Space-time observation of the dynamics of soliton collisions in a recirculating optical fiber loop

We present experiments performed in a recirculating fiber loop in which we realize the single-shot observation of the space and time interaction of two and three bright solitons. The space-time evolutions observed in experiments provide clear evidence of a nearly-integrable nonlinear wave dynamics that can be easily interpreted within the framework of the inverse scattering transform (IST) method. In particular collisions between solitons are found to be almost perfectly elastic in the sense that they occur without velocity change and with only a position (time) shift quantitatively well described by numerical simulations of the integrable nonlinear Schr\"odinger equation. Additionally our experiments provide the evidence that the position (time) shifts arising from the interaction among three solitons are determined by elementary pairwise interactions, as it is well known in the IST theory

Modulation instability in amplitude modulated dispersion oscillating fibers

International audienceWe investigate theoretically and experimentally the modulation instability process in a dispersion oscillating fiber characterized by an amplitude modulation of its group velocity dispersion. We developed an analytical model that allows us to calculate the parametric gain in these fibers and to predict the position of the quasi-phase matched modulation instability sidelobes. The two fundamental frequencies characterizing the dispersion profile lead to the splitting of the original multiple sidelobes generated in basic sinusoidally varying dispersion oscillating fibers. These theoretical predictions are confirmed by experiments

From modulational instability to focusing dam breaks in water waves

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wavepacket towards the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semi-classical limit of the 1D focusing nonlinear Schr"odinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semi-classical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system

Real-Time Characterization of Period-Doubling Dynamics in Uniform and Dispersion Oscillating Fiber Ring Cavities

International audienceModulational instability in passive optical resonators, the triggering mechanism of frequency comb and pulse train generation, is shown to exhibit transitions between regimes involving period-one (P1) versus period-two (P2) dynamical evolutions. The latter is a signature of parametric resonance occurring in the system, which can arise either from intrinsic cavity periodicity or from spatial modulation of the cavity parameters. We characterize the P1-P2 transition for both cases employing a fiber resonator where the intra-cavity fiber can be either uniform or dispersion modulated. The key element of our setup is a time lens which we exploit to resolve the temporal dynamics over successive round-trips, allowing crystal clear evidence of the existence of P1-P2 transitions for suitable changes of cavity parameters, as well as for the successful characterization of the relative temporal patterns. Our findings reveal new regimes where the averaged model known as Lugiato-Lefever equation turns out to be inadequate to explain the dynamics, whereas the results are correctly predicted and described on the basis of the full Ikeda map

Nonlinear Spectral Synthesis of Soliton Gas in Deep-Water Surface Gravity Waves

Soliton gases represent large random soliton ensembles in physical systems that exhibit integrable dynamics at the leading order. Despite significant theoretical developments and observational evidence of ubiquity of soliton gases in fluids and optical media, their controlled experimental realization has been missing. We report a controlled synthesis of a dense soliton gas in deep-water surface gravity waves using the tools of nonlinear spectral theory [inverse scattering transform (IST)] for the one-dimensional focusing nonlinear Schrödinger equation. The soliton gas is experimentally generated in a one-dimensional water tank where we demonstrate that we can control and measure the density of states, i.e., the probability density function parametrizing the soliton gas in the IST spectral phase space. Nonlinear spectral analysis of the generated hydrodynamic soliton gas reveals that the density of states slowly changes under the influence of perturbative higher-order effects that break the integrability of the wave dynamics

Instabilités modulationnelles dans les cavités fibrées passives à dispersion oscillante

