Geometrical Aspects of the Diffraction of Critically Incident Bulk Waves and Gaussian Beams

Abstract

This paper contains a study of some of the nonuniformities that can arise in the acoustic field radiated from a wavebearing boundary when it is insonified by either a bulk wave or a Gaussian beam. Particular attention is paid to cases of critical incidence for which the surface wave that can exist at the boundary is excited with maximum efficiency. By posing suitable diffraction problems local to the point of excitation of the surface wave, singular perturbation techniques are applied to establish the local structure of the total radiated field in this neighbourhood and these “inner” solutions are matched to “outer” solutions in which the various constituent waves can be unambiguously and independently identified. Doing so provides a geometrical methodology for predicting the region into which the radiation from the surface wave can penetrate. This is applied to the particular cases of bulk wave excitation of a supersonic “leaky” surface wave and of Gaussian beam insonification of a pure impedance plane. In the former case, the unusual spatial “cut-off” phenomenon is revealed and in the latter case, the lateral shifting of the geometrical axis of the recected beam is predicted. In all cases, the fine structure of the radiated fields are discussed and the many interesting diffraction effects generated by interferences between specularly reflected fields and surface wave radiation are ighlighted. Particular attention is paid to the geometrical aspects of these problems and it is shown how the solutions to the inner diffraction problems can be combined with ray theory to predict the various critical directions that arise in a natural and convenient way.