Efficient calculation of 1-D periodic Green´s functions for leaky-wave applications

In this paper an approach is described for the efficient computation of the mixed-potential scalar and dyadic Green´s functions for a one-dimensional periodic (periodic along x direction) array of point sources embedded in a planar stratified structure. Suitable asymptotic extractions are performed on the slowly converging spectral series. The extracted terms are summed back through the Ewald method, modified and optimized to efficiently deal with all the different terms. The accelerated Green´s functions allow for complex wavenumbers, and are thus suitable for application to leaky-wave antennas analysis. Suitable choices of the spectral integration paths are made in order to account for leakage effects and the proper/improper nature of the various space harmonics that form the 1-D periodic Green´s function.