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Nematicons
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Nematicons

Spatial Optical Solitons in Nematic Liquid Crystals

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Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

05.11.2012

Herausgeber

Gaetano Assanto

Verlag

John Wiley & Sons Inc

Seitenzahl

350

Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

05.11.2012

Herausgeber

Gaetano Assanto

Verlag

John Wiley & Sons Inc

Seitenzahl

350

Maße (L/B/H)

24/16.1/2.9 cm

Gewicht

847 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-0-470-90724-5

Weitere Bände von Wiley Series in Pure and Applied Optics

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Die Leseprobe wird geladen.
  • Nematicons
  • 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 Nematicon-Nematicon 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 Snyder-Mitchell Model 39

    2.2.3 An Accessible Soliton of the Snyder-Mitchell Model 42

    2.2.4 Breather and Soliton Clusters of the Snyder-Mitchell 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 Nematicon-Nematicon Interactions 54

    2.4 Conclusion 61

    Appendix 2.A: Proof of the Equivalence of the Snyder-Mitchell 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 Hermite-Gaussian Spatial Solitons 115

    4.3.2 Two-Dimensional Laguerre-Gaussian 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 Hermite-Gaussian 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 Interfaces 152

    5.6 Conclusions 156

    References 156

    Chapter 6. Dynamics of Optical Solitons in Bias-Free Nematic Liquid Crystals 159
    Yana V. Izdebskaya, Anton S. Desyatnikov, and Yuri S. Kivshar

    6.1 Summary 159

    6.2 Introduction 159

    6.3 From One to Two Nematicons 160

    6.4 Counter-Propagating Nematicons 162

    6.5 Interaction of Nematicons with Curved Surfaces 165

    6.6 Multimode Nematicon-Induced Waveguides 167

    6.7 Dipole Azimuthons and Charge-Flipping 170

    6.8 Conclusions 172

    References 173

    Chapter 7. Interaction of Nematicons and Nematicon Clusters 177
    Catherine Garc´?a-Reimbert, Antonmaria A. Minzoni, and Noel F. Smyth

    7.1 Introduction 177

    7.2 Gravitation of Nematicons 179

    7.3 In-Plane Interaction of Two-Color Nematicons 184

    7.4 Multidimensional Clusters 190

    7.5 Vortex Cluster Interactions 199

    7.6 Conclusions 205

    Appendix: Integrals 206

    References 206

    Chapter 8. Nematicons in Light Valves 209
    Stefania Residori, Umberto Bortolozzo, Armando Piccardi, Alessandro Alberucci, and Gaetano Assanto

    8.1 Introduction 209

    8.2 Reorientational Kerr Effect and Soliton Formation in Nematic Liquid Crystals 210

    8.2.1 Optically Induced Reorientational Nonlinearity 211

    8.2.2 Spatial Solitons in Nematic Liquid Crystals 211

    8.3 Liquid Crystal Light Valves 212

    8.3.1 Cell Structure and Working Principle 213

    8.3.2 Optical Addressing in Transverse Configurations 215

    8.4 Spatial Solitons in Light Valves 216

    8.4.1 Stable Nematicons: Self-Guided Propagation in the Longitudinal Direction 216

    8.4.2 Tuning the Soliton Walk-Off 218

    8.5 Soliton Propagation in 3D Anisotropic Media: Model and Experiment 220

    8.5.1 Optical Control of Nematicon Trajectories 224

    8.6 Soliton Gating and Switching by External Beams 224

    8.7 Conclusions and Perspectives 227

    References 229

    Chapter 9. Propagation of Light Confined via Thermo-Optical Effect in Nematic Liquid Crystals 233
    Marc Warenghem, Jean-Francois Blach, and Jean-Francois Henninot

    9.1 Introduction 233

    9.2 First Observation in NLC 235

    9.3 Characterization and Nonlocality Measurement 240

    9.4 Thermal Versus Orientational Self-Waveguides 246

    9.5 Applications 248

    9.5.1 Bent Waveguide 248

    9.5.2 Fluorescence Recovery 249

    9.6 Conclusions 250

    References 252

    Chapter 10. Discrete Light Propagation in Arrays of Liquid Crystalline Waveguides 255
    Katarzyna A. Rutkowska, Gaetano Assanto, and Miroslaw A. Karpierz

    10.1 Introduction 255

    10.2 Discrete Systems 256

    10.3 Waveguide Arrays in Nematic Liquid Crystals 258

    10.4 Discrete Diffraction and Discrete Solitons 263

    10.5 Optical Multiband Vector Breathers 265

    10.6 Nonlinear Angular Steering 267

    10.7 Landau-Zener Tunneling 268

    10.8 Bloch Oscillations 270

    10.9 Conclusions 272

    References 273

    Chapter 11. Power-Dependent Nematicon Self-Routing 279
    Alessandro Alberucci, Armando Piccardi, and Gaetano Assanto

