Theory of normal-incidence Brillouin scattering by acoustic phonons in a supported thin film

Abstract

The theory of Brillouin scattering by acoustic phonons in a thin film on a substrate is investigated. Only the back scattering of normally incident light is considered. The calculations start with the evaluation of the Green functions for the displacement-gradient components of the acoustic vibrations, and proceed to the differential cross section. It is shown that for isotropic or cubic symmetry of the film and substrate, scattering is by longitudinal vibrations only. Various limiting cases are included, in particular an unsupported film and a semi-infinite medium, and the results obtained for these agree with those derived previously. A detailed discussion is given of the special case in which the scattering takes place only in the film, which is taken to be transparent. The line is broadened because of the finite thickness of the film, and the lineshape is modulated by a periodic factor which arises from partial reflection of the phonons at the film-substrate interface. The results obtained give the first full expressions for these effects.