Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{\"o}dinger equations

It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{\"o}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{\"o}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The dynamics and characteristics of these generalized Peregrine soliton are analytically described in the case of a completely integrable modulation. A numerical investigation shows that their main properties persist in nonintegrable situations, where no exact analytical expression of the generalized Peregrine soliton is available. Our predictions are in good agreement with numerical findings for an interesting specific case of an experimentally realizable periodically dispersion modulated photonic crystal fiber. Our results therefore pave the way for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in the wide class of physical systems modeled by the nonlinear Schr{\"o}dinger equation

Localized Faraday patterns under heterogeneous parametric excitation

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schr\"odinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.Comment: 10 pages, 9 figures, Accepte

Periodic modulations controlling Kuznetsov-Ma soliton formation in nonlinear Schrödinger equations

International audienceWe analyze the exact Kuznetsov-Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov-Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kutzetsov-Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov-Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov-Ma soliton by a judicious choice of the amplitude and frequency of the modulation

Solitons dissipatifs des oscillateurs paramétriques optiques (instabilités convectives / absolues et effets non-linéaires du walk-off)

Les Oscillateurs Paramétriques Optiques (OPO) sont des sources optiques susceptibles de produire par interaction non linéaire à trois ondes au sein d'un cristal à forte sensibilité quadratique, des faisceaux de lumière cohérente et accordable en fréquence. Ils sont classés parmi les systèmes optiques à cavité non linéaire, dans lesquels des structures spatiales auto-organisées peuvent se former de façon spontanée dans la section transverse des faisceaux de sortie. Nous présentons ici, la capacité des OPO à générer de nouvelles structures, notamment celles conduisant à un confinement de l'énergie, appelées Structures Spatiales Localisées (SSL) ou solitons dissipatifs. Notre étude permet le contrôle et la manipulation des SSL à partir des caractéristiques du champ de pompe incident, et de l'interaction non lméaire des champs intra-cavité. Nous montrons, en particulier, que les inhomogénéités dans le pompage conduIsent à un piégeage des SSL, ce qui implique la quantification des seuils d'oscillation de l'OPO et une disparition des courbes neutre de stabIlité marginale, obtenues pour le cas idéal d'un pompage en ondes planes. Ce piégeage résiste à l'effet de dérive induit par le walk-off (double réfraction) et l'interaction entre ce dernier et les inhomogénéités fournit un moyen efficace pour contrôler aussi bien la vitesse que la position d'équilibre des SSL dans le plan transverse. L'étude des effets non linéaires du walk-off nous a permis de montrer qu'il est possible, en régIme monostable, d'abaisser le seuil d'émission de l'OPO sous le seuil linéaire classique. En régime bistable, nous avons révélé l'existence d'un terme de gradient non-linéaire pennettant ainsi la modélIsation de la dynamique spatio-temporelle des champs intra-cavité au-dessus du seuil. L'étude de ce nouveau modèle montre une autodépendance de la fréquence et de la vitesse d'entraînement des structures spatiales de l'OPO, vis à vis de leur intensité. Ce qui permet d'expliquer l'auto-décallage de fréquences, le freinage et la dissymétrie observés dans l'enveloppe des champs émis par l'OPO.LILLE1-BU (590092102) / SudocSudocFranceF

Localized states and non-variational Ising–Bloch transition of a parametrically driven easy-plane ferromagnetic wire

International audienc

Localized spatial structures in an optical parametric oscillator

8th Colloquium on Lasers and Quantum Optics, Toulouse, FRANCE, SEP 03-05, 200

Convection-induced stabilization of optical dissipative solitons

In spatially extended convective systems, the reflection symmetry breaking induced by drift effects leads to a striking nonlinear effect that drastically affects the formation and stability of dissipative solitons in optical parametric oscillators. The phenomenon of nonlinear-induced convection dynamics is revealed using a model of the complex quintic Ginzburg-Landau equation with nonlinear gradient terms in it. Mechanisms leading to stabilization of dissipative solitons by convection are singled out. The predictions are in very good agreement with numerical solutions found from the governing equations of the optical parametric oscillators.N. Akhmediev acknowledges the support of the Australian Research Council (Discovery Project DP0985394). This work was also partially supported by the Interuniversity Attraction Pole program of the Belgian government and the Conseil Regional Nord Pas de Calais

Time-delayed nonlocal response inducing traveling temporal localized structures

We show analytically and numerically that time-delayed nonlocal response induces traveling localized states in bistable systems. These states result from the interaction of fronts between homogeneous steady states. We illustrate this mechanism by considering an experimentally relevant system - the fiber cavity with the noninstantaneous Raman response. Close to the nascent bistability, we performed a derivation of a generic bistable model with a nonlocal delayed response. Analytical expressions of the width and the speed of traveling localized states are derived. Without a time-delayed nonlocal response, traveling localized states are excluded. In addition, we propose realistic parameters and perform numerical simulations of the governing model equation.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

NONVARIATIONAL ISING-BLOCH TRANSITION IN PARAMETRICALLY DRIVEN SYSTEMS

10th Latin American Workshop on Nonlinear Phenomena, Chilean Sci Inst, Fac Phys & Math Sci, Arica, CHILE, OCT 29-NOV 01, 200