WIAS Preprint No. 2355, (2016)

Scattering of general incident beams by diffraction gratings


  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78A45 78A40 65D30


  • diffraction, periodic structure, beam incidence, adaptive algorithm, cubature




The paper is devoted to the electromagnetic scattering of arbitrary time-harmonic fields by periodic structures. The Floquet-Fourier transform converts the full space Maxwell problem to a two-parameter family of diffraction problems with quasiperiodic incidence waves, for which conventional grating methods become applicable. The inverse transform is given by integrating with respect to the parameters over a infinite strip in ℝ². For the computation of the scattered fields we propose an algorithm, which extends known adaptive methods for the approximate calculation of multiple integrals. The novel adaptive approach provides autonomously the expansion of the incident field into quasiperiodic waves in order to approximate the scattered fields within a prescribed error tolerance. Some application examples are numerically examined.

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