Time-reversal focusing of an expanding soliton gas in disordered replicas

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.Comment: 7 Pages, 6 Figure

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schroedinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing new mechanisms of decay of antidark solitons.Comment: 8 pages, 10 figures, accepted in PR

Spontaneously generated X-shaped light bullets

We observe the formation of an intense optical wavepacket fully localized in all dimensions, i.e. both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is a X-shaped light bullet spontaneously generated from a standard laser wavepacket via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.Comment: 5 pages, 4 figures, submitted for publicatio

Optimal frequency conversion in the nonlinear stage of modulation instability

We investigate multi-wave mixing associated with the strongly pump depleted regime of induced modulation instability (MI) in optical fibers. For a complete transfer of pump power into the sideband modes, we theoretically and experimentally demonstrate that it is necessary to use a much lower seeding modulation frequency than the peak MI gain value. Our analysis shows that a record 95 % of the input pump power is frequency converted into the comb of sidebands, in good quantitative agreement with analytical predictions based on the simplest exact breather solution of the nonlinear Schr\"odinger equation

Modulational instability in dispersion-kicked optical fibers

We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been realized in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths much shorter than the period, which therefore approximate the ideal Dirac comb. Experimental spontaneous MI spectra recorded under quasi continuous wave excitation are in good agreement with the theory and with numerical simulations based on the generalized nonlinear Schr\"odinger equation

Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis

Active subnanometer spectral control of a random laser

We demonstrate an experimental technique that allows to achieve a robust control on the emission spectrum of a micro random laser and to select individual modes with sub-nanometer resolution. The presented approach relies on an optimization protocol of the spatial profile of the pump beam. Here we demonstrate not only the possibility to increase the emission at a wavelength, but also that we can isolate an individual peak suppressing unwanted contributions form other modes

Crossover dynamics of dispersive shocks in Bose-Einstein condensates characterized by two and three-body interactions

We show that the perturbative nonlinearity associated with three-atom interactions, competing with standard two-body repulsive interactions, can change dramatically the evolution of 1D dispersive shock waves in a Bose-Einstein condensate. In particular, we prove the existence of a rich crossover dynamics, ranging from the formation of multiple shocks regularized by coexisting trains of dark and antidark matter waves, to 1D soliton collapse. For a given scattering length, all these different regimes can be accessed by varying the number of atoms in the condensate.Comment: 4 pages, 5 figure