On the application of the Sommerfeld representation in a two-dimensional rotationally invariant anisotropic medium

A.J.W. Sommerfeld´s (1959) bundle of rays field representation is applied in a fictitious two-dimensional isotropic space that is mapped into a real rotationally invariant anisotropic region via a polarization-dependent coordinate transformation selected so as to obtain a field solution in the anisotropic region. Two elementary transformations are found, and the resulting representations (in the form of a modal angular spectrum or in terms of nonperiodic anisotropic ray bundles of complex trajectories) are analyzed. Field singularities are encountered and discussed in the context of their relation to the isotropic space rays. As an application, the solution to the canonical scattering problem of an anisotropically coated (ten material parameters, five for each polarization) circular cylinder is presented. Only H polarization is treated explicitly since the other (E) is obtainable via duality