Simple reflection and leaky waves in the vicinity of a line of exceptional bulk waves

Abstract

A study is made of the existence of two-component solutions of the reflection problem (simple reflection) and of leaky wave solutions in the vicinity of a line of exceptional bulk waves in a semi-infinite medium of arbitrary anisotropy. The line of exceptional waves is assumed to be associated with a Type 1 transonic state. It is found that generally one, three, and five simple reflections may appear, depending on the number of non-degenerate uniform partial modes at the transonic state. In the three-dimensional space of orientation angles specifying the geometry of the boundary-value problem, the set of configurations allowing simple reflection occupies two-dimensional surfaces. These surfaces pass through the line of exceptional waves. Leaky waves are shown to appear only near transonic states where there are two non-degenerate uniform partial modes, and their ‘geometries’ of propagation occupy two sectors confined between the surfaces of simple reflection. A criterion for the existence of leaky waves is derived. As an illustration of the general considerations, simple reflection and leaky waves in hexagonal media near the transverse isotropic direction are discussed.