Understanding the Far-Field Properties of Orbital Angular Momentum Beams through the Antenna Aperture Field Method

This work aims to provide insight into the far-field properties of orbital angular momentum (OAM) beams. Semi-analytical expressions for the far field of a general cylindrically-symmetric OAM aperture field are derived using the antenna aperture field method. The far-field properties of a circularly-polarized OAM carrying fields are considered. In particular, we derive analytical expression for the minimum theoretically achievable AR of a circularly-polarized OAM beam. For a common OAM-carrier aperture field distribution, i.e., the Laguerre-Gaussian distribution, analytical expressions of the fields are obtained in closed forms. The equations obtained in this paper show excellent agreement with predictions obtained from full-wave simulations. The derived analytical and semi-analytical formulas can potentially guide the design of OAM communication systems.