Nematicons

Name: Nematicons | Spatial Optical Solitons in Nematic Liquid Crystals
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Spatial Optical Solitons in Nematic Liquid Crystals

Gaetano Assanto(Autor*in)

Wiley (Verlag)

Erschienen am 1. Oktober 2012

456 Seiten

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Inhalt

Intro
Nematicons
Contents
Preface
Acknowledgments
Contributors
Chapter 1. Nematicons
1.1 Introduction
1.1.1 Nematic Liquid Crystals
1.1.2 Nonlinear Optics and Solitons
1.1.3 Initial Results on Light Self-Focusing in Liquid Crystals
1.2 Models
1.2.1 Scalar Perturbative Model
1.2.2 Anisotropic Perturbative Model
1.3 Numerical Simulations
1.3.1 Nematicon Profile
1.3.2 Gaussian Input
1.4 Experimental Observations
1.4.1 Nematicon-Nematicon Interactions
1.4.2 Modulational Instability
1.5 Conclusions
References
Chapter 2. Features of Strongly Nonlocal Spatial Solitons
2.1 Introduction
2.2 Phenomenological Theory of Strongly Nonlocal Spatial Solitons
2.2.1 The Nonlinearly Induced Refractive Index Change of Materials
2.2.2 From the Nonlocal Nonlinear Schrödinger Equation to the Snyder-Mitchell Model
2.2.3 An Accessible Soliton of the Snyder-Mitchell Model
2.2.4 Breather and Soliton Clusters of the Snyder-Mitchell Model
2.2.5 Complex-Variable-Function Gaussian Breathers and Solitons
2.2.6 Self-Induced Fractional Fourier Transform
2.3 Nonlocal Spatial Solitons in Nematic Liquid Crystals
2.3.1 Voltage-Controllable Characteristic Length of NLC
2.3.2 Nematicons as Strongly Nonlocal Spatial Solitons
2.3.3 Nematicon-Nematicon Interactions
2.4 Conclusion
Appendix 2.A: Proof of the Equivalence of the Snyder-Mitchell Model (Eq. 2.16) and the Strongly Nonlocal Model (Eq. 2.11)
Appendix 2.B: Perturbative Solution for a Single Soliton of the NNLSE (Eq. 2.4) in NLC
References
Chapter 3. Theoretical Approaches to Nonlinear Wave Evolution in Higher Dimensions
3.1 Simple Example of Multiple Scales Analysis
3.2 Survey of Perturbation Methods for Solitary Waves
3.3 Linearized Perturbation Theory for Nonlinear Schrödinger Equation
3.4 Modulation Theory: Nonlinear Schrödinger Equation
3.5 Radiation Loss
3.6 Solitary Waves in Nematic Liquid Crystals: Nematicons
3.7 Radiation Loss for The Nematicon Equations
3.8 Choice of Trial Function
3.9 Conclusions
Appendix 3.A: Integrals
Appendix 3.B: Shelf Radius
References
Chapter 4. Soliton Families in Strongly Nonlocal Media
4.1 Introduction
4.2 Mathematical Models
4.2.1 General
4.2.2 Nonlocality Through Response Function
4.3 Soliton Families in Strongly Nonlocal Nonlinear Media
4.3.1 One-Dimensional Hermite-Gaussian Spatial Solitons
4.3.2 Two-Dimensional Laguerre-Gaussian Soliton Families
4.3.3 Accessible Solitons in the General Model of Beam Propagation in NLC
4.3.4 Two-Dimensional Self-Similar Hermite-Gaussian Spatial Solitons
4.3.5 Two-Dimensional Whittaker Solitons
4.4 Conclusions
References
Chapter 5. External Control of Nematicon Paths
5.1 Introduction
5.2 Basic Equations
5.3 Nematicon Control with External Light Beams
5.3.1 Interaction with Circular Spots
5.3.2 Dielectric Interfaces
5.3.3 Comments
5.4 Voltage Control of Nematicon Walk-Off
5.4.1 Out-of-Plane Steering of Nematicons
5.4.2 In-Plane Steering of Nematicon
5.5 Voltage-Defined Interfaces
5.6 Conclusions
References
Chapter 6. Dynamics of Optical Solitons in Bias-Free Nematic Liquid Crystals
6.1 Summary
6.2 Introduction
6.3 From One to Two Nematicons
6.4 Counter-Propagating Nematicons
6.5 Interaction of Nematicons with Curved Surfaces
6.6 Multimode Nematicon-Induced Waveguides
6.7 Dipole Azimuthons and Charge-Flipping
6.8 Conclusions
References
Chapter 7. Interaction of Nematicons and Nematicon Clusters
7.1 Introduction
7.2 Gravitation of Nematicons
7.3 In-Plane Interaction of Two-Color Nematicons
7.4 Multidimensional Clusters
7.5 Vortex Cluster Interactions
7.6 Conclusions
Appendix: Integrals
References
Chapter 8. Nematicons in Light Valves
8.1 Introduction
8.2 Reorientational Kerr Effect and Soliton Formation in Nematic Liquid Crystals
8.2.1 Optically Induced Reorientational Nonlinearity
8.2.2 Spatial Solitons in Nematic Liquid Crystals
