Optics of Liquid Crystal Displays Second Edition

POCHIYEH CLAIRE GU

WILEY A John Wiley & Sons, Inc., Publication

Contents

Preface xiii Preface to the First Edition xv

Chapter 1. Preliminaries 1

1.1. Basic Components of LCDs 2 1.1.1. Polarizers 2 1.1.2. Transparent Electrodes 4 1.1.3. Liquid Crystal Cell 6 1.1.4. Birefringent Thin Film Compensators 7 1.1.5. Color Filters 8 1.1.6. Brightness Enhancement Films (BEFs) 9 1.1.7. AM and TFTs (Active Matrix and Thin Film

Transistors) 11 1.1.8. Diffusers 12 1.1.9. Backlights 14

1.2. Properties of Liquid Crystals 15 1.2.1. Orientational Order Parameter 20 1.2.2. Dielectric Constants 21 1.2.3. Refractive Index 24 1.2.4. Elastic Constants 26 1.2.5. Viscosity—Rotational Viscosity 27 1.2.6. Surface Alignment and Rubbing 27 1.2.7. Field-Induced Distortion—Electro-Optical Effect 30 1.2.8. Dynamics of Molecular Rotation—Rise Time

and Decay Time 39 References 47 Suggested Readings 48 Problems 48

Chapter 2. Polarization of Optical Waves 54

2.1. Monochromatic Plane Waves and Their Polarization States 54 2.1.1. Linear Polarization States 56 2.1.2. Circular Polarization States 57 2.1.3. Elliptical Polarization States 57

2.2. Complex Number Representation 61 2.3. Jones Vector Representation 62 2.4. 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. Pancharatnam Phase 77 References 78 Problems 78

Chapter 3. Electromagnetic Propagation in Anisotropic Media 82 3.1. Maxwell Equations and Dielectric Tensor 82

3.1.1. Lorentz Reciprocity Theorem 89 3.2. Plane Waves in Homogeneous Media and Normal Surface 90

3.2.1. к in the xy-Plane 95 3.2.2. к in the yz-Plane 95 3.2.3. к in the z*-Plane 96 3.2.4. Classification of Media 97 3.2.5. Power Flow in Anisotropic Media (I) 100 3.2.6. Power Flow in Anisotropic Media (II) 104

3.3. Light Propagation in Uniaxial Media 107 3.3.1. Propagation Perpendicular to the c-Axis 109 3.3.2. Propagation in the *г-Р1апе 110 3.3.3. Propagation along the c-Axis 111

3.4. Double Refraction at a Boundary 112 3.5. Anisotropic Absorption and Polarizers 126

3.5.1. Extinction Ratio and Real Sheet Polarizers 127 3.5.2. Field of View of Crossed Polarizers 128 3.5.3. Polarization States DO1 and Do2 130 3.5.4. Reflective Polarizers 133

3.6. Optical Activity and Faraday Rotation 139 3.6.1. Faraday Rotation 149

3.7. Light Propagation in Biaxial Media 151 3.7.1. Method of Index Ellipsoid 154 3.7.2. Perturbation Approach 158 3.7.3. Classification of Biaxial Crystals 160 References 162 Problems 163

Chapter 4. Jones Matrix Method 173 4.1. Jones Matrix Formulation 173

4.1.1. Example: A Half-Wave Retardation Plate 178 4.1.2. Example: A Quarter-Wave Plate 178 4.1.3. General Properties of the Jones Matrix 179 4.1.4. 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

4.2. Intensity Transmission Spectrum 199 4.2.1. Example: A Birefringent Plate Sandwiched

between Parallel Polarizers (an a-Plate between Parallel Polarizers) 201

4.2.2. Example: A Birefringent Plate Sandwiched between a Pair of Crossed Polarizers (an a-Plate between Crossed Polarizers) 202

4.2.3. Example: A Birefringent Plate Sandwiched between a Pair of Polarizers (an a-Plate between Two Polarizers) 203

4.2.4. Example: A Birefringent Plate Sandwiched between a Pair of Polarizers (a c-Plate between Two Polarizers) 204

4.2.5. Example: A Birefringent Plate Sandwiched between a Pair of Crossed Polarizers (a c-Plate between Crossed Polarizers) 204

4.2.6. Example: A Birefringent Plate Sandwiched between a Pair of Parallel Polarizers (a c-Plate between Parallel Polarizers) 204

4.2.7. An Alternative Approach 205 4.2.8. Method of Projection Operators and

Propagation Operators 206 4.3. Optical Properties of TN-LC (Adiabatic Following or

Waveguiding) 208 4.3.1. Adiabatic Following (Waveguiding in TN-LC) 210 4.3.2. 90° TN-LC 211 4.3.3. Transmission Properties of a General

TN-LCD 215 4.3.4. Normal Modes of Propagation in a General

TN-LC 218 4.4. Phase Retardation at Oblique Incidence 224

4.4.1. a-Plates 225 4.4.2. c-Plates 228

4.5. Conoscopy 229 4.5.1. a-Plate of Uniaxial Samples 229 4.5.2. c-Plate of Uniaxial Crystals 231 4.5.3. c-Cut Biaxial Plate 233

4.6. 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. Polarization States of Ordinary Mode in

Polarizers 252 4.8. Achromatic Wave Plates 254 4.9. Broadband Quasi-Circular Polarizers 264 4.10. Wide Field-of-View Elements 269

