Symmetries and modes of wave fields in inhomogeneous media

In this paper the 2D Helmholtz equation with space-dependent dielectric per mittivity and/or magnetic permeability is considered. The structure of the determining equations for the symmetry generator is analysed. It allows one to End many nontrivial spatial profiles of dielectric functions for which one can still separate variables in both the Helmholtz equation and corresp onding Hamilton-Jacobi equation. For the case of the Dirichlet problem of t he half-plane in an inhomogeneous medium the diffractive modes of the held are characterized. Several specific examples are provided.