Weakly localized waves on the corrugated surface of a medium of arbitrary anisotropy

Abstract

The existence of weakly localized surface and pseudosurface waves on the corrugated surface of a medium of arbitrary symmetry is studied. The localized solution originates from an exceptional bulk wave associated with a transonic state of positive or negative curvature. It is shown that the period of corrugation or the frequency of the wave can universally be chosen such that the solution will exist. The range of permissible periods (frequencies) is different for positive and negative curvature transonic states, it being wider near transonic states of positive curvature. The imaginary component of the pseudosurface wave velocity is found to vary as the height of grooves to period of corrugation ratio raised in fourth or sixth power, depending on the transonic state with which the exceptional wave is associated. A simple analytical expression is derived allowing estimations to be made of the penetration depth and the velocity of the localized wave.