Analyse de la dynamique de solitons photoréfractifs

Abstract : Laser beams propagating in a photorefractive crystal create spatial solitons called photorefractive solitons, in a phenomenon labelled filamentation. Their dynamics, complex and sensitive to initial conditions, make us assume the presence of spatial chaos, as would suggest beam propagation simulations. In order to characterize this assumed chaos, we first used a Modelling Program based upon a system interpretation of solitons ; Event Conformation Method then quantized the divergence between two dynamics from near but different solitons populations. Most results showed fast decorrelations ; but the dynamics we thus characterized cannot be labelled chaotic, because of their tendency to decay. Coming back to simulations, we built statistical estimators called ?divergence strengths? quantizing the divergence between two simulations ; these estimators show to be proportional to nonlinear coefficient, a parameter of the modelled crystal. Because of an identical decay, these dynamics cannot be qualified as chaotic ; nevertheless, the high initial condition sensitiveness is on par with a chaotic system. This method was then adapted to experimental data, where time and space decorrelation has been successfully characterized thanks to an innovative concept of multicorrelation. Then, using concepts based on fractal dimensions and estimators from econometrics, we characterized the organizing of solitons dynamics, node-wise and energy redistribution-wise. Thus we concluded that despite the absence of validation of a few chaos criteria, dynamics there show strong decorrelations whose numerical characterizations display empirical resemblance to a standard chaotic system
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Marc Grün. Analyse de la dynamique de solitons photoréfractifs. Autre [cond-mat.other]. Université Paul Verlaine - Metz, 2007. Français. ⟨NNT : 2007METZ003S⟩. ⟨tel-01748971⟩

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