OPTICAL SOLITONS: THEORETICAL CHALLENGES AND INDUSTRIAL PERSPECTIVES Les Houches Workshop, September 28- October 2,1998 Editors V.E. ZAKHAROV S. WABNITZ Springer-Verlag Berlin Heidelberg GmbH Centre de Physique des Bouches Books already published in this series 1 Porous Silicon Science and Technology 7 Scale Invariance and Beyond J.-C. VIAL and J. DERRIEN, Eds. 1995 B. DUBRULLE, F. GRANER and D. SORNETTE, Eds. 1997 2 Nonlinear Excitations in Biomolecules 8 New Non-Perturbative Methods and M. PEYRARD, Ed. 1995 Quantization on the Light Cone 3 Beyond Quasicrystals P. GRANGE, A. NEVEU, H.C. PAULI, S. PINSKY and E. WERNER, Eds. 1998 F. AXEL and D. GRATIAS, Eds. 1995 9 Starbursts Triggers, Nature, and Evolution 4 Quantum Mechanical Simulation Methods B. GUIDERDONI and A. KEMBHAV I, for Studying Biological Systems Eds. 1998 D. BICOUT and M. FIELD, Eds. 1996 10 Dynamical Networks in Physics and Biology 5 New Tools in Turbulence Modelling D. BEYSENS and G. FORGACS, Eds. 0. METAlS and J. FERZIGER, Eds. 1997 1998 11 Solid Interstellar Matter: 6 Catalysis by Metals The ISO Revolution A. J. RENOUPREZ L. d'HENDECOURT, C. JOBLIN and and H. JOBIC, Eds. 1997 A. JONES, Eds. 1999 Book series coordinated by Michele LEDUC Editors of "Optical Solitons: Theoretical Challenges and Industrial Perspectives " (No. 12) V.E. Zakharov (L.D. Landau Institute, Moscow, Russia) S. Wabnitz (LPUB, Universite de Bourgogne, Dijon, France) ISBN 978-3-540-66314-0 ISBN 978-3-662-03807-9 (eBook) DOI 10.1007/978-3-662-03807-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the French and German Copyright laws of March 11, 1957 and September 9, 1965, respectively. Violations fall under the prosecution act of the French and German Copyright Laws. ©Springer-Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg New York in 1999 FOREWORD V.E. Zakharov1 and S. Wabnitz2 1 L.D. Landau Institute for Theoretical Physics, 2 Kosygin Str., 117334 Moscow, Russia 2 Laboratoire de Physique, University of Bourgogne, 9 avenue A. Savary, 21078 Dijon, France After about a quarter of a century since the first theoretical predictions of op tical solitons, the industrial application of the optical soliton concept is near to reality in the booming field of modern telecommunications, where the de mand for high-speed data transmission and routing is of ever-growing. This book contains a set of lectures that were presented at a Les Houches school on optical solitons in September 1998. The school was successful in gathering among the lecturers most of the well-recognized world leaders in the field of optical solitons. A variety of different aspects of research into optical solitons was exposed in the lectures, ranging from the mathematical fundations of integrability theory to the rapidly evolving technological advances of fiber soliton-based telecommu nication systems. The overall impression that the participants and the students received from the school is that this field of research is an excellent example of the rapid transfer that occurs nowadays from basic science to the technological implementations of the first principles. The subjects that were covered by the lectures can be broadly grouped into four main categories: optical soliton the ory, fiber soliton telecommunications, optical soliton generation methods, and all-optical information processing via spatial solitons. The main issues that need to be solved for the practical deployment of solitons in real-world transmissions were outlined, such as timing jitters in duced by noise and by pulse interactions and collisions. Nowadays, the research on soliton telecommunications is basically focused on the solution provided by dispersion management or compensation. In this regime, optical pulse propa gation in the presence of fiber nonlinearity turns out to be extremely stable: a full theoretical understanding of the dynamics of these nonlinear pulses is still to be developed. IV Soliton-shaping effects play a key role in the generation of ultrashort optical pulses; a variety of effects and devices were described, ranging from stretched pulse lasers and fiber ring memories, to Bragg couplers and Raman or Brillouin soliton lasers. Another manifestation of optical solitons is given by spatial solitons; in this case, nonlinear self-focusing may balance the diffractive speading of a pulse in a dielectric. All-optical signal processing could be based on spatial soli ton effects, whereby light may induce reconfigurable waveguides in the form of arrays of bright or dark spatial solitons. For the stability of these pulses in a bulk medium, a saturable nonlinearity is required; as a possible physical mechanism for such nonlinear response, the photorefractive effect has recently received considerable attention. This effect has the merit of providing low soli ton powers, at the expense of long response times; moreover, soliton formation with incoherent (white) light was recently predicted. In summary, this book contains a unique panoramic review of recent theory and experiments in a rapidly evolving domain of applied physics, and should provide an interesting reference both for postgraduate students starting their research in the field and for researchers actively involved in nonlinear optics and optical communications. The school was carried out within the framework of the "Training and mo bility of researchers" summer school programme of the