An integral-equation method using interstitial currents devoted to the analysis of multilayered periodic structures with complex inclusions

An efficient surface integral equation-based method is proposed for the analysis of electromagnetic scattering from multilayered media containing complex periodic inclusions. The proposed method defines equivalent currents at the interfaces between layers in order to eliminate the need to compute the layered medium Green's function. Hence, the background medium in a given layer can be treated as a homogeneous unbounded medium for which the computation of the Green's function for an infinite doubly periodic array is sufficient. The resulting method-of-moments interaction matrix has a block tridiagonal structure, which leads to computational complexity proportional to the number of layers for both matrix filling and solution. When all layers are identical, the filling time essentially reduces to that of a single layer, and the interaction matrix has a Toeplitz structure. Numerical results are provided for the reflectivity of multilayered periodic arrays of spherical silver core-silica shell nanoparticles, excited by a plane wave at optical frequencies. Comparisons with results obtained with an FDTD-based commercial software validate the accuracy and efficiency of the proposed method.