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


On a Fast Integral Equation Method for Diffraction Gratings

A. Rathsfeld 1, G. Schmidt 1*, B. H. Kleemann 2

1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
2 Carl Zeiss AG, Corporate Research and Technology, Optical Design, 73446 Oberkochen, Germany.

Received 30 November 2005; Accepted (in revised version) 8 May 2006

Abstract

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 ratio 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 an example we present the simulation of echelle gratings which demonstrates the efficency of our approach.


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Key words: Diffraction gratings; integral equation method; preconditioning.


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Correspondence to: G. Schmidt , Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. Email: schmidt@wias-berlin.de
 

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