Comptes Rendus
no. 7
Équations aux dérivées partielles, Analyse numérique
Electromagnetic shielding by thin periodic structures and the Faraday cage effect
[Blindage électromagnétique par des structures fines et périodiques]
Bérangère Delourme1  ; David P. Hewett2
1 Université Sorbonne Paris Nord, Laboratoire Analyse Géométrie et Applications (UMR 7539), 93430 Villetaneuse, France
2 Department of Mathematics, University College London, London, United Kingdom
Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 777-784.

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.

Dans cette note, nous nous intéressons à la diffraction des ondes électromagnétiques (équations de Maxwell en régime harmonique) par une nappe perforée plane constituée de petit obstacles parfaitement conducteurs placée à l’interface entre deux milieux homogènes. La taille des obstacles et la distance séparant deux obstacles consécutifs sont du même ordre de grandeur δ, δ supposé petit. En étudiant trois configurations modèles ((i) obstacles « discrets », (ii) fils parallèles, (iii) maillage constitué de deux nappes de fils parallèles), nous montrons que la limite de la solution quand δ tend vers 0 dépend de la forme des obstacles constituant la nappe périodique, le phénomène de «  cage de Faraday » n’apparaissant que dans le cas du maillage de fils.

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Révisé le :
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DOI : 10.5802/crmath.59

Bérangère Delourme 1 ; David P. Hewett 2

1 Université Sorbonne Paris Nord, Laboratoire Analyse Géométrie et Applications (UMR 7539), 93430 Villetaneuse, France
2 Department of Mathematics, University College London, London, United Kingdom
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Electromagnetic shielding by thin periodic structures and the {Faraday} cage effect},
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Bérangère Delourme; David P. Hewett. Electromagnetic shielding by thin periodic structures and the Faraday cage effect. Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 777-784. doi : 10.5802/crmath.59. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.59/

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