Nematicons

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.

• Preface xv Acknowledgments xviiContributors xixChapter 1. Nematicons 1Gaetano Assanto, Alessandro Alberucci, and Armando Piccardi1.1 Introduction 11.1.1 Nematic Liquid Crystals 11.1.2 Nonlinear Optics and Solitons 31.1.3 Initial Results on Light Self-Focusing in Liquid Crystals 31.2 Models 41.2.1 Scalar Perturbative Model 51.2.2 Anisotropic Perturbative Model 91.3 Numerical Simulations 131.3.1 Nematicon Profile 131.3.2 Gaussian Input 141.4 Experimental Observations 171.4.1 Nematicon–Nematicon Interactions 221.4.2 Modulational Instability 261.5 Conclusions 31References 33Chapter 2. Features of Strongly Nonlocal Spatial Solitons 37Qi Guo, Wei Hu, Dongmei Deng, Daquan Lu, and Shigen Ouyang2.1 Introduction 372.2 Phenomenological Theory of Strongly Nonlocal Spatial Solitons 382.2.1 The Nonlinearly Induced Refractive Index Change of Materials 382.2.2 From the Nonlocal Nonlinear Schr¨odinger Equation to the Snyder–Mitchell Model 392.2.3 An Accessible Soliton of the Snyder–Mitchell Model 422.2.4 Breather and Soliton Clusters of the Snyder–Mitchell Model 452.2.5 Complex-Variable-Function Gaussian Breathers and Solitons 462.2.6 Self-Induced Fractional Fourier Transform 472.3 Nonlocal Spatial Solitons in Nematic Liquid Crystals 492.3.1 Voltage-Controllable Characteristic Length of NLC 502.3.2 Nematicons as Strongly Nonlocal Spatial Solitons 522.3.3 Nematicon–Nematicon Interactions 542.4 Conclusion 61Appendix 2.A: Proof of the Equivalence of the Snyder–Mitchell Model (Eq. 2.16) and the Strongly Nonlocal Model (Eq. 2.11) 61Appendix 2.B: Perturbative Solution for a Single Soliton of the NNLSE (Eq. 2.4) in NLC 62References 66Chapter 3. Theoretical Approaches to Nonlinear Wave Evolution in Higher Dimensions 71Antonmaria A. Minzoni and Noel F. Smyth3.1 Simple Example of Multiple Scales Analysis 713.2 Survey of Perturbation Methods for Solitary Waves 773.3 Linearized Perturbation Theory for Nonlinear Schr¨odinger Equation 813.4 Modulation Theory: Nonlinear Schr¨odinger Equation 833.5 Radiation Loss 883.6 Solitary Waves in Nematic Liquid Crystals: Nematicons 913.7 Radiation Loss for The Nematicon Equations 963.8 Choice of Trial Function 1013.9 Conclusions 105Appendix 3.A: Integrals 106Appendix 3.B: Shelf Radius 107References 108Chapter 4. Soliton Families in Strongly Nonlocal Media 111Wei-Ping Zhong and Milivoj R. Beli¸c4.1 Introduction 1114.2 Mathematical Models 1124.2.1 General 1124.2.2 Nonlocality Through Response Function 1134.3 Soliton Families in Strongly Nonlocal Nonlinear Media 1154.3.1 One-Dimensional Hermite–Gaussian Spatial Solitons 1154.3.2 Two-Dimensional Laguerre–Gaussian Soliton Families 1164.3.3 Accessible Solitons in the General Model of Beam Propagation in NLC 1184.3.4 Two-Dimensional Self-Similar Hermite–Gaussian Spatial Solitons 1254.3.5 Two-Dimensional Whittaker Solitons 1264.4 Conclusions 133References 135Chapter 5. External Control of Nematicon Paths 139Armando Piccardi, Alessandro Alberucci, and Gaetano Assanto5.1 Introduction 1395.2 Basic Equations 1405.3 Nematicon Control with External