European Commission. Additional institutions that gave their generous support to the event were Aka tel, CNET-France Telecom, the CNRS, the GDR-POAN, the Frency Ministry of Foreign Affairs, and the European Commission Cooperation Project on Sci ence and Technology (COST) 241. AUTHORS F.Kh. Abdullaev, Physical-Technical Institute, Academy of Sciences of Uzbekistan, Tashkent-84, G. Mavlyanov Str. 2-b, Uzbekistan J.S. Aitchison, Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8LQQ, U.K. N. Akmediev, Australian Photonics Cooperative Research Centre, Optical Sciences Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia G. Assanto, Department of Electronic Engineering, Terza University of Roma, and National Institute for the Physics of Matter, INFM-RM3 Division, via della Vasca Navale 84, 00146 Roma, Italy B. Biotteau, Alcatel Corporate Research Centre, route de Nozay, 91460 Marcoussis, France V. Cautaerts, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan J. Christou, Australian Photonics Cooperative Research Centre, Laser Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia S. Coen, Service d'Optique et d' Acoustique, Universite Libre de Bruxelles, CP. 194/5, 50 avenue F.D. Roosevelt, 1050 Bruxelles, Belgium C. Conti, Department of Electronic Engineering, Terza University of Roma, and National Institute for the Physics of Matter, INFM-RM3 Division, via della Vasca Navale 84,00146 Roma, Italy A. de Rossi, Department of Electronic Engineering, Terza University of Roma, and National Institute for the Physics of Matter, INFM-RM3 Division, via della Vasca Navale 84, 00146 Roma, Italy E. Desurvire, Alcatel Corporate Research Centre, route de Nozay, 91460 Marcoussis, France VI N.J. Doran, Photonics Research Group, School of Engineering and Applied Science, Aston University, Binningham B4 7ET, U.K. W. Forysiak, Photonics Research Group, School of Engineering and Applied Science, Aston University, Binningham B4 7ET, U.K. T. Georges, France Telecom/CNET, Lannion, France P. Grelu, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400, 2I 0 II Dijon, France M. Haeltennan, Service d'Optique et d' Acoustique, Universite Libre de Bruxelles, CP. 194/5, 50 avenue F.D. Roosevelt, 1050 Bruxeiies, Belgique, and, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400,21011 Dijon, France J.-P. Hamaide, Alcatel Corporate Research Centre, route de Nozay, 91460 Marcoussis, France H.A. Haus, Deparbnent of Electrical Engineering and Computer Science, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. A. Hasegawa, Kochi University of Technology, and NTT Science and Core Technology Laboratory Group, A TR Bldg. 2-2 Hikaridai Seikacho Sorakugun Kyoto-fu, 619-0288, Japan P.S. Jian, Deparbnent of Physics, Washington State University, Pullman, WA 99164-2814, U.S.A. Y. Kivshar, Australian Photonics Cooperative Research Centre, Optical Sciences Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia Y. Kodama, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan, and, Deparbnent of Mathematics, Ohio State University, Columbus, OH 43210, U.S.A. W. Krolikowski, Australian Photonics Cooperative Research Centre, Laser Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia E.A. Kuznetsov, L.D. Landau Institute for Theoretical Physics, 2 Kosygina Str., 117334 Moscow, Russia AUTHORS VII F. Lederer, lnstitut fi1r Festkorpertheorie und Theoretische Optik, Friedrich-Schiller Universitat Jena, Max-Wien-Platz 1, 07743 Jena, Germany J. Leon, Physique Mathematique et Theorique, UMR 5825 du CNRS, Universite de Montpellier 2, 34095 Montpellier, France B. Luther-Davies, Australian Photonics Cooperative Research Centre, Laser Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia A.l. Maimitsov, Moscow Engineering Physics Institute, Kashirskoe Sh. 31, Moscow, Russia V.G. Marikhin, L.D. Landau Institute for Theoretical Physics, 2 Kosygina Str., 117334 Moscow, Russia A. Maruta, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan V.K. Mezentsev, Photonics Research Group, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, U.K. A.V. Mikhailov, Applied Mathematics Department, University of Leeds, Leeds LS2 9JT, U.K., and, L.D. Landau Institute for Theoretical Physics, 142432 Chemogolovska, Russia G. Millot, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400,21011 Dijon, France C. Montes, Laboratoire de Physique de Ia Matiere Condensee, Centre National de Ia Recherche Scientifique, Universite de Nice-Sophia Antipolis, Pare Valrose, 06108 Nice Cedex 2, France J.H.B. Nijhof, Photonics Research Group, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, U.K. U. Peschel, lnstitut fi1r Festkorpertheorie und Theoretische Optik, Friedrich-Schiller Universitiit Jena, Max-Wien-Platz 1, 07743 Jena, Germany A. Picozzi, Service d'Optique et d' Acoustique, Universite Libre de Bruxelles, 50 avenue F.D. Roosevelt, CP. 194/5, 1050 Bruxelles, Belgium F. Pitel, Alcatel Corporate Research Centre, route de Nozay, 91460 Marcoussis, France VIII S. Pitois, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400,21011 Dijon, France T. Schafer, Photonics Research Group, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, U.K. M. Segev, Electrical Engineering Department and Center for Photonics and Opto Electronic Materials (POEM) and Princeton Materials Institute (PMI), Princeton University, Princeton, NJ 08544, U.S.A., and Solid State Institute and Physics Department, Technion - Israel Institute of Technology, Haifa 32000, Israel E. Seve, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400,21011 Dijon, France A.B. Shabat, L.D. Landau Institute for Theoretical Physics, 2 Kosygina Str., 117334 Moscow, Russia G.l. Stegeman, School of Optics and CREOL, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32826, U.S.A. H. Sugahara, Graduate School ofEngineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan P. Tchofo Dinda, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400, 21011 Dijon, France V. Tikhonenko, Australian Photonics Cooperative Research Centre, Laser Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia W.E. Torruellas, Department of Physics, Washington State University, Pullman, WA 99164-2814, U.S.A. S. Trillo, Dipartimento di Ingegneria, Universita di Ferrara, via Saragat 1, 44100 Ferrara, Italy, and, Fondazione Ugo Bordoni, via B. Castiglione 59, 00142 Roma, Italy S.K. Turitsyn, Photonics Research Group, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, U.K. S. Wabnitz, Laboratoire de Physique, Universite de Bourgogne, 9 avenue Savary, BP. 400, 21011 Dijon, France V.E. Zakharov, L.D. Landau Institute for Theoretical Physics, 2 Kosygina Str., 117334 Moscow, Russia CONTENTS LECTURE! Fundamentals of Optical Soliton Theory in Fibers by A. Hasegawa 1. Introduction............................................................................................. 1 2. Electromagnetic waves in dielectric materials........................................ 1 2.1 Polarization effects......................................................................... 1 2.2 Plane electromagnetic waves in dielectric materials...................... 3 2.3 Kerr effect and Kerr coefficient ..................................................... 5 2.4 Dielectric waveguides .................................................................... 6 3. Envelope of electromagnetic wave in dielectric materials...................... 10 3.1 Lightwave envelope in fibers-derivation of nonlinear Schrodinger equation...................................................................... 10 3.2 Evolution of the wave packet due to the group velocity dispersion 12 3.3 Evolution of wave packet due to the nonlinearity.......................... 14 3.4 Lax theorem.................................................................................... 15 3.5 The soliton solution of the nonlinear Schrooinger equation........... 15 4. Ultrafast communication based on optical solitons................................ 16 5. Conclusion.............................................................................................. 18 LECTURE2 Hamiltonian Theory of Backlund Transformation by V .G. Marikhin and A.B. Shabat 1. Introduction............................................................................................. 19 2. Lattice equations..................................................................................... 22 3. Canonical Backlund transformations...................................................... 25 4. First integrals .......................................................................................... 27 X LECTURE3 Stability of Solitons by E.A. Kuznetsov 1. Introduction............................................................................................. 31 2. Lyapunov stability.................................................................................. 33 2.1 Nonlinear Schrooinger equation..................................................... 33 2.2 The three-wave system................................................................... 36 2.3 Soliton solutions ofthe 3-wave system.......................................... 39 2.4 Nonlinear stability.......................................................................... 41 3. Linear stability........................................................................................ 43 3.1 Linear stability for 1D NLS solitons.............................................. 43 3.2 Solitons for the FF-SH interaction................................................. 46 LECTURE4 Chaotic Dynamics of Optical Solitons by F .Kh. Abdullaev 1. Introduction............................................................................................. 51 2. Variational approach to solitons dynamics in random media................. 52 2.1 Optical solitons in media with fluctuating quadratic potential....... 53 2.2 Spatial soliton in array with fluctuating parameters....................... 54 2.3 A random Kepler problem.............................................................. 55 3. Inverse scattering transform technique for solitons in random media.... 56 3.1 Single soliton propagation in random media.................................. 56 3.2 Interaction of optical solitons in random media............................. 59 4. Conclusion.............................................................................................. 61 LECTURES Variationalism and Empirio-Criticism. (Exact and Variational Approaches to Fibre Optics Equations) by A.V. Mikhailov 1. Introduction............................................................................................. 63 2. Variational approach............................................................................... 64 3. What is wrong with the variational approach?........................................ 68