THE CLASSICAL PARAMETRIC APPROXIMATION FOR 3-WAVE INTERACTIONS

We study sufficient conditions for the applicability of the classical parametric approximation in three-wave interactions when the pump inte nsity is very large compared to signal and idler intensity. To derive such conditions we express the exact classical solutions given by Jaco bian elliptic functions in terms of hyperbolic functions. Thereby the first minimum of the pump intensity is correctly described but the per iodicity is lost. We derive new approximations for the initial conditi ons using pump coordinate scaling and find the interval that defines c omplete pump depletion. We show that the classical parametric approxim ation with a fixed and sharp pump amplitude and phase can be used for an increasing fraction of this interval if the pump intensity is made to grow. By choosing higher and higher pump intensities the nonlineari ty is shifted to the end of that interval. As an instructive example f or the application of these findings the generation of two-mode squeez ing is briefly considered. (C) 1998 Elsevier Science B.V. All rights r eserved.