum Example: A Birefringent Plate Sandwiched between Parallel Polarizers (an a-plate between Parallel Polarizers) Example: A Birefringent Plate Sandwiched between a Pair of Crossed Polarizers (an a-plate between Crossed Polarizers) Example: A Birefringent Plate Sandwiched between a Pair of Polarizers (an a-plate between Two Polarizers) Example: A Birefringent Plate Sandwiched between a Pair of Polarizers (a c-plate between Two Polarizers) Example: A Birefringent Plate Sandwiched between a Pair of Crossed Polarizers (a c-plate between Crossed Polarizers) Example: A Birefringent Plate Sandwiched between a Pair of Parallel Polarizers (a c-plate between Parallel Polarizers) An Alternative Approach Method of Projection Operators and Propagation Operators Optical Properties of TN-LC (Adiabatic Following or Waveguiding) Adiabatic Following (Waveguiding in TN-LC) TN-LC Transmission Properties of a General TN-LCD Normal Modes of Propagation in a General TN-LC Phase Retardation at Oblique Incidence a-plates c-plates Conoscopy a-plate of Uniaxial Samples c-plate of Uniaxial Crystals c-cut Biaxial Plate Reflection Property of a General TN-LCD with a Back Mirror 234

VUl CONTENTS 4.7. Phase Retardation of a Biaxial Plate 242 4.7.1. Small 0 Approximation (Assume a «1, ß «1) 246 4.7.2. The Polarization States of Modes of Propagation 247 4.7.3.

5 VUl CONTENTS 4.7. Phase Retardation of a Biaxial Plate Small 0 Approximation (Assume a «1, ß «1) The Polarization States of Modes of Propagation Polarization States of Ordinary Mode in Polarizers Achromatic Wave Plates Broadband Quasi-Circular Polarizers Wide Field-of-View Elements Lyot-I Wide Field-of-View Elements Lyot-II Wide Field-of-View Elements Lyot-III Wide Field-of-View Elements 275 References 276 Suggested Readings 276 Problems 277 Chapter 5. Liquid Crystal Displays VA-LCDs Principle of Operation Transmission Property of Field-Off State Transmission Property of Field-On State Multidomain Vertically Aligned Liquid Crystal Display (MVA-LCD) IPS-LCDs Principles of Operation Transmission Property of Field-Off State Transmission Property of Field-On State TN-LCDs Principle of Operation Transmission Property of Field-Off State Transmission Property of Field-On State STN Displays Steepness of Electrodistortion Curves of STN Cell Transmission Properties of STN-LCD in the Field-Off State Transmission of STN-LCD in the Field-On State Nematic Liquid Crystal Display (N-LCD) Modes PA Cells Bend-Aligned (BA) Cells Polymer-Dispersed Liquid Crystal Displays (PD-LCDs) Reflective LCDs Transflective LCDs 407

CONTENTS 5.9. 5.10. 5.11. Projection Displays Other Display Systems 5.10.1. Ferroelectric LCDs 5.10.2. Cholesteric LCD 5.10.3.

6 CONTENTS Projection Displays Other Display Systems Ferroelectric LCDs Cholesteric LCD Liquid Crystal on Silicon (LCoS) Summary References Suggested Readings Problems ix »ter Matrix Addressing, Colors, and Properties of LCDs Multiplexed Displays Active Matrix (AM) Displays Principle of Thin Film Transistor (TFT) Operation Array Fabrication Cell Assembly Optical Throughput of TFT-LCDs Polarizers Color Filters Colors in LCDs Addition (or Mixing) of Colors and CIE 1976 Color Space (L*u*v*) References Suggested Readings Problems ter Optical Properties of Cholesteric Liquid Crystals Optical Phenomena in CLCs Dielectric Tensor of an Ideal CLC Exact Solutions at Normal Incidence Dispersion Relation Polarization States of Normal Modes Power Orthogonality Bragg Regime {n 0 p < X < n e p) Coupled-Mode Analysis Reflectance of CLCs Mauguin Regime (A, «0.5/?An) Circular Regime Short Wavelength Circular Regime (0.5npAn «X «p) Long Wavelength Circular Regime (nj> «X) References Suggested Readings Problems

$X CONTENTS Chapter 8. Extended Jones Matrix Method 485 8.1. Mathematical Formulation and Applications 486 8.1.1. Reflection and Refraction at the Interface 486 8.1.2. Matrix Formulation 493$

7 X CONTENTS Chapter 8. Extended Jones Matrix Method Mathematical Formulation and Applications Reflection and Refraction at the Interface Matrix Formulation Small Birefringence Approximation Comparison with the Conventional Jones Calculus Crossed Polarizers Arbitrary c-axis Orientation Application to LCDs Generalized Jones Matrix Method Another Extended Jones Matrix Method x4 Matrix Method Mathematical Formulation Reflection and Transmission Berreman's 4x4 Matrix Method General Properties of A 4 x 4 Matrix Mueller Matrix Algebra and Jones Matrix Algebra Reciprocity Theorem in Anisotropic Layered Media 562 References 567 Problems 567 Chapter 9. Optical Compensators for Liquid Crystal Displays Viewing Angle Characteristics of LCDs TN-LCDs VA-LCDs Multidomain VA-LCDs (MVA-LCDs) IPS-LCDs Origin of Leakage of Light in LCDs and Compensators Leakage of Light through Crossed Polarizers Leakage of Light due to LC Cell Birefringent Thin Film Compensators LCDs with Compensators CR Improvement in LCDs with Birefringence Compensators and Polarization Compensators Gray Level Performance of LCDs with Birefringence Compensators and Polarization Compensators Compensation Film with Positive Birefringence (O-Plate) Biaxial Compensation Film Materials for Optical Phase Retardation Compensation ö-plates oplates o-plates 659

CONTENTS XI 9.6.4. Form Birefringence 660 9.6.5. Form Birefringence in Thin-Layered Media 660 9.6.6. Form Birefringence in Composite Media 662 References 664 Problems 666 Appendix A.

8 CONTENTS XI Form Birefringence Form Birefringence in Thin-Layered Media Form Birefringence in Composite Media 662 References 664 Problems 666 Appendix A. Elastic and Electromagnetic Energy Density 674 Appendix B. Electro-Optical Distortion Tilt Mode 680 Appendix С. Electro-Optical Distortion Twist Mode 689 Appendix D. Electro-Optical Distortion in a TN-LC 694 Appendix E. Electro-Optical Distortion in an STN-LC 702 Appendix F. Form Birefringence of Composite Media 709 Appendix G. Spherical Trigonometry 712 Appendix H. Mie Scattering and Diffusers 721 Appendix I. Variational Principles and Lagrange's Equations 741 Author Index 745 Subject Index 749

Chap. 2. Polarization of Optical Waves

Chap. 2. Polarization of Optical Waves 2.1 Polarization States - Direction of the Electric Field Vector : r E = E xˆ + E yˆ E x x y ( ω t kz + ϕ ), E = E ( ωt kz + ϕ ) = E cos 0 x cos x y 0 y - Role :