WIAS Preprint No. 1090, (2006)

On a fast integral equation method for diffraction gratings


  • Rathsfeld, Andreas
  • Schmidt, Gunther
  • Kleemann, Bernd H.

2010 Mathematics Subject Classification

  • 78M15 78A45 65R99


  • Diffraction gratings, integral equation method, preconditioning, fundamental solution




The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple cross-section curves are considered. This method in its recent version is capable to tackle profile curves with corners, gratings with thin coated layers, and diffraction scenarios with unfavorably large ratios period over wavelength. We discuss special implementational issues including the efficient evaluation of the quasi-periodic Green kernels, the quadrature algorithm, and the iterative solution of the arising systems of linear equations. Finally, as application we present the simulation of coated echelle gratings which demonstrates the efficency of our approach.

Appeared in

  • Commun. Comput. Phys., 1 (2006) pp. 984-1009.

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