An iterative scheme for Gaussian beam expansion of electromagnetic waves

Point matching technique is applied to a pyramidal horn antenna to expand its aperture field in a wide angular range in terms of Gaussian beams using the Jacobi iterative method. The obtained far field pattern is compared with the results of Gabor's Gaussian beam expansion. Convergence, speed, the impact of initial condition and the selection of sample points is discussed. The implemented point matching scheme is almost as fast and accurate as the Gabor's expansion. It can even be faster and more accurate in some cases especially when the Gaussian beams are neither wide-waisted nor narrow-waisted.