Acoustic Green function for superlattices

Abstract

Classical response function theory is employed for the derivation of the displacement-gradient Green functions of a two-component superlattice. In particular, an exact result is derived for the Green function associated with acoustic waves whose wavevectors are perpendicular to the layers of the superlattice. This is shown to yield correct results for various known limiting cases. The characteristic spectrum includes contributions appropriate for the two bulk homogeneous samples plus multiple contributions. The latter follow a dispersion relation first derived by Rytov (1956), and arise from the folding of the Brillouin zone due to the macroscopic periodicity of the superlattice. The results are then discussed with reference to the GaAs-Ga_1-xAl_xAs superlattice for the case of small concentration parameter x. Explicit expressions are derived for this system in the case of equal thicknesses anticipating the application of the theory to light scattering by such superlattices.