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Supercontinuum generation and soliton dynamics milestone achieved
November 21, 2008
Unique fiber design enables first observation of two resonant dispersive waves on both sides of the emitting soliton A research team led by Fetah Benabid, University of Bath, has observed for the first time the simultaneous emission of two resonant dispersive waves by optical solitons (waves that maintain their shape while traveling at constant speeds). By designing a special fiber with an extremely small waveguiding feature located in the photonic crystal fiber cladding, the researchers were able to bring the theoretical prediction into the experimental demonstration, creating waves on both sides of the pump. This research appears in the current issue of the Optical Society's Optics Letters.
Summary
Since the 1980s, dispersive waves have been studied in the concept of solitons. The waves result due to perturbations that cause the soliton to lose some energy. Now, because of the flexibility in the design of Benabid's fiber, the waves are more general than they have been in the past. These "general" waves allow for a further degree of control over supercontinuum generation and have enabled a new way of generating coherent supercontinuum spectra, which is useful in a number of applications such as frequency combs. In addition, this new milestone introduces the opportunity for very compact femtosecond lasers.
Key Findings
# For the first time, two resonant dispersive waves have been observed on both sides of the pump, providing an experimental corroboration to what previously only had been theoretical.
# The unique design of the fiber itself - a nanometric-sized, rectangular-shaped waveguiding feature located in the photonic crystal fiber cladding - makes these waves more general than they have been in past experiments.
# The tight confinement along with the particular dispersion properties allow supercontinuum to be generated very efficiently and over very short length, creating the potential for very compact femtosecond lasers.
Optical Society of America
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Local And Global Analysis of Nonlinear Dispersive And Wave Equations (Cbms Regional Conference Series in Mathematics)
by Terence Tao (Author)
Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations. Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive...
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Methods of Wave Theory in Dispersive Media
by M. V. Kuzelev (Author), A. A. Rukhadze (Author)
This book presents the main mathematical methods of description and general problems in the theory of linear waves in dispersive systems and media, including equilibrium and nonequilibrium waves. To show how the general theory can be applied in practice, the authors give a unified description of the waves in all important physical systems which are traditionally studied in the mechanics of continuous media, electrodynamics, plasma physics, electronics and physical kinetics. Consideration is also given to the interaction of waves in coupled systems, the propagation and evolution of localized wave perturbations, and the emission of waves from dispersive media under the action of external sources moving in a prescribed manner. A general theory of instabilities of linear systems is given, in...
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Solitary Waves in Dispersive Complex Media
by Vasily Y. Belashov (Author), Sergey V. Vladimirov (Author)
This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced numerical, study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrödinger (NLS) and derivative NLS (DNLS) classes of equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for higher-order dispersion corrections, influence of dissipation, instabilities, and stochastic fluctuations of the wave fields. The book addresses researchers working in the theory and numerical simulations of dispersive complex...
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Large-Time Behavior of Solutions of Linear Dispersive Equations (Lecture Notes in Mathematics)
by Daniel B. Dix (Author)
This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.
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Non-linear Waves and Dispersive Media (Monographs in Natural Philosophy)
by V.I. Karpman (Author)
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Nonlinear Waves in One-Dimensional Dispersive Systems (Oxford Mathematical Monographs)
by Prabhu Lal Bhatnagar (Author)
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Singular Limits of Dispersive Waves (NATO Science Series: B:)
by N.M. Ercolani (Editor), I.R. Gabitov (Editor), C.D. Levermore (Editor), D. Serre (Editor)
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Nonlinear Dispersive Wave Systems: University of Central Florida, Orlando, Florida, 11-15 March, 1991 (Advanced Series in Nonlinear Dynamics)
by Lokenath Debnath (Editor)
This book brings together accounts of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schroedinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known teachers who have made significant contributions to nonlinear waves and nonlinear instability. This volume is aimed at applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and those interested in nonlinear dynamics.
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Nonlinear Waves in Dispersive and Dissipative Systems (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)
by Sergiy Korsunskyi (Author)
Investigates a wide range of problems where nonlinear wave phenomena play a crucial role, for instance in nonlinear acoustics, fluid dynamics, plasma physics and magnetohydrodynamics. Reviews the latest developments in the investigation of complex wave systems.
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Advances in Wave Interaction and Turbulence: Proceedings of an Ams-Ims-Siam Joint Summer Research Conference on Dispersive Wave Turbulence, Mount Holyoke ... June 11-15, 20 (Contemporary Mathematics)
by Paul A. Milewski (Editor), Leslie M. Smith (Editor), Fabian Waleffe (Editor), Esteban G. Tabak (Editor)
We often think of our natural environment as being composed of very many interacting particles, undergoing individual chaotic motions, of which only very coarse averages are perceptible at scales natural to us. However, we could as well think of the world as being made out of individual waves. This is so not just because the distinction between waves and particles becomes rather blurred at the atomic level, but also because even phenomena at much larger scales are better described in terms of waves rather than of particles: It is rare in both fluids and solids to observe energy being carried from one region of space to another by a given set of material particles; much more often, this transfer occurs through chains of particles, neither of them moving much, but...
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