Electromagnetic and optical behavior of two classes of dielectric lenses

Two families of spherically symmetric dielectric lenses are considered. Their optical properties are studied, and the radial eigenfunctions describing the electromagnetic field inside the lenses are found in terms of hypergeometric functions. Among the members of these two families are the Luneburg lens, the Maxwell fisheye, the isotropic lens of Eaton, and a lens that behaves like a metal reflector.