Analysis of large finite periodic structures using infinite periodicity methods

We present a method for studying large finite periodic structures using soft-
ware developed for infinite periodic structures. The method is based on the
Floquet-Bloch transformation, which splits the spatial description into one
microscopic spatial variable inside the unit cell, and one macroscopic wave
vector describing the variations on a scale encompassing many unit cells. The
resulting algorithm is iterative, and solves an infinite periodic problem in each
step, where the sources have been filtered through a windowing function. The
computational cost for the iterations is negligible compared to computing the
impedance matrices for the infinite periodic problems, and it is shown that
the algorithm converges if the periodic structure is large enough.