Search results for " solitons"
showing 10 items of 386 documents
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
2000
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …
Influence of spatial delay on the modulational instability in a composite system with a controllable nonlinearity.
2017
A theoretical investigation of the modulational instability (MI) in a composite system with a nonlocal response function is presented. A composite system of silver nanoparticles in acetone is chosen, whose nonlinearity can be delicately varied by controlling the volume fraction of the constituents, thus enabling the possibility of nonlinearity management. A pump-probe counterpropagation configuration has been assumed, and the interplay between the competing nonlinearities and the nonlocalities in the MI dynamics is systematically explored. A different class of nonlocalities have been considered, and the study reveals that the nonlocality critically depends on the kind of nonlocal function. …
Conditions for waveguide decoupling in square-lattice photonic crystals
2004
We study coupling and decoupling of parallel waveguides in two-dimensional square-lattice photonic crystals. We show that the waveguide coupling is prohibited at some wavelengths when there is an odd number of rows between the waveguides. In contrast, decoupling does not take place when there is even number of rows between the waveguides. Decoupling can be used to avoid cross talk between adjacent waveguides.
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
2012
International audience; The nonlinear Schro¨dinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important serie…
Polarization-domain-wall complexes in fiber lasers
2013
To study the possible build-up of polarization-domain-walls (PDWs) in fiber laser cavities, an erbium-doped fiber ring laser was used and a wide range of vector polarization dynamics that can be selected at a given pump power, by using the degrees of freedom of two intracavity polarization controllers (PC) was investigated. A simple theoretical model that explains polarization switching in fiber ring lasers featuring a normally dispersive cavity with a typical, moderate, level of birefringence is presented. Such polarization dynamics, based on a special class of polarization-domain-wall structures, agrees qualitatively well with experimental observations. The paper stresses on the complex a…
Modulational instability and generation of self-induced transparency solitons in resonant optical fibers
2009
International audience; We consider continuous-wave propagation through a fiber doped with two-level resonant atoms, which is described by a system of nonlinear Schrodinger-Maxwell-Bloch (NLS-MB) equations. We identify the modulational instability (MI) conditions required for the generation of ultrashort pulses, in cases of both anomalous and normal GVD (group-velocity dispersion). It is shown that the self-induced transparency (SIT) induces non-conventional MI sidebands. The main result is a prediction of the existence of both bright and dark SIT solitons in the anomalous and normal GVD regimes.
Thermodynamic approach of supercontinuum generation
2009
International audience; This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i. e., the state of maximum n…
Dark spatial solitary waves in a cubic-quintic-septimal nonlinear medium
2017
We consider the evolution of light beams in nonlinear media exhibiting nonlinearities up to the seventh order wherein the beam propagation is governed by the cubic-quintic-septimal nonlinear Schr\"odinger equation. An exact analytic solution that describes dark solitary wave propagation is obtained, based on a special ansatz. Unlike the well-known $\text{tanh}$-profile dark soliton in Kerr media, the present one has a functional form given in terms of ``${\text{sech}}^{2/3}$''. The requirements concerning the optical material parameters for the existence of this localized structure are discussed. This propagating solitary wave exists due to a balance among diffraction, cubic, quintic, and s…
Diffusion stabilizes cavity solitons in bidirectional lasers
2009
We study the influence of field diffusion on the spatial localized structures (cavity solitons) recently predicted in bidirectional lasers. We find twofold positive role of the diffusion: 1) it increases the stability range of the individual (isolated) solitons; 2) it reduces the long-range interaction between the cavity solitons. Latter allows the independent manipulation (writing and erasing) of individual cavity solitons.