General Solution of the Problem of Synthesis of a Geodesic Lens with Central Symmetry and Dielectric Filling

A solution is obtained for the problem of synthesis of a metal–dielectric geodesic lens with central symmetry and, in the general case, inhomogeneous dielectric filling, which transforms the field of a point source into a given geometric optical field. By way of example using the obtained solution, the problems of synthesis of a geodesic lens antenna with layered and gradient dielectric filling are considered. In particular, solutions are obtained for lens antennas with in-phase output front and out-of-phase front that forms a tableshaped radiation pattern. The solutions are analyzed with the aid of numerical simulation using the finite element method.