Ces travaux de thèse portent sur l’instabilité paramétrique survenant dans les cavités optiques fibrées passives en anneau, induite par une modulation longitudinale de la dispersion chromatique. Dans les cavités optiques, le processus d’instabilité modulationnelle est connu pour être susceptible de déstabiliser l’état stationnaire et de le transformer en un train stable d’impulsions. Nous décrivons dans ce travail comment une variation longitudinale de la dispersion à l’intérieur de la cavité enrichie la dynamique de ce type de dispositif en engendrant un régime d’instabilité paramétrique. Nous détaillons l’étude théorique de ce nouveau mécanisme ce qui nous permet d’en identifier les signatures spectrales et temporelles, parmi lesquels, la génération de multiples pics de résonances dans le spectre optique et l’apparition d’une dynamique de doublement de période dans le domaine temporel. Nous avons réalisé de tels résonateurs afin de confirmer expérimentalement nos prédictions. Le modèle que nous avons retenu consiste à réaliser un anneau en soudant entre elles des fibres uniformes présentant des dispersions différentes. En terme de résultats, nous avons tout d’abord observé pour la première fois l’apparition des instabilités modulationnelle et paramétrique dans un même système, pour ensuite s’intéresser à leur dynamique. Cette dernière est accessible grâce à des méthodes de détection en temps réel à la fois spectrale et temporelle. Nous avons ainsi pu observer avec une précision remarquable l’émergence des instabilités, le doublement de période associé au régime paramétrique ainsi que l’apparition d’un nombre record de résonances paramétriques dans notre système.This thesis work deals with the parametric instability occurring in passive optical fiber-ring cavities, which is induced by a longitudinal modulation of the chromatic dispersion. In optical cavities, the modulation instability process is known to potentially destabilize the stationary state and turn it into a stable train of pulses. We describe in this work how a longitudinal variation of the dispersion inside the cavity enriches the dynamics of this type of device by entailing a regime of parametric instability. We detail the theoretical study of this new mechanism, which allows us to identify its spectral and temporal signatures, among which, the generation of multiple resonance peaks in the optical spectrum and the appearance of a period doubling dynamics in the time domain. We have realized such resonators in order to confirm experimentally our predictions. The model we have chosen simply consists in building a ring by splicing together uniform fibers characterized by different dispersions. In terms of results, we first observed the emergence of both modulational and parametric instabilities in the same system, before investigating their dynamics. The latter is accessible thanks to real-time spectral and temporal detection methods. We thus observed with remarkable precision the emergence of the instabilities, the period doubling associated to the parametric regime and the appearance of a record number of parametric resonances in our system

The Physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: Rogue waves, modulation instability and self-focusing phenomena

International audienceWe review the different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schrödinger equation (1DNLSE) in the focusing regime. In this context, localized and coherent structures are very often associated to rogue wave events. We focus on one-dimensional optical experiments and in particular on (single mode) optical fibers experiments. In the focusing regime of 1DNLSE, the so-called modulation instability (MI), arising from nonlocal perturbation of the plane waves, is the most common phenomenon. Alongside the standard MI, other mechanisms are responsible for the emergence of rogue waves. We classify the different scenarii by considering those induced by small perturbations of unstable stationary state (the plane waves) and the ones arising from the self-focusing of large pulses without any perturbation. In the former case, the perturbations can be local, global, random or deterministic. In the latter case, the self-focusing dynamics can be observed both with isolated pulses or with large initial fluctuations of the optical power. We review the dynamics of emergence of localized structures in all these different scenarii

Modulation instability in the weak dispersion regime of dispersion oscillating fi\u9dber-ring cavities

We investigate modulation instability in a dispersion modulated passive \u9dfiber-ring cavity with a very low local dispersion. In this con\u9dguration, an unprecedented number of quasi-phase-matched spectral sidelobes are observed, related to Faraday parametric resonances

Parametric instabilities in modulated fiber ring cavities

We investigate modulational instability in inhomogeneous passive cavities modeled by the Ikeda map. The cavity boundary conditions and the modulation of the fiber dispersion force the system to develop parametric instabilities, which lead to the generation of simple, as well as period-doubled, temporal patterns. The analytical results obtained by means of the Floquet theory are validated through numerical solution of the Ikeda map, and the limitations of the mean-field Lugiato-Lefever model are highlighted

Roundtrip-to-roundtrip evolution of Faraday and Turing instabilities in dispersion oscillating fiber ring resonators

We study the roundtrip-to-roundtrip evolution of the output spectrum of a dispersion modulated passive fiber cavity using real time spectroscopy. Our experiments reveal that Faraday and Turing instabilities can be excited independently or coexist