Analysis of modified Luneberg lens using exact solutions

Analytical solutions have been obtained for the electromagnetic scattering by a modified Luneberg lens with the permittivity of arbitrary parabolic fu nction. They are expressed by four spherical vector wave functions for radi ally stratified medium which were introduced for the Luneberg lens by C.T.T ai. They consist of the confluent hypergeometric function and a "generalize d" confluent hypergeometric function, in which the parameters for the permi ttivity of arbitrary parabolic function are involved. The characteristics o f the modified Luneberg lens are numerically investigated using exact solut ions in comparison with that of the conventional Luneberg lens. The bistati c cross section, the forward cross section and the radar cross section are studied in detail. The near-field distribution is also investigated in orde r to study the focal properties of the Luneberg lens. The focal shifts defi ned by the distance between the geometrical focal point and the electromagn etic focal point are obtained for various ka (k is the wave number and a is the radius of the lens). The focal shift, normalized to the radius of the sphere becomes larger as Ica is smaller. However it drops down rapidly for k a < 2.5 because the power of convergence by the Luneberg lens becomes wea k when ka is small. The permittivities of a modified Luneberg lens are foun d versus ka > 5 when the peak of the electric field amplitude appears on th e surface of sphere.