Nematicons

The first book of its kind to introduce the fundamentals, basic features and models, potential applications and novel phenomena and its important applications in liquid crystal technology. Recognized leader in the field Gaetano Assanto outlines the peculiar characteristics of nematicons and the promise they have for the future growth of this captivating new field.

Autorentext

GAETANO ASSANTO, PhD, is Professor of Optoelectronics at the University of Rome, where he heads the Nonlinear Optics and OptoElectronics Lab. He is Fellow of the Optical Society of America and a Senior Member of the IEEE Photonics Society.

Klappentext

A pioneer in the field presents the first book on nematicons, spatial optical solitons in nematic liquid crystals

Little more than a decade after they were first demonstrated, nematicons have become an important area of research worldwide. This wide-ranging introduction is the first comprehensive collection of scientific work on optical spatial solitons in nematic liquid crystals, where they have been observed at powers of the order of milliwatts or lower, and have shown remarkable and peculiar features as compared to solitons in other media.

Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals features information on the background physics and relevant mathematics as well as numerical modeling, experimental approaches and results, and applications. It combines a review of the field with a considerable amount of original material as well as background information on liquid crystals.

This one-of-a-kind resource:

• Explores nematicons' nonlocal features, including their modeling, and experimental results on their mutual interactions
• Deals with models and numerics on light localization and spatial solitons, with emphasis on nematicons and their guiding properties
• Discusses experimental as well as theoretical work on nematicons and their trajectories, which can be modified in various ways and in several configurations
• Illustrates the physics and properties of nonlinear reorientation and thermo-optically localized waves
• Underlines the role of electronic nonlinearities and their synergy with reorientation in nematic liquid crystals, pinpointing the possibility of spatio-temporal solitons in these materials
  Complete with a vast bibliography of all the existing work in spatial solitons in nematic liquid crystals as well as actual photographs from experiments, Nematicons is a valuable tool for scientists, students, and scholars working on light localization and solitons, as well as on nonlinear optics in liquid crystals.

Inhalt
Preface xv Acknowledgments xvii

Contributors xix

Chapter 1. Nematicons 1
Gaetano Assanto, Alessandro Alberucci, and Armando Piccardi

1.1 Introduction 1

1.1.1 Nematic Liquid Crystals 1

1.1.2 Nonlinear Optics and Solitons 3

1.1.3 Initial Results on Light Self-Focusing in Liquid Crystals 3

1.2 Models 4

1.2.1 Scalar Perturbative Model 5

1.2.2 Anisotropic Perturbative Model 9

1.3 Numerical Simulations 13

1.3.1 Nematicon Profile 13

1.3.2 Gaussian Input 14

1.4 Experimental Observations 17

1.4.1 NematiconNematicon Interactions 22

1.4.2 Modulational Instability 26

1.5 Conclusions 31

References 33

Chapter 2. Features of Strongly Nonlocal Spatial Solitons 37
Qi Guo, Wei Hu, Dongmei Deng, Daquan Lu, and Shigen Ouyang

2.1 Introduction 37

2.2 Phenomenological Theory of Strongly Nonlocal Spatial Solitons 38

2.2.1 The Nonlinearly Induced Refractive Index Change of Materials 38

2.2.2 From the Nonlocal Nonlinear Schr¨odinger Equation to the SnyderMitchell Model 39

2.2.3 An Accessible Soliton of the SnyderMitchell Model 42

2.2.4 Breather and Soliton Clusters of the SnyderMitchell Model 45

2.2.5 Complex-Variable-Function Gaussian Breathers and Solitons 46

2.2.6 Self-Induced Fractional Fourier Transform 47

2.3 Nonlocal Spatial Solitons in Nematic Liquid Crystals 49

2.3.1 Voltage-Controllable Characteristic Length of NLC 50

2.3.2 Nematicons as Strongly Nonlocal Spatial Solitons 52

2.3.3 NematiconNematicon Interactions 54

2.4 Conclusion 61

Appendix 2.A: Proof of the Equivalence of the SnyderMitchell Model (Eq. 2.16) and the Strongly Nonlocal Model (Eq. 2.11) 61

Appendix 2.B: Perturbative Solution for a Single Soliton of the NNLSE (Eq. 2.4) in NLC 62

References 66

Chapter 3. Theoretical Approaches to Nonlinear Wave Evolution in Higher Dimensions 71
Antonmaria A. Minzoni and Noel F. Smyth

3.1 Simple Example of Multiple Scales Analysis 71

3.2 Survey of Perturbation Methods for Solitary Waves 77

3.3 Linearized Perturbation Theory for Nonlinear Schr¨odinger Equation 81

3.4 Modulation Theory: Nonlinear Schr¨odinger Equation 83

3.5 Radiation Loss 88

3.6 Solitary Waves in Nematic Liquid Crystals: Nematicons 91

3.7 Radiation Loss for The Nematicon Equations 96

3.8 Choice of Trial Function 101

3.9 Conclusions 105

Appendix 3.A: Integrals 106

Appendix 3.B: Shelf Radius 107

References 108

Chapter 4. Soliton Families in Strongly Nonlocal Media 111
Wei-Ping Zhong and Milivoj R. Beli¸c

4.1 Introduction 111

4.2 Mathematical Models 112

4.2.1 General 112

4.2.2 Nonlocality Through Response Function 113

4.3 Soliton Families in Strongly Nonlocal Nonlinear Media 115

4.3.1 One-Dimensional HermiteGaussian Spatial Solitons 115

4.3.2 Two-Dimensional LaguerreGaussian Soliton Families 116

4.3.3 Accessible Solitons in the General Model of Beam Propagation in NLC 118

4.3.4 Two-Dimensional Self-Similar HermiteGaussian Spatial Solitons 125

4.3.5 Two-Dimensional Whittaker Solitons 126

4.4 Conclusions 133

References 135

Chapter 5. External Control of Nematicon Paths 139
Armando Piccardi, Alessandro Alberucci, and Gaetano Assanto

5.1 Introduction 139

5.2 Basic Equations 140

5.3 Nematicon Control with External Light Beams 142

5.3.1 Interaction with Circular Spots 143

5.3.2 Dielectric Interfaces 145

5.3.3 Comments 146

5.4 Voltage Control of Nematicon Walk-Off 147

5.4.1 Out-of-Plane Steering of Nematicons 147

5.4.2 In-Plane Steering of Nematicon 149 5.5 Voltage-Defined Interface...