Surface acoustic waves of sagittal and shear-horizontal polarizations on large-amplitude gratings

By numerical solution of the corresponding dispersion relations we obtain the dispersion curves for acoustic waves of sagittal and shear-horizontal polarizations propagating normally to the grooves and ridges of a large-amplitude, periodically corrugated, stress-free surface of a semi-infinite, isotropic elastic medium. In the case of a surface defined by the equation x3 = ζ0cos (2πx1/d), it is found that when the ratio ζ0/d becomes sufficiently large the dispersion curves for surface acoustic waves of both polarizations acquire new, higher frequency, branches in addition to those obtained in earlier theoretical determinations of these dispersion curves. In the case of surface acoustic waves of shear-horizontal polarization, this conclusion confirms the same result obtained recently for surface acoustic waves propagating across a lamellar grating. The present calculations are based on the Rayleigh hypothesis, and the results obtained indicate that this method can in fact be used successfully in the study of the propagation of surface acoustic waves across periodically corrugated surfaces that are significantly rougher than those to which it has been applied in the past. A possible origin of the additional branches is briefly discussed.