Search results for "SOLITONS"
showing 10 items of 401 documents
Condensation of classical optical waves beyond the cubic nonlinear Schrodinger equation
2012
International audience; A completely classical nonlinear wave is known to exhibit a process of condensation whose thermodynamic properties are analogous to those of the genuine Bose-Einstein condensation. So far this phenomenon of wave condensation has been studied essentially in the framework of the nonlinear Schrodinger (NLS) equation with a pure cubic Kerr nonlinearity. We study wave condensation by considering two representative generalizations of the NLS equation that are relevant to the context of nonlinear optics, the nonlocal nonlinearity and the saturable nonlinearity. For both cases we derive analytical expressions of the condensate fraction in the weakly and the strongly nonlinea…
Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin
2008
We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.
Pattern formation driven by cross–diffusion in a 2D domain
2012
Abstract In this work we investigate the process of pattern formation in a two dimensional domain for a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka–Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, and hexagonal patterns.
A SUBCRITICAL BIFURCATION FOR A NONLINEAR REACTION–DIFFUSION SYSTEM
2010
In this paper the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms is investigated. Through a linear stability analysis we show that the cross-diffusion term allows the pattern formation. To predict the form and the amplitude of the pattern we perform a weakly nonlinear analysis. In the supercritical case the Stuart-Landau equation is found, which rules the evolution of the amplitude of the most unstable mode. With the increasing distance from the bifurcation value of the cross-diffusion parameter, the weakly nonlinear analysis fails and a Fourier–Galerkin approach is adopted. In the subcritical case the weakly nonlinear analysis must be pushed u…
Breather dynamics in a stochastic sine-Gordon equation: evidence of noise-enhanced stability
2023
The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influenc…
Supplementary optical phase transition in photorefractive coherent oscillator
2001
The semilinear photorefractive coherent oscillator with two counterpropagating pump waves may exhibit two optical phase transitions: one from a disordered state of wide-angle photorefractive scattering into a high-ordered state with the immobile photorefractive grating and the other one from the state with immobile grating into the state with two moving photorefractive gratings. We show, both experimentally and from calculations, that two these phase transitions are the second-order phase transitions.
Stability of laser cavity-solitons for metrological applications
2023
Laser cavity-solitons can appear in systems comprised of a nonlinear microcavity nested within an amplifying fiber loop. These states are robust and self-emergent and constitute an attractive class of solitons that are highly suitable for microcomb generation. Here, we present a detailed study of the free-running stability properties of the carrier frequency and repetition rate of single solitons, which are the most suitable states for developing robust ultrafast and high repetition rate comb sources. We achieve free-running fractional stability on both optical carrier and repetition rate (i.e., 48.9 GHz) frequencies on the order of [Formula: see text] for a 1 s gate time. The repetition r…
Modulational instability in resonant optical fiber with higher-order dispersion effect
2010
International audience; The modulational instability (MI) of an electromagnetic wave in a resonant optical fiber with a two-level system is investigated. In the normal dispersion regime, we find the occurrence of nonconventional MI sidebands which are induced by the two-level resonant atoms. We also observe that the MI gain spectra are suppressed by the higher-order dispersion effect in the anomalous dispersion regime.
Temporal Soliton “Molecules” in Mode-Locked Lasers: Collisions, Pulsations, and Vibrations
2008
A few years after the discovery of the stable dissipative soliton pairs in passively mode-locked lasers, a large variety of multi-soliton complexes were studied in both experiments and numerical simulations, revealing interesting new behaviors. This chapter focuses on the following three subjects: collisions between dissipative solitons, pulsations of dissipative solitons, and vibrations of soliton pairs. Different outcomes of collisions between a soliton pair and a soliton singlet are discussed, showing possible experimental control in the formation or dissociation of ‘soliton molecules’. Long-period pulsations of single and multiple dissipative solitons are presented as limit cycles and o…
Spectral incoherent solitons
2009
Solitons have been usually considered as inherently coherent localized structures and the discovery of incoherent optical solitons has represented a significant progress [1]. As occurs for standard coherent solitons, incoherent solitons are characterized by a confinement of the field in the spatial or in the temporal domain. We introduce here a novel type of incoherent solitons that are neither spatial nor temporal, i.e., the incoherent field does not exhibit any confinement in the spatiotemporal domain; however, the uncorrelated frequency components that constitute the incoherent field exhibit a localized soliton behavior in the frequency domain [2].