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

TL;DR

This paper develops and validates a finite element method for simulating surface plasmon-polaritons excited on conducting sheets like graphene, incorporating boundary conditions and numerical techniques for accurate modeling.

Contribution

It introduces a variational finite element formulation for Maxwell's equations with conducting sheets, enabling direct numerical simulation of surface plasmons with validation against exact solutions.

Findings

Validated finite element approach matches analytical solutions.

Incorporated boundary conditions for magnetic field discontinuities.

Discussed numerical techniques like PML and adaptive refinement.

Abstract

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.