Efficient computation of Green's functions for one-dimensional periodic structures in layered media

The development of computationally efficient Green's functions in layered-media environments is important when applying the method of moments (MoM) using the mixed-potential integral equation (MPIE) formulation (K. A. Michalski and D. Zheng, IEEE Trans. Antennas Propag., vol. 38, pp. 335-344, Mar. 1990). However, their computation poses difficulties in terms of accuracy and computation time due to the presence of slowly converging integrals and/or series. Extensive work has been carried out to accelerate the Green's function computation for the case of a single dipole source in a layered media. Considerably less effort has been devoted to accelerate the Green's functions due to a one-dimensional (1-D) periodic arrangement of dipole sources. These are required to study 1-D periodic structures in layered media, including scattering structures and guiding structures such as leaky-wave antennas (LWAs) made from layered media.