Disorder-induced resonance coupling of waves

General properties of a stochastic interaction between acoustic waves with a gapless spectrum and optic waves, the spectrum of which has a gap, are investigated in the region where their dispersion curves cross. The coupling parameter of these waves is considered as a random spatial zero-mean-value function with root-mean-square value λ and correlation radius ${\mathit{r}}_{\mathit{c}}$. This model only admits an interaction between the coherent waves and their scattered counterparts. It is shown that stochastic interaction leads to both dynamic and relaxation effects. The former are proportional to λ and promote degeneration removal and repulsion of the dispersion curves Δ at the crossing point, while the latter are proportional to ${\mathit{r}}_{\mathit{c}}^{\mathrm{-}1}$ and hinder this phenomenon. The values of Δ are different for the cases of coherent acoustic and optic waves. In the vicinity of the resonance point the relative stabilization of the fluctuation waves takes place due to the formation of long-living coupled states of the coherent and scattered waves.