Universal shape law of stochastic supercritical bifurcations: Theory and experiments

A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-like slice subjected to optical feedback are in excellent agreement.Comment: 5 pages, 5 figure

Control and removing of modulational instabilities in low dispersion photonic crystal fiber cavities

Taking up to fourth order dispersion effects into account, we show that fiber resonators become stable for large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for arbitrary small but nonzero fourth order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and opens the way to experimental implementation

INFLUENCE DU BRUIT ET DE LA BRISURE DE SYMÉTRIE DE RÉFLEXION SUR LES INSTABILITÉS DANS LES SYSTÈMES OPTIQUES SPATIALEMENT ÉTENDUS

Mes activités de recherche actuelles se situent dans le cadre de la morphogenèse optique et plus généralement de la dynamique non-linéaire. Les systèmes étudiés sont les milieux Kerr (cristaux liquides et fibres optiques) en cavité ou avec feedback optique. J'y étudie plus particulièrement les phénomènes d'instabilités temporelles et spatio-temporelles tels que : - la formation de structures transverses et les instabilités modulationnelles - les solitons dissipatifs et les structures localisées - les systèmes convectifs et leurs instabilités convectives et absolues - les effets du bruit sur ces instabilités, tels que les structures entretenues par le bruit

Experimental evidence of dynamical propagation for solitary waves in ultra slow stochastic non-local Kerr medium

We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z3/2 up to ten times the power threshold for solitary wave generation.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Experimental observation of front propagation in lugiato-lefever equation in a negative diffractive regime and inhomogeneous kerr cavity

info:eu-repo/semantics/publishe

Front pinning induced by spatial inhomogeneous forcing in a Fabry-Perot Kerr cavity with negative diffraction

Conference on Lasers and Electro-Optics Europe & International Quantum Electronics Conference (CLEO/Europe-IQEC), Munich, GERMANY, MAY 12-16, 2013International audienc

Spatiotemporal wave-train instabilities in nonlinear Schrodinger equation: revisited

A complete description of properties of the wave-train bifurcating from unstable basic oscillatory states (CW nonlinear stationary states) of the nonlinear Schrödinger equation are studied in the moving frames of reference as an initial value problem and using the methods of absolute and convective instabilities. The predictions are in excellent agreement with numerical solutions and may contribute understanding the nonlinear Schrödinger equation complex dynamics under various initial conditions including, localized and/or noisy initial conditions

Optical dam break problem in self-focusing stochastic nonlocal media

International audienc

Bifurcations of emerging patterns in the presence of additive noise

International audienceA universal description of the effects of additive noise on super-and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape