Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:339

Article

Maier, Matthias¹  Margetis, Dionisios^2,3,4  Luskin, Mitchell¹ 

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[3] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

[4] Univ Maryland, Ctr Sci Computat & Math Modeling, College Pk, MD 20742 USA

关键词: Time-harmonic Maxwell's equations;    Finite element method;    Surface plasmon polariton;    Weak discontinuity on hypersurface;   

DOI  :  10.1016/j.jcp.2017.03.014

来源: Elsevier

【 摘 要 】

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed. (C) 2017 Elsevier Inc. All rights reserved.

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