Propagation of surface acoustic waves across random gratings

The propagation of surface acoustic waves of sagittal and of shear horizontal polarization across the grooves of a random grating is investigated theoretically. It is found that the attenuation rate of a sagittally polarized surface acoustic wave in the long-wavelength limit is proportional to (ka)⁴, where k is the wave vector of the wave and a is the transverse correlation length of the surface roughness. This is in contrast with the (ka)⁵ dependence of the attenuation rate found in this limit for sagitally polarized surface acoustic waves propagating across a two-dimensional, randomly rough surface. The dominant contribution to the attenuation rate of such a surface acoustic wave comes from its scattering into bulk waves. The attenuation rate of surface acoustic waves of shear horizontal polarization is found to be proportional to (ka)⁵ in the long-wavelength limit. The surface roughness gives rise to the wave slowing of surface acoustic waves of both polarizations.