Wave Scattering from Infinite Penetrable Layers.
Armin Lechleiter

Abstract: We consider scattering of time-harmonic electromagnetic waves from an unbounded penetrable dielectric layer mounted on a perfectly conducting infinite plate. This model describes for instance propagation of monochromatic light through dielectric photonic assemblies mounted on a metal plate.

For the E- or H-mode the problem boils down to a scalar problem that can be solved variationally by Rellich identities. Already for these scalar problems, the Rellich identities introduce non-trapping conditions on the unbounded penetrable layer. For the full electromagnetic problem, the variational formulation of the problem in a suitable Sobolev space shows to be involved, since the radiation condition introduces singular weights on the artificial boundary. Again, Rellich identities show to be useful to obtain a-priori bounds on a solution to the problem and a limiting absorption argument implies existence of a solution to the problem.