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1 Liquid Crystals

3 Liquid Crystals Second Edition IAM-CHOON KHOO WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

4 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, , fax , or on the web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, , fax , or online at Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at , outside the United States at or fax 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 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 Liquid crystals. I. Title. QD923. K dc Printed in the United States of America

5 Contents Preface xiii Chapter 1. Introduction to Liquid Crystals Molecular Structures and Chemical Compositions Chemical Structures Electronic Properties Electronic Transitions and Ultraviolet Absorption Visible and Infrared Absorption Lyotropic, Polymeric, and Thermotropic Liquid Crystals Lyotropic Liquid Crystals Polymeric Liquid Crystals Thermotropic Liquid Crystals: Nematics, Cholesterics, and Smectics Other Liquid Crystalline Phases and Molecular Engineered Structures Mixtures and Composites Mixtures Dye-Doped Liquid Crystals Polymer-Dispersed Liquid Crystals Liquid Crystal Cells and Sample Preparation Bulk Thin Film Liquid Crystal Optical Slab Waveguide, Fiber, and Nanostructured Photonic Crystals 17 References 19 Chapter 2. Order Parameter, Phase Transition, and Free Energies Basic Concepts Introduction Scalar and Tensor Order Parameters Long- and Short-Range Order Molecular Interactions and Phase Transitions Molecular Theories and Results for the Liquid Crystalline Phase Maier-Saupe Theory: Order Parameter Near T c Nonequilibrium and Dynamical Dependence of the Order Parameter 29 v

6 vi CONTENTS 2.4. Isotropic Phase of Liquid Crystals Free Energy and Phase Transition Free Energy in the Presence of an Applied Field 33 References 35 Chapter 3. Nematic Liquid Crystals Introduction Elastic Continuum Theory The Vector Field: Direct Axis nˆ (r ) Elastic Constants, Free Energies, and Molecular Fields Dielectric Constants and Refractive Indices dc and Low-Frequency Dielectric Permittivity, Conductivities, and Magnetic Susceptibility Free Energy and Torques by Electric and Magnetic Fields Optical Dielectric Constants and Refractive Indices Linear Susceptibility and Local Field Effect Equilibrium Temperature and Order Parameter Dependences of Refractive Indices Flows and Hydrodynamics Hydrodynamics of Ordinary Isotropic Fluids General Stress Tensor for Nematic Liquid Crystals Flows with Fixed Director Axis Orientation Flows with Director Axis Reorientation Field-Induced Director Axis Reorientation Effects Field-Induced Reorientation without Flow Coupling: Freedericksz Transition Reorientation with Flow Coupling 61 References 62 Chapter 4. Cholesteric, Smectic, and Ferroelectric Liquid Crystals Cholesteric Liquid Crystals Free Energies Field-Induced Effects and Dynamics Twist and Conic Mode Relaxation Times Light Scattering in Cholesterics General Optical Propagation and Reflection: Normal Incidence Cholesteric Liquid Crystal as a One-Dimensional Photonic Crystal Cholesteric Liquid Crystals with Magneto-Optic Activity: Negative Refraction Effect 78

7 CONTENTS vii 4.3. Smectic and Ferroelectric Liquid Crystals: A Quick Survey Smectic-A Liquid Crystals Free Energy Light Scattering in SmA Liquid Crystals Smectic-C Liquid Crystals Free Energy Field-Induced Director Axis Rotation in SmC Liquid Crystals Smectic-C* and Ferroelectric Liquid Crystals Free Energy of Ferroelectric Liquid Crystals Smectic-C* Smectic-A Phase Transition 93 References 95 Chapter 5. Light Scatterings Introduction General Electromagnetic Formalism of Light Scattering in Liquid Crystals Scattering from Director Axis Fluctuations in Nematic Liquid Crystals Light Scattering in the Isotropic Phase of Liquid Crystals Temperature, Wavelength, and Cell Geometry Effects on Scattering Spectrum of Light and Orientation Fluctuation Dynamics Raman Scatterings Introduction Quantum Theory of Raman Scattering: Scattering Cross Section Brillouin and Rayleigh Scatterings Brillouin Scattering Rayleigh Scattering Nonlinear Light Scattering: Supraoptical Nonlinearity of Liquid Crystals 120 References 122 Chapter 6. Liquid Crystal Optics and Electro-Optics Introduction Review of Electro-Optics of Anisotropic and Birefringent Crystals Anisotropic, Uniaxial, and Biaxial Optical Crystals Index Ellipsoid in the Presence of an Electric Field: Linear Electro-Optics Effect Polarizers and Retardation Plate Basic Electro-Optics Modulation 130

