# Modal method in deep metal-dielectric gratings: the decisive role of hidden modes

Foresti 2006: In deep gratings mixing metal and dielectric, most TM-polarization features are explained by an astonishingly small number of true modes, yet…

Canonical: https://mcgrating.com/publications/foresti-2006-hidden-modes-deep-metal-dielectric-gratings.html


Maud Foresti, Ludivine Menez, Alexander V. Tishchenko

Maud Foresti, Ludivine Menez and Alexander V. Tishchenko, “Modal method in deep metal-dielectric gratings: the decisive role of hidden modes”, J. Opt. Soc. Am. A **23**, 2501 (2006). [https://doi.org/10.1364/josaa.23.002501](https://doi.org/10.1364/josaa.23.002501)

In deep gratings mixing metal and dielectric, most TM-polarization features are explained by an astonishingly small number of true modes, yet convergence can still fail. This paper identifies the culprit: "hidden" modes that carry the field along the metal walls and are easy to miss in the mode search, and shows that including them restores agreement.

A result that shapes how the modal codes select and check the modes they keep.

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

**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 [9]](https://mcgrating.com/references.html#ref-9)

**Full text**: [Modal method in deep metal-dielectric gratings: the decisive role of hidden modes](https://mcgrating.com/references/ref09.pdf) (PDF, 525 KB)

© 2006 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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