Search results for "Stability"
showing 10 items of 3085 documents
The nonlinear Schrodinger equation and the propagation of weakly nonlinear waves in optical fibres and on the water surface
2015
International audience; The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional par…
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
2011
International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.
Nonlinear parametric resonances in quasiperiodic dispersion oscillating fibers
2015
We numerically study the evolution of the spectrum of parametric resonance or modulation instability sidebands in quasiperiodic dispersion oscillating fibers. We separately consider a linear variation along the fiber of either the spatial period, the average dispersion, or the amplitude of the dispersion oscillation. We found that this linear variation of the dispersion oscillating fiber parameters may provide different novel mechanisms for the splitting of the resonance sideband spectrum, owing to coherent interference between quasi-resonant waves that are generated at different points along the fiber. (C) 2015 Elsevier B.V. All rights reserved.
Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics
2014
International audience; The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. W…
Energy and frequency dependence of the alpha particle redistribution produced by internal kink modes
2014
International audience; The redistribution of alpha particles due to internal kink modes is studied. The exact particle trajectories in the total fields, equilibrium plus perturbation, are calculated. The equilibrium has circular cross section and the plasma parameters are similar to those expected in ITER. The alpha particles are initially distributed according to a slowing down distribution function and have energies between 18 keV and 3.5 MeV. The (1, 1), (2, 2), and (2, 1) modes are included and the effect of changing their amplitude and frequency is studied. When only the (1, 1) mode is included, the spreading of high energy ( E≳1 MeV) alpha particles increases slowly with the energy …
Operation conditions and stability of a degenerate two-photon laser
1993
Abstract The presence of a far off-resonant intermediate level in a degenerate three-level two-photon laser model manifests through a steady pump-dependent and a dynamic frequency shift on the laser equations. The steady shift strongly affects the pump threshold necessary for emission, preventing it in certain cases. The dynamic shift makes the frequency pulling/pushing to be intensity-dependent and substantially modify the domains of existence and stability of the lasing solution permitting stable operation for large cavity losses in certain cases.
Experimental observation of the generation of cutoff solitons in a discreteLCnonlinear electrical line
2014
We address the problem of supratransmission of waves in a discrete nonlinear system, driven at one end by a periodic excitation at a frequency lying above the phonon band edge. In an experimental electrical transmission line made of 200 inductance-capacitance LC cells, we establish the existence of a voltage threshold for a supratransmission enabling the generation and propagation of cut-off solitons within the line. The decisive role of modulational instability in the onset and development of the process of generation of cut-off solitons is clearly highlighted. The phenomenon of dissipation is identified as being particularly harmful for the soliton generation, but we show that its impact …
Chaotic-like behavior of modulated waves in a nonlinear discrete LC transmission line
2003
International audience; Modulational instability (MI) in a discrete nonlinear LC transmission line is investigated. The higher order nonlinear Schrodinger (NLS) equation modeling modulated waves propagation in the network allows to predict the MI conditions, with additional features, compared to the standard NLS model. More precisely, a chaotic-like behavior of the system, which is observed in a particular frequency domain, is related to the nonrepeatability of the numerical experiments.
Polarization instability in anisotropic-cavity degenerate four-wave mixing
2000
Abstract The emission and stability properties of a plane-wave model of intracavity degenerate four-wave mixing including self- and cross-phase modulation are studied. A Kerr medium inside an anisotropic cavity in which a linearly polarized field is injected is considered. Cavity anisotropy leads to qualitative new phenomena such as a subcritical polarization instability.
Modulation instability scenario in negative index materials
2010
We present an investigation of the critical frequency windows permitting modulation instability in negative index materials. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective dispersive magnetic permeability in addition to the effective dielectric permittivity determining the propagation model for ultrashort pulses in negative index materials. We emphasize the influence of nonlinear dispersion terms, arising out of the combinatorial effect of the dispersive permeability with the nonlinear polarization, over the MI phenomena, the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has be…