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JWUS_LC-Khoo_Prelims.qxd 1/19/2007 12:32 PM Page i Liquid Crystals JWUS_LC-Khoo_Prelims.qxd 1/19/2007 12:32 PM Page ii JWUS_LC-Khoo_Prelims.qxd 1/19/2007 12:32 PM Page iii Liquid Crystals Second Edition IAM-CHOON KHOO WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION JWUS_LC-Khoo_Prelims.qxd 1/19/2007 12:32 PM Page iv Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, or online at http://www.wiley.com/go/permission. 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For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at 877-762-2974, outside the United States at 317-572-3993 or fax 317- 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Wiley Bicentennial Logo : Richard J. Pacifico Library of Congress Cataloging-in-Publication Data: Khoo, Iam-Choon. Liquid crystals / Iam-Choon Khoo. —2nd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-471-75153-3 1. Liquid crystals. I. Title. QD923. K49 2007 530.4’29—dc22 2006048260 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 JWUS_LC-Khoo_Contents.qxd 1/9/2007 3:31 PM Page v Contents Preface xiii Chapter 1. Introduction to Liquid Crystals 1 1.1. Molecular Structures and Chemical Compositions 1 1.1.1. Chemical Structures 1 1.2. Electronic Properties 3 1.2.1. Electronic Transitions and Ultraviolet Absorption 3 1.2.2. Visible and Infrared Absorption 4 1.3. Lyotropic,Polymeric,and Thermotropic Liquid Crystals 6 1.3.1. Lyotropic Liquid Crystals 6 1.3.2. Polymeric Liquid Crystals 6 1.3.3. Thermotropic Liquid Crystals:Nematics, Cholesterics,and Smectics 7 1.3.4. Other Liquid Crystalline Phases and Molecular Engineered Structures 10 1.4. Mixtures and Composites 11 1.4.1. Mixtures 12 1.4.2. Dye-Doped Liquid Crystals 13 1.4.3. Polymer-Dispersed Liquid Crystals 14 1.5. Liquid Crystal Cells and Sample Preparation 14 1.5.1. Bulk Thin Film 15 1.5.2. Liquid Crystal Optical Slab Waveguide,Fiber, and Nanostructured Photonic Crystals 17 References 19 Chapter 2. Order Parameter,Phase Transition,and Free Energies 22 2.1. Basic Concepts 22 2.1.1. Introduction 22 2.1.2. Scalar and Tensor Order Parameters 23 2.1.3. Long- and Short-Range Order 25 2.2. Molecular Interactions and Phase Transitions 26 2.3. Molecular Theories and Results for the Liquid Crystalline Phase 26 2.3.1. Maier-Saupe Theory:Order Parameter Near T 27 c 2.3.2. Nonequilibrium and Dynamical Dependence of the Order Parameter 29 v JWUS_LC-Khoo_Contents.qxd 1/9/2007 3:31 PM Page vi vi CONTENTS 2.4. Isotropic Phase of Liquid Crystals 32 2.4.1. Free Energy and Phase Transition 32 2.4.2. Free Energy in the Presence of an Applied Field 33 References 35 Chapter 3. Nematic Liquid Crystals 36 3.1. Introduction 36 3.2. Elastic Continuum Theory 36 3.2.1. The Vector Field:Direct Axis nˆ ((cid:1)r) 36 3.2.2. Elastic Constants,Free Energies,and Molecular Fields 38 3.3. Dielectric Constants and Refractive Indices 41 3.3.1. dc and Low-Frequency Dielectric Permittivity, Conductivities,and Magnetic Susceptibility 41 3.3.2. Free Energy and Torques by Electric and Magnetic Fields 44 3.4. Optical Dielectric Constants and Refractive Indices 45 3.4.1. Linear Susceptibility and Local Field Effect 45 3.4.2. Equilibrium