Symmetry analysis of the numerical instabilities in the transfer matrix method

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.Nordic Innovation Center 09053Ministerio de Economía y Competitividad MAT2011-23593, CSD2007-00007Junta de Andalucía FQM- 3579, FQM-524

Symmetry analysis of the numerical instabilities in the transfer matrix method

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. © 2013 IOP Publishing Ltd.This work was partially funded by the Nordic Innovation Center project NORDIC DSC (no. 09053) and the CNB-E project of the TKK/Aalto University Multidisciplinary Institute of Digitalisation and Energy MIDE. H.M. thanks the Spanish Ministry of Economy and Competitiveness for funding under grants MAT2011-23593 and Consolider CSD2007-00007 and Junta de Andalucia for funding under grants FQM- 3579 and FQM-5247. H.M. also thanks the European Research Council for a Starting Grant (POLIGHT).Nordic Innovation CenterTKK/Aalto University Multidisciplinary Institute of Digitalisation and EnergySpanish Ministry of Economy and CompetitivenessJunta de AndaluciaEuropean Research CouncilPeer Reviewe