# Grating theory: new equations in Fourier space leading to fast converging results for TM polarization

Popov 2000: Applies Li's factorization theorems to the differential theory of gratings, which for thirty years had used a product rule that does not…

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Evgeni Popov, Michel Nevière

Evgeni Popov and Michel Nevière, “Grating theory: new equations in Fourier space leading to fast converging results for TM polarization”, J. Opt. Soc. Am. A **17**, 1773 (2000). [https://doi.org/10.1364/josaa.17.001773](https://doi.org/10.1364/josaa.17.001773)

Applies Li's factorization theorems to the differential theory of gratings, which for thirty years had used a product rule that does not converge everywhere in TM polarization. New equations in Fourier space, correct for arbitrary profiles rather than only lamellar ones, restore fast convergence for metallic gratings.

Cited by the software's history, together with the next two papers, for the automatic generation of the normal-vector field in Modal Crossed.

**Implemented in**: [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)

**Bibliography**: [Reference [21]](https://mcgrating.com/references.html#ref-21)

**Full text**: [Grating theory: new equations in Fourier space leading to fast converging results for TM polarization](https://mcgrating.com/references/ref21.pdf) (PDF, 258 KB)

© 2000 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.

MC Grating is Windows software that computes diffraction gratings by [the modal method](https://mcgrating.com/features/modal-method.html) and [the C method](https://mcgrating.com/features/c-method.html). [The download page](https://mcgrating.com/download.html) has the current release, which runs in demo mode without a license key.