Lenses and graded films for focusing and guiding acoustic surface waves

Two novel schemes for guiding acoustic surface waves along curved paths on isotropic substrates are described. One involves the deposition of a slowing film of graded thickness along the intended path on a dielectric substrate. Paraxial-ray equations are developed to describe the ray paths adjacent to the axis of the guiding film, which are determined by the slowing factor resulting from a variable-thickness deposited film. Diffraction is taken into account through an approximation developed by Pierce for optical beams. It is shown that very thin films are sufficient for a substantial amount of directional control. The other guidance system employs a series of lenses in analogy with the lens guides developed for millimeter waves and optical beams. Some comments are made about thin-film lenses and the theory is developed for the focusing action of a lens formed by a spherical depression in (or protrusion from) the surface of a substrate. A simple analog for determining ray paths over generally nonplanar surfaces is described and applied to nonspherical depressions to evaluate their focusing properties.