Search results for "Dispersion."

Three dimensional reductions of four-dimensional quasilinear systems

2017

In this paper we show that integrable four dimensional linearly degenerate equations of second order possess infinitely many three dimensional hydrodynamic reductions. Furthermore, they are equipped infinitely many conservation laws and higher commuting flows. We show that the dispersionless limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking Soliton equations introduced by O.I. Bogoyavlenski) are one and two component reductions (respectively) of one of these four dimensional linearly degenerate equations.

A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

2012

Abstract We study numerically the small dispersion limit for the Korteweg–de Vries (KdV) equation u t + 6 u u x + ϵ 2 u x x x = 0 for ϵ ≪ 1 and give a quantitative comparison of the numerical solution with various asymptotic formulae for small ϵ in the whole ( x , t ) -plane. The matching of the asymptotic solutions is studied numerically.

Nonlinear higher-order polariton topological insulator

2020

We address the resonant response and bistability of the exciton-polariton corner states in a higher-order nonlinear topological insulator realized with kagome arrangement of microcavity pillars. Such states are resonantly excited and exist due to the balance between pump and losses, on the one hand, and between nonlinearity and dispersion in inhomogeneous potential landscape, on the other hand, for pump energy around eigen-energies of corresponding linear localized modes. Localization of the nonlinear corner states in a higher-order topological insulator can be efficiently controlled by tuning pump energy. We link the mechanism of corner state formation with symmetry of the truncated kagome…

Scaling guidelines of a soliton-based power limiter for 2R-optical regeneration applications

2010

International audience; In this work, we report scaling rules for the design of an all-fibered soliton-based power limiter for reamplification and reshaping (2R) regeneration process. In particular, we propose general guidelines to fix the optimum fiber length and initial power of the regenerator. We quantitatively point out the optical power limiting effect of the device enabling a significant reduction of the amplitude jitter of a degraded signal. Influence of the initial level of amplitude jitter is discussed and the results are compared with a self-phase modulation-based configuration working in the normal dispersion regime. Realistic numerical simulations in the context of 160 Gbit/s s…

Design of All-Normal Dispersion Microstructured Optical Fiber on Silica Platform for Generation of Pulse-Preserving Supercontinuum Under Excitation a…

2017

We investigated numerically the possibility of all normal dispersion fiber design for near-infrared supercontinuum generation based on a standard air-silica microstructure. The design procedure includes finding of target dispersion profile and subsequent finding of appropriate geometrical fiber design by inverse dispersion engineering. It was shown that the tailoring of dispersion profile could increase the spectral width of generated supercontinuum while maintaining perfect spectral flatness. Conditions necessary for wide and flat supercontinuum generation as well as restrictions imposed by chosen materials were discussed. As a result of design and optimization procedure, an air-silica des…

Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths

2008

International audience; In this work, we report the experimental observation of a polarization attraction process which can occur in optical fibers at telecommunication wavelengths. More precisely, we have numerically and experimentally shown that a polarization attractor, based on the injection of two counter-propagating waves around 1.55 mu m into a 2-m long high nonlinear fiber, can transform any input polarization state into a unique well-defined output polarization state.

All-fiber based chaotic polarization scrambler

2014

We present a fiber-based polarization scrambler founded on the nonlinear interaction between a signal and its backward replica generated and amplified by a reflective loop. The output polarization dynamic turns out to be chaotic.

Refinement of the Dispersion Equations of the Nonlinear Biaxial Crystals KTiOAsO/sub 4/, RbTiOAsO/sub 4/ and CsTiOAsO/sub 4/. Method and Measurements

2005

How to standardize (if you must)

2017

In many situations we are interested in appraising the value of a certain characteristic for a given individual relative to the context in which this value is observed. In recent years this problem has become prominent in the evaluation of scientific productivity and impact. A popular approach to such relative valuations consists in using percentile ranks. This is a purely ordinal method that may sometimes lead to counterintuitive appraisals, in that it discards all information about the distance between the raw values within a given context. By contrast, this information is partly preserved by using standardization, i.e., by transforming the absolute values in such a way that, within the s…

Plasmon mass scale in classical nonequilibrium gauge theory

2017

Classical lattice Yang-Mills calculations provide a good way to understand different nonequilibrium phenomena in nonperturbatively overoccupied systems. Above the Debye scale the classical theory can be matched smoothly to kinetic theory. The aim of this work is to study the limits of this quasiparticle picture by determining the plasmon mass in classical real time Yang-Mills theory on a lattice in 3 spatial dimensions. We compare three methods to determine the plasmon mass: a hard thermal loop expression in terms of the particle distribution, an effective dispersion relation constructed from fields and their time derivatives, and by measuring oscillations between electric and magnetic fiel…