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

Observation of the stepwise blue shift of a dispersive wave preceding its trapping by a soliton

International audienceThe trapping of a weak dispersive wave by an intense soliton is a complex process occurring at the early stage of supercontinuum generation. It is theoretically predicted to arise from multiple soliton-dispersive wave interactions, producing a stepwise frequency blue shift of the dispersive wave. We report here the first experimental evidence of this frequency blue shift using a tapered fiber which acts as a prism, allowing to disperse the blue spectral components in order to identify unambiguously each soliton-dispersive wave collision

Soliton annihilation into a polychromatic dispersive wave

International audienceWe investigate the propagation of a soliton in an axially-varying optical fiber with a progressive change from anomalous to normal dispersion regimes. Spectral and temporal measurements provide evidence for a complete annihilation of the soliton, which explodes into a polychromatic dispersive wave. This interpretation is confirmed by numerical solution of the generalized nonlinear Schrödinger equation

Geometric parametric instability in periodically modulated graded-index multimode fibers

International audienceWe present a theoretical and numerical study of light propagation in graded-index (GRIN) mul-timode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows to induce a Moiré-like pattern, which modifies the geometric parametric instability gain observed in homogeneous GRIN fibers

Solitonization of a dispersive wave

International audienceWe report the observation of a nonlinear propagation scenario in which a dispersive wave is transformed into a fundamental soliton in an axially-varying optical fiber. The dispersive wave is initially emitted in normal dispersion region and the fiber properties change longitudinally so that the dispersion becomes anomalous at the dispersive wave wavelength, which allows it to be transformed into a soliton. The solitonic nature of the field is demonstrated by solving the direct Zakharov-Shabat scattering problem. Experimental characterization performed in spectral and temporal domains show evidence of the solitonizatin process in an axially-varying photonic crystal fiber

Bouncing of a dispersive wave in a solitonic cage

International audienceWe report the experimental observation of a weak dis-persive wave trapping within a cage formed by two solitons in an optical fiber. We show that the disper-sive wave bouncing is accompanied by a back and forth wavelength conversion of the probe to an idler wave. Besides, we observed the destruction of the soliton cage when dispersive wave power is increased, leading to the collision of the solitons