Abstract
In this paper we present an electric field volume integral equation approach to simulate surface plasmon propagation along metal/dielectric interfaces. Metallic objects embedded in homogeneous dielectric media are considered. Starting point is a so-called weak-form of the electric field integral equation. This form is discretized on a uniform tensor-product grid resulting in a system matrix whose action on a vector can be computed via the fast Fourier transform. The GMRES iterative solver is used to solve the discretized set of equations and numerical examples, illustrating surface plasmon propagation, are presented. The convergence rate of GMRES is discussed in terms of the spectrum of the system matrix and through numerical experiments we show how the eigenvalues of the discretized volume scattering operator are related to plasmon propagation and the medium parameters of a metallic object.
Highlights
While photons and phonons are quanta of energy for light and mechanical vibrations, plasmons result from the quantization of plasma oscillations in a conductor
To illustrate the performance of our integral equation approach, we present two numerical experiments in which we simulate surface plasmon propagation
The discretization of the integral equation was discussed in detail and by formulating the discretized set of equations in terms of Kronecker products, it was shown that the discretized system matrix has a similar structure as the continuous volume scattering operator
Summary
While photons and phonons are quanta of energy for light and mechanical vibrations, plasmons result from the quantization of plasma oscillations in a conductor. In this paper we use a global volume integral approach, since we are interested in electromagnetic fields operating in steadystate and electromagnetic field strength unknowns are defined on the scattering domain only. The singular Green’s function is weakened in a manner that is consistent with the finitedifference approximation error and we make use of the Kronecker product to show that the discretized set of equations has a similar structure as the continuous volume integral operator. The discretized set of equations is solved using the Generalized Minimum Residuals (GMRES) iterative solver [7] and a numerical analysis of its convergence rate for plasmonic configurations is presented as well
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