Exact cascading nonlinearity in quasi-phase-matched quadratic media

The evolution of light pulses and beams in a quasi-phase-matched (QPM) quadratic medium is usually described by considering only the spatial harmonic of the QPM grating that minimizes the residual phase-mismatch. I show that, for strongly phase-mismatched interactions (the cascading regime), several harmonics need to be accounted for in order to obtain the correct value of the effective cubic nonlinearity, of which I find a simple analytical expression. I discuss the effects of the higher order harmonics of the grating on solitary wave propagation

The multi-resonant Lugiato-Lefever model

We introduce a new model describing multiple resonances in Kerr optical cavities. It perfectly agrees quantitatively with the Ikeda map and predicts complex phenomena such as super cavity solitons and coexistence of multiple nonlinear states

Resonant radiation shed by dispersive shock waves

We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing nonlinear Schroedinger equation, giving criteria for calculating the radiated frequency based on the estimate of the shock velocity, revealing also a diversity of possible scenarios depending on the order and magnitude of the dispersive corrections

Modulational instability in dispersion oscillating fiber ring cavities

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

Parametric Frequency Conversion of Short Optical Pulses Controlled by a CW Background

We predict that parametric sum-frequency generation of an ultra-short pulse may result from the mixing of an ultra-short optical pulse with a quasi-continuous wave control. We analytically show that the intensity, time duration and group velocity of the generated idler pulse may be controlled in a stable manner by adjusting the intensity level of the background pump

Parametric excitation of multiple resonant radiations from localized wavepackets

Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A remarkable property of such driving is that it can induce the localized (bound) states to resonantly couple to the continuum. Therefore experiments that allow for enlightening and controlling the mechanisms underlying such coupling are of paramount importance. We implement such an experiment in a special fiber optics system characterized by a dispersion oscillating along the propagation coordinate, which mimics "time". The quasi-momentum associated with such periodic perturbation is responsible for the efficient coupling of energy from the localized wave-packets sustained by the fiber nonlinearity into free-running linear dispersive waves (continuum), at multiple resonant frequencies. Remarkably, the observed resonances can be explained by means of a unified approach, regardless of the fact that the localized state is a soliton-like pulse or a shock front

Fast and accurate modelling of nonlinear pulse propagation in graded-index multimode fibers

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics

Extreme high-intensity and ultrabroadband interactions in anisotropic β-BaB_2O_4 crystals

International audienceWe derive unidirectional pulse propagation equations to describe extreme high-intensity and ultra-broadband optical interactions in uniaxial crystals, showing both second-and third-order nonlinear optical susceptivities. We focus our attention on the anisotropic nature of the quadratic and cubic nonlinear response of β−BaB 2 O 4 (BBO) crystals. Two nonlinearly coupled first order (in the propagation coordinate) equations describe the dynamics and interactions of the ordinary and extraordinary field polarizations, and are valid for arbitrarily wide pulse bandwidth. We exploit this model to predict harmonic and supercontinuum generation in BBO crystals under strong and competing influence of quadratic and cubic susceptivities

Random telegraph dispersion-management: modulational instability

We study modulational instability in a fiber system resembling a dispersion-managed link where the sign of the group-velocity dispersion varies randomly according to a telegraph process. We find that the instability gain of stochastic origin converges, for long fiber segment mean length (the inverse of the transition rate between the two values), to the conventional values found in a homogeneous anomalous dispersion fiber. For short fiber segments, the gain bands are broadened and the maximum gain decreases. By employing correlation splitting formulas, we obtain closed form equations that allow us to estimate the instability gain from the linearized nonlinear Schr\"odinger equation. We compare the analytical to the numerical results obtained in a Monte Carlo spirit. The analysis is proven to be correct not only for a fluctuating group-velocity dispersion, but also including fourth-order dispersion (both constant or varying according to a synchronous or independent telegraph process). These results may allow researchers to tailor and control modulational instability sidebands, with applications in telecommunications and parametric photon sources.Comment: 12 pages, 6 figure

Complex dispersion relation of a double chain of lossy metal nanoparticles

International audienceWe study the propagation characteristics of optical signals in waveguides composed of a double chain of metallic nanoparticles embedded in a dielectric host. We find that the complex Bloch band diagram for the guided modes, derived by the Mie scattering theory including material losses, exhibits strong differences with respect to the previously studied single chain. The results of the model are validated through finite element solution of Maxwell's equations