Search results for "Pattern Formation"
showing 10 items of 408 documents
Spatial localization and pattern formation in discrete optomechanical cavities and arrays
2020
We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig & Marquardt [Phys. Rev. Lett. 101, 073603 (2013)]. Also, we study the connections between both types of models and continuous OM models. While all three types of models merge naturally in the limit of a large number of densely distribu…
Effective kink-kink interaction in a one-dimensional model mediated by phonon exchange
1994
The general 1D double-well model with anharmonic interaction is considered in the displacive limit. Expansion of the Hamiltonian around a multikink state results in a phonon-kink Hamiltonian. It is shown that at rather low temperatures and short wave lengths the phonon-kink interaction can be treated in Born approximation, leading to a decomposition of the multikink-phonon Hamiltionian. Elimination of the phonons results in an effective potential for the kink-kink interaction, which corresponds to the one-dimensional analog of the RKKY interaction. This long-range interaction is inherent only for models with anharmonic on-site potentials and not in case of a double-parabola model.
Numerical study of the stability of the Peregrine solution
2017
International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.
Light self-confinement via second harmonic generation in a 2D nonlinear photonic crystal waveguide
2007
Spatial solitary waves induced by quadratic nonlinearities have been the subject of many theoretical and experimental investigations in the last decade, with extensive studies being devoted to soliton formation in 1D nonlinear photonic crystals (NPC) such as PPLN (periodically poled LiNbO3). Here we present results on a new class of (1 + 1)D spatial solitary waves, the first examples of quadratic self-confinement in a 2D NPC.
Four-wave mixing instabilities in telecom fibers
2012
Instabilities in fiber four-wave mixing are investigated, revealing the formation of colliding dispersive shock waves in the normal GVD regime and collective modulation instabilities in the anomalous GVD regime.
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.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
2009
[EN] We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance
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…
Generating ultra-short high-energy pulses using dissipative soliton resonance: Pulse compression schemes
2011
Dissipative soliton resonance (DSR) refers to a phenomenon where the energy of the stable soliton solution increases to extremely large values in a nonlinear dissipative system modeled by the complex cubic-quintic Ginzburg-Landau equation (CGLE) [1]. It occurs in the vicinity of a specific hyper-surface in the multi-dimensional space of the CGLE parameters. The phenomenon has applications in designing laser oscillators generating ultra-high energy pulses, since the dynamics of such lasers can be well-modeled by the CGLE. The DSR was first found in normally-dispersive media, in concordance with the current design trend for high-energy mode-locked laser oscillators [2–4]. However, we have sho…
Optimization of soliton transmissions in dispersion-managed fiber links
1998
We propose a simple optimization criterion (including the best launch point position in-between amplifiers) for the design of soliton transmission lines. The present approach is shown to minimize energy scattering from the solitons into the continuum.