Surface elastic waves in superlattices: Sagittal localized and resonant modes

We investigate the existence and behavior of localized and resonant acoustic modes of sagittal polarization associated with the surface of a semi-infinite superlattice. These modes appear as well-defined peaks of the density of states, either inside the minigaps or inside the bulk bands of the superlattice. The densities of states, which are calculated as functions of the frequency {ω} and the wave vector k_∥ (parallel to the interfaces), are obtained from an analytic determination of the Green function for a semi-infinite superlattice. We show the existence of {δ} peaks of weight -1/2 at the limits of any bulk band. The conservation of the total number of states leads to the necessary existence of surface localized modes inside the gaps, but also of semilocalized modes which appear as well-defined resonances inside the bulk bands of the superlattice.