Electromagnetic Wave Scattering from Rough Penetrable Layers

Houssem Haddar 1 Armin Lechleiter 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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. We give a variational formulation for the electromagnetic scattering problem in a suitable Sobolev space of functions defined in an unbounded domain containing the dielectric structure. Further, we derive a Rellich identity for a solution to the variational formulation. For simple material configurations and under suitable non-trapping and smoothness conditions, this integral identity allows to prove an a-priori estimate for such a solution. A-priori estimates for solutions to more complicated material configurations are then shown using a perturbation approach. While the estimates derived from the Rellich identity show that the electromagnetic rough surface scattering problem has at most one solution, a limiting absorption argument finally implies existence of a solution to the problem.
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Houssem Haddar, Armin Lechleiter. Electromagnetic Wave Scattering from Rough Penetrable Layers. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43, pp.2418-2443. ⟨10.1137/100783613⟩. ⟨hal-00743734⟩

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