Effect of damping on nonlinear three−wave interaction

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Abstract
We examine the nonlinear evolution of three coherent positive energy waves interacting resonantly in a homogeneous lossy medium. Assuming that only the low−frequency wave is appreciably damped, we establish a necessary and sufficient condition for unidirectional energy transfer from the pump to the two other waves in terms of a critical damping factor. We then find asymptotic solutions and solutions in the weakly and strongly damped regimes. Also, we examine the pump wave depletion time as a function of the damping rate and initial pump wave intensity.