An efficient integral equation method using interstitial currents for the analysis of electromagnetic scattering from multilayered periodic structures with complex inclusions

In this article, an efficient surface integral equation-based method is proposed for the analysis of electromagnetic scattering from multilayered, doubly periodic arrays of three-dimensional (3D) penetrable objects which are either embedded in or located above layered dielectric media. In the proposed method, the surface equivalence principle is used to define the equivalent electric and magnetic currents on the interfaces between the layers, thus, as opposed to the similar studies in literature, eliminates the need to calculate the Green's function for layered dielectric media. Interfaces can be physical or fictional. In the case where the interfaces are physical, the background medium in a given layer can be treated as a homogeneous unbounded medium for which the computation of the two-dimensional (2-D) periodic Green's function is sufficient. The resulting method of moments (MoM) interaction matrix has a block-tridiagonal form which leads to computational complexity that is linear in the number of layers for both matrix filling and matrix equation solution. When the nonlinear computational complexity in literature is considered, the presented method is advantageous. The numerical results obtained through the proposed method are validated by comparison with the results obtained using commercial software based on FDTD (Finite Differences in Time Domain).