Fast and accurate electromagnetic solutions of finite periodic optical structures.

Electromagnetic applications of periodic materials have become popular in many modern optical and RF applications. The accurate computation of the electromagnetic response of large structures requires solving problems with high number of unknowns. Fast methods are useful to deal with such big problems, but, in general they do not take advantage of the periodicity properties. Based on the behaviour of impedance matrices involved in the solution of the surface integral equations with the Method of Moments, an accelerated solution based on the FFT is implemented. The presented approach slots the original impedance matrix and it applies the FFT to calculate the exact solution of the matrix vector product in an iterative process. The proposed solution achieves a linear memory cost proportional to 𝒪(N) and a computing time of 𝒪(N log N), where N is the problem number of unknowns. Also, in this paper, the advantages of this technique are shown in the developed applications.