• Volume 57, Issue 5-6

      November 2001,   pages  839-1180

    • Preface

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    • Introduction to solitons

      Miki Wadati

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      As an introduction to the special issue on nonlinear waves, solitons and their significance in physics are reviewed. The soliton is the first universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized.

    • Optical fiber communication—An overview

      M Arumugam

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      This paper deals with the historical development of optical communication systems and their failures initially. Then the different generations in optical fiber communication along with their features are discussed. Some aspects of total internal reflection, different types of fibers along with their size and refractive index profile, dispersion and loss mechanisms are also mentioned. Finally the general system of optical fiber communication is briefly mentioned along with its advantages and limitations. Future soliton based optical fiber communication is also highlighted.

    • Fundamentals of nonlinear optical materials

      D Arivuoli

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      In this article, we briefly review the fundamental aspects of nonlinear optical materials and their role in modern communication.

    • Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations

      M Lakshmanan T Kanna

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      Coupled nonlinear Schrödinger equations (CNLS) very often represent wave propagation in optical media such as multicore fibers, photorefractive materials and so on. We consider specifically the pulse propagation in integrable CNLS equations (generalized Manakov systems). We point out that these systems possess novel exact soliton type pulses which are shape changing under collision leading to an intensity redistribution. The shape changes correspond to linear fractional transformations allowing for the possibility of construction of logic gates and Turing equivalent all optical computers in homogeneous bulk media as shown by Steiglitz recently. Special cases of such solitons correspond to the recently much discussed partially coherent stationary solitons (PCS). In this paper, we review critically the recent developments regarding the above properties with particular reference to 2-CNLS.

    • A variational approach to nonlinear evolution equations in optics

      D Anderson M Lisak A Berntson

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      A tutorial review is presented of the use of direct variational methods based on Rayleigh-Ritz optimization for finding approximate solutions to various nonlinear evolution equations. The practical application of the approach is demonstrated by some illustrative examples in connection with the nonlinear Schrödinger equation.

    • Periodic wavetrains for systems of coupled nonlinear Schrödinger equations

      Kwok W Chow Derek WC Lai

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      Exact, periodic wavetrains for systems of coupled nonlinear Schrödinger equations are obtained by the Hirota bilinear method and theta functions identities. Both the bright and dark soliton regimes are treated, and the solutions involve products of elliptic functions. The validity of these solutions is verified independently by a computer algebra software. The long wave limit is studied. Physical implications will be assessed.

    • Completely integrable models of nonlinear optics

      Andrey I Maimistov

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      The models of the nonlinear optics in which solitons appeared are considered. These models are of paramount importance in studies of nonlinear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency and parametric interaction of three waves. At present there are a number of theories based on completely integrable systems of equations, which are, both, generations of the original known models and new ones. The modified Korteweg-de Vries equation, the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation. Sine-Gordon equation, the reduced Maxwell-Bloch equation. Hirota equation, the principal chiral field equations, and the equations of massive Thirring model are some soliton equations, which are usually to be found in nonlinear optics theory.

    • Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers

      Ajit Kumar

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      Switching between the bistable soliton states in a doubly and inhomogeneously doped fiber system is studied numerically. Both the cases of lossless as well as lossy couplers are considered. It is shown that both up-switching (from the low state to the high state) and down-switching (from the high state to the low state) of solitons between bistable states are realizable, if the amplification of the input soliton for up-switching and the extraction of energy from it for down-switching are suitably adjusted.

    • Stable complex solitary waves of Sasa Satsuma equation

      Sasanka Ghosh

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      Existence of a new class of complex solitary waves is shown for Sasa Satsuma equation. These solitary waves are found to be stable in a certain domain of the parameter and become chaotic if the parameter exceeds the value 2.4. Significantly, the complex solitary waves propagate at higher bit rate over the most stable solitons under the same conditions of the input parameters.

    • Nonlinear compression of optical solitons

      MN Vinoj VC Kuriakose

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      In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.

    • Soliton models in resonant and nonresonant optical fibers

      K Porsezian

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      In this review, considering the important linear and nonlinear optical effects like group velocity dispersion, higher order dispersion, Kerr nonlinearity, self-steepening, stimulated Raman scattering, birefringence, self-induced transparency and various inhomogeneous effects in fibers, the completely integrable concept and bright, dark and self-induced transparency soliton models in nonlinear fiber optics are discussed. Considering the above important optical effects, the different completely integrable soliton models in the form of nonlinear Schrödinger (NLS), NLS-Maxwell-Bloch (MB) type equations reported in the literature are discussed. Finally, solitons in stimulated Raman scattering (SRS) system is briefly discussed.

    • Spinning solitons in cubic-quintic nonlinear media

      Lucian-Cornel Crasovan Boris A Malomed Dumitru Mihalache

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      We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.

    • Stable helical solitons in optical media

      Boris A Malomed G D Peng P L Chu Isaac Towers Alexander V Buryak Rowland A Sammut

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      We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations.

      In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes.

      In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.

    • Self-trapped optical beams: Spatial solitons

      Andrey A Sukhorukov Yuri S Skivshar

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      We present a brief overview of the basic concepts of the theory of spatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.

    • Soliton-based ultra-high speed optical communications

      Akira Hasegawa

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      Multi-terabit/s, ultra-high speed optical transmissions over several thousands kilometers on fibers are becoming a reality. Most use RZ (Return to Zero) format in dispersion-managed fibers. This format is the only stable waveform in the presence of fiber Kerr nonlinearity and dispersion in all optical transmission lines with loss compensated by periodic amplifications. The nonlinear Schrödinger equation assisted by the split step numerical solutions is commonly used as the master equation to describe the information transfer in optical fibers. All these facts are the outcome of research on optical solitons in fibers in spite of the fact that the commonly used RZ format is not always called a soliton format. The overview presented here attempts to incorporate the role of soliton-based communications research in present day ultra-high speed communications.

    • Spatiotemporal solitons in quadratic nonlinear media

      Frank W Wise

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      Recent developments in the study of optical spatiotemporal solitons are reviewed.

    • Spatial solitons in nonlinear liquid waveguides

      R Barillé G Rivoire

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      Spatial solitons are studied in a planar waveguide filled with nonlinear liquids. Spectral and spatial measurements for different geometries and input power of the laser beam show the influence of different nonlinear effects as stimulated scatterings on the soliton propagation and in particular on the beam polarization. The stimulated scattering can be used advantageously to couple the two polarization components. This effect can lead to multiple applications in optical switching.

    • List of Contributors

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    • Subject Index

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    • Author Index

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