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arXiv · 1908.08457

Electromagnetic wave scattering from local perturbed periodic inhomogeneous layers

Alexander Konschin
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Abstract

We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At first, we derive a variational formulation for the electromagnetic scattering problem in a suitable Sobolev space on an unbounded domain and reformulate the problem into a family of bounded domain problems using the Bloch-Floquet transform. For this family we can show the unique existence of the solution by applying a carefully designed Helmholtz decomposition. Afterwards, we split the differential operator into a coercive part and a compact perturbation and apply the Fredholm theory. Having that, the Sherman-Morrison-Woodbury formula allows to construct the solution of the whole problem handling the singularities of the Calderon operator on the boundary. Moreover, we show some regularity results of the Bloch-Floquet transformed solution w.r.t. the quasi-periodicity.

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Alexander Konschin. 2019-08-22. Electromagnetic wave scattering from local perturbed periodic inhomogeneous layers. https://arxiv.org/abs/1908.08457

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