This book presents a comprehensive treatment of the fundamentals and applied aspects of optical physics, light scatterings, electro-optics and nonlinear optics of liquid crystals. The opening chapters cover the basic physics and optical properties of liquid crystals critical to understanding more advanced content. The author then moves on to review the current display and non-display optical applications of liquid crystals, including new topics such as photonic crystals, negative index materials, and more. He also includes a thorough review of the advanced computational methods for light propagation through liquid crystalline and anisotropic materials/devices. Later chapters provide a uniquely comprehensive treatment of nonlinear optics of liquid crystals. Several sections have been added or expanded in this new edition to provide the most up-to-date resource on the topic.

Iam Choon Khoo, PhD, is the William E. Leonhard Professor of Electrical Engineering at Pennsylvania State University, USA. He is a Life Fellow of the Institute of Electrical and Electronics Engineers (IEEE), and a Fellow of the Optical Society of America, UK Institute of Physics and The Electromagnetic Academy.

LIQUID CRYSTALS [3^rd Edition] – I. C. Khoo

PREFACE   

1.            INTRODUCTION TO LIQUID CRYSTALS 

1.1.        Molecular Structures and Chemical Compositions

      1.2.  Optical properties

1.2.1.     Electronic Optical Transitions and Ultraviolet Absorption

1.2.2.     Visible and Infrared Absorption; Terahertz, Microwave

1.3.        Lyotropic, Polymeric, and Thermotropic Liquid Crystals

1.3.1.     Lyotropic Liquid Crystals

1.3.2.     Polymeric Liquid Crystals

1.3.3.     Thermotropic Liquid Crystals: Smectic, Nematic, Cholesteric, and Blue-Phase Liquid Crystals

1.3.4      Functionalized and Discotic Liquid Crystals

1.4.        Mixtures, Polymer-Dispersed and Dye-doped Liquid Crystals

1.4.1.     Mixtures

1.4.2.     Dye-Doped Liquid Crystals

1.4.3.     Polymer-Dispersed and polymer-stabilized Liquid Crystals

1.5.        Liquid Crystal Cells Fabrication 

1.5.1.     Nematic LC cells assembly

1.5.2.     Cholesteric Liquid crystal Cell Assembly

1.5.3    Blue-phase liquid crystal cell assembly

1.5.4.     Photosensitive and Tunable Optical Waveguide, Photonic Crystals and Metamaterial Nanostructures

1.5.5.   Isotropic Liquid Crystal Cored Fiber Array

References

2.            ORDER PARAMETER, PHASE TRANSITION, AND FREE ENERGIES

2.1.        Basic Concepts

2.1.1.     Introduction

2.1.2.     Scalar and Tensor Order Parameter

2.1.3.     Long- and Short-Range Order

2.2.        Molecular Interactions and Phase Transitions

2.3.        Molecular Theories and Results for the Liquid Crystalline Phase

2.3.1.     Maier-Saupe Theory: Order Parameter Near Tc

2.3.2.     Nonequilibrium and Dynamical l Dependence of the Order Parameter

2.4.        Isotropic Phase of Liquid Crystals

2.4.1.     Free Energy and Phase Transition

2.4.2.     Free Energy in the Presence of an Applied Field

References

3.            NEMATIC LIQUID CRYSTALS

3.1.        Introduction

3.2.        Elastic Continuum Theory

3.2.1.     The Vector Field: Direct Axis  

3.2.2.     Elastic Constants, Free Energies and Molecular Fields

3.3.        Dielectric Constants at low frequency

3.3.1.     DC and Low-Frequency Dielectric Permittivities, Conductivities, and Magnetic Susceptibility

3.3.2.     Free Energy and Torques by Electric and Magnetic Fields

3.4.        Optical Dielectric Constants and Refractive Indices

3.4.1.     Linear Susceptibility and Local Field Effect

3.4.2.     Equilibrium Temperature and Order Parameter Dependence of   Refractive Indices

3.5.        Flows and Hydrodynamics

3.5.1.     Hydrodynamics of Ordinary Isotropic Fluids

3.5.2.     General Stress Tensor for Nematic Liquid Crystals

3.5.3.     Flows with Fixed Director Axis Orientation

3.5.4.     Flow with Direct Axis Reorientation

3.6.        Field-Induced Director Axis Reorientation Effects

3.6.1.     Field-Induced Reorientation without Flow Coupling – Freedericksz Transition

3.6.2.     Reorientation with Flow Coupling

References

4.            CHOLESTERIC (including Blue-Phase), SMECTIC, AND FERROELECTRIC LIQUID CRYSTALS

4.1.        Cholesteric Liquid Crystals

4.1.1.     Free Energies

4.1.2.     Field-Induced Effects and Dynamics

4.1.3.     Twist and Conic Mode Relaxation Times

4.2.        Optical Properties of Cholesterics

4.2.1.     Bragg Regime (Optical Wavelength » Pitch)

4.2.2.     General Optical Propagation and Reflection: Normal Incidence

4.2.3    Cholesteric Liquid Crystal as a 1-Dimensional Photonic Crystals.

4.2.4.     Cholesteric liquid crystals with magneto-optic activity: negative refraction effect

4.2.5      Polarization Rotation and Switching by high period number CLC -adiabatic rotation and circular Bragg resonance

