2019/08/22 by Alexander Konschin, Konschin, Alexander
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1908.08457
openalex publication_date 2019/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.