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Volume 1, Issue 6
On a Fast Integral Equation Method for Diffraction Gratings

A. Rathsfeld, G. Schmidt & B. H. Kleemann

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

Published online: 2006-01

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  • 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 efficiency of our approach.

  • Keywords

Diffraction gratings integral equation method preconditioning.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-1-984, author = {A. Rathsfeld, G. Schmidt and B. H. Kleemann}, title = {On a Fast Integral Equation Method for Diffraction Gratings}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {6}, pages = {984--1009}, 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 efficiency of our approach.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7991.html} }
TY - JOUR T1 - On a Fast Integral Equation Method for Diffraction Gratings AU - A. Rathsfeld, G. Schmidt & B. H. Kleemann JO - Communications in Computational Physics VL - 6 SP - 984 EP - 1009 PY - 2006 DA - 2006/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7991.html KW - Diffraction gratings KW - integral equation method KW - preconditioning. AB -

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 efficiency of our approach.

A. Rathsfeld, G. Schmidt and B. H. Kleemann. (2006). On a Fast Integral Equation Method for Diffraction Gratings. Communications in Computational Physics. 1 (6). 984-1009. doi:
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