# Normal vector method for convergence improvement using the RCWA for crossed gratings

Schuster 2007: The normal-vector method for crossed gratings. Fourier factorization needs to know, at every point of the unit cell, which field component is…

Canonical: https://mcgrating.com/publications/schuster-2007-normal-vector-method-rcwa.html


Thomas Schuster, Johannes Ruoff, Norbert Kerwien, Stephan Rafler, Wolfgang Osten

Thomas Schuster, Johannes Ruoff, Norbert Kerwien, Stephan Rafler and Wolfgang Osten, “Normal vector method for convergence improvement using the RCWA for crossed gratings”, J. Opt. Soc. Am. A **24**, 2880 (2007). [https://doi.org/10.1364/josaa.24.002880](https://doi.org/10.1364/josaa.24.002880)

The normal-vector method for crossed gratings. Fourier factorization needs to know, at every point of the unit cell, which field component is continuous across the material boundary; a smooth field of normal vectors defined over the whole cell supplies that information for arbitrary two-dimensional shapes, and the paper shows the resulting convergence improvement for RCWA.

Modal Crossed generates this NV field automatically from the pillar geometry, and its documentation has a topic devoted to it.

**Implemented in**: [Modal Crossed](https://mcgrating.com/products.html#modal-crossed)

**Cited on**: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) · [Use of Fourier series in the analysis of discontinuous periodic structures](https://mcgrating.com/publications/li-1996-fourier-series-discontinuous.html) · [Publications](https://mcgrating.com/references.html)

**Bibliography**: [Reference [23]](https://mcgrating.com/references.html#ref-23)

**Full text**: [Normal vector method for convergence improvement using the RCWA for crossed gratings](https://mcgrating.com/references/ref23.pdf) (PDF, 1.1 MB)

© 2007 Optica Publishing Group. This copy is hosted for the convenience of MC Grating users; the version of record is the publisher's, at the DOI above.

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