Surface acoustic waves in a periodically patterned layered structure

Dispersion relations of surface acoustic modes in a supported film with periodic mass loading at the surface are calculated using the plane wave expansion method. The model captures the salient features of recent experiments on the laser excitation of surface waves in periodically patterned thin film structures, such as a bandgap inside the Brillouin zone arising from the hybridization and avoided crossing of the Rayleigh and Sezawa modes. We demonstrate that the ellipticity of the particle motion in the surface waves plays an important role in determining the width of the bandgaps. In particular, bandgaps at the Brillouin zone boundary close completely when the surface particle motion in a given acoustic mode becomes circular. Another interesting finding is that of an isolated point within the leaky Rayleigh-Sezawa branch where the periodicity-induced attenuation vanishes.