Temperature and Order Parameter Dependences of Refractive Indices 47 3.5. Flows and Hydrodynamics 51 3.5.1. Hydrodynamics of Ordinary Isotropic Fluids 52 3.5.2. General Stress Tensor for Nematic Liquid Crystals 55 3.5.3. Flows with Fixed Director Axis Orientation 55 3.5.4. Flows with Director Axis Reorientation 57 3.6. Field-Induced Director Axis Reorientation Effects 58 3.6.1. Field-Induced Reorientation without Flow Coupling:Freedericksz Transition 58 3.6.2. Reorientation with Flow Coupling 61 References 62 Chapter 4. Cholesteric,Smectic,and Ferroelectric Liquid Crystals 64 4.1. Cholesteric Liquid Crystals 64 4.1.1. Free Energies 64 4.1.2. Field-Induced Effects and Dynamics 66 4.1.3. Twist and Conic Mode Relaxation Times 69 4.2. Light Scattering in Cholesterics 70 4.2.1. General Optical Propagation and Reflection: Normal Incidence 70 4.2.2. Cholesteric Liquid Crystal as a One-Dimensional Photonic Crystal 74 4.2.3. Cholesteric Liquid Crystals with Magneto-Optic Activity:Negative Refraction Effect 78 JWUS_LC-Khoo_Contents.qxd 1/9/2007 3:31 PM Page vii CONTENTS vii 4.3. Smectic and Ferroelectric Liquid Crystals:A Quick Survey 80 4.4. Smectic-A Liquid Crystals 82 4.4.1. Free Energy 82 4.4.2. Light Scattering in SmA Liquid Crystals 84 4.5. Smectic-C Liquid Crystals 86 4.5.1. Free Energy 86 4.5.2. Field-Induced Director Axis Rotation in SmC Liquid Crystals 87 4.6. Smectic-C* and Ferroelectric Liquid Crystals 88 4.6.1. Free Energy of Ferroelectric Liquid Crystals 89 4.6.2. Smectic-C*–Smectic-A Phase Transition 93 References 95 Chapter 5. Light Scatterings 97 5.1. Introduction 97 5.2. General Electromagnetic Formalism of Light Scattering in Liquid Crystals 98 5.3. Scattering from Director Axis Fluctuations in Nematic Liquid Crystals 100 5.4. Light Scattering in the Isotropic Phase of Liquid Crystals 104 5.5. Temperature,Wavelength,and Cell Geometry Effects on Scattering 107 5.6. Spectrum of Light and Orientation Fluctuation Dynamics 109 5.7. Raman Scatterings 111 5.7.1. Introduction 111 5.7.2. Quantum Theory of Raman Scattering: Scattering Cross Section 112 5.8. Brillouin and Rayleigh Scatterings 115 5.8.1. Brillouin Scattering 117 5.8.2. Rayleigh Scattering 119 5.9. Nonlinear Light Scattering:Supraoptical Nonlinearity of Liquid Crystals 120 References 122 Chapter 6. Liquid Crystal Optics and Electro-Optics 124 6.1. Introduction 124 6.2. Review of Electro-Optics of Anisotropic and Birefringent Crystals 125 6.2.1. Anisotropic,Uniaxial,and Biaxial Optical Crystals 125 6.2.2. Index Ellipsoid in the Presence of an Electric Field:Linear Electro-Optics Effect 127 6.2.3. Polarizers and Retardation Plate 128 6.2.4. Basic Electro-Optics Modulation 130 JWUS_LC-Khoo_Contents.qxd 1/9/2007 3:31 PM Page viii viii CONTENTS 6.3. Electro-Optics of Nematic Liquid Crystals 131 6.3.1. Director Axis Reorientation in Homeotropic and Planar Cells:Dual-Frequency Liquid Crystals 131 6.3.2. Freedericksz Transition Revisited 133 6.3.3. Field-Induced Refractive Index Change and Phase Shift 136 6.4. Nematic Liquid Crystal Switches and Displays 138 6.4.1. Liquid Crystal Switch:On-Axis Consideration for Twist,Planar,and Homeotropic Aligned Cells 139 6.4.2. Off-Axis Transmission,Viewing