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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

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.

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.

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.

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.

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.

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

We consider the existence and propagation of nondiffractive and nondispersive spatiotemporal optical wavepackets in nonlinear Kerr media. We report analytically and confirm numerically the properties of spatiotemporal dark line solitary wave solutions of the (2 + 1)D nonlinear Schrödinger equation (NLSE). Dark lines represent holes of light on a continuous wave background. Moreover, we consider non-trivial web patterns generated under interactions of dark line solitary waves,which give birth to dark X solitary waves. These solitary waves are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the (2 + 1)D type II Kadomtsev-Petviashvili (KP-II) equation. This finding opens a novel path for the excitation and control of optical solitary waves, of hydrodynamic nature.

International audience; We experimentally investigate the roundtrip-to-roundtrip dynamics of the modulation instability spectrum in a passive fiber ring cavity presenting an inhomogeneous dispersion profile. By implementing a real-time spectroscopy technique we are able to record successive single-shot spectra, which display the evolution of the system toward a stationary state. We find that the two instability regimes (Turing and Faraday) that compete in this kind of inhomogeneous cavities not only differ by their characteristic frequency but also by their dynamical behaviour. The dynamic transition between those two regimes of instability is also presented.

International audience; We present a theoretical and experimental study of the modulation instability process in a dispersion oscillating passive fiber-ring resonator in the low dispersion region. Generally, the modulation of the dispersion along the cavity length is responsible for the emergence of a regime characterised by multiple parametric resonances (or Faraday instabilities). We show that, under weak dispersion conditions, a huge number of Faraday sidebands can grow under the influence of fourth order dispersion. We specifically designed a piecewise uniform fiber-ring cavity and report on experiments that confirm our theoretical predictions. We recorded the dynamics of this system revealing strong interactions between the different sidebands in agreement with numerical simulations.

International audience; We report on the experimental generation of Riemann waves in an optical fiber system, allowing for the controlled formation of shock waves, as analytically described by a seminal equation of fluid dynamics: the so-called Inviscid Burgers’ Equation.

International audience; We investigate the nonlinear stage of modulational instability in dispersion oscillating fibers in normal dispersion regime. We unveil a heteroclinic structure leading to the excitability of superbreathers and parametric amplification outside the linear gain bandwidth.

We experimentally report the observation of dispersive shock waves from a short pulse superimposed to a small cw background in optical fibers. The visibility of intensity oscillations inherent to shock waves is strongly enhanced.

We report on the experimental observation of inviscid Burgers’ equation dynamics and Riemann wave formation when a properly tailored optical pulse is coupled into a nonlinear fiber. Experimental results clearly show controllable pulse front steepening and shock formation.

International audience; We investigate the nonlinear stage of modulational instability in dispersion oscillating fibers in normal dispersion regime. We unveil a heteroclinic structure leading to the excitability of superbreathers and parametric amplification outside the linear gain bandwidth.

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrodinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

Contrary to conventional coherent shocks, we show theoretically and experimentally that nonlocal turbulent flows lead to the emergence of large-scale incoherent shock waves, which constitute a collective phenomenon of the incoherent field as a whole.

Numerical integration schemes of time-domain Maxwell equations in optical dispersive and nonlinear media are considered. In this context, we study quantitatively the impact of numerical dispersion on a typical nonlinear parametric conversion process, comparing the widely used finite difference (FDTD) approach and pseudo-spectral (PSTD) methods. Our results show that, unless using very dense grid, only fourth-order PSTD gives results in good quantitative agreement with standard coupled-mode theory.

We experimentally study modulational instability in a dispersion oscillating passive fiber ring cavity. This dispersion profile leads to new high-frequency gain bands that can be used for the generation of ultra-high repetition rate pulse trains.

Understanding turbulent flows arising from random dispersive waves that interact strongly through nonlinearities is a challenging issue in physics. Here we report the observation of a characteristic transition: strengthening the nonlocal character of the nonlinear response drives the system from a fully turbulent regime, featuring a sea of coherent small-scale dispersive shock waves (shocklets) towards the unexpected emergence of a giant collective incoherent shock wave. The front of such global incoherent shock carries most of the stochastic fluctuations and is responsible for a peculiar folding of the local spectrum. Nonlinear optics experiments performed in a solution of graphene nano-flakes clearly highlight this remarkable transition. Our observations shed new light on the role of long-range interactions in strongly nonlinear wave systems operating far from thermodynamic equilibrium, which reveals analogies with, for example, gravitational systems, and establishes a new scenario that can be common to many turbulent flows in photonic quantum fluids, hydrodynamics and Bose–Einstein condensates., Understanding turbulent flows arising from random dispersive waves that interact through nonlinearities is a challenging issue in physics. Here, the authors model and observe experimentally in a nonlinear optics set-up the transition between a sea of small-scale shocklets and a giant collective shock wave.

