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 function. They are expressed by four spherical vector wave functions for radially stratified medium which were introduced for the Luneberg lens by C.T.Tai. They consist of the confluent hypergeometric function and a "generalized" confluent hypergeometric function, in which the parameters for the permittivity of arbitrary parabolic function are involved. The characteristics of the modified Luneberg lens are numerically investigated using exact solutions in comparison with that of the conventional Luneberg lens. The bistatic cross section, the forward cross section and the radar cross section are studied in detail. The near-field distribution is also investigated in order to study the focal properties of the Luneberg lens. The focal shifts defined by the distance between the geometrical focal point and the electromagnetic 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 weak when ka is small. The permittivities of a modified Luneberg lens are found versus ka > 5 when the peak of the electric field amplitude appears on the surface of sphere.