Use of Fourier series in the analysis of discontinuous periodic structures

The mathematical foundation of every modern FMM/RCWA implementation. Li proves the rules governing the Fourier factorization of products of discontinuous functions: when the product's coefficients may be formed by Laurent's rule and when the inverse rule must be used instead. The Lalanne–Morris and Granet–Guizal reformulations converge because they obey these rules uniformly at the material boundaries.

The FMM in the modal codes is built on these factorization rules; the crossed-grating code applies them through the normal-vector field of Schuster et al. 2007.

Implemented in

Modal Collinear, Modal Conical, Modal Crossed

Cited on

The modal method (RCWA / FMM) · Highly improved convergence of the coupled-wave method for TM polarization · Publications

Bibliography

Reference [11]

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Use of Fourier series in the analysis of discontinuous periodic structures (PDF, 262 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.

MC Grating is Windows software that computes diffraction gratings by the modal method and the C method. The download page has the current release, which runs in demo mode without a license key.