doi abstract bibtex

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 algorithmsare 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.

@article{li_formulation_1996, title = {Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings}, volume = {13}, issn = {1084-7529}, doi = {10.1364/JOSAA.13.001024}, 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 algorithmsare 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.}, number = {5}, journal = {Journal of the Optical Society of America A}, author = {Li, Lifeng}, year = {1996}, pages = {1024}, file = {Li_1996_Formulation and comparison of two recursive matrix algorithms for modeling.pdf:/Users/baptiste/Library/Application Support/Zotero/Profiles/d9rq1atq.default/zotero/storage/6UQGIVA7/Li_1996_Formulation and comparison of two recursive matrix algorithms for modeling.pdf:application/pdf} }

Downloads: 0