WIAS Preprint No. 1296, (2008)

Integral equations for conical diffraction by coated gratings


  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 35Q60 31A10, 35J05, 35K50, 45F15, 78A45


  • Diffraction, periodic structure, integral equation method, oblique incidence, system of singular integral equations




The paper is devoted to integral formulations for the scattering of plane waves by diffraction gratings under oblique incidence. For the case of coated gratings Maxwell's equations can be reduced to a system of four singular integral equations on the piecewise smooth interfaces between different materials. We study analytic properties of the integral operators for periodic diffraction problems and obtain existence and uniqueness results for solutions of the systems corresponding to electromagnetic fields with locally finite energy.

Appeared in

  • J. Integral Equations Appl., 23 (2011) pp. 71--112.

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