# Physics of near-wavelength high contrast gratings

Karagodsky 2012: A simple theory of high-contrast gratings in the near-wavelength regime. A phase selection rule explains both their very broadband high…

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Vadim Karagodsky, Connie J. Chang-Hasnain

Vadim Karagodsky and Connie J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings”, Opt. Express **20**, 10888 (2012). [https://doi.org/10.1364/oe.20.010888](https://doi.org/10.1364/oe.20.010888)

A simple theory of high-contrast gratings in the near-wavelength regime. A phase selection rule explains both their very broadband high reflectivity and their ultra-high-Q resonances, and reveals the crossing and anti-crossing of the grating modes; the analytical results agree with simulations and with measurements on VCSELs using such a grating as the top reflector.

The grating-mode interference this paper describes is what the Modes Interference window of the modal codes lets a user examine mode by mode.

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

**Cited on**: [Modes interference in high-contrast gratings](https://mcgrating.com/modes-interference.html)

**Bibliography**: [Modes-interference reference [5]](https://mcgrating.com/modes-interference.html#mi-ref-5)

**Full text**: [Physics of near-wavelength high contrast gratings](https://mcgrating.com/files/modesint/ref05.pdf) (PDF, 1.2 MB)

© 2012 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.