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It is known that the modulation instability (MI) is a focusing mechanism responsible for the formation of rogue waves (RWs). Such dynamics are initiated from the injection of sidebands, which translates into an amplitude modulation (AM) of the wave field. The nonlinear stage of unstable wave evolution can be described by exact breather solutions of the nonlinear Schrödinger equation (NLSE). In fact, the amplitude modulation of such coherent RW structures is connected to a particular phase-shift seeded in the carrier wave, i.e. a particular form of localized frequency modulation (FM). By seeding only the local FM information of a deterministic breather to a regular wave train, our experiments show that such an FM localization can indeed trigger pure breather-type RW dynamics. Results of an experimental study on identifying spontaneous RWs in a random wave field by isolating the respective FM and AM dynamics will also be discussed.

We address the recurrent regime of depleted two-color modulational instability in second-harmonic generation in the cascading limit. We validate a description based on simple algebraic formulas, based on asymptotic matching, establishing quantitatively the limit of validity of this approach. In the low mismatch regime, where such description breaks down, the system is found to undergo pseudo-stochastic alterations between two types of deterministic recurrence.

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wavenumber, we obtain low-frequency MI sidelobes which converge to those given by a white noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVD, 12 pages, 6 figures submitted

We present a systematic investigation of the resonant radiation emitted by localized soliton-like wave-packets supported by second-harmonic generation in the cascading regime. We emphasize a general mechanism which allows for the resonant radiation to grow without the need for higher-order dispersion, primarily driven by the second-harmonic component, while radiation is also shed around the fundamental-frequency component through parametric down-conversion processes. The ubiquity of such a mechanism is revealed with reference to different localized waves such as bright solitons (both fundamental and second-order), Akhmediev breathers, and dark solitons. A simple phase matching condition is put forward to account for the frequencies radiated around such solitons, which agrees well with numerical simulations performed against changes of material parameters (say, phase mismatch, dispersion ratio). The results provide explicit understanding of the mechanism of soliton radiation in quadratic nonlinear media.

International audience; Fermi Pasta Ulam (FPU) recurrence process describes the ability of a nonlinear system to excite multiple modes and then to return to its initial state. In fiber optics, such process has been investigated within the framework of modulation instability (MI) [1], corresponding to growth of weak perturbations at the expense of a strong pump. Nonlinear stage of MI and FPU recurrences in optical fibers have been widely investigated and many results have been obtained with an efficient compensation of the losses [2]. Investigations on water waves [3] demonstrated that dissipation of their water tank forces the system to operate in a single regime. Here, we provide a deeper and complete study on the impact of dissipation of the FPU dynamics. Thanks to a fiber optics system, we have been able to control the loss coefficient, allowing us to trigger the different corresponding FPU regimes. Using a setup similar to the one in [2] and based on a multiple HOTDR system, we managed to record FPU recurrences in power and phase along the fiber length as a function of the loss, Fig. 1. The dissipation is controlled thanks to a counter-propagating Raman pump whose power is tuned to get an effective loss coefficient. A direct relation between the Raman pump power and effective loss coefficient is obtained, allowing a direct comparison between experiments (left panel) and simulations (right panel). Three different regions are discernible. In the 3 rd

International audience; We report recent results obtained with a novel optical fiber experimental setup based on a heterodyne optical time-domain reflectometer in the context of FPU recurrence process. Moreover, we actively compensate the dissipation of the system. We show that we can observe several FPU recurrences by monitoring the power and relative phase evolutions of the main discrete frequency components involved in the process.

The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both, optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here., 9 pages, 10 figures

We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schr\"odinger equation framework and show that an Akhmediev breather envelope, which is at the core of Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events, can be frozen into a steady periodic (dnoidal) wave by a suitable variation of a single external physical parameter. We experimentally demonstrate this general approach in the particular case of surface gravity water waves propagating in a wave flume with an abrupt bathymetry change. Our results highlight the influence of topography and waveguide properties on the lifetime of nonlinear waves and confirm the possibility to control them., Comment: 6 pages, 3 figures (main text); 8 pages, 8 figures (supplemental material)

A coherently pumped, passive cavity supports, in the normal dispersion regime, the propagation of still interlocked fronts or switching waves that form invariant localized temporal structures. We address theoretically the problem of the excitation of this type of wave packet. First, we map all the dynamical behaviors of the switching waves as a function of accessible parameters, namely, the cavity detuning and input energy deficiency, using box-like excitation of the intracavity field. Then we show how a good degree of control can be obtained by applying a negative or positive external pulsed excitation.

