Nonuniform Luneburg and two-shell lens antennas: radiation characteristics and design optimization

Abstract
Design optimization of radially nonuniform spherical lens antennas is the focus of this paper. In particular, special attention is given to the optimal design of nonuniform Luneburg (1964) lens antennas. One of the important engineering objectives of designing an optimal Luneburg lens antenna is to use as small number of shells as possible while maintaining an acceptable gain and sidelobe performance. In a typical radially uniform design, by reducing the number of shells, the gain is decreased and the grating lobes are increased. This deficiency in the radiation performance of the uniform lens antenna can be overcome by designing the nonuniform lens antenna. This necessitates the optimum selection of each layer thickness and permittivity. A genetic algorithm (GA) optimizer with adaptive cost function is implemented to obtain the optimal design. In this manner, the GA optimizer simultaneously determines the optimal material and its thickness for each shell by controlling the gain and sidelobes envelope of the radiation pattern. Various lens geometries, including air gaps and feed offset from the lens surface, are analyzed by using the dyadic Green's functions of the multilayered dielectric sphere. Many useful engineering design guidelines have been suggested for the optimum construction of the lens. The results have been satisfactory and demonstrate the utility of the GA/adaptive cost-function algorithm. Additionally, the radiation characteristics of a novel two-shell lens antenna have been studied, and its performance is compared to the Luneburg lens.

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