A homogenization procedure for microstructured resistive sheets

A thin resistive sheet is described by its sheet conductance, and the electric and magnetic dipole moments per unit area. All three properties can be controlled by the material parameters and geometry of the sheet, for instance by making a periodic pattern of holes in it. A mathematical analysis of the low frequency limit of Maxwell's equations in a periodic setting generates a hierarchy of local problems which can be used to compute the conductance and electric and magnetic polarizability per unit area of the microstructured sheet. We present results from a numerical implementation of these local problems, and discuss the region of validity for the asymptotic solution.