On the homogenization of bulk and sheet metamaterials

A metamaterial is an artificial structure with dielectric or metallic inclusions periodically or randomly distributed in a host matrix. The interest in the metamaterial concept resides fundamentally in the fact that it potentially allows molding of the electrodynamics of the structure, and in this way may help improving the performance of a number of devices. The paper discusses the difference between the homogenization of bulk metamaterial and a thin metamaterial slab, and shows that in some cases it is possible to characterize how a complex surface interacts with radiation directly from knowledge of the effective parameters of the bulk material. To this end, we propose an analytical formalism that is adequate to characterize the scattering from plane waves by a metamaterial slab, provided the bulk effective parameters are known or can be computed numerically. In order to illustrate the application of the results, we homogenize a crossed wire mesh "surface". We obtained an excellent agreement between our method and full wave simulations. The method can be used to homogenize slabs of arbitrary thickness.