Dispersion and attenuation of surface shear acoustic waves with horizontal polarization on the free statistically rough surface of the hexagonal crystal

Expressions for dispersion of the phase velocity and inverse damping depth of surface acoustic waves with shear horizontal polarization are derived in an analytical form within perturbation theory using the modified mean-field method for the Z-cut hexagonal crystal with a free statically rough surface. Both two-and one-dimensionally rough surfaces are considered. The one-dimensionally rough surface is considered as a special case of the two-dimensionally rough surface. It is shown that shear surface waves with horizontal polarization cannot exist on the flat surface of the Z-cut hexagonal crystal. The derived expressions are studied analytically and numerically in the entire frequency range accessible in perturbation theory. The long-wavelength limit (most interesting from the experimental point of view) is considered, where the wavelength is much longer than the roughness correlation radius. The conditions for the existence of SH-polarized waves are determined for both roughness types. It is shown that dispersion and attenuation of SH polarized waves are qualitatively similar in character to those we considered previously for an isotropic medium.