Conical diffraction by multilayer gratings: a recursive integral equation approach |
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Authors: | Gunther Schmidt |
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Institution: | 1. Weierstrass Institute for Applied Mathematics and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany
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Abstract: | 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 ?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 2×2 operator matrices on each interface. Necessary and sufficient conditions for the applicability of the algorithm are derived. |
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