Angle,and Birefringence Compensation 139 6.4.3. Liquid Crystal Display Electronics 141 6.5. Electro-Optical Effects in Other Phases of Liquid Crystals 142 6.5.1. Surface Stabilized FLC 142 6.5.2. Soft-Mode FLCs 144 6.6. Nondisplay Applications of Liquid Crystals 146 6.6.1. Liquid Crystal Spatial Light Modulator 146 6.6.2. Tunable Photonic Crystals with Liquid Crystal Infiltrated Nanostructures 148 6.6.3. Tunable Frequency Selective Planar Structures 148 6.6.4. Liquid Crystals for Molecular Sensing and Detection 150 6.6.5. Beam Steering,Routing,and Optical Switching and Laser Hardened Optics 152 References 153 Chapter 7. Electromagnetic Formalisms for Optical Propagation 157 7.1. Introduction 157 7.2. Electromagnetism of Anisotropic Media Revisited 158 7.2.1. Maxwell Equations and Wave Equations 158 7.2.2. Complex Refractive Index 159 7.2.3. Negative Index Material 160 7.2.4. Normal Modes,Power Flow,and Propagation Vectors in a Lossless Isotropic Medium 163 7.2.5. Normal Modes and Propagation Vectors in a Lossless Anisotropic Medium 164 7.3. General Formalisms for Polarized Light Propagation Through Liquid Crystal Devices 168 7.3.1. Plane-Polarized Wave and Jones Vectors 169 7.3.2. Jones Matrix Method for Propagation Through a Nematic Liquid Crystal Cell 173 7.3.3. Oblique Incidence:4(cid:1)4 Matrix Methods 175 7.4. Extended Jones Matrix Method 177 JWUS_LC-Khoo_Contents.qxd 1/9/2007 3:31 PM Page ix CONTENTS ix 7.5. Finite-Difference Time-Domain Technique 181 7.5.1. The Implementation of FDTD Methods 181 7.5.2. Example:FDTD Computations of the Twisted Nematic Cell in One Dimension 186 References 188 Chapter 8. Laser-Induced Orientational Optical Nonlinearities in Liquid Crystals 190 8.1. General Overview of Liquid Crystal Nonlinearities 190 8.2. Laser-Induced Molecular Reorientations in the Isotropic Phase 193 8.2.1. Individual Molecular Reorientations in Anisotropic Liquids 193 8.2.2. Correlated Molecular Reorientation Dynamics 196 8.2.3. Influence of Molecular Structure on Isotropic Phase Reorientational Nonlinearities 198 8.3. Molecular Reorientations in the Nematic Phase 200 8.3.1. Simplified Treatment of Optical Field-Induced Director Axis Reorientation 201 8.3.2. More Exact Treatment of Optical Field-Induced Director Axis Reorientation 204 8.3.3. Nonlocal Effect and Transverse Dependence 205 8.4. Nematic Phase Reorientation Dynamics 206 8.4.1. Plane Wave Optical Field 206 8.4.2. Sinusoidal Optical Intensity 210 8.5. Laser-Induced Dopant-Assisted Molecular Reorientation and Trans-Cis Isomerism 211 8.6. DC Field Aided Optically Induced Nonlinear Optical Effects in Liquid Crystals:Photorefractivity 213 8.6.1. Orientational Photorefractivity:Bulk Effects 215 8.6.2. Some Experimental Results and Surface Charge/Field Contribution 220 8.7. Reorientation and Nonelectronic Nonlinear Optical Effects in Smectic and Cholesteric Phases 221 8.7.1. Smectic Phase 221 8.7.2. Cholesteric Phase 222 References 223 Chapter 9. Thermal,Density,and Other Nonelectronic Nonlinear Mechanisms 227 9.1. Introduction 227 9.2. Density and Temperature Changes Induced by Sinusoidal Optical Intensity 230 9.3. Refractive Index Changes:Temperature and Density Effects 233