    11.1 Introduction 279

    11.2 Nematicons: Governing Equations 280

    11.2.1 Perturbative Regime 282

    11.2.2 Highly Nonlinear Regime 284

    11.2.3 Simplified (1 + 1)D Model in a Planar Cell 285

    11.3 Single-Hump Nematicon Profiles 287

    11.3.1 (2 + 1)D Complete Model 288

    11.3.2 (1 + 1)D Simplified Model 289

    11.4 Actual Experiments: Role of Losses 290

    11.4.1 BPM (1 + 1)D Simulations 291

    11.4.2 Experiments 292

    11.5 Nematicon Self-Steering in Dye-Doped NLC 293

    11.6 Boundary Effects 298

    11.7 Nematicon Self-Steering Through Interaction with Linear Inhomogeneities 302

    11.7.1 Interfaces: Goos-H¨anchen Shift 303

    11.7.2 Finite-Size Defects: Nematicon Self-Escape 304

    11.8 Conclusions 305

    References 306

    Chapter 12. Twisted and Chiral Nematicons 309
    Urszula A. Laudyn and Miroslaw A. Karpierz

    12.1 Introduction 309

    12.2 Chiral and Twisted Nematics 310

    12.3 Theoretical Model 312

    12.4 Experimental Results 314

    12.4.1 Nematicons in a Single Layer 314

    12.4.2 Asymmetric Configuration 315

    12.4.3 Multilayer Propagation 317

    12.4.4 Influence of an External Electric Field 317

    12.4.5 Guiding Light by Light 319

    12.4.6 Nematicon Interaction 319

    12.5 Discrete Diffraction 321

    12.6 Conclusions 323

    References 323

    Chapter 13. Time Dependence of Spatial Solitons in Nematic Liquid Crystals 327
    Jeroen Beeckman and Kristiaan Neyts

    13.1 Introduction 327

    13.2 Temporal Behavior of Different Nonlinearities and Governing Equations 328

    13.2.1 Reorientational Nonlinearity 328

    13.2.2 Thermal Nonlinearity 331

    13.2.3 Other Nonlinearities 333

    13.3 Formation of Reorientational Solitons 333

    13.3.1 Bias Voltage Switching Time 334

    13.3.2 Soliton Formation Time 336

    13.3.3 Experimental Observation of Soliton Formation 337

    13.3.4 Influence of Flow Effects 341

    13.4 Conclusions 344

    References 344

    Chapter 14. Spatiotemporal Dynamics and Light Bullets in Nematic Liquid Crystals 347
    Marco Peccianti

    14.1 Introduction 347

    14.1.1 (2 + 1 + 1)D Nonlinear Wave Propagation in Kerr Media 348

    14.2 Optical Propagation Under Multiple Nonlinear Contributions 349

    14.2.1 Multiple Nonlinearities and Space-Time Decoupling of the Nonlinear Dynamics 349

    14.2.2 Suitable Excitation Conditions 350

    14.3 Accessible Light Bullets 351

    14.3.1 From Nematicons to Spatiotemporal Solitons 351

    14.3.2 Experimental Conditions for Accessible Bullets Observation 353

    14.4 Temporal Modulation Instability in Nematicons 355

    14.5 Soliton-Enhanced Frequency Conversion 355

    14.6 Conclusions 357

    References 358

    Chapter 15. Vortices in Nematic Liquid Crystals 361
    Antonmaria A. Minzoni, Luke W. Sciberras, Noel F. Smyth, and Annette L. Worthy

    15.1 Introduction 361

    15.2 Stabilization of Vortices in Nonlocal, Nonlinear Media 364

    15.3 Vortex in a Bounded Cell 373

    15.4 Stabilization of Vortices by Vortex-Beam Interaction 378

    15.5 Azimuthally Dependent Vortices 382

    15.6 Conclusions 387

    References 389

    Chapter 16. Dispersive Shock Waves in Reorientational and Other Optical Media 391
    Tim R. Marchant

    16.1 Introduction 391

    16.2 Governing Equations and Modulational Instability 392

    16.3 Existing Experimental and Numerical Results 394

    16.4 Analytical Solutions for Defocusing Equations 396

    16.5 Analytical Solutions for Focusing Equations 398

    16.5.1 The 1 + 1 Dimensional Semianalytical Soliton 400

    16.5.2 Uniform Soliton Theory 402

    16.5.3 Comparisons with Numerical Solutions 403

    16.6 Conclusions 406

    References 407

    Index 411