Light Beams 1425.3.1 Interaction with Circular Spots 1435.3.2 Dielectric Interfaces 1455.3.3 Comments 1465.4 Voltage Control of Nematicon Walk-Off 1475.4.1 Out-of-Plane Steering of Nematicons 1475.4.2 In-Plane Steering of Nematicon 1495.5 Voltage-Defined Interfaces 1525.6 Conclusions 156References 156Chapter 6. Dynamics of Optical Solitons in Bias-Free Nematic Liquid Crystals 159Yana V. Izdebskaya, Anton S. Desyatnikov, and Yuri S. Kivshar6.1 Summary 1596.2 Introduction 1596.3 From One to Two Nematicons 1606.4 Counter-Propagating Nematicons 1626.5 Interaction of Nematicons with Curved Surfaces 1656.6 Multimode Nematicon-Induced Waveguides 1676.7 Dipole Azimuthons and Charge-Flipping 1706.8 Conclusions 172References 173Chapter 7. Interaction of Nematicons and Nematicon Clusters 177Catherine Garc´ýa-Reimbert, Antonmaria A. Minzoni, and Noel F. Smyth7.1 Introduction 1777.2 Gravitation of Nematicons 1797.3 In-Plane Interaction of Two-Color Nematicons 1847.4 Multidimensional Clusters 1907.5 Vortex Cluster Interactions 1997.6 Conclusions 205Appendix: Integrals 206References 206Chapter 8. Nematicons in Light Valves 209Stefania Residori, Umberto Bortolozzo, Armando Piccardi, Alessandro Alberucci, and Gaetano Assanto8.1 Introduction 2098.2 Reorientational Kerr Effect and Soliton Formation in Nematic Liquid Crystals 2108.2.1 Optically Induced Reorientational Nonlinearity 2118.2.2 Spatial Solitons in Nematic Liquid Crystals 2118.3 Liquid Crystal Light Valves 2128.3.1 Cell Structure and Working Principle 2138.3.2 Optical Addressing in Transverse Configurations 2158.4 Spatial Solitons in Light Valves 2168.4.1 Stable Nematicons: Self-Guided Propagation in the Longitudinal Direction 2168.4.2 Tuning the Soliton Walk-Off 2188.5 Soliton Propagation in 3D Anisotropic Media: Model and Experiment 2208.5.1 Optical Control of Nematicon Trajectories 2248.6 Soliton Gating and Switching by External Beams 2248.7 Conclusions and Perspectives 227References 229Chapter 9. Propagation of Light Confined via Thermo-Optical Effect in Nematic Liquid Crystals 233Marc Warenghem, Jean-Francois Blach, and Jean-Francois Henninot9.1 Introduction 2339.2 First Observation in NLC 2359.3 Characterization and Nonlocality Measurement 2409.4 Thermal Versus Orientational Self-Waveguides 2469.5 Applications 2489.5.1 Bent Waveguide 2489.5.2 Fluorescence Recovery 2499.6 Conclusions 250References 252Chapter 10. Discrete Light Propagation in Arrays of Liquid Crystalline Waveguides 255Katarzyna A. Rutkowska, Gaetano Assanto, and Miroslaw A. Karpierz10.1 Introduction 25510.2 Discrete Systems 25610.3 Waveguide Arrays in Nematic Liquid Crystals 25810.4 Discrete Diffraction and Discrete Solitons 26310.5 Optical Multiband Vector Breathers 26510.6 Nonlinear Angular Steering 26710.7 Landau–Zener Tunneling 26810.8 Bloch Oscillations 27010.9 Conclusions 272References 273Chapter 11. Power-Dependent Nematicon Self-Routing 279Alessandro Alberucci, Armando Piccardi, and Gaetano Assanto11.1 Introduction 27911.2 Nematicons: Governing Equations 28011.2.1 Perturbative Regime 28211.2.2 Highly Nonlinear Regime 28411.2.3 Simplified (1 + 