Asymptotic of the Green function for the diffraction by a perfectly conducting plane perturbed by a sub-wavelength rectangular cavity

Abstract

Rapport de recherche. A paraitre dans MMASInternational audienceThis work is aimed at understanding the amplification and confinement of electromagnetic fields in open sub-wavelength metallic cavities. We present a theoretical study of the electromagnetic diffraction by a perfectly conducting planar interface, which contains a sub-wavelength rectangular cavity. We derive a rigorous asymptotic of the Green function associated with the Helmholtz operator when the width of the cavity shrinks to zero. We show that the limiting Green function is that of a perfectly conducting plane with a dipole in place of the cavity. We give an explicit description of the effective dipole in terms of the wavelength and of the geometry of the cavity

Enhancement of Electromagnetic Fields Caused by Interacting Subwavelength Cavities

“…The limiting Green function turns out to be that of an infinite half plane on which a dipole is placed. The present paper extends the analysis of [8] to two sub-wavelength cavities separated by a sub-wavelength distance, and studies the interaction between the cavities. Let us briefly summarize our analysis and the main results.…”

“…Experimental results suggest that the amplification factors of the fields depend on the width of the cavities. In [8], the case of a half plane containing a single cavity of width w was considered. The authors studied the asymptotic of the Green function as w tends to zero using techniques based on integral representation [3,18,10], which are well adapted to such geometry.…”

“…Let us briefly summarize our analysis and the main results. Due to geometrical considerations and to the choice of a time harmonic incident field [5,8], the scattering problem can be reduced to a Helmholtz equation. Using the Green formula we reformulate the Helmholtz equation as a system of integral equations (2.11)-(2.12) defined on the aperture of the two cavities, for the normal derivatives of the solution u.…”

A Survey of Open Cavity Scattering Problems

“…In the TE polarization, the open cavity scattering problem can be reduced to the following boundary value problem: 14) which has the variational formulation: Find u ∈ H 1 (Ω) such that 15) where the sesquilinear form…”

“…Related optimal design problems can be found in [8][9][10], which was to design the shape of the cavity so as to minimize the RCS. We also refer to [5,15] for the study on the electromagnetic field enhancement by interacting subwavelength cavities.…”