Modal methods often used to model lamellar gratings that include infinitely or highly conducting metallic parts encounter numerical instabilities in some situations. In this paper, the origin of these numerical instabilities is determined, and then a stable algorithm solving this problem is proposed. In order to complete this analysis, the different geometries that can be handled without numerical instabilities are clearly defined. Numerical tests of the exact modal method implemented with the proposed solution are also presented. A test of convergence shows the efficiency of the method while the comparison with the fictitious sources method shows its accuracy.
© 2008 Optical Society of America
Diffraction and Gratings
Original Manuscript: June 16, 2008
Revised Manuscript: September 18, 2008
Manuscript Accepted: September 25, 2008
Published: November 25, 2008
Boris Gralak, Raphaël Pierre, Gérard Tayeb, and Stefan Enoch, "Solutions of Maxwell's equations in presence of lamellar gratings including infinitely conducting metal," J. Opt. Soc. Am. A 25, 3099-3110 (2008)