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Liquid Crystals Liquid Crystals Third Edition IAM-CHOON KHOO Pennsylvania State University University Park, Pennsylvania Thiseditionfirstpublished2022 ©2022JohnWiley&Sons,Inc. EditionHistory Wiley-Interscience,2e2007;Wiley,1e1994 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform orbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,exceptaspermittedbylaw.Adviceon howtoobtainpermissiontoreusematerialfromthistitleisavailableathttp://www.wiley.com/go/permissions. TherightofIam-ChoonKhootobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewithlaw. RegisteredOffice JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,USA EditorialOffice 111RiverStreet,Hoboken,NJ07030,USA Fordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWileyproducts,visitusat www.wiley.com. 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LibraryofCongressCataloging-in-PublicationData Names:Khoo,Iam-Choon,author. Title:Liquidcrystals/Iam-ChoonKhoo,PennsylvaniaStateUniversity, UniversityPark,Pennsylvania. Description:Thirdedition.|Hoboken,NJ:JohnWiley&Sons,Inc.,[2022] |Series:Wileyseriesinpureandappliedoptics|Includes bibliographicalreferencesandindex. Identifiers:LCCN2021038545(print)|LCCN2021038546(ebook)|ISBN 9781119705826(hardback)|ISBN9781119705857(adobepdf)|ISBN 9781119705796(epub) Subjects:LCSH:Liquidcrystals–Congresses. Classification:LCCQD923.L531592021 (print)|LCCQD923 (ebook)|DDC 530.4/29–dc23 LCrecordavailableathttps://lccn.loc.gov/2021038545 LCebookrecordavailableathttps://lccn.loc.gov/2021038546 Coverimage:©Sensvector/Shutterstock ImagerybyIam-ChoonKhoo CoverdesignbyWiley Setin10/12ptTimesbyStraive,Pondicherry,India 10 9 8 7 6 5 4 3 2 1 Contents Preface xiii Chapter 1. Introduction to Liquid Crystals 1 1.1. Molecular Structuresand Chemical Compositions 1 1.2. Optical Properties 3 1.2.1. Electronic Optical Transitions and UVAbsorption 3 1.2.2. Visible and Infrared Absorption; Terahertz, Microwave 4 1.3. Lyotropic, Polymeric, and Thermotropic Liquid Crystals 6 1.3.1. Lyotropic Liquid Crystals 6 1.3.2. Polymeric Liquid Crystals 7 1.3.3. Thermotropic Liquid Crystals: Smectic, Nematic, Cholesteric, and Blue-phase Liquid Crystals 8 1.3.4. Functionalized and Discotic Liquid Crystals 11 1.4. Mixtures, Polymer-dispersed, andDye-dopedLiquid Crystals 11 1.4.1. Mixtures 12 1.4.2. Dye-doped Liquid Crystals 14 1.4.3. Polymer-dispersedandPolymer-stabilizedLiquidCrystals 14 1.5. Liquid Crystal Cells Fabrication 16 1.5.1. Nematic LC Cells Assembly 16 1.5.2. Cholesteric Liquid Crystal Cell Assembly 18 1.5.3. Blue-phaseLiquid CrystalCell Assembly 20 1.5.4. Photosensitive and Tunable Optical Waveguide, Photonic Crystals, and Metamaterial Nanostructures 22 1.5.5. Isotropic Liquid Crystal Cored Fiber Array 24 References 25 Chapter 2. Order Parameter,Phase Transition, and Free Energies 29 2.1. Basic Concepts 29 2.1.1. Introduction 29 2.1.2. Scalar and Tensor Order Parameters 30 2.1.3. Long- andShort-range Order 32 2.2. Molecular Interactionsand Phase Transitions 33 2.3. Molecular Theories and Results for the Liquid CrystallinePhase 34 2.3.1. Maier–Saupe Theory: Order Parameter Near T 34 c 2.3.2. Nonequilibrium and Dynamical Dependence of the Order Parameter 36 v vi CONTENTS 2.4. Isotropic Phase of Liquid Crystals 39 2.4.1. Free Energyand Phase Transition 40 2.4.2. Free Energyin the Presenceof an Applied Field 41 References 43 Chapter 3. Nematic Liquid Crystals 44 3.1. Introduction 44 3.2. Elastic Continuum Theory 44 3.2.1. The Vector Field: Director Axis 44 3.2.2. Elastic Constants, Free Energies, and Molecular Fields 46 3.3. Dielectric Constants and Refractive Indices 49 3.3.1. DC and Low-frequency Dielectric Permittivity, Conductivities, and Magnetic Susceptibility 49 3.3.2. FreeEnergyandTorquesbyElectricandMagneticFields 52 3.4. Optical Dielectric Constants and Refractive Indices 53 3.4.1. Linear Susceptibility andLocal Field Effect 53 3.4.2. Equilibrium Temperature andOrder Parameter Dependences of Refractive Indices 56 3.5. Flows andHydrodynamics 60 3.5.1. Hydrodynamics of