Existence and uniqueness in the reflection-transmission problem

The sextic Stroh formalism is applied to the analysis of reflection and transmission problems for inhomogeneous plane waves at a plane interface between viscoelastic anisotropic half-spaces. The direction of a wave is taken to be that of the time-averaged energy flux and hence compatibility of the equations for reflection and transmission coefficients is investigated. Sufficient conditions are determined for existence and uniqueness of the solution to the reflection-transmission problem. The occurrence of surface or interface waves is shown to provide either incompatibility or non-uniqueness of the solution, depending on the incident wave. The phenomenon of the Brewster angle, related to a zero reflection coefficient, is also pointed out.