Soliton complexes in dissipative systems: vibrating, shaking and mixed soliton pairs

We show, numerically, that coupled soliton pairs in nonlinear dissipative systems modeled by the cubic-quintic complex Ginzburg-Landau equation can exist in various forms. They can be stationary, or they can pulsate periodically, quasiperiodically, or chaotically, as is the case for single solitons. In particular, we have found various types of vibrating and shaking soliton pairs. Each type is stable in the sense that a given bound state exists in the same form indefinitely. New solutions appear at special values of the equation parameters, thus bifurcating from stationary pairs. We also report the finding of mixed soliton pairs, formed by two different types of single solitons. We present regions of existence of the pair solutions and corresponding bifurcation diagrams

Optical bullets and double bullet complexes in dissipative systems

We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial separation between the two bullets and the bullet shape in time domain is also detailed

Extreme wave dynamics in ultrashort fiber lasers

Conferencia invitada; IS-PALD 2015, Metz, France, November 4- 6, 2015; http://ispald.web2.ncku.edu.tw/We review recent experiments that demonstrate the existence of optical wave transients of unusually high amplitude in fiber lasers operated in the vicinity of mode locking. These transients are analyzed in the context of optical rogue wave formation, with an important role played by the constraints of ultrafast measurements. From these investigations, a universal rogue wave mechanism is highlighted, which results from the evolution of a chaotic bunch of pulses or sub-pulses, subjected to numerous inelastic collisions, while traveling round the laser cavity.Peer Reviewe

Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes

Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation.N.A. acknowledges support from the Australian Research Council. The work of J.M.S.-C. was supported by the M.E.y C. under Contract No. FIS2006-03376 and P.G. acknowledges support from Agence Nationale de la Recherche

Baseband modulation instability as the origin of rogue waves

We study the existence and properties of rogue wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider Fokas-Lenells equation, the defocusing vector nolinear Schr\"odinger equation, and the long-wave-short-wave resonance equation. We show that rogue wave solutions in all of these models exist in the subset of parameters where modulation instability is present, if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations

Superlocalization reveals long-range synchronization of vibrating soliton molecules

We implement a super-localization method in the time domain that allows the observation of the external motion of soliton molecules in a fiber ring cavity laser with unprecedented accuracy. In particular, we demonstrate the synchronization of two oscillating soliton molecules separated by several nanoseconds, with inter-molecules oscillations following the same pattern as the intramolecular motion of the individual molecules. These experimental findings indicate an interplay between the different interaction mechanisms that coexist inside the laser cavity, despite their very different characteristic ranges, timescales, strengths, and physical origins.Comment: This work was supported by the French "Investissements d'Avenir" program / project ISITE-BFC (contract ANR-15-IDEX-0003), and by the Agence Nationale de la Recherche (ANR) project "CoMuSim" (contract ANR-17-CE24-0010-01

Chaotic internal dynamics of dissipative optical soliton molecules

When a laser cavity supports the propagation of several ultrashort pulses, these pulses interact and can form compact bound states called soliton molecules. Soliton molecules are fascinating objects of nonlinear science, which present striking analogies with their matter molecules counterparts. The soliton pair, composed of two identical pulses, constitutes the chief soliton molecule of fundamental interest. The relative timing and phase between the two propagating pulses are the most salient internal degrees of freedom of the soliton molecule. These two internal degrees of freedom allow self-oscillating soliton molecules, which have indeed been repeatedly observed, whereas the lowdimensional chaotic dynamics of a soliton-pair molecule remains elusive, noting that it would require at least three degrees of freedom. We here report the observation of chaotic soliton-pair molecules within an ultrafast fiber laser, by means of a direct measurement of the relative optical pulse separation with sub-femtosecond precision in real time. Moreover, we demonstrate an all-optical control of the chaotic dynamics followed by the soliton molecule, by injecting a modulated optical signal that resynchronizes the internal periodic vibration of soliton molecule.Comment: 11 pages, 5 figure

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber

The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality

Stationary and pulsating dissipative light bullets from a collective variable approach

A collective variable approach is used to map domains of existence for (3+1)-dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation time