How to select the dimensionless radius to realize the strongest abruptly autofocusing ability of circular Airyprime beams

Abruptly autofocusing performance of a circular Airyprime beam (CAPB) is investigated by changing the dimensionless radius of the primary ring R₀. With increasing R₀, the abruptly autofocusing ability of CAPBs first increases and the decreases. An optimal value for R₀ with the strongest autofocusing ability is selected out. With the increase of the exponential decay factor a, the optimal value for R₀ decreases. When a = 0.05 and R₀ = 26.0, the abruptly autofocusing ability of a CAPB is as high as 1822.49. When a = 0.10 and R₀ = 13.5, the abruptly autofocusing ability of a CAPB is further enhanced by 8.42% compared with the previously reported result. Such relationship between the abruptly autofocusing ability and the dimensionless radius also exists in a circular Airy beam (CAB). The difference is that the optimal value for R₀ of a CAPB is greater than that of a CAB. The experimental measurement of abruptly autofocusing ability of CAPBs and CABs confirms the above conclusions. The physical mechanism of the relationship between the abruptly autofocusing ability and the dimensionless radius is qualitatively interpreted by the lateral acceleration and quantitatively explained by simulating the Fresnel zone plate lens. Our research provides a new scheme for how to select the dimensionless radius to realize the strongest abruptly autofocusing ability. This finding provides a new insight into the practical application of circular abruptly autofocusing beams.