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This paper investigates the orbital angular momentum (OAM) mode of a vortical radio wave generated by a circular antenna array. Theoretical formulations of the radiation fields are deduced, and factors affecting the mode distribution are identified. Because the array antenna cannot ideally generate a pure mode, two indicators, namely, the fundamental mode energy ratio and the degree of intensity deviation, are defined to evaluate the quality of the radiated vortex beams. The relationship between mode purity and the array parameters, OAM mode number and elevation angle, is shown through both theoretical analysis and numerical experiments. Given a threshold of mode purity, the boundary of the pure mode region is determined, and the minimum number of elements is obtained to ensure that the main lobe is located in the pure region. An X-band experimental setup for vortical radio beams is created, and the radiation field is measured to validate the theoretical results. The theoretical analysis can benefit the array design and application of vortical radio waves.
Yuan et al. (2016) studied this question.