Electromagnetic shielding by thin periodic structures and the Faraday cage effect
Résumé
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 $\delta$. 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 $\delta\to0$ 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.
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