Reflection by a Concave Parabolic Mirror

The diffraction of a plane electromagnetic wave axially incident on the concave side of a perfectly conducting parabolic reflector is solved exactly and in closed form in the frequency domain. The method of solution follows the technique originally proposed by Lamb in 1906, who, however, was unable to solve the problem addressed herein. The present solution is obtained by matching the left- and right-propagating fields at the focal line of the mirror.