Geodesic
Conical diffraction by multilayer gratings: A recursive integral equation approach
Applications of Mathematics, Tome 58 (2013) no. 3, pp. 279-307.

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The paper is devoted to an integral equation algorithm for studying 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 $\mathbb R^2$ 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.
DOI : 10.1007/s10492-013-0014-6
Classification : 35J05, 45E05, 78A45, 78M15
Keywords: diffraction; periodic structure; multilayer grating; singular integral formulation; recursive algorithm 
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Schmidt, Gunther. Conical diffraction by multilayer gratings: A recursive integral equation approach. Applications of Mathematics, Tome 58 (2013) no. 3, pp. 279-307. doi : 10.1007/s10492-013-0014-6. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0014-6/

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