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 experiment shows that, at such optimal modulation frequency, a record 95 % of the output 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 Schrodinger equation. (c) 2015 Optical Society of America

International audience; In this review we present recent theoretical and experimental progresses on modulation instability and parametric amplification processes in dispersion oscillating fibers. These optical fibers are characterized by longitudinal periodic variations of their outer diameter engineered over the meter-long scale, which provides an additional degree of freedom to the system and leads to the generation of multiple MI side band pairs. Main results published in single pass configurations and in passive cavities are summarized in this review.

We investigate wave collapse in the generalized nonlinear Schrodinger (NLS) equation and in the presence of a non vanishing background. Through the use of virial identities, we establish a new criterion for blow-up.

We review different formalisms describing incoherent waves: the wave turbulence kinetic equation, the Vlasov equation in analogy with Gravitation, the weak Langmuir turbulence equation describing spectral solitons and incoherent dispersive shocks.

International audience; We show that the use of a dispersion oscillating fiber in passive cavities significantly extend modulational instability to novel high-frequency bands, which also destabilize the branches of the steady response which are stable with homogeneous dispersion. By means of Floquet theory, we obtain exact explicit expression for the sideband gain, and a simple analytical estimate for the frequencies of maximum gain. Numerical simulations show that stable stationary trains of pulses can be excited in the cavity.

International audience; We show that passive Kerr resonators pumped close to zero dispersion wavelengths on the normal dispersion side develop the resonant generation of linear waves driven by cavity (mixed dispersive-dissipative) shock waves. The resonance mechanism can be successfully described in the framework of the generalized Lugiato-Lefever equation with higher-order dispersive terms. Substantial differences with radiation from cavity solitons and purely dispersive shock waves dispersion are highlighted.

A nonlinear optical response coupled with feedback mechanisms is able to support optical multistability in various material systems and geometries. In periodically perturbed waveguides such as distributed feedback gratings (DFBG), a Bragg resonance coupling counterpropagating fields can associate with a Kerr or a parametric nonlinearity to give rise to transmissive nonlinear eigenstates within the otherwise propagation-forbidden photonic bandgap [1-5]. These correspond to energy localization states in the form of stationary or slowly travelling "gap-solitons" when properly excited, they can be viewed as optical bits trapped within the DFBG for shortor long-term storage depending on their propagation speed. Due to the rapidly growing interest in transparent optical networks and all-optical memories, the possibility of stationary localized states or "still" gap-solitons in DFBGs is an intriguing one. In this paper, after introducing two-color quadratic gap-solitons or gap-simultons in a channel waveguide for frequency doubling, we address the problem of excitation of slowly moving or stationary states in singly (srDFBG) or doubly resonant gratings (drDFBG), showing that the feasibility of read/write all-optical memories is within experimental reach. In a material system with a quadratically

Self-guided multi-frequency waves or simultons can form and propagate in media exhibiting a quadratic nonlinear susceptibility and, specifically, able to generate second harmonic. Some of their relevant properties are discussed, illustrating beam cleanup, instability, switching, steering, collisional interactions and other features in the spatial and temporal domains, including energy localization and gap solitons in periodic structures.

The stability of optical gap solitons is investigated in the framework of the generalized massive Thirring model. The self-phase modulation can induce either oscillatory or nonoscillatory types of instability, the latter mechanism being described by an explicit criterion, and unfolded geometrically to reveal gap soliton multistability, as well as different nonlinear evolution scenarios.

We address theoretically and numerically pump-probe switching in a nonlinear semiconductor nanocavity where tuning is achieved via a dominant mechanism of free-carrier plasma dispersion. By using coupled-mode approach we give a set of guidelines to optimize the switching performances both in terms of avoiding self-pulsation and keeping switching power to the minimum, ending up by showing that such devices can achieve high-performances with relatively low-power consumption.

