WIAS Preprint No. 1601, (2011)

Conical diffraction by multilayer gratings: A recursive integral equations approach


  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78A45 78M15 45E05 35J05


  • Diffraction, periodic structure, multilayer grating, singular integral formulation, recursive algorithm




In this paper we consider an integral equation algorithm to study the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in $R^2$ coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with an arbitrary number of material layers we present the extension of a recursive procedure developed by Maystre for normal incidence, which transforms the problem to a sequence of equations with $2 times 2$ operator matrices on each interface. Necessary and sufficient conditions for the applicability of the algorithm are derived.

Appeared in

  • Appl. Math., 58 (2013) pp. 279--307.

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