Brillouin-scattering cross sections of off-axis phonons in CdS

Abstract

Incorporating the rotational contribution to the direct photoelastic effect and the angular deviation of the Poynting vector from the wave vector of the diffracted light a Brillouin-scattering theory, valid for a general anisotropic scattering kinematics in a hexagonal crystal, is derived. From the basic theory Brillouin-scattering cross sections of off-axis pure transverse ($T_1$), quasitransverse ($T_2$), and quasilongitudinal ($L$) phonons are calculated in the cases where the optic axis lies in the scattering plane and the incident light is polarized either parallel or perpendicular to this plane. The frequency dependence and the angular dependence of the cross section for visible light (${\lambda }_0=6328\mathrm{}$ Å) in CdS are evaluated for a number of important cases. The main emphasis of the numerical calculations is devoted to the $T_1$ mode for which the scattering cross section has one, two, or four branches. For certain scattering geometries the cross section equals zero for selected phonon frequencies and off-axis angles. It is shown that an experimental determination of the relative signs of the symmetric photoelastic tensor components conveniently can be based on a localization of the zeros for the $L$-phonon scattering cross section. The formulas derived in the present paper are very useful for an analysis of the frequency spectrum and the angular distribution of the phonons in acoustoelectrically active or inactive off-axis domains in hexagonal crystals like CdS and ZnO.