Studies on certain modified Luneberg lenses

The solution for the electromagnetic field in the presence of certain modified Luneberg lenses is obtained analytically. The permittivity profiles are selected to improve the lens directivity at low frequencies, where the lens diameter is of the order of the wavelength. For a Huygens´ source excitation their directivity, as a function of profile parameters, is computed and the degree of improvements are indicated. Radiation patterns are also computed and are compared with those of the standard Luneberg lens. To examine their performance with a practical source an open ended rectangular waveguide is then used and the computed radiation patterns are presented. In the latter case, to simplify computation, the exciting waveguide is represented by a two-dimensional Huygens´ source array.