Fast Eigensolver for Plasmonic Metasurfaces

Fast Eigensolver for Plasmonic Metasurfaces

Finding the wavevectors (eigenvalues) and wavefronts (eigenvectors) in nanostructured metasurfaces is cast as a problem of finding the complex roots of a non-linear equation. A new algorithm is introduced for solving this problem; example eigenvalues are obtained and compared against the results fro...

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Veröffentlicht in:Optical materials express 2014-02, Vol.4 (2), p.288-299
Hauptverfasser: Korotkevich, Alexander O., Ni, Xingjie, Kildishev, Alexander V.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Computation
Eigenvalues
Mathematical analysis
Plasmonics
Roots
Solvers
Wave fronts
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container_title Optical materials express
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creator Korotkevich, Alexander O.
Ni, Xingjie
Kildishev, Alexander V.
description Finding the wavevectors (eigenvalues) and wavefronts (eigenvectors) in nanostructured metasurfaces is cast as a problem of finding the complex roots of a non-linear equation. A new algorithm is introduced for solving this problem; example eigenvalues are obtained and compared against the results from a popular, yet much more computationally expensive method built on a matrix eigenvalue problem. In contrast to the conventional solvers, the proposed method always returns a set of 'exact' individual eigenvalues. First, by using the Lehmer-Schur algorithm, we isolate individual complex roots from others, then use a zero-polishing method applied at the very final stage of ultimate eigenvalue localization. Exceptional computational performance, scalability, and accuracy are demonstrated.
doi_str_mv 10.1364/OME.4.000288
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source DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals
subjects Algorithms
Computation
Eigenvalues
Mathematical analysis
Plasmonics
Roots
Solvers
Wave fronts
title Fast Eigensolver for Plasmonic Metasurfaces
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