Phase Mode Analysis of Radio Beams Carrying Orbital Angular Momentum

We present a full analysis of radio beams carrying orbital angular momentum (OAM) generated by a circular array. The vector potential of the array is decomposed into a series of phase modes, which are orthogonal to each other. These phase modes are used to analyze the OAM modes of the generated beam, which reveals the fundamental physics behind the phenomenon of why pure OAM modes can only be realized in the main lobe of the antenna array and why the design condition is set to be |l| <; N/2. Furthermore, to verify the phase mode analysis, an optimized circular array is simulated and analysed.