We experimentally investigate the influence of optical fiber loss on the dynamics of the FPU process. We show that the symmetry of the FPU process can be broken several times by tuning the fiber loss value.

We show that two-color Peregrine solitary waves in quadratic nonlinear media can resonantly radiate dispersive waves even in the absence of higher-order dispersion, owing to a phase-matching mechanism that involves the weaker second-harmonic component. We give very simple criteria for calculating the radiated frequencies in terms of material parameters, finding excellent agreement with numerical simulations.

International audience; We report the experimental observation of more than four Fermi-Pasta-Ulam-Tsingou recurrences in an optical fiber thanks to an ultra-low loss optical fiber and to an active loss compensation system. We observe both regular (in-phase) and symmetry-broken (phase-shifted) recurrences, triggered by the input phase. Experimental results are confirmed by numerical simulations.

We report the first, to the best of our knowledge, experimental observation of doubly periodic first-order solutions of the nonlinear Schrödinger equation in optical fibers. We confirm, experimentally, the existence of A -type and B -type solutions. This is done by using the initial conditions that consist of a strong pump and two weak sidebands. The evolution of power and phase of the main spectral components is recorded using heterodyne time-domain reflectometry. Another important part of our experiment is active loss compensation. We reach a good agreement between theory and experiment.

Soliton and breather solutions of the nonlinear Schr\"odinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such exact solutions is the proper generation of the exact initial phase-shift profile in the carrier wave, as defined by the NLSE envelope at a specific time or location. Here, we show experimentally the significance of such initial exact phase excitation during the hydrodynamic propagation of localized envelope solitons and breathers, which modulate a plane wave of constant amplitude (finite background). Using the example of stationary black solitons in intermediate water depth and pulsating Peregrine breathers in deep-water, we show how these localized envelopes disintegrate while they evolve over a long propagation distance when the initial phase shift is zero. By setting the envelope phases to zero, the dark solitons will disintegrate into two gray-type solitons and dispersive elements. In the case of the doubly-localized Peregrine breather the maximal amplification is considerably retarded; however locally, the shape of the maximal focused wave measured together with the respective signature phase-shift are almost identical to the exact analytical Peregrine characterization at its maximal compression location. The experiments, conducted in two large-scaled shallow-water as well as deep-water wave facilities, are in very good agreement with NLSE simulations for all cases., Comment: (14 pages, 12 figures)

We report the first experimental observation of four Fermi-Pasta-Ulam-Tsingou recurrences along an optical fiber thanks to an active compensation of the losses.

In optical fibres, weak modulations can grow at the expense of a strong pump to form a triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such conversion and back-conversion constitute a manifestation of the universal nonlinear phenomenon known as Fermi–Pasta–Ulam recurrence. However, it remains a major challenge to observe the coexistence of different types of recurrences owing to the spontaneous symmetry-breaking nature of such a phenomenon. Here, we implement a novel non-destructive technique that allows the evolution in amplitude and phase of frequency modes to be reconstructed via post-processing of the fibre backscattered light. We clearly observe how control of the input modulation seed results in different recursive behaviours emerging from the phase-space structure dictated by the spontaneously broken symmetry. The proposed technique is an important tool to characterize other mixing processes and new regimes of rogue-wave formation and wave turbulence in fibre optics.

International audience; We experimentally investigate two cycles of Fermi-Pasta-Ulam-Tsingou recurrence in optical fibers. Using three waves input we characterize the distance of maximum compression points against sideband amplitude and relative phase, outlining the qualitative changes of the dynamics due to separatrix crossing. Experimental results are in good agreement with numerical simulations and analytical predictions.

International audience; Modulational 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.

The piston problem, i.e. the dynamics of a uniform gas at rest under the action of a moving piston, is fundamental in shock wave physics [1,2]. In conservative systems, shock waves are regularized by the formation, owing to dispersion, of rapidly oscillating non-stationary structures, called dispersive shock waves (DSWs) [3–6].

