WIAS Preprint No. 1980, (2014)

An integral equation approach for electromagnetic scattering by biperiodic structures


  • Bugert, Beatrice

2010 Mathematics Subject Classification

  • 31B10 35Q60 35Q61 45A05 78A45


  • biperiodic scattering problems, Maxwell's equations, boundary integral equations, Lipschitz domains




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.

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