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Symmetry analysis of the numerical instabilities in the transfer matrix method

AuthorsLuque-Raigón, J. M.; Halme, Janne; Míguez, Hernán ; Lozano, Gabriel
Issue Date15-Nov-2013
PublisherInstitute of Physics Publishing
CitationJournal of Optics 15 (12): 2013
AbstractThis paper discusses the numerical exponential instability of the transfer matrix method (TMM) in the framework of the symmetry formalism. This numerical weakness is attributed to a series of increasingly extreme exponentials that appear in the TMM when it is applied to geometries involving total internal reflection (TIR) or very high absorption. We design a TMM formalism that identifies the internal symmetries of the multilayer geometry. These symmetries suggest particular transformations of a reference system in the TMM that improve its ill-conditioned exponentials. To illustrate the numerical improvements, we present examples with calculations of electric fields. © 2013 IOP Publishing Ltd.
Identifiersdoi: 10.1088/2040-8978/15/12/125719
issn: 2040-8978
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