Electromagnetic shielding by thin periodic structures and the Faraday cage effect

TL;DR

This paper analyzes how thin periodic structures of conducting obstacles influence electromagnetic wave scattering, revealing that a wire mesh uniquely produces a Faraday cage effect, with the behavior depending on the layer's topology.

Contribution

It derives homogenized interface conditions for different configurations, showing the topology-dependent emergence of the Faraday cage effect in the limit as obstacle size shrinks.

Findings

Full shielding occurs only with wire mesh topology.

Homogenized interface conditions depend on obstacle configuration.

The Faraday cage effect is topology-dependent.

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 $\delta$, $\delta$ being small. 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.