Electromagnetic shielding by thin periodic structures and the Faraday cage effect

Abstract

In this note we consider the scattering of electromagnetic waves (governed by the time-harmonic Maxwell equations) by a thin periodic layer of perfectly conducting obstacles. The size of the obstacles and the distance between neighbouring obstacles are of the same small order of magnitude δ. By deriving homogenized interface conditions for three model configurations, namely (i) discrete obstacles, (ii) parallel wires, (iii) a wire mesh, we show that the limiting behaviour as δ → 0 depends strongly on the topology of the periodic layer, with full shielding (the so-called “Faraday cage effect”) occurring only in the case of a wire mesh.