Nematicons E-Book

Gaetano Assanto

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Pure and Applied Optics
• Sprache: Englisch

Seitenzahl: 717

Veröffentlichungsjahr: 2012

Beschreibung

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.

Leseprobe

Table of Contents

Series

Title Page

Copyright

Dedication

Preface

Acknowledgments

Contributors

Chapter 1: Nematicons

1.1 Introduction

1.2 Models

1.3 Numerical Simulations

1.4 Experimental Observations

1.5 Conclusions

References

Chapter 2: Features of Strongly Nonlocal Spatial Solitons

2.1 Introduction

2.2 Phenomenological Theory of Strongly Nonlocal Spatial Solitons

2.3 Nonlocal Spatial Solitons in Nematic Liquid Crystals

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

4.3 Soliton Families in Strongly Nonlocal Nonlinear Media

4.4 Conclusions

References

Chapter 5: External Control of Nematicon Paths

5.2 Basic Equations

5.3 Nematicon Control with External Light Beams

5.4 Voltage Control of Nematicon Walk-Off

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

Acknowledgments

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

8.2 Reorientational Kerr Effect and Soliton Formation in Nematic Liquid Crystals

8.3 Liquid Crystal Light Valves

8.4 Spatial Solitons in Light Valves

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

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

9.2 First Observation in NLC

9.3 Characterization and Nonlocality Measurement

9.4 Thermal Versus Orientational Self-Waveguides

9.5 Applications

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

11.2 Nematicons: Governing Equations

11.3 Single-Hump Nematicon Profiles

11.4 Actual Experiments: Role of Losses

11.5 Nematicon Self-Steering in Dye-Doped NLC

11.6 Boundary Effects

11.7 Nematicon Self-Steering Through Interaction with Linear Inhomogeneities

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

12.5 Discrete Diffraction

12.6 Conclusions

References

Chapter 13: Time Dependence of Spatial Solitons in Nematic Liquid Crystals

13.2 Temporal Behavior of Different Nonlinearities and Governing Equations

13.3 Formation of Reorientational Solitons

13.4 Conclusions

References

Chapter 14: Spatiotemporal Dynamics and Light Bullets in Nematic Liquid Crystals

14.1 Introduction

14.2 Optical Propagation Under Multiple Nonlinear Contributions

14.3 Accessible Light Bullets

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

16.2 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

16.6 Conclusions

References

index

bseries

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Library of Congress Cataloging-in-Publication Data:

Nematicons : spatial optical solitons in nematic liquid crystals / [edited by]

Gaetano Assanto.

pages cm. – (Wiley series in pure and applied optics ; 74)

Includes bibliographical references.

ISBN 978-0-470-90724-5

1. Solitons. 2. Nematic liquid crystals. 3. Liquid crystals–Spectra. I.

Assanto, Gaetano, 1958-

QC174.26.W28N46 2012

530.12′4–dc23

2012010716

To my parents

Preface

Solitons in physics and solitons in optics are well-established contemporary topics, addressed in a large number of scientific papers and several books. Spatial optical solitons form a specific class, as optics in space is characterized by diffraction rather than dispersion, beam size rather than pulse duration, one or two transverse dimensions rather than one in the temporal domain. For a long time, the available experimental observations of optical solitons in space were limited by the magnitude of the material nonlinearities, until molecular and photorefractive media allowed investigating them at low power and with continuous-wave sources, including incoherent ones. Among the well-known molecular dielectrics exhibiting a large optically nonlinear response were liquid crystals, typically employed in thin samples. It was realized in the early days of both nonlinear optics and liquid crystals that the reorientational response of nematic liquid crystals could lead to quite impressive effects, both in the electro-optic and all-optical domains. Later on, beam propagation over extended distances in nematic liquid crystals was exploited to demonstrate self-focusing and related phenomena, until it became clear that optical spatial solitons could be supported by such a response at the molecular level. I came across light self-localization in nematic liquid crystals during international meetings, where I attended the inspiring presentations by Prof. M. Karpierz (Poland) and Prof. M. Warenghem (France) on light self-confinement in nematic liquid crystals, and decided to get involved in research on nematicons. The discussions with Prof. I. C. Khoo were enlightening and the collaboration with Prof. C. Umeton allowed the program to get started on the right foot. The term “nematicon” was actually coined during a car trip in Poland as I was having a conversation on the topic with M. Karpierz and G. I. Stegeman. The Greek root νϵματικoσ means “filament-like” or “spaghetti-like,” appropriate to both the topic and the culinary culture of someone like me, of Italian birth and upbringing.

