Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides

Yuntian Chen, Torben Roland Nielsen, Niels Gregersen, Peter Lodahl, Jesper Mørk

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    Abstract

    We develop a self-consistent finite-element method to quantitatively study spontaneous emission from emitters in nanoscale proximity of plasmonic waveguides. In the model, it is assumed that only one guided mode is dominatingly excited by the quantum emitter, while the cross section of the plasmonic waveguide can be arbitrary. The fraction of the energy coupled to the plasmonic mode can be calculated exactly, which can be used to determine the efficiency with which single optical plasmons are generated. We apply our numerical method to calculate the coupling of a quantum emitter to a cylindrical metallic nanowire and a square metallic waveguide, and compare the cylindrical metallic nanowire with previous work that employs quasistatic approximation. For the cylindrical metallic nanowire we observe good agreement with the quasistatic approximation for radii below 10 nm, but for increasing radius the spontaneous emission β factor and the plasmonic decay rate deviate substantially, by factors of up to 5–10 for a radius of ∼100 nm, from the values obtained in the quasistatic approximation. We also show that the quasistatic approximation is typically valid when the radius is less than the skin depth of the metals at optical frequencies. For the square metallic waveguide we estimate an optimized value for the spontaneous emission β factor up to 80%.
    Original languageEnglish
    JournalPhysical Review B Condensed Matter
    Volume81
    Issue number12
    Pages (from-to)125431
    ISSN0163-1829
    DOIs
    Publication statusPublished - 2010

    Bibliographical note

    Copyright 2010 American Physical Society

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