Efficient Computation of Green's Function for 1-D Periodic Structures

In this letter, the computation of the Green's function for one-dimensional (1-D) periodic structures is presented via a fast and accurate algorithm based on the philosophy of Kummer's decomposition (KD). The KD uses an optimal value for a quasi-periodicity parameter. An approximate optimal balance between direct summation and acceleration is constructed when necessary. The algorithm has been designed for easy extraction and analytical analysis of the irregular structure of the Green's function including logarithmic singularity. The shown numerical results for low- and quite high-frequency values demonstrate the high efficiency and accuracy of the algorithm in comparison with other known approaches. In particular, numerical comparisons to Ewald's and other methods are discussed.