We propose a simple method based on the Aperture Antennas Theory to understand in a simple fashion limitations of OAM antennas in far-field links. Additional insight is also given by analyzing the properties of the operators relating source and farfield distributions for a given order of the vortex. The outcomes fully agree with the results recently achieved by Edfors, Craeye, and co-authors, and emphasize some additional draw-back. The 'degrees of freedom' of the fields associated to the different orders of the vortices are also discussed.
Index Terms-Antenna theory, Orbital Angular Momentum.
I. A PREMISEAmongst the novel techniques developed for utilizing the radio spectrum with maximum efficiency, great attention has been recently devoted to Orbital Angular Momentum (OAM) antennas [1]- [20]. Such systems have been in some cases proposed as means to improve almost "indefinitely" the channel capacity in a link amongst two antennas [2].Roughly speaking, the idea is to take profit from the fact that an antenna could simultaneously generate different fields each one associated to a different amount of 'orbital momentum', i.e., to a different angular variation of the phase around the target direction (such as e jϕ , e 2jϕ , and so on, ϕ denoting the azimuth angle in the observation domain). Then, by associating a different information to each of these patterns, one could realize an "OAM multiplexing" [17] and eventually enlarge "at will" the channel capacity [2]. Saying it in other words, it is like using different modes of a channel, where the modes are associated to a free space link rather than to a guiding structure.A large interest has been devoted to such a topic, including spectacular public demonstrations for mass media (e.g., Piazza San Marco, Venice, Italy, June 24 th 2011 [2]) as well as contributions on top scientific journals, e.g., [3]-[6].Since then, doubts [7] and objections [8],[10] have begun to appear, emphasizing some expected limitations.In the attempt to contribute to such a debate, in the following we propose a very simple yet instructive point of view on the subject. In particular, we focus on the actual possibility to get such a multiplication of channels [2] in the far-field zone, which is the usual framework for antenna links. In this respect, we will focus on the case of aperture antennas. Notably, this assumption does not impair the general validity of the following discussion. In fact, any antenna can be regarded as an aperture antenna by a proper choice of the aperture plane [21]. Also, the arguments below could be rephrased in terms of multipole expansions as well as in terms of the appropriate radiation integrals. Then, additional insight is also given by an analysis of the operators relating source and field behaviors for a given order of the vortex. The outcomes confirm limitations indicated in [7],[8], and emphasize some further draw-backs of the proposed multiplexing scheme.The paper is organized as follows. In Sections II and III, respectively, we review some properties of the H...