Discussion on the efficient evaluation of the Green´s functions of point sources inside infinite parallel plate waveguides

In this paper, we examine several techniques for computing the Green´s functions inside infinite parallel plate waveguides considering point sources. The basic spectral and spatial domain approaches are reviewed, showing their main particularities. Next, the Ewald method is applied for the evaluation of these functions, in order to enhance the convergence in singular situations. Besides, a novel alternative method based on the Kummer´s transformation is also proposed. Several convergence and validation results are included to compare the efficiency of the different techniques presented.