An optimum design of a ring Airyprime beam array based on dimensionless eccentric position

The beam array with abruptly autofocusing capability weakens the turbulence effect in free space optical (FSO) communication systems with relatively low complexity, thereby improving the communication quality of FSO communication systems. Based on the perspective of dimensionless eccentric position B, the design of a ring Airyprime beam array (RAPBA) is optimized to achieve the strongest autofocusing capability. When B increases from zero, the autofocusing capability of a RAPBA first increases, then reaches a maximum value, and finally decreases. With given the exponential decay factor a, an optimum value of B under which the autofocusing capability is the strongest is searched out. With the decrease of a, the optimum value of B increases. When a = 0.05, the autofocusing capability of a RAPBA with the optimum B is enhanced by 373.66 % compared with the maximum autofocusing capability of a circular Airyprime beam, while the corresponding focal length is only shortened by 4.73 %. Also, we construct a concise experimental optical setup for the acquisition and the measurement of a RAPBA. The measured results support the theoretical predictions. The physical logical principles underlying the autofocusing capability and the dimensionless eccentric position is interpreted. This research offers a novel approach for an optimum design of a RAPBA with the strongest autofocusing capability. A similar variation pattern of autofocusing capability and dimensionless eccentric position exists in a ring Airy beam array (RABA). Accordingly, our proposed scheme is also suitable for the optimum design of a RABA.