Feed polarization for parallel currents in reflectors generated by conic sections

The family of surfaces of revolution obtained from conic sections are the sphere, ellipsoid, paraboloid, hyperboloid, and plane. These "conic" surfaces find various uses as reflectors in antenna systems because of their focusing or imaging properties. When any of the "conic" reflectors are used, it is of interest to specify an "ideal" polarization of the incident field such that the currents induced in the reflector flow in parallel paths. This specification will permit the reflector to be formed by parallel conducting wires or slats. This paper presents a method for determining the "ideal" feed polarization that should be incident upon a "conic" reflector. It is specified in terms of the polarization characteristics of elemental electric and magnetic dipoles. It will be shown that for any "conic" surface, the "ideal" polarization can always be specified in terms of crossed electric and magnetic dipoles whose relative intensities are related to the eccentricity of the "conic" reflector.