Explicit solutions of the four-wave mixing model

DOI10.1088/1751-8113/42/19/192003zbMATH Open1165.78315arXiv0903.5476OpenAlexW3124747819MaRDI QIDQ3630092

Svetlana Bugaychuk, Robert Conte

Publication date: 2 June 2009

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: The dynamical degenerate four-wave mixing is studied analytically in detail. By removing the unessential freedom, we first characterize this system by a lower-dimensional closed subsystem of a deformed Maxwell-Bloch type, involving only three physical variables: the intensity pattern, the dynamical grating amplitude, the relative net gain. We then classify by the Painleve' test all the cases when singlevalued solutions may exist, according to the two essential parameters of the system: the real relaxation time tau, the complex response constant gamma. In addition to the stationary case, the only two integrable cases occur for a purely nonlocal response (Real(gamma)=0), these are the complex unpumped Maxwell-Bloch system and another one, which is explicitly integrated with elliptic functions. For a generic response (Re(gamma) not=0), we display strong similarities with the cubic complex Ginzburg-Landau equation.

Full work available at URL: https://arxiv.org/abs/0903.5476

Mathematics Subject Classification ID

Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (2)

ANALYTIC STRUCTURE OF THE FOUR-WAVE MIXING MODEL IN PHOTOREACTIVE MATERIAL ⋮ Four-wave interaction equations: Hamiltonian formulation, conservation laws and the Hirota method

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