Resonant frequencies for a narrow strip grating

Abstract

This paper deals with the existence and the distribution of the resonances associated with the Maxwell system in a periodic infinite structure, obtained by loading a substrate with a periodic perturbation. We give an integral formulation of the homogeneous diffraction problem. By boundary integral operators method, the existence and distribution of resonances is reduced to the determination of the characteristic values of two meromorphic operator valued functions. We give existence results on complex resonances close to the resonances of the substrate and also on real resonances. Copyright © 1999 John Wiley & Sons, Ltd.

Acoustic and Electromagnetic Equations

“…The above theorem is also essentially valid in an open exterior set ne in ]R2 ; but a logarithmic weight enters in the definition of the space W~,-l(ne) in that case.•We can now state Theorem 2.5 15. The exterior Neumann problem…”