4. 3.       Cholesteric Blue Phase Liquid crystals

4.3.1.     Free Energies and Equation of Motion under an applied Field

4.3.2   Field-induced lattice distortion and new crystalline structures

4.3.3   Polymer-stabilization and electro-optical properties of non-cubic BPLC

4.4         Smectic and Ferroelectric Liquid Crystals: A brief Survey

               4.4.1   Smectic-A Liquid Crystals; Free Energy; Light Scattering 

4.4.2   Smectic-C Liquid Crystals; Free Energy; Field-Induced Director    axis rotation

4.4.3 Smectic-C* and Ferroelectric Liquid Crystals; Free Energy 

4.4.4 Smectic-C*-Smectic-A Phase Transition

References

5.            LIGHT Scatterings

5.1.        Introduction

5.2.        Electromagnetic Formalism of Light Scattering in Liquid Crystals

5.3.        Scattering from Director Axis Fluctuations in Nematic Liquid Crystals

5.4.        Light Scattering in the Isotropic Phase of Liquid Crystals

5.5.        Temperature, Wavelength, and Cell Geometry Effects on Scattering

5.6.        Spectrum of Light and Orientation Fluctuation Dynamics

5.7         Raman Scatterings

5.7.1    Introduction

5.7.2   Quantum Theory of Spontaneous and Stimulated Raman Scattering: Scattering Cross Section

       5.8 Brillouin and Rayleigh Scatterings

                              5.8.1    Brillouin Scattering

                              5.8.2   Rayleigh Scattering 

5.9         A brief introduction to nonlinear Light Scattering 

References

6.            LIQUID CRYSTALS OPTICS AND ELECTRO-OPTICS 

6.1 Introduction 

      6.2 Review of Electro-Optics of Anisotropic and Birefringent Crystals

6.2.1 Anisotropic, uniaxial and biaxial optical crystals

6.2.2 Index Ellipsoid in the presence of an electric field –Electro-                        Optics Effect

6.2.3 Polarizers and Retardation plate

6.2.4 Basic Electro-Optics Modulation

6.3. Electro-Optics of Nematic Liquid Crystals

6.3.1 Director Axis reorientation in Homeotropic and Planar Cell; Dual frequency Liquid Crystals 

6.3.2 Freedericksz transition revisited

6.3.3 Field Induced Refractive Index Change and Phase Shift.

6.4 Liquid crystals switches for display applications

6.4.1 Liquid crystal switch – on axis consideration for Twist, Planar and Homeotropic aligned cells

6.4.2 Off-axis transmission, viewing angle and birefringence compensation.

6.4.3 Liquid crystal Display Electronics

6.5 Electro- Optical Effects in Other Phases of Liquid crystals

6.5.1 Surface Stabilized FLC

6.5.2 Soft-Mode FLCs

6.6 Non-display Applications of Liquid Crystals

                        6.6.1 Liquid Crystal Spatial Light Modulator

6.6.2. Tunable Photonic Crystals with Liquid Crystal Infiltrated Nanostructure

