Search results for "soliton"
showing 10 items of 534 documents
Dissipative Optical Breather Molecular Complexes
2020
We demonstrate different types of breathing soliton complexes in a mode-locked fibre laser: multi-breather molecules, and molecular complexes arising from the binding of two breather-pair molecules or a breather-pair molecule and a single breather.
Stationary and pulsating dissipative light bullets from a collective variable approach
2009
A collective variable approach is used to map domains of existence for (3+1) -dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation tim…
Two-stage linear-nonlinear shaping of an optical frequency comb as rogue nonlinear-Schrödinger-equation-solution generator
2014
International audience; We report a wave generator of complex solutions of the nonlinear Schrödinger equation (NLSE) combining both intensity and phase spectral shaping of an initial optical frequency comb with subsequent nonlinear propagation in an optical fiber. We apply the explicit analytical form of the two-breather solutions of the NLSE as a linear spectral filter to shape ideal modulation of a continuous wave. The additional nonlinear propagation of the tailored wave provides experimental evidence of both the growth and decay of the fundamental second-order periodic breather solution. The temporal and spectral profiles of the higher-order breather are in excellent agreement with the …
Seeded and spontaneous higher-order modulation instability
2012
International audience; We report on the dynamics of the higher-order modulation instability in optical fibers and show that it is the very same phenomenon that underpins the emergence of rogue waves in the early stage of supercontinuum generation.
Experimental Study of Modulational Instability and Vector Solitons in Optical Fibers
2003
This chapter brings forth the experimental study of modulational instability and vector solitons in optical fibers.
Baseband modulation instability as the origin of rogue waves
2015
International audience; We study the existence and properties of rogue-wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider the Fokas-Lenells equation, the defocusing vector nonlinear Schrödinger equation, and the long-wave-shortwave resonance equation. We show that rogue-wave solutions in all of these models exist in the subset of parameters where modulation instability is present if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whe…
Optical bullets and double bullet complexes in dissipative systems
2006
We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial s…
Higher-Order Modulation Instability in Nonlinear Fiber Optics
2011
International audience; We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution r…
The nonlinear Schrodinger equation and the propagation of weakly nonlinear waves in optical fibres and on the water surface
2015
International audience; The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional par…
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
2011
International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.