Full experimental characterization of short pulses (with discrete line spectra) of the electric field (phase+intensity) in optical fibers is of high interest to get a detailed description of a large variety of nonlinear phenomena governed by the general nonlinear Schrodinger equation such as rogue wave formation or frequency comb generation. Recently, new techniques allowing real-time full-field characterization has been shown in the context of rogue waves [1] and laser dynamics [2]. However, experimental methods were limited so far to localized characterization of the field.

We provide the first longitudinal characterization in phase and amplitude of the nonlinear stage of Modulation instability in optical fibers by means of a heterodyne optical time domain reflectometer. This original setup allows to report the symmetry breaking of the process due to an initial condition change.

Full-field longitudinal characterization of picosecond pulse train formation in optical fibers is reported. The spatio-temporal evolution is obtained via fast and non-invasive distributed measurements in phase and intensity of the main spectral components of the pulses. To illustrate the performance of the setup, we report, to the best of our knowledge, the first time-domain experimental observation of the symmetry breaking of Fermi-Pasta-Ulam recurrences. The experimental results are in good agreement with numerical simulations.

We investigate the nonlinear stage of modulational instability reporting experimental evidence for symmetry breaking of recurrent evolutions entailing growth and decay of sideband combs, and discussing its breakdown resulting from temporal confinement of the perturbation.

Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence process describes the ability of a multimodal system experiencing complex nonlinear dynamics to come back to its initial state, instead of reaching thermalization. In optics, it has particularly been investigated in the context of modulation instability (MI) [1], which plays a key role in many nonlinear phenomena such as rogue wave formation or supercontinuum generation. Recently, we reported a novel experimental setup [2] consisting in a heterodyne time-domain detection system which allows to perform along an optical fiber distributed measurement in phase and intensity of a pump wave and its modulation sidebands. Thanks to an active compensation of the losses, it enabled the observation of two FPUT recurrences cycle for the first time (Fig. 1(b,c)). Moreover, Grinevich and Santini recently reported [3] an advanced theoretical model to predict the characteristics of these recurrences which have been verified experimentally in a 3D photorefractive crystal [4]. Based on the setup described in [2], we report here its verification in an optical fiber.

International audience; We investigate the generation of symmetric and asym-metric pairs of breathers from localized disturbances in the nonlinear stage of modulational instability governed by the nonlinear Schrödinger equation. An asymptotic matching approach allows us to predict with great accuracy how their emergence and their evolution depend on the parameters of the perturbation. The same approach turns out to be applicable to other classes of perturbations, which, due to their different decay in time, do not give rise to breathers.

We study the small dispersion limit of the Korteweg–de Vries (KdV) equation with periodic boundary conditions and we apply the results to the Zabusky–Kruskal experiment. In particular, we employ a WKB approximation for the solution of the scattering problem for the KdV equation [i.e., the time-independent Schrodinger equation] to obtain an asymptotic expression for the trace of the monodromy matrix and thereby of the spectrum of the problem. We then perform a detailed analysis of the structure of said spectrum (i.e., band widths, gap widths and relative band widths) as a function of the dispersion smallness parameter ϵ . We then formulate explicit approximations for the number of solitons and corresponding soliton amplitudes as a function of ϵ . Finally, by performing an appropriate rescaling, we compare our results to those in the famous Zabusky and Kruskal’s paper, showing very good agreement with the numerical results.

We investigate the phenomenon of resonant radiation emitted by Peregrine solitons. We show that, unlike bright or dark solitons of the nonlinear Schrödinger equation, the radiation process is affected by the intrinsic local longitudinal variation of the soliton wavenumber. We give a phase-matching condition that allows the prediction of the multiple spectral peaks of the resonant radiation.

International audience; The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrödinger equation. It is showed that the development of associated spatio-temporal patterns is strongly affected by the shape and the parameters of the perturbation. Different scenarios are presented that involve an auto-modulation developing in a characteristic wedge, possibly coexisting with breathers which lie inside or outside the wedge.

We experimentally and numerically report on the formation of ballistic dispersive shock waves that mimic superfluid behavior in optical fibers. The shock wave is triggered by a strong nonlinear phase shift induced by a high power pump pulse on a cross-polarized continuous-wave probe field, and it exhibits a central void surrounded by two oscillating fronts moving away from each other with opposite velocities. The impact of disorder in the continuous-wave background as well as the difference of group-velocities between the two orthogonally polarized waves is also investigated. Our experimental observations are in very good agreement with theoretical and numerical predictions derived from the Manakov model.

