Synthesizing metamaterials with angularly independent effective medium properties based on an anisotropic parameter retrieval technique coupled with a genetic algorithm

In this paper, we present a method to retrieve the effective electromagnetic parameters of a slab of anisotropic metamaterial from reflection and transmission coefficients (or scattering parameters). In this retrieval method, calculated or measured scattering parameters are employed for plane waves incident obliquely on a metamaterial slab at different angles. Useful analytical expressions are derived for extracting the homogeneous anisotropic medium parameters of a metamaterial. To validate the method, the effective permittivity and permeability tensor parameters for a composite split-ring resonator-wire array are retrieved and shown to be consistent with observations previously reported in the literature. This retrieval method is further incorporated into a genetic algorithm (GA) to synthesize an infrared zero-index-metamaterial with a wide field-of-view, demonstrating the utility of the new design approach. The anisotropic parameter retrieval algorithm, when combined with a robust optimizer such as GA, can provide a powerful design tool for exploiting the anisotropic properties in metamaterials to achieve specific angle dependant or independent responses.