We demonstrate that wave-breaking dramatically affects the dynamics of nonlinear frequency conversion processes that operate in the regime of high efficiency (strong multiple four-wave mixing). In particular, by exploiting an all-optical-fiber platform, we show that input modulations propagating in standard telecom fibers in the regime of weak normal dispersion lead to the formation of undular bores (dispersive shock waves) that mimic the typical behavior of dispersive hydrodynamics exhibited, e.g., by gravity waves and tidal bores. Thanks to the nonpulsed nature of the beat signal employed in our experiment, we are able to clearly observe how the periodic nature of the input modulation forces adjacent undular bores to collide elastically

We analyze the modulation instability induced by periodic variations of group velocity dispersion and nonlinearity in optical fibers, which may be interpreted as an analogue of the well-known parametric resonance in mechanics. We derive accurate analytical estimates of resonant detuning, maximum gain and instability margins, significantly improving on previous literature on the subject. We also design a periodically tapered photonic crystal fiber, in order to achieve narrow instability sidebands at a detuning of 35 THz, above the Raman maximum gain peak of fused silica. The wide tunability of the resonant peaks by variations of the tapering period and depth will allow to implement sources of correlated photon pairs which are far-detuned from the input pump wavelength, with important applications in quantum optics.

We investigate the impact of nonlocality, owing to diffusive behavior, on transverse instabilities of a dark\ud stripe propagating in a defocusing cubic medium. The nonlocal response turns out to have a strongly stabilizing\ud effect both in the case of a single soliton input and in the regime where dispersive shock waves develop\ud multisoliton regime. Such conclusions are supported by the linear stability analysis and numerical simulation\ud of the propagation

We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis. [12,13]. While the concept of PR originates in the linear world [14], PRs deeply impact also the behavior of nonlinear conservative systems. However, the full nonlinear dynamics of PRs is relatively well understood only for lowdimensional Hamiltonian systems [2,15,16]. Conversely, the analysis of extended systems described by PDEs with periodicity in the evolution variable [17] is essentially limited to determine the region of parametric instability (Arnold tongues) via Floquet analysis [18][19][20][21], while the nonlinear stage of PR past the linearized growth of the unstable modes remains mostly unexplored.In this letter, taking the periodic defocusing nonlinear Schrödinger equation (NLSE) as a widespread example describing, e.g. periodic management of atom condensates [12,19,20,22], optical beam propagation in layered media [21], or optical fibers with periodic dispersion [18,23,24], we show that the PR gives rise to quasi-periodic evolutions which exhibit on average FermiPasta-Ulam (FPU) recurrence [25] with a remarkably complex (but ordered) underlying phase-plane structure. Such structure describes the continuation into the nonlinear regime of the modulational instability (MI) of a background solution, uniquely due to the parametric forcing (with zero forcing the defocusing NLSE is stable). A byproduct of this structure is the existence of breatherlike solutions [26]. This fact suggests the intriguing possibility of observing rogue waves [27], which are commonly associated with breathers [28], in the defocusing NLSE [29]. On the other hand, the richness of such structure allows us to remarkably predict that optimal parametric amplification occurs at a critical frequency where the system lies off-resonance (outside the PR bandwidth). Our approach retains its validity in the most interesting regime of strong parametric driving, where the system is found to exhibit a remarkably ordered structure despite its broken translational symmetry and integrability. In this sense the physics differs from other integrable models exhibiting a complex nonlinear dynamics of MI already in the undriven regime (e.g. focusing NLSE [26,[30][31][32][33][34][35][36]), around which chaos can develop under weak periodic perturbations [31,37,38].We consider the following periodic NLSEreferring, without loss of genera...

We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate the model by comparing it to numerical simulation, we distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model.

We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.

Nondeterministic giant waves, denoted as rogue, killer, monster, or freak waves, have been reported in many different branches of physics. Their physical interpretation is however still debated: despite massive numerical and experimental evidence, a solid explanation for their spontaneous formation has not been identified yet. Here we propose that rogue waves [more precisely, rogue solitons (RSs)] in optical fibers may actually result from a complex dynamical process very similar to well-known mechanisms such as glass transitions and protein folding. We describe how the interaction among optical solitons produces an energy landscape in a highly dimensional parameter space with multiple quasi-equilibrium points. These configurations have the same statistical distribution of the observed rogue events and are explored during the light dynamics due to soliton collisions, with inelastic mechanisms enhancing the process. Slightly different initial conditions lead to very different dynamics in this complex geometry; a RS turns out to stem from one particularly deep quasi-equilibrium point of the energy landscape in which the system may be transiently trapped during evolution. This explanation will prove to be fruitful to the vast community interested in freak waves. (C) 2015 Optical Society of America

Raman effect in gases can generate an extremely long-living wave of coherence that can lead to the establishment of an almost perfect temporal periodic variation of the medium refractive index. We show theoretically and numerically that the equations, regulate the pulse propagation in hollow-core photonic crystal fibers filled by Raman-active gas, are exactly identical to a classical problem in quantum condensed matter physics - but with the role of space and time reversed - namely an electron in a periodic potential subject to a constant electric field. We are therefore able to infer the existence of Wannier-Stark ladders, Bloch oscillations, and Zener tunneling, phenomena that are normally associated with condensed matter physics, using purely optical means.