This is the first book specifically dealing with spatial optical solitons in nematic liquid crystals. It is a multiauthor contribution to the field and contains review as well as original (previously unpublished) material, from theoretical models to advanced numerical simulations and from experimental observations to applications. The various contributors and chapters have been selected and invited in order to cover most of the relevant activities in this field over the past 12 years.

G. Assanto

Italy

February 2012

Acknowledgments

Prof. Glenn Boreman and his wife, Maggie, friends since my PhD studies at the University of Arizona in Tucson, Arizona, encouraged me to consider preparing a Wiley book on nematicons. George Telecki soon joined them in keeping up the necessary pressure. Thanks a lot. I hope you were right and that readers will enjoy this book.

I thank all the authors who kindly accepted my invitation to contribute one or more chapters, and to subject themselves to a number of requests concerning contents, style, mode of presentation, and deadlines. I express my gratitute to all the students and colleagues who do not appear as book contributors but are coauthors of papers and precious actors inspiring various portions of the scientific activities. They include R. Asquini, R. Barboza, I. Burgess, O. Buchnev, G. Coschignano, D. Christodoulides, A. d'Alessandro, A. de Luca, R. Dabrowski, A. Dyadyusha, A. Fratalocchi, M. Kaczmarek, I. C. Khoo, M. Kwasny, L. Lucchetti, R. Morandotti, E. Nowinowski-Kruszelnicki, A. Pasquazi, K. A. Rutkowska, S. V. Serak, F. Simoni, G. I. Stegeman, N. Tabiryan, M. Trotta, and C. Umeton.

Finally, I pay a special tribute to Alessandro Alberucci and Armando Piccardi for greatly supporting me in the no less important task of arranging, organizing, managing, and editing the manuscript.

GA

Contributors

Alessandro Alberucci, Nonlinear Optics and OptoElectronics Lab, University ROMA TRE, Rome, Italy

Gaetano Assanto, Nonlinear Optics and OptoElectronics Lab, University ROMA TRE, Rome, Italy

Jeroen Beeckman, Department of Electronics and Information Systems, Ghent University, Ghent, Belgium

Milivoj R. Beli, Science Program, Texas A&M University at Qatar, Doha, Qatar

Jean-Francois Blach, Unité de Catalyse et de Chimie du Solide, Faculté des Sciences, Université d'Artois, Lens, France

Umberto Bortolozzo, INLN, Université de Nice-Sophia Antipolis, CNRS, Valbonne, France

Dongmei Deng, Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Photoelectronic Science and Engineering, South China Normal University, Guangzhou, China

Anton S. Desyatnikov, Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, ACT, Australia

Catherine García-Reimbert, Department of Mathematics and Mechanics, IIMAS, Fenomenos Nonlineales y Mecánica, Universidad Nacional Autónoma de México, Mexico D.F., Mexico

Qi Guo, Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Photoelectronic Science and Engineering, South China Normal University, Guangzhou, China

Jean-Francois Henninot, Unité de Catalyse et de Chimie du Solide, Faculté des Sciences, Université d'Artois, Lens, France

Wei Hu, Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Photoelectronic Science and Engineering, South China Normal University, Guangzhou, China

Yana V. Izdebskaya, Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, ACT, Australia

Miroslaw A. Karpierz, Warsaw University of Technology, Warsaw, Poland

Yuri S. Kivshar, Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, ACT, Australia

Urszula A. Laudyn, Warsaw University of Technology, Warsaw, Poland

Daquan Lu, Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Photoelectronic Science and Engineering, South China Normal University, Guangzhou, China

Tim R. Marchant, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia

Antonmaria A. Minzoni, Department of Mathematics and Mechanics, IIMAS, Fenomenos Nonlineales y Mecánica, Universidad Nacional Autónoma de México, Mexico D.F., Mexico

Kristiaan Neyts, Department of Electronics and Information Systems, Ghent University, Ghent, Belgium

Shigen Ouyang, Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Photoelectronic Science and Engineering, South China Normal University, Guangzhou, China

