Thermalization of the dispersive three-wave interactionS. Lagrange, H. R. Jauslin and A. Picozzi
CNRS-Institut Carnot de Bourgogne, UMR 5209 - Dijon, France
received 21 March 2007; accepted in final form 27 July 2007; published September 2007
published online 21 August 2007
We investigate the role of dispersion effects on the long-term evolution of the nonlinear three-wave interaction. We show that the three waves exhibit, as a general rule, an irreversible evolution towards a thermodynamic equilibrium state in which they propagate with identical velocities. As a result of this thermalization process, the three-wave system is driven away from spatio-temporal resonance, so that the equilibrium state does not satisfy the (phase-matching) resonant conditions of energy and momentum conservation for the averaged frequencies. Moreover, we show that the interplay between temporal dispersion and spatial diffraction leads to the emergence of a peculiar equilibrium state characterized by an X-shaped spatio-temporal spectrum.
42.65.Sf - Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics.
05.45.-a - Nonlinear dynamics and chaos.
42.25.Kb - Coherence.
© Europhysics Letters Association 2007