Ordinary Isotropic Fluids 61 3.5.2. General Stress Tensor for Nematic Liquid Crystals 64 3.5.3. Flows with Fixed Director Axis Orientation 65 3.5.4. Flows with Director Axis Reorientation 66 3.6. Field-inducedDirector Axis Reorientation Effects 67 3.6.1. Field-inducedReorientation Without Flow Coupling: Freedericksz Transition 68 3.6.2. Reorientation with Flow Coupling 70 References 72 Chapter 4. Cholesteric, Smectic, and Ferroelectric Liquid Crystals 73 4.1. Cholesteric Liquid Crystals 73 4.1.1. Free Energies 73 4.1.2. Field-inducedEffectsand Dynamics 75 4.1.3. Twist andConic Mode Relaxation Times 78 4.2. Optical Properties of Cholesterics 79 4.2.1. BraggRegime (OpticalWavelength Pitch) 79 4.2.2. Reflection and Transmission of Polarized Light: Normal Incidence 79 4.2.3. Cholesteric Liquid Crystal as a One-dimensional Photonic Crystal,Photonic Bandgap, and Dispersion 84 4.2.4. Cholesteric Liquid Crystals with Magneto-optic Activity: Negative Index of Refraction 89 CONTENTS vii 4.2.5. Polarization Rotation andSwitching by High Period Number CLC –Adiabatic Rotation and Circular Bragg Resonance 90 4.3. Cholesteric Blue Phase Liquid Crystals 97 4.3.1. Free Energies andEquation of Motion under anApplied Field 97 4.3.2. Field-inducedLattice Distortion and New Crystalline Structures 98 4.3.3. Polymer-stabilization and Electro-optical Properties of Non-cubic BPLC 99 4.4. Smectic and Ferroelectric Liquid Crystals: A Brief Survey 100 4.4.1. Smectic-A Liquid Crystals 101 4.4.2. Smectic-C Liquid Crystals 104 ∗ 4.4.3. Smectic-C and Ferroelectric Liquid Crystals 106 4.4.4. Smectic-C∗–Smectic-A Phase Transition 111 References 113 Chapter 5. Light Scattering 115 5.1. Introduction 115 5.2. Electromagnetic Formalism of Light Scattering in Liquid Crystals 115 5.3. Scattering From Director AxisFluctuations in Nematic Liquid Crystals 118 5.4. Light Scattering in the Isotropic Phase of Liquid Crystals 122 5.5. Temperature,Wavelength, and Cell Geometry Effectson Scattering 125 5.6. Spectrum of Light andOrientation Fluctuation Dynamics 127 5.7. Raman Scatterings 129 5.7.1. Introduction 129 5.7.2. Quantum Theory of Spontaneous and Stimulated RamanScattering: Scattering Cross-section 130 5.7.3. Spontaneous Raman Scattering 132 5.7.4. Stimulated Raman Scattering 132 5.8. Brillouin and Rayleigh Scatterings 133 5.8.1. Brillouin Scattering 135 5.8.2. Rayleigh Scattering 137 5.9. A Brief Introduction to Nonlinear Light Scattering 138 References 140 Chapter 6. Liquid Crystals Optics and Electro-optics 142 6.1. Introduction 142 6.2. Review of Electro-Optics of Anisotropic and Birefringent Crystals 143 viii CONTENTS 6.2.1. Anisotropic, Uniaxial andBiaxial Optical Crystals 143 6.2.2. Index Ellipsoid in the Presence of an Electric Field–Electro-optics Effect 145 6.2.3. Polarizers andRetardation Plate 146 6.2.4. Basic Electro-optics Modulation 148 6.3. Electro-Opticsof Nematic Liquid Crystals 149 6.3.1. Director Axis Reorientation in Homeotropic and PlanarCell; Dual Frequency Liquid Crystals 149 6.3.2. Freedericksz Transition Revisited 151 6.3.3. Field-inducedRefractive Index Change and Phase Shift 154 6.4. Nematic Liquid Crystal Switches for Display Application 156 6.4.1. Liquid Crystal Switch –on AxisConsideration for Twist, Planar, andHomeotropic Aligned Cells 156 6.4.2. Off-axis Transmission, Viewing Angle, and Birefringence Compensation 157 6.4.3. Liquid Crystal Display Electronics 159 6.5. Electro-Optical Effectsin Other Phases of Liquid Crystals 159 6.5.1. SurfaceStabilized FLC 160 6.5.2. Soft-mode FLCs 161 6.6. Non-Display Applications of Liquid Crystals 163 6.6.1. Liquid Crystal Spatial Light Modulator 164 6.6.2. Tunable Photonic Crystals with Liquid Crystal Infiltrated Nanostructures 165 6.6.3. Tunable FrequencySelective Structures, Metamaterial, and Metasurfaces 167 6.6.4. Liquid Crystals for Molecular Sensing and Detection 168 6.6.5. Beam Steering, Routing, and Tunable Micro-ring Resonator, and High-power Laser Optics 170 References 171 Chapter 7. Optical Propagation in Anisotropic Materials 175 7.1. Electromagnetic Formalisms for Optical