Mathematical And Numerical Modelling Of Dispersion Managed Solitons Autosolitons And Self Similar Optical Pulses

During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

This dissertation, "Solitons and Wave Propagation in Hydrodynamical and Optical Media" by Chun-chung, Mak, 麥振忠, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstractofthesisentitled SolitonsandWavePropagation inHydrodynamicalandOpticalMedia submittedby Chun-ChungMAK forthedegreeofMasterofPhilosophy attheUniversityofHongKong inAugust2004 Solitons, which have been extensively studied over the past five decades, rep- resent one of the most important concepts in nonlinear science. These particle-like nonlinearwaveshavebeendemonstratedboththeoreticallyandexperimentally, and arebelievedtohavehighengineeringpotentialinsomeapplications. Theaimofthis studywastostudythesolitonswhichexistinsomeconfigurationsofhydrodynam- ical and optical media. In particular, soliton solutions of a number of completely integrablenonlinearevolutionequationsarenewlyobtainedorre-derived. The Hirota's bilinear method is adopted to obtain the exact soliton solutions in this study. This differentiation-based method, which requires no sophisticated mathematics, isabletoderiveexact, analyticsolutionsefficiently. An optical fiber system with decaying/amplifying and broadening/compressing effects is modelled by a variable coefficient nonlinear Schro]dinger (NLS) equa- tion. This equation is also able to describe the propagation of optical pulses in a dispersion-managed fiber system, averaged over one dispersion map. Bright anddark, one- and two-soliton solutions are obtained. These solitons are shown to havevaryingwavenumberandfrequencyintheirsolitonexpansions. Inadditionto the decaying and broadening effects, the bright solitons also demonstrate a special property, namely that the trajectory of their center of mass can have three possible modesinthex-t domain. A coupled NLS system with a group velocity mismatch is considered to be the relevant equation for a three-layer stratified shear flow. While the coupled NLS systemhasbeenstudiedindetail, theeffectofaddingagroupvelocitymismatchis still unknown. Dark one- and two-soliton solutions are obtained for an integrable system. TheSasa-Satsumaequationisoneintegrablesettingofthemoregeneralhigher- orderNLSequation, whichtakesintoaccounthigher-ordernonlineareffects. Adark one-solitonsolutionisobtained, butitisfoundtohaveonelessarbitraryparameter than its NLS counterpart. Because of this additional constraint, a dark two-soliton solutionisnotfound. Somespecialexpansionseriesmaybeneededforthebilinear formtoobtainmulti-solitonsolutions, andtheseareleftforfuturestudies. Inmicrochannelflows, interfacialeffectssuchastheelectricdoublelayercannot be neglected. This layer will interact with the ions and hence the liquid flow in the microchannel. The associated electric potential is shown to be modelled by the sinh-Poisson equation, a different version of which also has applications in vortex dynamics. Techniques from nonlinear waves are applied to solve for one- to three- solitonsolutions, buttheyarefoundtobethesameasthoseobtainedforthecontexts of vortex dynamics. A comparison is also made between an exact doubly periodic solutionandanapproximatesolutionfromtheDebye-Hu]ckelapproximation, anda considerableamountofdifferenceisfoundinsomeregions. DOI: 10.5353/th_b3051366 Subjects: Solitons Fiber optics Hydrodynamics

With this book, we aim to capture different perspectives of researchers on nonlinear optics and optical devices and we intend to cover the latest developments in optics from theoretical, numerical, and experimental aspects. The eleven selected chapters cover a variety of topics related to nonlinear optics including bright, dark, kink solitary waves in various media, magnetic solitons, lattice solitons, rogue-waves, solid-state lasers, laser cladding, optical sensors, optical vortices, and molecular switches. The book is intended to draw the attention of scientists in academia, as well as researchers and engineers in industry, since the field has a significant potential for the production and design of novel optical devices and other technological applications.

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Erbium Fiber Amplifiers is a comprehensive introduction to the increasingly important topic of optical amplification. Written by three Bell Labs pioneers, the book stresses the importance of the interrelation of materials properties, optical properties, and systems aspects of optical fiber amplifiers. All disc-based content for this title is now available on the Web. Key Features * Explains the theory of noise in optically amplified systems in an intuitive way * The book contains a discussion of components used in amplifier fabrication and of the attendant technologies used in real systems * The book provides basic tools for amplifier design as well as systems engineering, including the latest developments in WDM and soliton systems * The book discusses the fundamentals of rare earth ions for the reader desiring more depth in the topic * The book is for either the novice of experienced reader * The chapter have links between them to allow the reader to understand the relationship between the amplifier characteristics, noise, and systems applications * The book contains extensive references

Nonlinearity is a fascinating element of nature whose importance has been appreciated for many years when considering large-amplitude wave motions observed in various fields ranging from fluids and plasmas to solid-state, chemical, biological, and geological systems. Localized large-amplitude waves called solitons, which propagate without spreading and have particle-like properties, represent one of the most striking aspects of nonlinear phenomena. Although a wealth of literature on the subject, including theoretical and numerical studies, is available in good recent books and research journals, very little material has found its way into introductory texbooks and curricula. This is perhaps due to a belief that nonlinear physics is difficult and cannot be taught at an introductory level to undergraduate students and practitioners. Consequently, there is considerable interest in developing practical material suitable for students, at the lowest introductory level. This book is intended to be an elementary introduction to the physics of solitons, for students, physicists, engineers and practitioners. We present the modeling of nonlinear phenomena where soliton-like waves are involved, together with applications to a wide variety of concrete systems and experiments. This book is designed as a book of physical ideas and basic methods and not as an up-to-the minute book concerned with the latest research results. The background in physics and the amount of mathematical knowledge assumed of the reader is within that usually accumulated by junior or senior students in physics.

The development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments. The book presents sound coverage of the fundamentals of lightwave technology, along with material on pulse compression techniques and rare-earth-doped fiber amplifiers and lasers. The extensively revised chapters include information on fiber-optic communication systems and the ultrafast signal processing techniques that make use of nonlinear phenomena in optical fibers. New material focuses on the applications of highly nonlinear fibers in areas ranging from wavelength laser tuning and nonlinear spectroscopy to biomedical imaging and frequency metrology. Technologies such as quantum cryptography, quantum computing, and quantum communications are also covered in a new chapter. This book will be an ideal reference for: R&D engineers working on developing next generation optical components; scientists involved with research on fiber amplifiers and lasers; graduate students and researchers working in the fields of optical communications and quantum information. The only book on how to develop nonlinear fiber optic applications Two new chapters on the latest developments; Highly Nonlinear Fibers and Quantum Applications Coverage of biomedical applications