We report a novel experimental setup to perform distributed characterization in intensity and phase of the nonlinear stage of modulation instability by means of a non-invasive experimental setup : a heterodyne time domain reflectometer.

International audience; We provide a direct observation of a period-doubling phenomenon associated to the modulation instability in both uniform and dispersion oscillating passive fiber ring cavities. This has been done by performing roundtrip-to-roundtrip measurements of the temporal pattern generated through the instability.

International audience

We provide a clear demonstration of a period-doubling phenomenon associated to the modulation instability in dispersion oscillating fiber cavities. This has been done by performing roundtrip-to-roundtrip measurements of the temporal pattern generated through the instability.

International audience; We investigate the optical analogous of the piston shock problem in gas dynamics. Using fast temporal measurements, we recorded dispersive shock waves formed by the propagation of a bi-chromatic photon fluid along an optical fiber. OCIS codes: (190.4370) Nonlinear optics fibers, (190.5530) Pulse propagation and temporal solitons.

International audience; We provide the first longitudinal characterization in phase and amplitude of the Fermi Pasta Ulam recurrence in optical fibers by means of a heterodyne optical time domain reflectometer. This original setup allows to report the symmetry breaking of the process due to an initial condition change.

International audience; We investigate analytically, numerically and experimentally the spectral broadening of pulses that undergo the formation of dispersive shocks, addressing in particular pulses in the range of tens of ps generated via electro-optic modulation of a continuous-wave laser. We give an analytical estimate of the maximal spectral extension and show that super-Gaussian waveforms favor the generation of flat-topped spectra. We also show that the weak residual background of the modulator produces undesired spectral ripples. Spectral measurements confirm our estimates and agree well with numerical integration of the nonlinear Schrödinger equation.

Water dam breaking (or dam failure) triggered by the nature disasters such as earthquakes or heavy rainfall can cause huge damage in terms of human lives and properties. Not only for realizing its formation process to evaluate the potential consequences, but also because of the intrinsic rich mathematical and numerical interest, this classical problem has attracted a lot of attention [1-3]. However, clear and accurate experimental investigations are still lacking. In this communication, based on our previous observation of dispersive shock waves (DSW) [4], we revisited the classical dam-breaking problem in nonlinear fiber optics. We studied the propagation of a short optical pulse with an intensity-jump in a dispersion compensating fiber (DCF) that mimics water height jump in hydrodynamics. A sketch of the experimental setup is shown in Fig. 1 (a). We used an electro-optical modulator to generate a step like pulse of 1 ns duration with a background level equals to 15% of the powerful part of the pulse (Fig. 1 (c)). It is then amplified in an erbium doped fiber amplifier to reach 0.6 W peak power and launched inside a DCF whose parameters are listed in Fig. 1's caption. Linear losses of the fiber are almost totally compensated by launching a counter-propagating Raman pump at 1480 nm. The intensity profile at the output of this lossless DCF has been recorded by using an optical sampling oscilloscope, as shown in Fig.1 (e). We clearly see that the optical dam decays into a pair of oppositely propagating DSW (on the left) and rarefaction wave (RW, on the right), separated by a short plateau between them.

International audience; The emergence of long-range phase coherence among random nonlinear waves is a fascinating effect that characterizes fundamental phenomena such as the condensation of nonlinear waves and the related manifestation of superfluidity of certain turbulent flows. Here we report a previously unrecognized phenomenon of spontaneous emergence of long-range phase coherence among incoherent waves interacting through a nonlocal nonlinearity. The theory reveals that the establishment of long-range phase coherence constitutes a generic property of a conservative (Hamiltonian) system of highly nonlocal random waves that evolve in the strongly nonlinear regime. Aside from phase coherence, the field exhibits intensity fluctuations whose coherence length is shown to increase in a dramatic way during the evolution of the system. The analysis can be transposed to the temporal domain, revealing the emergence of temporal phase coherence among incoherent waves propagating in nonlinear materials featured by a noninstantaneous nonlinear response

International audience; We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the step-like input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state. The detailed observation of the cavitating state dynamics allows for a fully quantitative test of the Whitham modulation theory applied to the universal defocusing nonlinear Schrödinger equation.