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Symmetry analysis of the numerical instabilities in the transfer matrix method

 

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Opened Access Symmetry analysis of the numerical instabilities in the transfer matrix method
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Author: Luque Raigón, J M
Halme, Janne
Míguez García, Hernán Ruy
Lozano Barbero, Gabriel Sebastián
Date: 2013
Published in: Journal of Optics, 15 (12), 125719-.
Document type: Article
Abstract: This 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.
Cite: Luque Raigón, J.M., Halme, J., Míguez García, H.R. y Lozano Barbero, G.S. (2013). Symmetry analysis of the numerical instabilities in the transfer matrix method. Journal of Optics, 15 (12), 125719-.
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URI: https://hdl.handle.net/11441/70137

DOI: 10.1088/2040-8978/15/12/125719

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