Design of a non-homogeneous wire media lens using genetic algorithms

Artificial materials, such as wire media, open the possibility of synthesizing a medium with certain desired electromagnetic properties. In the case of wire media, long thin perfect electrical conductors (PEC) are distributed periodically in a 3D lattice forming a crystal. Provided that the wavelength of radiation is much greater than the dimensions of the crystal´s basic cell, the medium behaves as an anisotropic dielectric (natural) medium. By controlling the length of the wire inclusions, we can design an anisotropic homogenous artificial medium with a prescribed effective permittivity in the z-direction. A non-homogeneous medium may be synthesized by varying the length of wires from cell to cell in the wire crystal. We present an evaluation study on the design of a lens antenna whose substrate is a non-homogeneous anisotropic medium. The design method assumes that the lens is electrically large in order that geometrical optics describes well the propagation of electromagnetic waves. Then, our objective is to compute the lens profile such that a given feed pattern is transformed by the lens into a prescribed target pattern. We propose a versatile and powerful method, based on genetic algorithms, which overcomes the drawbacks found previously when using an integral equation method (see Silveirinha, M. and Fernandes, C., AP-S Symp., vol.3, p.62, 2001).