# Highly improved convergence of the coupled-wave method for TM polarization

Lalanne 1996: The coupled-wave (RCWA) method had always converged slowly for TM polarization on metallic lamellar gratings. Lalanne and Morris found that…

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Philippe Lalanne, G. Michael Morris

Philippe Lalanne and G. Michael Morris, “Highly improved convergence of the coupled-wave method for TM polarization”, J. Opt. Soc. Am. A **13**, 779 (1996). [https://doi.org/10.1364/josaa.13.000779](https://doi.org/10.1364/josaa.13.000779)

The coupled-wave (RCWA) method had always converged slowly for TM polarization on metallic lamellar gratings. Lalanne and Morris found that using the Fourier matrix of the *inverse* permittivity for the right field component makes the same truncated expansion converge dramatically faster, with no other change to the method.

The Fourier Modal Method (FMM) of the three modal codes uses this formulation; [Li 1996](https://mcgrating.com/publications/li-1996-fourier-series-discontinuous.html) explains why it works.

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

**Cited on**: [About MC Grating Software](https://mcgrating.com/about.html) · [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) · [Publications](https://mcgrating.com/references.html)

**Bibliography**: [Reference [10]](https://mcgrating.com/references.html#ref-10)

**Full text**: [Highly improved convergence of the coupled-wave method for TM polarization](https://mcgrating.com/references/ref10.pdf) (PDF, 422 KB)

© 1996 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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