Introduction of fractal absorbing boundary conditions in electromagnetic simulation by SMM

Abstract

In a series of previous papers, we have shown that the spectral moments method (SMM) may be a powerful tool for solving problems of propagation and diffraction of electromagnetic waves. In this work, we demonstrate the ability of this method to incorporate fractal absorbing boundary conditions. First, we describe the SMM principle when eigenvalues of the dynamical matrix are complex, and present the absorbing boundary conditions used. We show that fractal boundary absorbing conditions improve stability and allow us to deal with small discretized domains, with the possibility of extending the computation to three-dimensional systems. Furthermore, the method does not require the introduction of Huyghens surfaces to simulate propagation of plane waves. The efficiency and accuracy of the method is analysed by comparing the results obtained by SMM with the analytical solution.