Abstract

Two recursive and numerically stable matrix algorithms for modeling layered diffraction gratings, the S-matrix algorithm and the R-matrix algorithm, are systematically presented in a form that is independent of the underlying grating models, geometries, and mountings. Many implementation variants of the algorithms are also presented. Their physical interpretations are given, and their numerical stabilities and efficiencies are discussed in detail. The single most important criterion for achieving unconditional numerical stability with both algorithms is to avoid the exponentially growing functions in every step of the matrix recursion. From the viewpoint of numerical efficiency, the S-matrix algorithm is generally preferred to the R-matrix algorithm, but exceptional cases are noted.

© 1996 Optical Society of America

Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings

Lifeng Li
J. Opt. Soc. Am. A 11(11) 2829-2836 (1994)

Enhanced R-matrix algorithms for multilayered diffraction gratings

Eng Leong Tan
Appl. Opt. 45(20) 4803-4809 (2006)

Note on the S-matrix propagation algorithm

Lifeng Li
J. Opt. Soc. Am. A 20(4) 655-660 (2003)

Note on formulation of the enhanced scattering- (transmittance-) matrix approach

Eng Leong Tan
J. Opt. Soc. Am. A 19(6) 1157-1161 (2002)

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

Maxim Pisarenco, Joseph Maubach, Irwan Setija, and Robert Mattheij
J. Opt. Soc. Am. A 28(7) 1364-1371 (2011)