Efficient computation of the 2-D Green's function for 1-D periodic line sources in planar multilayered media

Periodic Green's function (PGF) of an infinite 1-D periodic array of line sources in planar multilayered media is calculated by the use of the of the 3-level discrete complex image method (DCIM) together with the surface wave pole (SWP) extraction. The Ewald's method is then applied to accelerate the evaluation of the PGF. The recipe to choose the Ewald's splitting parameter is also given. It is shown that the Ewald's transformation needs a few terms to approximate the PGF with high accuracy. The SWP contributions, which are extracted before the DCIM application, are added to this approximation. The spatial domain surface wave pole contributions are observed to be highly oscillatory and converge to zero. The numerical results are provided to demonstrate the efficiency and the accuracy of the procedure followed.