Towards a unified approach to electromagnetic analysis of objects embedded in multilayers

According to the surface equivalence theorem [1], any enclosed surface with electric and magnetic current densities enforced on it can generate exactly the same fields as the original problem. The problem is how to construct the current sources. In this paper, an efficient and accurate unified approach with an equivalent current density enforced on the outermost boundary is proposed to solve transverse magnetic (TM) scattering problems by objects embedded in multilayers. In the proposed approach, an equivalent current density is derived after the surface equivalence theorem is recursively applied on each boundary from innermost to outermost interfaces. Then, the objects are replaced by the background medium and the equivalent electric current density only on the outermost boundary is derived. The scattering problems by objects embedded in multilayers can be solved with the electric field integral equation (EFIE). Compared with the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and other dual source formulations, the proposed approach shows significant benefits: only the surface electric current density instead of both the electric and magnetic current densities is required to model the complex objects in the equivalent problem. Furthermore, the electric current density is only enforced on the outermost boundary of objects. Therefore, the overall count of unknowns can be significantly reduced. At last, several numerical experiments are performed to validate its accuracy and efficiency. Although overhead is required to construct the intermediate matrices, the overall performance improvement is still significant as numerical results are shown. Therefore, it shows great potential useful in the practical engineering applications.