Generation of Laguerre-Gaussian Modes by Aperture or Array Sources

This paper investigates the generation of Laguerre-Gaussian (LG) modes at radio frequencies (RFs) by utilizing either a continuous aperture or a discrete array. The mode generation can be performed with or without sidelobe control, and superdirectivity is avoided by properly selecting the system geometry and regularizing the associated inverse problem. For an individual mode, a continuous aperture source is first determined based on the singular value decomposition of the wave system. This continuous source is subsequently discretized following the construction of a 2-D quadrature rule, which, in the two extreme cases of no and maximum sidelobe suppression, results in an array grid that inherently requires a minimum number of antenna elements. A tradeoff can be made between the adopted array element number and the realized sidelobe level. A method to use a single array with a conserved number of elements to generate and multiplex multiple modes simultaneously is also developed. Full-wave simulations are used to demonstrate the application of the developed theories to arrays of realistic antennas with mutual coupling included. The study shows that, despite their origin in optics, LG modes can be accurately generated in the RF regime, and therefore still play a crucial role in orbital angular momentum (OAM)-based radio.