Enhancement of Electromagnetic Fields Caused by Interacting Subwavelength Cavities

This article is devoted to the asymptotic analysis of the electromagnetic fields 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 fields 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-field and the near-field are given.