An efficient alternating direction implicit-based Fourier spectral method for the simulation of dispersive metallic structures

In this article we present a novel spectral method for the simulation of dispersive materials. Metals that can be described with the Drude-model or multi-pole Lorentzian models can be simulated efficiently with our algorithm. The proposed method is based on the alternating direction implicit (ADI) scheme in order to soften restrictions for the maximum stable time-step, which is imposed for explicit methods by the Courant limit. We derive a new system of auxiliary differential equations for the material dispersion that is compatible with the ADI method. The use of the Fourier differentiation technique allows for the efficient evaluation of the implicit equations by removing the need to solve a linear system of equations. Combining the ADI technique with the spectral approach leads to a fast algorithm that shows both exponential spatial convergence and second order-accuracy in time. High accuracy for time-steps of an order of magnitude larger than the Courant limit is demonstrated for a wide frequency range.