Ionic Brillouin Effect

A theory is presented of the inelastic scattering of monochromatic infrared radiation by the long-wavelength acoustic vibration modes of an arbitrary crystal possessing infrared-active optical modes. Central to the theory is a lattice-dynamical calculation of the ionic contribution to the photoelastic constants of a crystal, i.e., the fourth-rank-tensor coefficients which relate the change in the dielectric tensor to the parameters describing a homogeneous deformation of the crystal. The results of this calculation show that the photoelastic tensor is not symmetric in the second pair of indices, in general, in agreement with recent predictions of Nelson and Lax. The general expression for the ionic contribution to the photoelastic tensor has a resonant character for frequencies of the incident light close to the frequencies of the infrared-active optical modes of the crystal. This general expression is specialized to the case of diatomic cubic crystals, and the magnitude of the ionic contribution to the photoelastic constants is estimated for GaAs and KCl on the basis of simple lattice-dynamical models. From these results the scattering efficiencies for these two crystals are determined. It is found for each of these crystals that the integrated scattering efficiency for Stokes (or anti-Stokes) scattering exceeds ${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ ${\mathrm{sr}}^{-1\mathrm{}}$ for frequencies of the incident light within 5% of the frequency of the transverse-optical mode.