The Gaussian expansion of the Green's function of an electric current in a parallel-plate waveguide

In this paper, a novel closed form expression is derived to find the Green' s function of a horizontal electric current in a parallel-plate waveguide. It is achieved by expanding the Green' s function into a series of Gaussian functions. This new method is called the Gaussian Green' s function (GGF) method. The main advantage of the GGF method lies in its precision as well as rapid convergence. Numerical results confirm that the closed form expression yields less than 0.2% error compared to the numerical integration of the spectral integral. Furthermore, it is verified that this method can be in excellent agreement with the complex images (CI) method.