# Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media

Popov 2001: The most general form of the fast-Fourier-factorization idea: differential equations for the Fourier components of the field diffracted by an…

Canonical: https://mcgrating.com/publications/popov-2001-maxwell-equations-fourier-space.html


Evgeny Popov, Michel Nevière

Evgeny Popov and Michel Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media”, J. Opt. Soc. Am. A **18**, 2886 (2001). [https://doi.org/10.1364/josaa.18.002886](https://doi.org/10.1364/josaa.18.002886)

The most general form of the fast-Fourier-factorization idea: differential equations for the Fourier components of the field diffracted by an arbitrarily shaped, periodic, anisotropic medium, written so that the truncated series converge quickly. Classic isotropic gratings, crossed gratings and photonic-crystal slabs all appear as particular cases.

One of the three papers behind the normal-vector field that Modal Crossed generates automatically for a two-dimensional unit cell.

**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)

**Bibliography**: [Reference [22]](https://mcgrating.com/references.html#ref-22)

**Full text**: [Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media](https://mcgrating.com/references/ref22.pdf) (PDF, 188 KB)

© 2001 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.