Homogenization of Lossy Artificial Structures with Mirror Cells

In this paper, we present a novel numerical approach for computing the quasi-static effective parameters of lossy artificial structures with mirror cells in two directions. The study is reduced to an elementary cell which is considered as a TEM rectangular waveguide. The computation of the local electromagnetic properties is realized in the cell with adequate boundary conditions using the finite element method. The effective parameters are expressed as function of macroscopic properties which are deduced from local properties. The obtained numerical results, produced by personal software, are confronted to Maxwell-Garnett mixing formula predictions and the multi-scale homogenization method.