Efficient numerical approach to electromagnetic scattering from three-dimensional periodic array of dielectric spheres using sequential accumulation

An effective numerical solution is presented for the plane wave scattering by multilayered periodic arrays of dielectric spheres. The treated structure is a fundamental model of photonic crystals having three-dimensional periodicity. The problem is analyzed by the mode matching method, where the electromagnetic fields in the air and dielectric regions are approximated by using the Floquet harmonics and vector spherical wave functions, respectively. They are matched on the junction surfaces in the least squares sense. Introduction of sequential accumulation in the process of QR decomposition reduces the computation time from O(Q(3)) to O(Q(1)) and the memory requirement from O(Q(2)) to O(Q(1)), with Q being a number of sphere layers. Numerical results are given for CPU time, speed of convergence, and some band gap characteristics.