Synthesis for OAM Vortex Electromagnetic Waves Based on Fourier–Bessel Expansion

Abstract

In this article, we proposed a method for low sidelobe vortex wave synthesis. Using Fourier–Bessel series expansion, arbitrary radiation pattern function can be synthesized. Fortunately, the radiation pattern of concentric annulus array for vortex wave is a finite series involving Bessel functions of the first kind, which exactly suits for the Fourier–Bessel series expansion. Considering that a radiation pattern of vortex beam has a null depth in the center, it is similar to the difference pattern of monopulse radar. Therefore, we use the Bayliss difference pattern function as the objective pattern. By calculating Fourier–Bessel expansion coefficients, concentric annulus arrays can be used to effectively generate low sidelobe vortex beams. Our synthesis method may provide a theoretical reference for secure vortex communication and vortex radars in the future.