Using a sensitive two-color heterodyne pump-probe technique, we investigate the carrier dynamics of an InP photonic crystal nanocavity. The heterodyne technique provides unambiguous results for all wavelength configurations, including the degenerate case, which cannot be investigated with the widely used homodyne technique. A model based on coupled mode theory including two carrier distributions is introduced to account for the relaxation dynamics, which is assumed to be governed by both diffusion and recombination.

We report on 10 GHz operation of an all-optical gate based on an Indium Phosphide Photonic Crystal Molecule. Wavelength conversion and all-optical mixing of microwave signals are demonstrated using the 2 mW output of a mode locked diode laser. The spectral separation of the optical pump and signal is crucial in suppressing optical cross-talk.

International audience; We show that, by properly adjusting the relative state of polarization of the pump and of a weak modulation, with a frequency such that at least one of its even harmonics falls within the band of modulation instability, one obtains a fully modulated wave at the second or higher even harmonic of the initial modulation. An application of this principle to the generation of a 80-GHz optical pulse train with high extinction ratio from a 40-GHz weakly modulated pump is experimentally demonstrated using a nonzero dispersion shifted fiber in the telecom C band.

We report experimental and theoretical studies of Raman-induced cross-phase modulational instabilities (XPMI) in a high-birefringence, normally dispersive optical fiber. Experimental results reveal that the Raman-Stokes wave, generated by a quasi-CW pump beam, interacts with the latter to create a novel type of XPMI sidebands. These sidebands are characterized by a narrow gain bandwidth. The sideband frequencies are well reproduced by a linear stability analysis as well as by full numerical solutions of the coupled generalized nonlinear Schrödinger equations.

International audience; We show that pulses undergoing wave-breaking in nonlinear weakly dispersive fibers radiate, owing to phase-matching, assisted by higher-order dispersion, of linear dispersive waves with the shock wave front. Our theoretical results perfectly explain the radiation recently observed from pulses propagating in the normal dispersion (i.e. non solitonic) regime.

We predict that self-sustained oscillations can be generated in a semiconductor nanocavity in which the dominant effect is band-filling dispersion. Linear stability analysis, validated through numerical integration of a mean-field model, leads us to envisage oscillations typically at tens of gigahertz, with onset at much lower input power (∼ 100 μW) compared with those driven by two-photon absorption.

Modulational instabilities and optical solitons are analyzed for dispersive (or diffractive) media with competing quadratic (χ(2)) and cubic (χ(3)) nonlinearities. Such a competition between the nonlinearities is expected for the parametric interaction between the fundamental and second harmonics that originates the so-called cascaded nonlinearity. It is shown that strong interplay between the nonlinearities can occur for both large and small values of the phase mismatch and, for example, the influence of χ(2) nonlinearities may have dramatic effect on modulational instability of continuous waves and properties of optical solitons. Solitons supported by such competing nonlinearites are analyzed, and an exact analytical solution for bright solitons is presented for special relations between parameters. It is also demonstrated that even a small contribution of quadratic nonlinearity breaks degeneracy of optical solitons and also make some of them unstable.

Cherenkov radiation and Soliton Self Frequency Shift are reported in (1.5mm-long) Photonic Crystal waveguides. The picosecond and picojoule pulses used here and the absence of Raman-induced frequency shift are peculiar of this new nonlinear material.

We investigate dispersive shock dynamics in materials with competing cubic-quintic nonlinearities. Whitham theory of modulation, hydrodynamic analysis and numerics demonstrate a rich physical scenario, ranging from multi-shock generation to collapse.

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schr¨ odinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose-Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

We show that a model based on anticrossing between highly group velocity-mismatched gap-guided and index-guided modes describes gap soliton propagation in photonic crystal waveguides. Such nonlinear solutions can be exploited for exploring new regimes such as all-optical control of group velocity (dispersionless slow light) over a submillimeter length scale, and propagation beyond the linear modal cutoff. The results are validated by means of finite-difference time domain simulations.

In the regime of normal dispersion and low-frequency detunings (or high powers), four-wave mixing is shown to undergo a hydrodynamic type of instability. Such instability involves the formation of shocks (steep fronts) from smooth initial data that are regularized through the appearance of trains of fast oscillations, which exhibit solitonlike behavior, colliding elastically.