Search results for "Linear system"
showing 10 items of 1558 documents
Nonlinear theory of slow light.
2011
In the framework of the nonlinear Λ model, propagation of solitons was analysed in atomic vapours and Bose–Einstein condensates. The complicated nonlinear interplay between fast and slow-light solitons in a Λ -type medium was shown to facilitate control of its optical transparency and formation of optical gates. An exact analytical description was given for the deceleration, stopping and revival of slow-light solitons in the experimentally relevant non-adiabatic regime. A stopping slow-light soliton imprints a localized immobile polarization pattern in the medium, which, as explicitly demonstrated here, can be used as a bit of readable optical memory. The whole process can be controlled wi…
Stationary and Pulsating Dissipative Optical Bullets
2006
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media. Beyond the domain where stable bullets are found, unstable bullets show unusual behaviors, like "optical rockets", pulsating solutions or pattern formation.
Switching dynamics of dark-pulse Kerr frequency comb states in optical microresonators
2021
Dissipative Kerr solitons are localized structures that exist in nonlinear optical cavities. They lead to the formation of microcombs - chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion cavities. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we explore dark-pulse Kerr combs generated in normal dispersion optical microresonators and report the discovery of reversible switching between coherent dar…
Analytical investigation of solitary waves in nonlinear Kerr medium
2004
Abstract We study analytically the solution of nonlinear equation which result from the propagation of electromagnetic waves within a nonlinear Kerr medium. The medium is characterized by a dielectric constant which varies periodically and depends on the local field intensity. As a first step, we detail the resolution of the nonlinear equations with a quadratic nonlinearity. After that, we apply the slowly varying envelope approximation to obtain a Sine–Gordon equation. In this kind of nonlinearity, a gap solitons occurs. Moreover we verify that the solutions of the nonlinear equation for all frequencies within the gap are solitons solutions. After that we study the conditions of apparition…
Magnetism in lowdimensional systems
1991
Abstract Magnetism in lowdimensional systems is characterized by the importance of space and time dependent correlations with respect to static long range order which does not exist for finite temperatures in such systems except for the 2D-Ising model. Typical properties of these strongly fluctuating systems will be discussed and compared to the behaviour of normal magnets. Strongly nonlinear effects can be observed, like solitons and new quantum groundstates as in the 1D-Heisenberg antiferromagnet for S=1. As real crystals with quasi-lowdimensional magnetic behaviour can be obtained, experiments in this field have significantly advanced our understanding of collective processes in systems …
Truncated thermalization of incoherent optical waves through supercontinuum generation in photonic crystal fibers
2013
We revisit the process of optical wave thermalization through supercontinuum generation in photonic crystal fibers. We report theoretically and numerically a phenomenon of `truncated thermalization': The incoherent optical wave exhibits an irreversible evolution toward a Rayleigh-Jeans thermodynamic equilibrium state characterized by a compactly supported spectral shape. The theory then reveals the existence of a frequency cut-off which regularizes the ultraviolet catastrophe inherent to ensembles of classical nonlinear waves. This phenomenon sheds new light on the mechanisms underlying the formation of bounded supercontinuum spectra in photonic crystal fibers.
Reservoir Computing with Random Skyrmion Textures
2020
The Reservoir Computing (RC) paradigm posits that sufficiently complex physical systems can be used to massively simplify pattern recognition tasks and nonlinear signal prediction. This work demonstrates how random topological magnetic textures present sufficiently complex resistance responses for the implementation of RC as applied to A/C current pulses. In doing so, we stress how the applicability of this paradigm hinges on very general dynamical properties which are satisfied by a large class of physical systems where complexity can be put to computational use. By harnessing the complex resistance response exhibited by random magnetic skyrmion textures and using it to demonstrate pattern…
Real lattices modelled by the nonlinear Schrödinger equation and its generalizations
2006
We present the analysis of two dimerized lattices : a bi-inductance electrical network with macroscopic wave modes, an antiferromagnetic chain whith microscopic spin waves. Using the multiple scale technique of reductive perturbation we show that the original discrete equations of motion can be reduced to a Nonlinear Schrodinger equation with complex coefficients for the first system and two coupled Nonlinear Schrodinger equations for the second system. The possible solutions of these equations are discussed in relation with our numerical simulations and real experiments.
LÉVY FLIGHT SUPERDIFFUSION: AN INTRODUCTION
2008
After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of self-similarity converts the infinitely divisible characteristic function of the L\'{e}vy process into a stable characteristic function of the L\'{e}vy motion. The L\'{e}vy motion generalizes the Brownian motion on the base of the $\alpha$-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. Th…
Higher-order correlation functions and nonlinear response functions in a gaussian trap model.
2012
The four-time correlation function of a general dynamical variable obeying Gaussian statistics is calculated for the trap model with a Gaussian density of states. It is argued that for energy-independent variables this function is reminiscent of the four-time functions that have been discussed earlier in the interpretation of the results of four-dimensional NMR experiments on supercooled liquids. Using an approximative relation between the four-time correlation function and the cubic response function the nonlinear susceptibility is calculated and the results are compared with the corresponding ones resulting from an exact calculation. It is found that the results of the approximation chang…