Efficient computation of the 2D Green´s function for 1D periodic layered structures using the Ewald method

We present an alternative direct procedure for applying the Ewald approach to obtain the Green´s function for an array of line sources with 1D periodicity. The approach is the 2D analog of that of Wilton, Jackson and Champagne (see URSI Int. Sym. on Electrom. Theory, Thessaloniki, Greece, May 1998). Furthermore, we derive an algorithm for choosing the Ewald splitting parameter E that extends the efficiency of the method when the periodicity is somewhat larger than a wavelength. The case of periodic 2D multilayered media is also treated analogously done by Wilton et al. for the 3D case. In particular, the dyadic Green´s function formalism of Michalski (1990), which yields mixed potential integral equations for layered media, is combined with the Ewald method.