Abstract
We investigate the existence and behavior of localized and resonant acoustic modes of sagittal polarization associated with the interface between an isotropic medium and a superlattice, consisting of alternating isotropic layers of two materials. These modes appear as well-defined peaks in the density of states. The local and total densities of states are obtained from an analytical determination of the Green function for the superlattice/substrate system. The reflection coefficients in the substrate are also derived and compared to the density of states. We show that the existence and dispersion of interface modes are dependent upon the relative parameters of the substrate and the superlattice, but also upon the nature of the film in the superlattice, which is in contact with the substrate.
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