8.3 Liquid Crystal Light Valves
8.3.1 Cell Structure and Working Principle
8.3.2 Optical Addressing in Transverse Configurations
8.4 Spatial Solitons in Light Valves
8.4.1 Stable Nematicons: Self-Guided Propagation in the Longitudinal Direction
8.4.2 Tuning the Soliton Walk-Off
8.5 Soliton Propagation in 3D Anisotropic Media: Model and Experiment
8.5.1 Optical Control of Nematicon Trajectories
8.6 Soliton Gating and Switching by External Beams
8.7 Conclusions and Perspectives
References
Chapter 9. Propagation of Light Confined via Thermo-Optical Effect in Nematic Liquid Crystals
9.1 Introduction
9.2 First Observation in NLC
9.3 Characterization and Nonlocality Measurement
9.4 Thermal Versus Orientational Self-Waveguides
9.5 Applications
9.5.1 Bent Waveguide
9.5.2 Fluorescence Recovery
9.6 Conclusions
References
Chapter 10. Discrete Light Propagation in Arrays of Liquid Crystalline Waveguides
10.1 Introduction
10.2 Discrete Systems
10.3 Waveguide Arrays in Nematic Liquid Crystals
10.4 Discrete Diffraction and Discrete Solitons
10.5 Optical Multiband Vector Breathers
10.6 Nonlinear Angular Steering
10.7 Landau-Zener Tunneling
10.8 Bloch Oscillations
10.9 Conclusions
References
Chapter 11. Power-Dependent Nematicon Self-Routing
11.1 Introduction
11.2 Nematicons: Governing Equations
11.2.1 Perturbative Regime
11.2.2 Highly Nonlinear Regime
11.2.3 Simplified (1 + 1)D Model in a Planar Cell
11.3 Single-Hump Nematicon Profiles
11.3.1 (2 + 1)D Complete Model
11.3.2 (1 + 1)D Simplified Model
11.4 Actual Experiments: Role of Losses
11.4.1 BPM (1 + 1)D Simulations
11.4.2 Experiments
11.5 Nematicon Self-Steering in Dye-Doped NLC
11.6 Boundary Effects
11.7 Nematicon Self-Steering Through Interaction with Linear Inhomogeneities
11.7.1 Interfaces: Goos-Hänchen Shift
11.7.2 Finite-Size Defects: Nematicon Self-Escape
11.8 Conclusions
References
Chapter 12. Twisted and Chiral Nematicons
12.1 Introduction
12.2 Chiral and Twisted Nematics
12.3 Theoretical Model
12.4 Experimental Results
12.4.1 Nematicons in a Single Layer
12.4.2 Asymmetric Configuration
12.4.3 Multilayer Propagation
12.4.4 Influence of an External Electric Field
12.4.5 Guiding Light by Light
12.4.6 Nematicon Interaction
12.5 Discrete Diffraction
12.6 Conclusions
References
Chapter 13. Time Dependence of Spatial Solitons in Nematic Liquid Crystals
13.1 Introduction
13.2 Temporal Behavior of Different Nonlinearities and Governing Equations
13.2.1 Reorientational Nonlinearity
13.2.2 Thermal Nonlinearity
13.2.3 Other Nonlinearities
13.3 Formation of Reorientational Solitons
13.3.1 Bias Voltage Switching Time
13.3.2 Soliton Formation Time
13.3.3 Experimental Observation of Soliton Formation
13.3.4 Influence of Flow Effects
13.4 Conclusions
References
Chapter 14. Spatiotemporal Dynamics and Light Bullets in Nematic Liquid Crystals
14.1 Introduction
14.1.1 (2 + 1 + 1)D Nonlinear Wave Propagation in Kerr Media
14.2 Optical Propagation Under Multiple Nonlinear Contributions
14.2.1 Multiple Nonlinearities and Space-Time Decoupling of the Nonlinear Dynamics
14.2.2 Suitable Excitation Conditions
14.3 Accessible Light Bullets
14.3.1 From Nematicons to Spatiotemporal Solitons
14.3.2 Experimental Conditions for Accessible Bullets Observation
14.4 Temporal Modulation Instability in Nematicons
14.5 Soliton-Enhanced Frequency Conversion
14.6 Conclusions
References
Chapter 15. Vortices in Nematic Liquid Crystals
15.1 Introduction
15.2 Stabilization of Vortices in Nonlocal, Nonlinear Media
15.3 Vortex in a Bounded Cell
15.4 Stabilization of Vortices by Vortex-Beam Interaction
15.5 Azimuthally Dependent Vortices
15.6 Conclusions
References
Chapter 16. Dispersive Shock Waves in Reorientational and Other Optical Media
16.1 Introduction
16.2 Governing Equations and Modulational Instability
16.3 Existing Experimental and Numerical Results
16.4 Analytical Solutions for Defocusing Equations
16.5 Analytical Solutions for Focusing Equations
16.5.1 The 1 + 1 Dimensional Semianalytical Soliton
16.5.2 Uniform Soliton Theory
16.5.3 Comparisons with Numerical Solutions
16.6 Conclusions
References
Index

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