6.6.3 Tunable Frequency Selective Structures, metamaterial and metasurfaces

6.6.4 Liquid Crystals for Molecular Sensing and Detection

6.5.5 Beam Steering, Routing and Tunable Micro-ring resonator and    high-power laser optics

References

7. Optical Propagation in Anisotropic Materials

      7.1 Electromagnetic Formalisms for Optical Propagation

                              7.1.1 Maxwell Equations and Wave Equations in Anisotropic Media 

                              7.1.2 Complex Refractive Index– Real and Imaginary Components

                              7.1.3 Negative Index Material

7.1.4 Normal modes, power flow and propagation vectors in a lossless isotropic medium

7.1.5 Normal modes and propagation vectors in a lossless anisotropic medium

7.2 Polarized Light propagation in Liquid Crystal Display Panel

                              7.2.1. Plane Polarized Wave and Jones Vectors  

7.2.2 Jones Matrix Method

                              7.2.3 Oblique incidence - 4x4 Matrix methods  

7.3 Extended Jones Matrix Method

7.4 Finite-Difference Time-Domain Technique

7.5 Nonlinear Light propagation in Liquid Crystals – a first look

7.6 Systems of units

References

8.            Laser-induced reorientation nonlinear optical effects

      8.1   Introduction

8.2         Laser-Induced Molecular Reorientations in the Isotropic Phase

8.2.1      Individual Molecular Reorientations in Anisotropic Liquids

8.2.2      Correlated Molecular Reorientation Dynamics

8.2.3      Influence of Molecular Structures on Reorientation Nonlinearities

8.3         Molecular Reorientations in the Nematic Phase

8.3.1      Simplified Treatment of Optical Field-Induced Director Axis Reorientation

8.3.2      More Exact Treatment of Optical Field-Induced Director Axis Reorientation

8.3.3    Nonlocal Director Axis Reorientation and Optical Nonlinearity

8.4         Nematic Phase Reorientation Dynamics

8.4.1      Plane Wave Optical Field

8.4.2      Sinusoidal Optical Intensity

8.4.3 Polarization grating with uniform optical intensity

8.5         Laser-induced director axis realignment in dye-doped liquid crystals

                              8.5.1 Reorientation caused by inter-molecular torque

                              8.5.2 Laser induced Trans-Cis isomerism in dye-doped liquid crystals

8.6 DC Field aided Optically Induced Nonlinear Optical Effects in Liquid Crystals – Photorefractivity

8.6.1      Orientation Photorefractivity – Bulk effects

8.6.2      Some Experimental Results and surface charge/field contribution

8.7 Reorientation in other Phases of pristine (undoped) liquid Crystals

References

9             Thermal, Density, Lattice Distortion Optical Nonlinearities in Nematic, Cholesteric and Blue-phase Liquid Crystals

