In this work we treat in detail the acceleration of the freespace scalar Green’s function in three dimensional (3-D) structures with one dimensional (1-D) periodicity. We analyze the methods able to deal with a complex phase shift, necessary to study complex waves in periodic structures. We present a spectral Kummer-Poisson’s decomposition; then we extend the application of the Ewald’s method by performing an optimization of the relevant splitting parameter, and we also ﬁnd an integral representation. Comparisons among the various acceleration methods are performed, thus providing fundamental information on their actual efﬁciency.
Baccarelli, P., & Galli, A. (2006). 3-D Green’s function in 1-D periodic structures: a comparative analysis of acceleration techniques. In Proceedings I European Conference on Antennas and Propagation 2006 (pp.1-5). Eur Space Agency Spec Publ ESA SP [10.1109/EUCAP.2006.4584480].