A fast algorithm for calculating the radiation pattern in the longitudinal plane of antennas with cylindrical structure by applying asymptotic waveform evaluation in a spectrum of two-dimensional solutions

When dealing with electromagnetic problems of small three-dimensional (3-D) elements, such as dipole, microstrip patches and slots, in the vicinity of two-dimensional (2-D) structures, it is very efficient to find the radiation characteristics of the 3-D elements by using a spectrum of 2-D solutions (S2DS). Only one 2-D solution in the spectral domain is needed to obtain the radiation pattern in the transverse plane defined by θ=90°. For the radiation in a longitudinal plane defined by a fixed azimuth angle φ, one 2-D problem has to be solved for each value of the polar angle θ. This paper presents a fast algorithm by which the radiation pattern in the longitudinal plane can be computed more efficiently. The algorithm applies the method of asymptotic waveform evaluation (AWE) in the 2-D spectral domain. For the cases shown in the paper, the algorithm needs only three 2-D solutions to determine the complete radiation pattern in the longitudinal plane.