Surface shear horizontal waves associated with a periodic array of wires deposited on a substrate

The vibrational and electronic spectra of a semi-infinite crystal with a pl anar surface are modified by the presence of surface inhomogeneities or rou ghness such as ridges or grooves, quantum wires or tips. We develop a Green 's function formalism to investigate the localized and resonant acoustic mo des of shear horizontal polarization associated with the surface of a subst rate supporting a single and a periodic array of wires. Each material is as sumed to be an isotropic elastic medium. The calculation can be applied to an arbitrary choice of the shape and elastic parameters of the wires. The s urface modes are obtained as well-defined peaks of the densities of states (DOS). In this paper, we calculate the variation of the density of states a ssociated with the adsorption of a single wire, and the dispersion curves o f the surface modes for a periodic array of wires on the flat surface of a substrate. We discuss their behaviors as a function of the elastic paramete rs and the relationship between resonant modes of the single wire and dispe rsion curves of the surface modes for a periodic structure.