Eigenvalue system for the scattering from rough surfaces – Saving in computation time by a physical approach

The curvilinear coordinate method is an efficient theoretical tool for analysing rough surfaces. It consists on solving Maxwell’s equations written in a nonorthogonal coordinate system. The C method leads to eigenvalue systems and the scattered fields can be expanded as a linear combination of eigensolutions. The boundary conditions allow the combination coefficients to be determined. The dominant computational cost for the C method is the eigenvalue problem solution which is of order of N3 where N is the size of eigenvalue systems. In this paper, we propose a new approach based on the association of the C method with the beam simulation method (BSM) in order to reduce the computational time. The BSM is based on decomposing a large incident beam into narrower subbeams and then synthesizing the large beam by coherent superposition. The adopted procedure consists of two stages. First, the surface fields are obtained by the C method associated with each elementary beam illuminating smaller surfaces. Second, the total surface field is deduced from a coherent superposition of elementary surface current densities. The far-field and the scattering coefficients are derived from the Huygens principle applied to the total surface fields. We confirm the efficiency and the validity of the approach and show that the BSM applied with the C method allows a significant saving in computation time.