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.