Resolution of Maxwell's equations by spectral moments method. Local approach

Abstract

In previous work, we have presented a computation method based on the determination of the Green functions of the electromagnetic field with the help of the spectral moments method (SMM). In this method, the Green functions are calculated in the form of continued fractions, and one determines the coefficients of their development. Two approaches have been presented: one, we call global approach, where all space is discretized in a box, the other, we call the local approach, where only the diffracting item is considered. In this work we present the results obtained for the one, two and three-dimensional cases by the local approach. We first develop the necessary tools for the computing. We establish the analytical form of the Green functions of the continuous vacuum and of the discretized vacuum, the dispersion curves and the selection rules which appear. We show that the real part of the diagonal Green functions is directly linked to the vibrational density of states and therefore perfectly determined whatever dimension the space is. Longitudinal, non physical modes are found to play a subsequent role. As regards scattering, we principally report a series of tests on some canonical systems, such as cylinders or spheres, showing that the backscattering cross- section and the impulsional response obtained with SMM are in very good agreement with the analytical results. Bi-static scattering cross section is also studied.