8 viii CONTENTS 6.3. Electro-Optics of Nematic Liquid Crystals Director Axis Reorientation in Homeotropic and Planar Cells: Dual-Frequency Liquid Crystals Freedericksz Transition Revisited Field-Induced Refractive Index Change and Phase Shift Nematic Liquid Crystal Switches and Displays Liquid Crystal Switch: On-Axis Consideration for Twist, Planar, and Homeotropic Aligned Cells Off-Axis Transmission, Viewing Angle, and Birefringence Compensation Liquid Crystal Display Electronics Electro-Optical Effects in Other Phases of Liquid Crystals Surface Stabilized FLC Soft-Mode FLCs Nondisplay Applications of Liquid Crystals Liquid Crystal Spatial Light Modulator Tunable Photonic Crystals with Liquid Crystal Infiltrated Nanostructures Tunable Frequency Selective Planar Structures Liquid Crystals for Molecular Sensing and Detection Beam Steering, Routing, and Optical Switching and Laser Hardened Optics 152 References 153 Chapter 7. Electromagnetic Formalisms for Optical Propagation Introduction Electromagnetism of Anisotropic Media Revisited Maxwell Equations and Wave Equations Complex Refractive Index Negative Index Material Normal Modes, Power Flow, and Propagation Vectors in a Lossless Isotropic Medium Normal Modes and Propagation Vectors in a Lossless Anisotropic Medium General Formalisms for Polarized Light Propagation Through Liquid Crystal Devices Plane-Polarized Wave and Jones Vectors Jones Matrix Method for Propagation Through a Nematic Liquid Crystal Cell Oblique Incidence: 4 4 Matrix Methods Extended Jones Matrix Method 177

9 CONTENTS ix 7.5. Finite-Difference Time-Domain Technique The Implementation of FDTD Methods Example: FDTD Computations of the Twisted Nematic Cell in One Dimension 186 References 188 Chapter 8. Laser-Induced Orientational Optical Nonlinearities in Liquid Crystals General Overview of Liquid Crystal Nonlinearities Laser-Induced Molecular Reorientations in the Isotropic Phase Individual Molecular Reorientations in Anisotropic Liquids Correlated Molecular Reorientation Dynamics Influence of Molecular Structure on Isotropic Phase Reorientational Nonlinearities Molecular Reorientations in the Nematic Phase Simplified Treatment of Optical Field-Induced Director Axis Reorientation More Exact Treatment of Optical Field-Induced Director Axis Reorientation Nonlocal Effect and Transverse Dependence Nematic Phase Reorientation Dynamics Plane Wave Optical Field Sinusoidal Optical Intensity Laser-Induced Dopant-Assisted Molecular Reorientation and Trans-Cis Isomerism DC Field Aided Optically Induced Nonlinear Optical Effects in Liquid Crystals: Photorefractivity Orientational Photorefractivity: Bulk Effects Some Experimental Results and Surface Charge/Field Contribution Reorientation and Nonelectronic Nonlinear Optical Effects in Smectic and Cholesteric Phases Smectic Phase Cholesteric Phase 222 References 223 Chapter 9. Thermal, Density, and Other Nonelectronic Nonlinear Mechanisms Introduction Density and Temperature Changes Induced by Sinusoidal Optical Intensity Refractive Index Changes: Temperature and Density Effects 233

10 x CONTENTS 9.4. Thermal and Density Optical Nonlinearities of Nematic Liquid Crystals in the Visible-Infrared Spectrum Steady-State Thermal Nonlinearity of Nematic Liquid Crystals Short Laser Pulse Induced Thermal Index Change in Nematics and Near-T c Effect Thermal and Density Optical Nonlinearities of Isotropic Liquid Crystals Coupled Nonlinear Optical Effects in Nematic Liquid Crystals Thermal-Orientational Coupling in Nematic Liquid Crystals Flow-Orientational Effect 247 References 251 Chapter 10. Electronic Optical Nonlinearities Introduction Density Matrix Formalism for Optically Induced Molecular Electronic Polarizabilities Induced Polarizations Multiphoton Absorptions Electronic Susceptibilities of Liquid Crystals Linear Optical Polarizabilities of a Molecule with No Permanent Dipole Second-Order Electronic Polarizabilities Third-Order Electronic Polarizabilities Electronic Nonlinear Polarizations of Liquid Crystals Local Field Effects and Symmetry Symmetry Considerations Permanent Dipole and Molecular Ordering Quadrupole Contribution and Field-Induced Symmetry Breaking Molecular Structural Dependence of Nonlinear Susceptibilities 269 References 271 Chapter 11. Introduction to Nonlinear Optics Nonlinear Susceptibility and Intensity-Dependent Refractive Index Nonlinear Polarization and Refractive Index Nonlinear Coefficient and Units General Nonlinear Polarization and Susceptibility Convention and Symmetry Coupled Maxwell Wave Equations 282

