On Evaluation of the Green Function for Periodic Structures in Layered Media

A hybrid scheme is developed to efficiently calculate the periodic Green function for planar stratified structures. The technique is based on a combination of Ewald's method and the Shank transformation. It begins with using the matrix pencil-of-function (MPOF) to approximate the periodic Green function via a sum of exponential series that converges slowly. The slowly converging series can be accelerated through Ewald's method. After the slowly converging series is removed, the Shank transformation is then used to sum the remaining spectral terms. As a result, the proposed technique greatly accelerates summation of the periodic Green function and significantly reduces the computational time when compared with the spectral summation and straightforward Shank transformation. Some numerical examples are preformed to demonstrate rapidity and accuracy of the proposed technique.