Exploring the upper limit of the number of vortices loaded onto a ring Airyprime vortex beam array to achieve the strongest auto-focusing ability.

An Airy-like vortex beam array achieves the encoding and transmission of information through its auto-focusing property and the carriage of orbital angular momentum. However, the study of its auto-focusing ability, especially how this ability is affected by the number of vortices uploaded, has rarely been explored. This study delves into the effect of the number of vortices loaded onto a ring Airyprime vortex beam array (RAPVBA) on its auto-focusing ability. Two types of vortices, namely vortices with identical and opposite vortices, are studied, respectively. Regardless of whether the identical or opposite vortices are uploaded, for the number of vortices loaded onto the RAPVBA to achieve the strongest auto-focusing ability exists an upper limit, which can be interpreted by the flow of energy fluxes (also known as the Poynting vector). Overloading and underloading of the number of vortices will not achieve the strongest auto-focusing ability. Finally, the RAPVBA is experimentally generated, and the effect of the number of vortices on auto-focusing ability is measured. The experimental results match the theoretical predictions closely, confirming the accuracy of the theoretical model. This study provides a scheme for accurately controlling the number of vortices to generate a vortex beam array with the strongest auto-focusing ability, which can be potentially used in atmospheric optical communication.