11 CONTENTS xi Nonlinear Optical Phenomena Stationary Degenerate Four-Wave Mixing Optical Phase Conjugation Nearly Degenerate and Transient Wave Mixing Nondegenerate Optical Wave Mixing: Harmonic Generations Self-Focusing and Self-Phase Modulation Stimulated Scatterings Stimulated Raman Scatterings Stimulated Brillouin Scatterings Stimulated Orientational Scattering in Liquid Crystals Stimulated Thermal Scattering (STS) 316 References 317 Chapter 12. Nonlinear Optical Phenomena Observed in Liquid Crystals Self-Focusing, Self-Phase Modulation, and Self-Guiding Self-Focusing and Self-Phase Modulation and cw Optical Limiting with Nematic Liquid Crystals Self-Guiding, Spatial Soliton, and Pattern Formation Optical Wave Mixing Stimulated Orientational Scattering and Polarization Self-Switching: Steady State Stimulated Orientational Scattering: Nonlinear Dynamics Optical Phase Conjugation with Orientation and Thermal Gratings Self-Starting Optical Phase Conjugation Liquid Crystals for All-Optical Image Processing Liquid Crystals as All-Optical Information Processing Materials All-Optical Image Processing Intelligent Optical Processing Harmonic Generations and Sum-Frequency Spectroscopy Optical Switching Nonlinear Absorption and Optical Limiting of Short Laser Pulses in Isotropic Phase Liquid Crystals and Liquids Introduction Nonlinear Fiber Array RSA Materials (C60 Doped ILC) Optical Limiting by TPA Materials (L34 Fiber Core Liquid) Conclusion 358 References 358 Index 365

12 Preface Liquid crystal science and applications now permeate almost all segments of the society from large industrial displays to individual homes and offices. Nondisplay applications in nonlinear optics, optical communication, and data/signal/image processing are receiving increasing attention and are growing at a rapid pace. Since the last edition (1995), tremendous progress has been made in the study of optics of liquid crystals, and advances are measured by orders of magnitude rather than small increments. Feature sizes have shrunk from microns to nanometers; optical nonlinearities, such as the refractive index coefficient, have grown a millionfold from 10 3 to 10 3 cm 2 /W. This book is intended to capture the essentials of these fundamental breakthroughs and point out new exciting possibilities, while providing the reader a basic overall grounding in liquid crystal optics. This edition of Liquid Crystals, consisting of ten original book chapters that have been completely revised with the addition of the latest concepts, devices, applications, literature, and two new chapters, provides a comprehensive coverage of the fundamentals of liquid crystal physical, optical, electro- and nonlinear optical properties, and related optical phenomena. It is intended for students in their final years of undergraduate studies in the sciences and beginning graduate students and researchers. It will also serve as a general useful introductory guide to all newcomers to the field of liquid crystals and contemporary optics and photonics materials and devices. Studies of liquid crystals are highly inter- and multidisciplinary, encompassing physics, materials science, optics, and engineering. Liquid crystal science and technologies are rapidly advancing. As such, details of actual devices and applications may likely change or become obsolete. In order to present a treatment that is useful and more readily understandable to the intended readers, I have limited the discussion to only the fundamentals that can withstand the passage of time. Wherever possible and without loss of the physics, I have replaced vigorous theoretical formalisms with their simplified versions, for the sake of clarity. Chapters 1 5 cover the basic physics and optical properties of liquid crystals intended for beginning workers in liquid crystal related areas. Although the major focus is on nematics, we have included sufficient discussions on other mesophases of liquid crystals such as the smectics, ferroelectrics, and cholesterics to enable the readers to proceed to more advanced or specialized topics elsewhere. New sections have also been added. For example, in Chapter 4, a particularly important addition is a quantitative discussion of the optical properties and fundamentals of one-dimensional photonic crystal band structures. Dispersion is added to fill in an important gap in most treatments of cholesteric liquid crystals. In Chapter 6, we explore the fundamentals of liquid crystals for electro-optics and display, and nondisplay related applications such as sensing, switching and specialized xiii

13 xiv PREFACE nanostructured tunable photonic crystals and frequency selective surfaces. In Chapter 7 we provide a thorough account of the various theoretical and computational techniques used to describe optical propagation through liquid crystals and anisotropic materials. Chapters 8 12 provide the most comprehensive self-contained treatment of nonlinear optics of liquid crystals available anywhere, and have greatly expanded on the coverage of the same subject matter in the previous edition of the book with updated literature reviews and fundamental discussions. In particular, readers will find quantitative and complete theories and analysis of important nonlinear optical processes such as photorefractivity, various all-optical image/beam processing, stimulated scattering and optical phase conjugation, nonlinear multiphoton absorptions, and optical limiting of short laser pulses and continuous-wave lasers. During the course of writing this book, as in my other work, I have enjoyed valuable encouragement and support from a wide spectrum of people. First and foremost is my wife, Chor San. Her patience, understanding, and unqualified support are important sources of strength and motivation. I would also like to express my gratitude to my present and former students and co-authors for valuable contributions to the advances we have made together and the rewarding life experiences. Support from the National Science Foundation, Army Research Office, Air Force Office of Scientific Research, Defense Advanced Research Projects Agency, and Naval Air Development Center over the years is also gratefully acknowledged. IAM-CHOON KHOO University Park, Pennsylvania

Liquid Crystals IAM-CHOON 1(1100 .,4 WILEY 2007 WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION. 'i; Second Edition. n z

Liquid Crystals IAM-CHOON 1(1100 .,4 WILEY 2007 WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION. 'i; Second Edition. n z Liquid Crystals Second Edition IAM-CHOON 1(1100.,4 z 'i; BICENTCNNIAL 1 8 0 7 WILEY 2007 DICENTENNIAL n z z r WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents Preface xiii Chapter 1.