Design and realization of an autofocusing Airyprime beams array

Abstract

An Airyprime beams array that consists of four centrosymmetric Airyprime beamlets is designed for the first time, and the analytical expression of the Airyprime beams array propagating in free space is derived. The Airyprime beams array is shown to possess the autofocusing property. The effects of the transverse displacement parameter, the exponential decay factor and the scaling factor on the autofocusing ability and the focus position of the Airyprime beams array are investigated in detail. The autofocusing ability of the Airyprime beams array is improved by increasing the transverse displacement parameter or reducing the exponential decay factor. Further, the autofocusing ability of the Airyprime beams array in the case of nonzero off-centre position can be enhanced by decreasing the scaling factor. The focus position of the Airyprime beams array can be controlled by adjusting the transverse displacement parameter or the scaling factor. The autofocusing evolutionary process of the Airyprime beams array is quite different from that of the Airy beams array. The trajectory of the peak intensity for the Airyprime beams array is more regular than that for the Airy beams array. The Airyprime beams array has stronger autofocusing ability and smaller focusing dominant spot than the Airy beams array with the same beam parameters. Moreover, we experimentally generate the Airyprime beams array, and the autofocusing properties of the Airyprime beams array are demonstrated. The Airyprime beams array will find important potential applications in free space optical communication and so on.