Josselin Garnier

Modulational instability of electromagnetic waves in inhomogeneous and in discrete media

Publisher Summary This chapter discusses the modulational instability (MI) of electromagnetic waves in inhomogeneous and in discrete media. MI exists because of the interplay between the nonlinearity and dispersion/diffraction effects. Important models for investigating MI of electromagnetic waves in nonlinear media represent the scalar and vectorial nonlinear Schrodinger (NLS) equations, the system describing evolution of the envelopes of fundamental and second harmonics waves in quadratically nonlinear media, and sine-Gordon equation. The methods such as periodic solutions of the NLS equation and the coupled-mode theory with three modes are discussed. The chapter discusses the MI of electromagnetic waves in optical media with periodic inhomogeneities. The origin of the random fluctuations of parameters in optical fibers and other nonlinear optical media is described. MI in fibers with random amplification and dispersion and MI in randomly birefringent fibers are discussed. The chapter discusses the MI of electromagnetic waves in nonlinear discrete optical systems such as an array of planar waveguides and fibers. Particular cases of MI in discrete media with cubic nonlinearity and quadratic nonlinearity are investigated.

Statistical analysis of pulse propagation driven by polarization mode dispersion

The linear propagation of pulses driven by random polarization-mode dispersion is considered. Analytical expressions are derived for the probability-density functions of the pulse width, timing displacement, and degree of polarization. The study is performed in Stokes space, and frequency correlation between modes is shown to play an important role in it.

Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity

The dynamics of a metastable attractive Bose-Einstein condensate trapped by a system of laser beams is analyzed in the presence of small fluctuations of the laser intensity. It is shown that the condensate will eventually collapse. The expected collapse time is inversely proportional to the integrated covariance of the time autocorrelation function of the laser intensity and it decays logarithmically with the number of atoms. Numerical simulations of the stochastic three-dimensional Gross-Pitaevskii equation confirm analytical predictions for small and moderate values of mean-field interaction.

Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length

The collective oscillations of one-dimensional (1D) repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean-field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean-field regime we predict bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point. We confirm the analytical predictions by direct numerical simulations of the 1D GrossPitaevskii equation and the effective nonlinear Schrodinger equation with quintic nonlinearity and trap potential.

Propagation of partially coherent light with the Maxwell–Debye equation

We deal with the propagation of broadband Schell-model sources in nonlinear media with finite relaxation time. The approach is based on a study of the Wigner distribution function and on a separation of scales technique between the microscopic random fluctuations of the field and the macroscopic intensity profile. The regime in which the nonlinearity is strong and slow is considered. Precise results are obtained for the small- and large-scale characteristics of the pulse: optical intensity profile, speckle radius, and typical intensity profile of the speckle spots.

Optical solitons in random media

Publisher Summary This chapter provides a description of the present status of theory and experiment about propagation and interaction of optical solitons in random media. A short derivation of the main equations describing the evolution of optical solitons in the presence of a cubic or a quadratic nonlinearity is presented and the dynamics of solitonic pulses in fibers with random parameters is discussed. The propagation of standard optical solitons as well as dispersion-managed solitons under random fluctuations of dispersion and nonlinearity is examined. The inverse scattering transform, the variational approach, and averaging of the nonlinear Schrodinger equation (NLSE) in the frequency domain9 are applied for the investigation of solitonic processes in fibers with these types of inhomogeneities. The chapter describes the influence of random birefringence on the propagation of optical solitons. Polarization mode dispersion (PMD) is a limiting factor for long-distance optical fiber communication systems. It can be overcome by solitonic propagation. The propagation can be analyzed by averaging the original system of coupled NLSEs over the rapid variations of the birefringence. The resulting system is the randomly perturbed Manakov system. For vector optical solitons, radiative effects, and internal motion, the chapter describes their propagation using the inverse scattering transform (ist) approach. Analytical and numerical results are discussed for two types of fluctuations along the propagation direction: random mismatch and fluctuating nonlinearity.

A multiscale analysis of the hotspot dynamics during the deceleration phase of inertial confinement capsules

This paper is devoted to the study of the deceleration phase of inertial confinement capsules. First the self-similar flow exhibited by Betti et al. [Phys. Plasmas 8, 5257 (2001)] is proved to be an attractor in the sense that arbitrary initial conditions converge towards this solution. The convergence rate depends on the ablation process and heat conductivity and it is shown to be a power law of the increase rate of the hotspot mass. Second the thin layer that separates the hotspot from the cold shell is described and it is shown that it also converges to a locally self-similar profile. By using and generalizing a shell model introduced by Betti et al. [Phys. Plasmas 9, 2277 (2002)] a closed system of ordinary differential equations for the main hydrodynamic variables is derived. Finally the linear growth rates of the deceleration phase Rayleigh‐Taylor instabilities are computed taking into account ablation and spherical convergence. Significant differences are exhibited between directly and indirectly driven capsules.

Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap

This paper is devoted to the study of the dynamics of two weakly coupled Bose-Einstein condensates confined in a double-well trap and perturbed by random external forces. The energy diffusion due to random forcing is quantitatively analyzed. The energy distribution is shown to evolve to a stationary distribution which depends on the initial state of the condensate only through the total number of atoms. This loss of memory of the initial conditions allows a simple and complete description of the stationary dynamics of the condensate. In particular, when the number of atoms exceeds a threshold value, the condensate temporarily localizes into one of the wells and jumps into the other well according to a Markovian dynamics. This localization occurs even in the presence of dissipation.

Collapse in Bose-Einstein condensates induced by fluctuations of the laser intensity

The dynamics of an attractive BEC trapped by an optical trap is analyzed in the presence of fluctuations of the laser intensity. The condensate will eventually collapse for time is inversely proportional to noise intensity.