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Author: Bugert, Beatrice × Subject: Lipschitz domains ×

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    Analytical investigation of an integral equation method for electromagnetic scattering by biperiodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bugert, Beatrice; Schmidt, Gunther
    This paper is concerned with the study of a new integral equation formulation for electromagnetic scattering by a 2π-biperiodic polyhedral Lipschitz profile. Using a combined potential ansatz, we derive a singular integral equation with Fredholm operator of index zero from time-harmonic Maxwell's equations and prove its equivalence to the electromagnetic scattering problem. Moreover, under certain assumptions on the electric permittivity and the magnetic permeability, we obtain existence and uniqueness results in the special case that the grating is smooth and, under more restrictive assumptions, in the case that the grating is of polyhedral Lipschitz regularity.
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    An integral equation approach for electromagnetic scattering by biperiodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Bugert, Beatrice
    The objective of this paper is the analytical investigation of an integral equation formulation for electromagnetic scattering by 2π-biperiodic multilayered structures with polyhedral Lipschitz regular interfaces. Extending the combined potential ansatz from Preprint No. 1882 for the electric fields in the before mentioned electromagnetic scattering problem from single to N profile scattering yields an equivalent system of N integral equations. We present a uniqueness and two existence results for this system depending on the values of the electromagnetic material parameters of the considered biperiodic scatterer. This in particular includes the proof that the system of integral equations is of zero Fredholm index. The general case that the grating interfaces are of polyhedral Lipschitz regularity requires more strict assumptions than the special case of smooth grating interfaces. We exploit the solvability results of this work in a subsequent paper featuring a recursive integral equation algorithm for the 2π-biperiodic multilayered electromagnetic scattering problem.