Abstract
We study the interaction of three modes in χ (2) media in the classical as well as in the quantum picture. We show that it is possible to distinguish two basic forms of phase-space motion depending on the value of the integral of motion Γ in the classical formulation or the (initial) mean value of the interaction Hamiltonian in the quantum formulation. The quantum and classical pictures are compared using a simulation of the Husimi Q function via classical trajectories for an ensemble of phase-space points. The very good correspondence between the two pictures is shown to last for a significant interaction time and can be investigated for arbitrary initial intensities.
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