WIAS Preprint No. 1882, (2013)

Analytical investigation of an integral equation method for electromagnetic scattering by biperiodic structures


  • Bugert, Beatrice
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 31B10 35Q60 35Q61 45A05 78A45


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




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.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. S, 8 (2015) pp. 435--473.

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