Martine Le Berre

Kinetics of domain walls in the degenerate optical parametric oscillator

The kinetics of the domain walls that occur in the degenerate optical parametric oscillator are studied within the propagation model. The formation of large intensity peaks for null and positive signal mistuning is shown to be associated with a dynamical scaling law ~t1/3. In the parameter range where the degenerate optical parametric operator reduces to potential systems, the growth law ~t1/2 is observed. It is also obtained for negative mistuning of order unity, and up to three times above the threshold, i.e.?beyond the validity range of the Swift-Hohenberg model equation. In addition, we describe the labyrinth formation which displays self-similar growth with the law ~t1/5.

Role of the phase mismatch on the structures generated in an optical parametric oscillator

The effects of the phase mismatch are analysed within the propagation model for the degenerate optical parametric oscillator (DOPO). The transverse structures generated via a modulational instability are found to be strongly dependent on the mistuning of the signal and the phase mismatch. Islands of squares, quasi-hexagons and zigzags are found to emerge from a sea of stripes, in the plane defined by the two mistunings.

Gain and reflectivity characteristics of self-oscillations in self- feedback and delayed feedback devices

Abstract In counterpropagating waves devices, multiwave mixing involves gain and reflectivity properties for the forward and the backward probes and idlers that are shown to be related to both gain and reflectivity of the intrinsic system without any mirror. In the later case, gain and reflectivity of a probe field are shown to vary strongly with the angular frequency of the probe; actually the reflectivity is especially depending on whether it is associated with a convective instability or an absolute instability, vanishing in the first case but diverging in the second case. The occurrence of a self-oscillation at a given frequency in either a half-cavity device or a Fabry-Perot interferometer is demonstrated to depend not only on the gain that such a probe would realize through the system without mirrors but also on its reflectivity properties at the cell exit. For example the self-oscillation in a Fabry-Perot interferometer occurs in the Rabi frequency domain not because a probe might be strongly amplified, as usually stated, but because its reflectivity at the cell exit has to be negligible. Differently, the half-cavity device chooses its own threshold frequency for the self-oscillation to occur where the probe reflectivity matrix has elements of magnitude of order unit, irrespective of its gain. In both cases the behaviour is seen to be a consequence of the boundary conditions imposed by the optics.

Turbulence: Does Energy Cascade Exist?

To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These tests are applied to real Eulerian data of a turbulent velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype model equation for wave turbulence. First we demonstrate the irreversible character of the flow by using multi-time correlation function at a given point of space. Moreover the unexpected behavior of the test function leads us to connect irreversibility and finite time singularities (intermittency). Secondly we show that turbulent cascade exists, and is a dynamical process, by using a test function depending on time and frequency. The cascade shows up only in the inertial domain where the kinetic energy is transferred more rapidly (on average) from the wavenumber

Supernovae: An example of complexity in the physics of compressible fluids

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Wave-breaking and generic singularities of nonlinear hyperbolic equations

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Chaos dans des systmes optiques raction retarde

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