Theoretical Analyses and Design of Circular Array to Generate Orbital Angular Momentum

Uniform circular array (UCA) is a pioneering approach to generate radio twisted beams carrying orbital angular momentum (OAM). However, faulty antenna elements in a UCA could render the array into an imperfect UCA (IUCA), consequently creating distortion for OAM-based communication or radar systems. To analyze the effects of an IUCA on generating OAM, elementary wave function and wave transformation are derived to obtain field equations of a general circular array. Further derivation of IUCA shows that the field of an IUCA is a superposition of OAM modes, which is caused by polluted orthogonalities of OAM modes. To achieve pure OAM modes, the orthogonal matching pursuit algorithm, the convex optimization tool, and the analytical solution are employed to design a feeding network to retrieve the orthogonal property at the cost of strong gain loss. Then, the reduced constraints method is proposed for the IUCA to achieve high-purity and low-loss OAM mode. Finally, four circular arrays with different shapes are explored for limited installation space to generate twisted beams.