New single-source surface integral equation for solution of electromagnetic problems in multilayered media

Abstract

This thesis presents a novel single source-surface integral equation (SSSIE) formulation for 2-D and 3-D electromagnetic fields analysis in complex multilayered media. The new integral equation named SVS-EFIE provides a solution for magneto-quasi-static analysis of 2-D transmission lines above lossy layered substrates. Traditionally, the solution of the modelling current flow in 2-D conductors is obtained through the volume electric field integral equation (V-EFIE) which has unknown current density in the cross-section of conductors. The proposed integral equation is transformed from this classical V-EFIE, and it has single unknown current density on the boundary of the conductors. Further, the pole-residual representation of the 2-D spectrum domain Green's function is introduced to enable evaluation of the required spatial Green's function in closed form in both shielded and open media. SVS-EFIE is also developed for full wave analysis of homogeneous 3-D scattering objects situated in multilayered media. Traditionally, the solution of scattering problems is obtained through the two-source surface integral equations. In this case, the curl operators acting on dyadic Green's functions cannot be eliminated through gradient or divergence theorems. As the result, the derivatives from the curl operator need to be moved into the Sommerfeld integrals and make the convergence of Sommerfeld integrals harder. Unlike the traditional surface integral equations, the new integral equation has only electric field dyadic Green's function due to the single unknown fictitious electric surface current density on the boundary of the scatterer. After moving gradient and divergence operators to the basis and testing functions, the novel layered media integral equation does not have derivatives on the Green's function. Consequently, it can be formulated in Michalski-Zheng's mixed-potential form with the spectrum domain layered medium Green's function in the mixed-potential form obtained from the transmission-line network theory. Coupling of the SVS-EFIE formulation stated for the dielectric regions with the popular Mixed Potential Integral Equation (MPIE) stated for metal regions introduces new coupled integral equations formulation termed SVS-S-EFIE for the complex metal-dielectric composite structures embedded in multilayered media.