1)D Model in a Planar Cell 28511.3 Single-Hump Nematicon Profiles 28711.3.1 (2 + 1)D Complete Model 28811.3.2 (1 + 1)D Simplified Model 28911.4 Actual Experiments: Role of Losses 29011.4.1 BPM (1 + 1)D Simulations 29111.4.2 Experiments 29211.5 Nematicon Self-Steering in Dye-Doped NLC 29311.6 Boundary Effects 29811.7 Nematicon Self-Steering Through Interaction with Linear Inhomogeneities 30211.7.1 Interfaces: Goos-H¨anchen Shift 30311.7.2 Finite-Size Defects: Nematicon Self-Escape 30411.8 Conclusions 305References 306Chapter 12. Twisted and Chiral Nematicons 309Urszula A. Laudyn and Miroslaw A. Karpierz12.1 Introduction 30912.2 Chiral and Twisted Nematics 31012.3 Theoretical Model 31212.4 Experimental Results 31412.4.1 Nematicons in a Single Layer 31412.4.2 Asymmetric Configuration 31512.4.3 Multilayer Propagation 31712.4.4 Influence of an External Electric Field 31712.4.5 Guiding Light by Light 31912.4.6 Nematicon Interaction 31912.5 Discrete Diffraction 32112.6 Conclusions 323References 323Chapter 13. Time Dependence of Spatial Solitons in Nematic Liquid Crystals 327Jeroen Beeckman and Kristiaan Neyts13.1 Introduction 32713.2 Temporal Behavior of Different Nonlinearities and Governing Equations 32813.2.1 Reorientational Nonlinearity 32813.2.2 Thermal Nonlinearity 33113.2.3 Other Nonlinearities 33313.3 Formation of Reorientational Solitons 33313.3.1 Bias Voltage Switching Time 33413.3.2 Soliton Formation Time 33613.3.3 Experimental Observation of Soliton Formation 33713.3.4 Influence of Flow Effects 34113.4 Conclusions 344References 344Chapter 14. Spatiotemporal Dynamics and Light Bullets in Nematic Liquid Crystals 347Marco Peccianti14.1 Introduction 34714.1.1 (2 + 1 + 1)D Nonlinear Wave Propagation in Kerr Media 34814.2 Optical Propagation Under Multiple Nonlinear Contributions 34914.2.1 Multiple Nonlinearities and Space–Time Decoupling of the Nonlinear Dynamics 34914.2.2 Suitable Excitation Conditions 35014.3 Accessible Light Bullets 35114.3.1 From Nematicons to Spatiotemporal Solitons 35114.3.2 Experimental Conditions for Accessible Bullets Observation 35314.4 Temporal Modulation Instability in Nematicons 35514.5 Soliton-Enhanced Frequency Conversion 35514.6 Conclusions 357References 358Chapter 15. Vortices in Nematic Liquid Crystals 361Antonmaria A. Minzoni, Luke W. Sciberras, Noel F. Smyth, and Annette L. Worthy15.1 Introduction 36115.2 Stabilization of Vortices in Nonlocal, Nonlinear Media 36415.3 Vortex in a Bounded Cell 37315.4 Stabilization of Vortices by Vortex–Beam Interaction 37815.5 Azimuthally Dependent Vortices 38215.6 Conclusions 387References 389Chapter 16. Dispersive Shock Waves in Reorientational and Other Optical Media 391Tim R. Marchant16.1 Introduction 39116.2 Governing Equations and Modulational Instability 39216.3 Existing Experimental and Numerical Results 39416.4 Analytical Solutions for Defocusing Equations 39616.5 Analytical Solutions for Focusing Equations 39816.5.1 The 1 + 1 Dimensional Semianalytical Soliton 40016.5.2 Uniform Soliton Theory 40216.5.3 Comparisons with Numerical Solutions 40316.6 Conclusions 406References 407Index 411