Volume 79, Number 6, September 2007
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||21 August 2007|
Thermalization of the dispersive three-wave interaction
CNRS-Institut Carnot de Bourgogne, UMR 5209 - Dijon, France
Accepted: 27 July 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.
PACS: 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
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