Slender-body theory for plasmonic resonance
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Accepted version
Author(s)
Ruiz, M
Schnitzer, O
Type
Journal Article
Abstract
We develop a slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips. We adopt a modal approach where one first solves the plasmonic eigenvalue problem, a geometric spectral problem which governs the surface-plasmon modes of the particle; then, the latter modes are used, in conjunction with spectral-decomposition, to analyse localized-surface-plasmon resonance in the quasi-static limit. We show that the permittivity eigenvalues of the axisymmetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime. For that family of modes, we use matched asymptotics to derive an effective eigenvalue problem, a singular non-local Sturm–Liouville problem, where the lumped one-dimensional eigenfunctions represent axial voltage profiles (or charge line densities). We solve the effective eigenvalue problem in closed form for a prolate spheroid and numerically, by expanding the eigenfunctions in Legendre polynomials, for arbitrarily shaped particles. We apply the theory to plane-wave illumination in order to elucidate the excitation of multiple resonances in the case of non-spheroidal particles.
Date Issued
2019-09-04
Date Acceptance
2019-08-16
ISSN
1364-5021
Publisher
Royal Society, The
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
475
Issue
2229
Copyright Statement
2019 The Author(s) Published by the Royal Society. All rights reserved.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/R041458/1
Subjects
localized-surface-plasmon resonance
plasmonic eigenvalue problem
slender-body theory
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2019-09-18