The purpose of the method described in this paper is to identify with precision sharp phenomena and to produce reliable solutions for various kinds of one-dimensional grating problems in the resonance domain, without limitation in the geometry or the electromagnetic parameters. The theory lies in the use of finite elements and Rumsey’s variational principle for matching the Rayleigh expansions on both sides of the inhomogeneous region. The numerical implementation is checked by classical tests and by comparisons with existing numerical data. In particular, solutions are given for difficult cases where there is a lack of numerical results. The basic principle of the generalization to two-dimensional gratings and an example of a numerical result are given.
© 1993 Optical Society of America
Original Manuscript: November 23, 1992
Revised Manuscript: May 10, 1993
Manuscript Accepted: May 12, 1993
Published: December 1, 1993
T. Delort and D. Maystre, "Finite-element method for gratings," J. Opt. Soc. Am. A 10, 2592-2601 (1993)