Marco Peccianti, Institute for Complex Systems, ISC-CNR, Rome, Italy

Armando Piccardi, Nonlinear Optics and OptoElectronics Lab, University ROMA TRE and CNISM, Rome, Italy

Stefania Residori, INLN, Université de Nice-Sophia Antipolis, CNRS, Valbonne, France

Katarzyna A. Rutkowska, Warsaw University of Technology, Warsaw, Poland

Luke W. Sciberras, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia

Noel F. Smyth, School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, Scotland, United Kingdom

Marc Warenghem, Unité de Catalyse et de Chimie du Solide, Faculté des Sciences, Université d'Artois, Lens, France

Annette L. Worthy, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia

Wei-Ping Zhong, Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde, China

Chapter 1: Nematicons

Gaetano Assanto, Alessandro Alberucci and Armando Piccardi

Nonlinear Optics and OptoElectronics Lab, University ROMA TRE, Rome, Italy

1.1 Introduction

The term nematicon was coined to denote the material, nematic liquid crystals (NLC), supporting the existence of optical spatial solitons via a molecular response to light, a reorientational nonlinearity. Nematicons was first used in the title of Reference 1, after three years since the first publication on reorientational spatial optical solitons in NLC [2]. Since then, a large number of results, including experimental, theoretical, and numerical, have been presented in papers and conferences and formed a body of literature on the subject. In this chapter we attempt to summarize the most important among them, leaving the details to the specific articles but trying to provide a feeling of the amount of work carried out in slightly more than a decade.

1.1.1 Nematic Liquid Crystals

Liquid crystals are organic mesophases featuring various degrees of spatial order while retaining the basic properties of a fluid. In the absence of absorbing dopants, they are excellent dielectrics, transparent from the ultraviolet to the mid-infrared, with highly damaged thresholds, relatively low electronic susceptibilities, and significant birefringence at the molecular level and in the nematic phase. In the latter phase, their elongated molecules have the same average angular orientation, although their individual location is randomly distributed as they are free to move (Fig. 1.1a). NLC exhibit a molecular nonlinearity; when an electric field is present, the electrons in the molecular orbitals tend to oscillate with it and give rise to dipoles which, in turn, react to and tend to align with the field in order to minimize the resulting Coulombian torque [35] (Fig. 1.1b–c). This torque is counteracted by the elastic forces stemming from intermolecular links: equilibrium is established when the free energy of the system is minimized, as modeled by a set of Euler–Lagrange equations. Because the polarizability of the molecules is higher along their major axes, their reorientation toward the field will increase the optical density, both at the microscopic and macroscopic levels. It is noteworthy that an initial orthogonality between the field and the induced molecular dipoles corresponds to a threshold effect known as Freedericksz transition [3]. For static or low frequency fields, reorientation leads to a large electro-optic response with a positive refractive index variation for light polarized in the same plane of the field lines and the long molecular axes [3]. For fields at optical frequencies, the average angular orientation or molecular director in the nematic phase corresponds to the optic axis of the equivalent uniaxial crystal; hence, the refractive index for extraordinarily polarized electric fields (i.e., with field vector coplanar with both optic axis and wave-vector) will increase with the orientation angle θ (Fig. 1.1c–d for wave-vectors along z).

The reorientational mechanism described above is neither instantaneous nor fast (see Chapter 13), but can be very large, with effective Kerr coefficients n2 of about 10−4 cm/W2 [6], that is, eight to twelve orders of magnitude larger than that in CS2 and in electronic media, respectively [7]. Therefore, nonlinear effects can be observed in NLC even with continuous wave lasers, at variance with many other nonlinear dielectrics often requiring pulsed excitations.

Nevertheless, the reorientational response is not the only available response in NLC. Owing to their fluidic nature, a high electric field can change the portion of molecules aligned to the director, that is, can affect the order parameter [8], particularly in the presence of dye dopants [9]. Doped NLC also features an enhanced reorientational nonlinearity because of the Janossy effect [10]. As a result of thermo-optic effect, a nonlinear response also stems from temperature changes, modifying the refractive indices mainly via the order parameter in phase transitions [6] (see Chapter 9). Moreover, NLC can show the photorefractive effect [4] and fast electronic nonlinearities (see Chapter 14).

1.1.2 Nonlinear Optics and Solitons