Parametric interaction of waves in a randomly nonhomogeneous dissipative medium

The steady-state parametric interaction of three plane waves in an absorbing medium containing random inhomogeneities is investigated in order to extend to absorbing media the results of Abramovich and Tamoikin's (1980) study of the effect of fluctuations of a medium's dielectric constant on parametric wave decay and coalescence. Exact solutions for the mean intensities of the interacting waves are found, with the frequency dependence of the absorption factor taken into account. For parametric decay, an exact expression for the threshold pump intensity is obtained, and the dependence of the decay instability threshold on the level of the fluctuations is determined. It is shown that in a strongly inhomogeneous medium where multiple scattering is substantial, the rate of change in the mean wave intensities may be altered considerably when even a small amount of absorption is present.