Macroscopic theory of dielectric solids. II. The theory of Brillouin scattering from rare gas crystals

We extend the macroscopic theory of dielectric solids to include the description of the Brillouin scattering of light by deriving expressions for the dielectric constant in the absence of strains, and for the Pockels elasto-optic coefficients, from a microscopic model appropriate for the rare gas crystals. The constituent atoms are regarded as polarizable particles coupled by the dipole–dipole interaction, which we treat by introducing the usual microscopic effective electric field, and by the short-range higher multipole and Vander Waals interactions, which are included in the microscopic model by associating with each atom an effective polarizability that depends on the distance between the atom and its nearest neighbors. We define the macroscopic fields by space averaging over volume elements of linear dimensions Δ satisfying a [Formula: see text], where a is the interatomic spacing and λ the wavelength in vacuo; using a new theorem relating the microscopic effective electric field and macroscopic electric and polarization fields, we are able to derive a constitutive relation, involving the strain tensor, from our microscopic model. While the largest contribution to the Pockels coefficients appearing in this relation is due to variations in the dielectric tensor that result from deviations of the macroscopic density from its value in the absence of strains, we find that two other contributions appear because strain fields affect the dielectric tensor by changing both the local field and the values of the effective polarizabilities. If the short-range interactions are neglected, our theory leads to the same ratios of Pockels coefficients obtained from the microscopic scattering theory of Werthamer (when an error in that theory is corrected), but the values of the Pockels coefficients we obtain contain a local field correction, which the microscopic scattering theory does not take into account. The contribution of the short-range interactions to the Pockels coefficients is estimated by obtaining values of the effective polarizabilities from calculations of the polarizabilities of pairs of rare-gas atoms; we find that the contribution is non-negligible and thus demonstrate that new information on these short-range interactions can be obtained from the results of Brillouin scattering experiments.