The problem of scattering of a time-harmonic electromagnetic wave by a perfectly conducting elliptic cylinder embedded in a uniaxially anisotropic medium is being investigated. The optical axis of the medium is assumed perpendicular to the cylinder’s generating line, and the electromagnetic sources are assumed parallel to it, giving rise to a two dimensional problem. Magnetic current line sources radiate E modes, for which a boundary value problem is formulated. A method described by Felsen is utilized to transform this boundary value problem to the familiar Helmholtz equation with a Neumann boundary condition. The solution is found and expanded for the long wave (or small obstacle) range, and interpreted in simple physical terms. The leading terms of the scattered field correspond to radiation by equivalent multipole sources. It is shown that the strength of these sources depends on the orientation of the scatterer with respect to the optical axis, and on the ray refractive index of the medium. If the uniaxial medium represents an ionized gas in a strong magnetic field, some elements of the dielectric tensor may be negative or complex. Our results are shown to remain valid in this case.
BENJAMIN RULF, "Electromagnetic Scattering by an Elliptic Cylinder Embedded in a Uniaxially Anisotropic Medium," J. Opt. Soc. Am. 56, 595-601 (1966)