Elastic vibrations of planar and deterministic rough surfaces

We present a few recent or new theoretical results about surface acoustic localized and resonant modes associated with planar or deterministic rough surfaces. The following composite systems are considered: one or two adlayers deposited on a semi-infinite substrate and wires or grooves integrated near a planar surface. The surface modes can be obtained as well-defined features of the density of states resulting from a calculation of the Green functions in these heterostructures. In this work, the materials are described in the framework of the elasticity theory.