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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 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.

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; 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.

We show that the intracavity field evolving in an externally driven passive Kerr resonator subject to weak normal dispersion undergoes wave-breaking, thus forming dispersive shock waves. At variance with the cavity-less propagation, such dispersive wave-breaking turns out to be strongly favored by cavity bistability and coexisting modulational instability.

We show that the saturation of defocusing nonlinearities leads to qualitative changes in the onset of wave breaking, determining double shock formation whose regularization occurs in terms of antidark solitons. In a given material, the crossover between different regimes can be controlled by changing the input intensity.

International audience; We investigate wave-breaking and dispersive shock wave formation driven by a pulse undergoing second-harmonic generation in a quadratic medium. We show that the process is accessible in the regime of high phase-mismatch (cascading limit) and weak dispersion. Insight into the phenomenon is obtained by means of a suitable hydrodynamic reduction of the equations that govern the mixing.

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.

We investigate second-harmonic generation beyond the scalar approximation. We show that the tensorial nature of the second-order susceptibility may lead to the onset of spatial chaos in the polarization evolution of the interacting fields. We discuss the effect of chaos on situations of interest.

A stability analysis of the nonlinear dynamics of two-wave parametric mixing in a quadratic nonlinear medium in the presence of self- and cross-phase modulation reveals a novel symmetry-breaking instability. This instability may be lead to abrupt changes, as a function of the beam intensity, in the transfer of power between the fundamental and its second harmonic.

A synchronously pumped modulational-instability ring laser with a nonlinear dispersive fiber can be operated in both the anomalous and the normal dispersion regimes. We obtain simple analytical expressions for the sideband gain in the cavity by using an average pulse formalism. The numerical simulations indicate that stable stationary trains of pulses may be formed in the cavity. This is independent of the sign of the dispersion.

A geometric analysis of modulational instability reveals that spatiotemporally stable amplitude and frequency modulations may propagate in a nonlinear dispersive fiber, owing to self-injected locking of the temporal modes. We describe the close connection between the coherent nonlinear switching of an intense carrier by means of a weak modulating signal and similar instabilities in birefringent fibers and nonlinear directional couplers.

We predict all-optical switching of solitons between the two linear modes of a nonlinear coherent coupler made from a dual-core fiber operating in the anomalous dispersion regime.

We show that the Standard map governs near-separatrix evolution of the polarization state for an intense light wave traveling along a fiber whose linear birefringence has a periodic modulation. This allows us to estimate analytically, in good agreement with numerical experiments, the minimum angle to the unstable axis of a linearly polarized input beam in order to avoid chaotic power-dependent switching of the output polarization state.

Solutions of coupled-mode equations describing intensity-induced Bragg coupling of counterpropagating modes in a nonlinear distributed-feedback structure may become spatially unstable. Instability leads to nonpassing plateaus in the intensity transmission characteristics. This induces strong optical limiting action in the transmission mode and lower thresholding in the reflection mode.

We show that self-transparent or gap solitons with leading-order components at fundamental frequency can be generated in a singly resonant Bragg grating by second-harmonic generation. We discuss the conditions required for exciting these localized waves.

In a doubly resonant degenerate optical parametric oscillator below threshold the signal beam can be trapped in the form of stable bright temporal or spatial solitons. We characterize these soliton families and discuss how to excite them.

We predict that nearly resonant optical parametric oscillators support stable topological spatial solitons as a result of the interplay between diffraction and parametric amplification due to chi((2)) nonlinearities. Robust soliton stripes are observed in two transverse dimensions. Their stability is ensured by the phase-sensitive nature of the underlying parametric process.

We show that one-dimensional parametric spatial solitons undergo temporal instability that leads to their breakup into spatiotemporal patterns with a characteristic snakelike shape.

We address the important problem of excitation of gap solitons of a parametric nature, which are sustained in periodically corrugated frequency-doubling media near Bragg resonance with both the fundamental frequency and its second harmonic. We demonstrate that a zero-velocity soliton can be trapped in a finite Bragg structure by the quiescence of two counterpropagating moving solitons, which in turn might be formed by injection of appropriate light pulses at a single carrier frequency.

We present a study of the dynamics of multiple soliton bound states in diffractive media with second-order nonlinearity. A numerical stability analysis of these bound states reveals that wave propagation in quadratic materials exhibits spatial symmetry-breaking instabilities.

It is shown that second-harmonic generation in a grating allows one to cancel the group-velocity difference between two polarization components at fundamental by means of nonlinearly induced phase shifts. This occurs when a new type of cascading soliton propagates on resonance.

A symbiotic pair of dark (second-harmonic) and bright (fundamental frequency) solitons sustain each other and travel locked in second-harmonic generation dominated by group-velocity difference or spatial walk-off. The conditions of existence of the soliton pair are determined, and its stability in the presence of dispersion is discussed.

It is demonstrated that optical solitons can propagate in a dispersive (or diffractive) medium with competing quadratic [i.e., chi((2))] and cubic [i.e., chi((3))] nonlinearities. Strong interplay between the nonlinearities leads to novel effects, in particular the following: (i) stable bright solitons can still exist in a self-defocusing (owing to cubic nonlinearity) medium supported by quadratic parametric interactions and (ii) chi((2)) nonlinearity can lead to instabilities of chi((3)) solitons.

We show that the eigenmodes of the two-wave interaction in a dispersive quadratic medium are unstable with respect to periodic perturbations. This mechanism represents a novel kind of modulational instability that involves the spontaneous generation of sideband pairs around both the fundamental and the second-harmonic frequencies.

We study the nonlinear evolution in optical fibers of a modulationally unstable continuous wave. We find that a good description of the propagation can be analytically obtained by a simple truncated three-wave model. The dynamic viewpoint may give an important physical insight in different processes, such as frequency conversion of modulated signals, all-optical generation of temporal codes, and the onset of spatiotemporal chaos.

We predict that the third-order parametric mixing of a pump with a pair of orthogonally polarized sidebands in a birefringent single-mode optical fiber may be spatially unstable. The interaction may exhibit both periodic and nonperiodic energy conversion and period doubling. This analysis allows us to propose a new scheme for all-optical switching as well as to predict the most efficient conditions for energy conversion when pump depletion is accounted for.

We show that an optical pulse can propagate undistorted as a bright solitary wave in the normal dispersion regime when it couples through cross-phase modulation to a dark pulse in the anomalous dispersion regime.

Self-induced birefringence effects in a periodically modulated nonlinear medium are investigated. An input beam linearly polarized along the axis of a fiber polarization-rocking filter undergoes a spatial instability as the input power crosses a threshold value that scales linearly with the coupling strength. We describe the potential use of this effect for relatively low-power intensity discrimination, all-optical polarization switching, and small-signal amplification using linearly polarized beams. The wavelength for maximum polarization conversion between the axes can be tuned by varying the input power, and the filter bandwidth narrows with increasing power.