9.1         Introduction

9.2 Electrostriction and flows in non-absorbing liquid crystals – a general overview.

9.3         Laser induced density and temperature modulations in liquid crystals

9.3.1 Modulations by Sinusoidal Optical Intensity

               9.3.2 Refractive Index Changes: Temperature and Density Effects

               9.4         Optical Nonlinearities of Nematic Liquid Crystals

9.4.1      Steady-State Thermal Nonlinearity of Nematic Liquid Crystals

9.4.2      Short Laser Pulse Induced Thermal Index Change in Nematics and Near-T_c Effect

9.4.3    Optical Nonlinearities of Isotropic Liquid Crystals

9.5         Coupled Nonlinear Optical Effects in Nematic Liquid Crystals

9.5.1      Thermal-Orientation Coupling Effect

9.5.2      Flow-Orientational Effect

9.6 Nonlinear optical responses of cholesteric blue-phase liquid crystals

                              9.6.1 General overview

9.6.2. Non-electronics optical nonlinearities of BPLC

References

10           ELECTRONIC OPTICAL NONLINEARITIES

10.1 Introduction to Quantum Mechanical Treatment of molecules

10.2 Density Matrix Formalism for Optical Induced Molecular Electronic Polarizabilities

10.2.1    Field Induced Polarizations – First and Higher Orders

10.2.2    Linear and Nonlinear Absorptions

      10.3 Electronic Susceptibilities of Liquid Crystals

10.3.1    Linear Optical Polarizabilities of a Molecular

10.3.2    Complex Susceptibilities and Index of Refraction – Dispersion, Absorption and Amplification of Light, Lasers

10.3.3    Second-Order Electronic Polarizabilities

10.3.4    Third-Order Electronic Polarizabilities

10.3.5    Local Field Effects and Symmetry

10.3.6 Symmetry Considerations

10.3.7    Permanent Dipole and Molecular Ordering

10.3.8 Quadrupole Contribution and Field-Induced Symmetry Breaking

10.3.9 Influence of Molecular Structures

10.4 Intensity dependent refractive index change and nonlinear absorption 

References

11           Nonlinear Optics

            11.1          Introduction

11.1.1    General Nonlinear Polarization and Susceptibility

11.1.2    Convention and Symmetry

11.2       Coupled Maxwell Wave Equations

11.3       Nonlinear Optical Phenomena

11.3.1    Stationary Degenerate Four-Wave Mixing

11.3.2    Optical Phase Conjugation

11.3.3    Transient and Nearly Degenerate Wave Mixing

11.3.4    Non-degenerate Optical Wave Mixing; Harmonic Generations

11.3.5 Stationary Self-Phase Modulation and Self-Action

11.4       Stimulated Scatterings

11.4.1    Stimulated Raman Scatterings

11.4.2    Stimulated Brillouin Scattering

11.4.3    Stimulated Orientational Scattering in Liquid Crystals

11.4.4    Stimulated Thermal Scattering (STS)

               11.5       Ultrafast laser pulse self-action effects in cholesteric liquid crystals

11.5.1Coupled wave equations for forward and backward propagating waves

5.1.2 Ultrafast pulse modulations – compression, stretching and recompression

       References

12 NONLINEAR OPTICAL PROCESSES OBSERVED IN LIQUID CRYSTALS

12.1 Self-action nonlinear optical processes

12.1.1 Self-induced spatial and temporal phase shift

12.1.2 Self-phase modulation, Self-focusing, -defocusing of CW or Pulsed Laser

12.1.3 Self-guiding, spatial soliton and pattern formation

12.1.4 Pulse modulations, polarization rotation of and switching by ultrafast (picosecond -femtoseconds) laser.

               12.2    Optical Wave Mixings

12.2.1 Stimulated Orientational Scattering and Polarization self-switching      – steady state 

               12.2.2 Stimulated Orientational Scattering – Nonlinear Dynamics 

12.2.3 Optical Phase Conjugation with orientation and thermal gratings

12.2.4 Self-Starting Optical Phase conjugation

          12.3 Liquid Crystals for all-optical image processing

12.3.1 Liquid Crystals as all-optical information processing materials

12.3.2. All-Optical Image Processing

12.3.3 Intelligent Optical Processing

                         12.4 Harmonic generations and sum-frequency spectroscopy

             12.5 Optical Switching

    12.6 Nonlinear absorption and optical limiting of short laser pulses

                              12.6.1 Introduction

12.6.2 Nonlinear fiber array- an intensity dependent spatial frequency   filter

                              12.6.3 Optical limiting action of fiber array containing RSA materials

12.6.4 Optical limiting action of fiber array containing TPA materials

12.7 Concluding Remarks

References