Propagation 175 7.1.1. Maxwell Equations andWave Equations in Anisotropic Media 176 7.1.2. Complex Refractive Index –Real and Imaginary Components 177 7.1.3. Negative Index Material 178 7.1.4. Normal Modes, Power Flow and Propagation Vectors in a Lossless Isotropic Medium 179 7.1.5. Normal Modes and Propagation Vectors in a Lossless Anisotropic Medium 181 7.2. Polarized LightPropagation in Liquid CrystalDisplay Panel 185 7.2.1. Pane Polarized Wave and Jones Vectors 185 CONTENTS ix 7.2.2. Jones Matrix Method 189 7.2.3. Oblique Incidence – 4× 4Matrix Methods 191 7.3. Extended Jones Matrix Method 193 7.4. Finite-difference Time-domain technique 196 7.5. Nonlinear Light Propagation in Liquid Crystals –a First Look 197 7.6. Systems of Units 198 References 200 Chapter 8. Laser-induced Reorientation Nonlinear Optical Effects 203 8.1. Introduction 203 8.2. Laser-Induced Molecular Reorientations in the Isotropic Phase 204 8.2.1. IndividualMolecular Reorientations in Anisotropic Liquids 204 8.2.2. Correlated Molecular Reorientation Dynamics 207 8.2.3. Influence of Molecular Structure on Isotropic Phase Reorientation Nonlinearities 210 8.3. Molecular Reorientations in the Nematic Phase 212 8.3.1. Simplified Treatmentof Optical Field-inducedDirector AxisReorientation 213 8.3.2. More Exact Treatment of Optical Field-inducedDirector AxisReorientation 215 8.3.3. Nonlocal Director AxisReorientation and Nonlocal Optical Nonlinearity 217 8.4. Nematic Phase Reorientation Dynamics 219 8.4.1. Plane Wave Optical Field 219 8.4.2. Sinusoidal Optical Intensity 222 8.4.3. Polarization Grating with Uniform Optical Intensity 224 8.5. Laser-Induced Director Axis Realignment in Dye-Doped Liquid Crystals 225 8.5.1. Reorientation Caused byInter-Molecular Torque 225 8.5.2. Laser-induced Trans–Cis Isomerism in Dye-doped Liquid Crystals 226 8.6. DC Field Aided Optically Induced Nonlinear Optical Effects in Liquid Crystals –Photorefractivity 226 8.6.1. Orientation Photorefractivity– Bulk Effects 229 8.6.2. Experimental Results and Surface Charge/Field Contribution 233 8.7. Reorientation in Other Phases of Pristine (Undoped)Liquid Crystals 234 8.7.1. Smectic Phase 234 8.7.2. Cholesteric andBlue-phase Liquid Crystals 235 References 236 x CONTENTS Chapter 9. Thermal, Density, Lattice Distortion Optical Nonlinearities in Nematic, Cholesteric, and Blue-phase LiquidCrystals 241 9.1. Introduction 241 9.2. Electrostrictionand Flows in Non-Absorbing Liquid Crystals – a General Overview 242 9.3. Laser-Induced Density and Temperature Modulations in Liquid Crystals 245 9.3.1. Modulations bySinusoidal Optical Intensity 247 9.3.2. Refractive Index Changes: Temperature and Density Effects 250 9.4. Optical Nonlinearities of Nematic Liquid Crystals 254 9.4.1. Steady-State Thermal Nonlinearity of Nematic Liquid Crystals 256 9.4.2. ShortLaser Pulse-induced Thermal Index Change in Nematics and Near-T Effect 257 c 9.4.3. Optical Nonlinearities of Isotropic Liquid Crystals 258 9.5. Coupled Nonlinear Optical Effects in Nematic Liquid Crystals 260 9.5.1. Thermal Orientation Coupling Effect 261 9.5.2. Flow-reorientation Effect 262 9.6. Nonlinear Optical Responses of Cholesteric Blue-Phase Liquid Crystals 266 9.6.1. General Overview 266 9.6.2. Non-electronics Optical Nonlinearitiesof BPLC 268 References 272 Chapter 10. ElectronicOptical Nonlinearities 275 10.1. Introduction to Quantum Mechanical Treatmentof Molecules 275 10.2. Density Matrix Formalism for Optical Induced Molecular Electronic Polarizabilities 278 10.2.1.Field-inducedPolarizations –First and Higher Orders 280 10.2.2.Linear andNonlinear Absorptions 280 10.3. Linear andNonlinear Electronic Susceptibilities 282 10.3.1.Linear Optical Polarizabilities of a Molecule 282 10.3.2.Complex Susceptibilities and Index of Refraction – Dispersion, Absorption,and Amplification of Light, Lasers 286 10.3.3.Second-order Electronic Polarizabilities 289 10.3.4.Third-order Electronic Polarizabilities 290 10.3.5.Local Field Effects and Symmetry 292 10.3.6.Symmetry Considerations 293 10.3.7.Permanent Dipole and Molecular Ordering 294