Enhancement of electromagnetic fields caused by interacting subwavelength cavities

Jean-François Babadjian (1) , Eric Bonnetier (2) , Faouzi Triki (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 EDP - Equations aux Dérivées Partielles

This article is devoted to the asymptotic analysis of the electromagnetic elds scattered by a perfectly conducting plane containing two sub-wavelength rectangular cavities. The problem is formulated through an integral equation, and a spectral analysis of the integral operator is performed. Using the generalized Rouché theorem on operator valued functions, it is possible to localize two types of resonances, symmetric and anti-symmetric, in a neighborhood of each zero of some explicit function, associated to the limiting geometry. For the symmetric modes, the elds in the cavities interact in phase, and the system of two cavities essentially acts as a dipole. In the anti-symmetric case, the fields oscillate in anti-phase, and the system behaves like a quadripole. Asymptotic expansions of the resonances, the far-eld and the near-eld are given.

Mots clés: Resonances; Generalized Rouché theorem; Integral operator; Asymptotic expansion

Domaines: Analyse numérique [cs.NA]; Equations aux dérivées partielles [math.AP]

Jean-François Babadjian, Eric Bonnetier, Faouzi Triki. Enhancement of electromagnetic fields caused by interacting subwavelength cavities. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2010, 8 (4), pp.1383-1418. ⟨10.1137/100787659⟩. ⟨hal-00463102⟩