Slender-body theory for plasmonic resonance

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Title: Slender-body theory for plasmonic resonance
Authors: Ruiz, M
Schnitzer, O
Item 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.
Issue Date: 4-Sep-2019
Date of Acceptance: 16-Aug-2019
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/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/R041458/1
Keywords: localized-surface-plasmon resonance
plasmonic eigenvalue problem
slender-body theory
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Online Publication Date: 2019-09-18
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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