Modified S-matrix algorithm for the aperiodic Fourier modal method in contrast-field formulation

M. Pisarenco, J.M.L. Maubach, I.D. Setija, R.M.M. Mattheij

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17 Citations (Scopus)
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Abstract

The Fourier modal method (FMM) is a method for efficiently solving Maxwell’s equations with periodic boundary conditions. In order to apply the FMM to nonperiodic structures, perfectly matched layers need to be placed at the periodic boundaries, and the Maxwell equations have to be formulated in terms of a contrast (scattered) field. This reformulation modifies the structure of the resulting linear systems and makes the direct application of available stable recursion algorithms impossible. We adapt the well-known S-matrix algorithm for use with the aperiodic FMM in contrast-field formulation. To this end, stable recursive relations are derived for linear systems with nonhomogeneous structure. The stability of the algorithm is confirmed by numerical results.
Original languageEnglish
Pages (from-to)1364-1371
JournalJournal of the Optical Society of America A, Optics, Image Science and Vision
Volume28
Issue number7
DOIs
Publication statusPublished - 2011

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