4.10.1. Lyot-I Wide Field-of-View Elements 271 4.10.2. Lyot-II Wide Field-of-View Elements 273 4.10.3. Lyot-III Wide Field-of-View Elements 275 References 276 Suggested Readings 276 Problems 277

Chapter 5. Liquid Crystal Displays 290

5.1. VA-LCDs 291 5.1.1. Principle of Operation 291 5.1.2. Transmission Property of Field-Off State 293 5.1.3. Transmission Property of Field-On State 294 5.1.4. Multidomain Vertically Aligned Liquid Crystal

Display (MVA-LCD) 312 5.2. IPS-LCDs 316

5.2.1. Principles of Operation 317 5.2.2. Transmission Property of Field-Off State 320 5.2.3. Transmission Property of Field-On State 324

5.3 TN-LCDs 331 5.3.1. Principle of Operation 332 5.3.2. Transmission Property of Field-Off State 335 5.3.3. Transmission Property of Field-On State 339

5.4. STN Displays 365 5.4.1. Steepness of Electrodistortion Curves of STN

Cell 367 5.4.2. Transmission Properties of STN-LCD in the

Field-Off State 374 5.4.3 Transmission of STN-LCD in the Field-On

State 381 5.5. Nematic Liquid Crystal Display (N-LCD) Modes 388

5.5.1. PA Cells 389 5.5.2. Bend-Aligned (BA) Cells 394

5.6. Polymer-Dispersed Liquid Crystal Displays (PD-LCDs) 398 5.7. Reflective LCDs 404 5.8. Transflective LCDs 407

CONTENTS ix

5.9. 5.10.

5.11.

»ter 6.

6.1. 6.2.

6.3.

6.4.

•ter 7.

7.1. 7.2. 7.3.

7.4.

7.5. 7.6.

Projection Displays Other Display Systems 5.10.1. Ferroelectric LCDs 5.10.2. Cholesteric LCD 5.10.3. Liquid Crystal on Silicon (LCoS) Summary References Suggested Readings Problems

Matrix Addressing, Colors, and Properties of LCDs

Multiplexed Displays Active Matrix (AM) Displays 6.2.1. Principle of Thin Film Transistor (TFT)

Operation 6.2.2. Array Fabrication 6.2.3. Cell Assembly Optical Throughput of TFT-LCDs 6.3.1. Polarizers 6.3.2. Color Filters Colors in LCDs 6.4.1. Addition (or Mixing) of Colors and CIE 1976

Color Space (L*u*v*) References Suggested Readings Problems

Optical Properties of Cholesteric Liquid Crystals

Optical Phenomena in CLCs Dielectric Tensor of an Ideal CLC Exact Solutions at Normal Incidence 7.3.1. Dispersion Relation 7.3.2. Polarization States of Normal Modes 7.3.3. Power Orthogonality Bragg Regime {n0p < X < nep)—Coupled-Mode Analysis 7.4.1. Reflectance of CLCs Mauguin Regime (A, « 0.5/?An) Circular Regime 7.6.1. Short Wavelength Circular Regime

(0.5npAn « X « p) 7.6.2. Long Wavelength Circular Regime (nj> « X) References Suggested Readings Problems

410 412 412 416 417 419 419 421 422

426

426 430

431 440 445 446 446 448 450

452 457 458 458

461

461 462 465 466 467 471 471 475 477 479

479 479 481 481 481

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 8.1.3. Small Birefringence Approximation 495 8.1.4. Comparison with the Conventional Jones

Calculus 500 8.1.5. Crossed Polarizers 502 8.1.6. Arbitrary c-Axis Orientation 505 8.1.7. Application to LCDs 509 8.1.8. Generalized Jones Matrix Method 517

8.2. Another Extended Jones Matrix Method 523 8.3. 4 x 4 Matrix Method 526

8.3.1. Mathematical Formulation 526 8.3.2. Reflection and Transmission 530 8.3.3. Berreman's 4 x 4 Matrix Method 532

8.4. General Properties of A 4 x 4 Matrix 533 8.5. Mueller Matrix Algebra and Jones Matrix Algebra 546 8.6. Reciprocity Theorem in Anisotropic Layered Media 562

References 567 Problems 567

Chapter 9. Optical Compensators for Liquid Crystal Displays 570

9.1. Viewing Angle Characteristics of LCDs 571 9.1.1. TN-LCDs 572 9.1.2. VA-LCDs 579 9.1.3. Multidomain VA-LCDs (MVA-LCDs) 589 9.1.4. IPS-LCDs 589

9.2. Origin of Leakage of Light in LCDs and Compensators 595 9.2.1. Leakage of Light through Crossed Polarizers 598 9.2.2. Leakage of Light due to LC Cell 601 9.2.3. Birefringent Thin Film Compensators 605

9.3. LCDs with Compensators 614 9.3.1. CR Improvement in LCDs with Birefringence

Compensators and Polarization Compensators 615 9.3.2. Gray Level Performance of LCDs with

Birefringence Compensators and Polarization Compensators 631

9.4. Compensation Film with Positive Birefringence (O-Plate) 648 9.5. Biaxial Compensation Film 654 9.6. Materials for Optical Phase Retardation Compensation 659

9.6.1. ö-Plates 659 9.6.2. oPlates 659 9.6.3. 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. 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