Dipole Excitation of Surface Plasmon on a Conducting Sheet: a Finite Element Study

By using a suitable rescaled form of time-harmonic Maxwell’s equations, we numerically simulate the propagation of a slowly decaying electromagnetic wave, called surface plasmonpolariton, excited along a large conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. For this purpose, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the 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 test our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as local refinement and a-posteriori error control are discussed.