Airy transformation is a useful technique to modulate amplitude and phase of a light beam, which has important applications in particle trapping/manipulation, optical communications and optical imaging. However, most of the studies only focused on the Airy transform of Gaussian beams and other vortex-free beams in the past. In this paper, the Airy transform of Gaussian vortex beams, which are the most common vortex beams, is investigated. A universal analytical expression of the Gaussian vortex beams with topological charge (TC) m passing through an Airy transform optical system is derived. We carry out a detailed study on the output beams’ characteristics after the Airy transform of the Gaussian vortex beams with m = ± 1 and ± 2. The analytical expressions for the centroid, the beam spot size, the divergence angle and the beam propagation factor of the output beams are derived. The effects of the Airy control parameters and the TC on the normalized intensity distribution, the phase distribution, the centroid, the beam spot size and the beam propagation factor of the output beams are investigated both theoretically and experimentally. The experimental results agree reasonably well with the theoretical results which illustrate the properties of Airy transform of the Gaussian vortex beams.

艾里变换是一种调制光束振幅和相位的有用技术，在粒子捕获/操纵、光通信和光学成像中具有重要应用。然而，以往的研究大多只集中在高斯光束和其他无涡旋光束的艾里变换上。在本文中，研究了最常见的涡旋光束高斯涡旋光束的艾里变换。推导出具有拓扑电荷(TC) m的高斯涡旋光束通过艾里变换光学系统的通用解析表达式。我们对具有m的高斯涡旋光束进行艾里变换后的输出光束特性进行了详细研究= ± 1 和 ± 2。导出光束的质心、光束光斑尺寸、发散角和光束传播因子的解析表达式。从理论上和实验上研究了艾里控制参数和 TC 对归一化强度分布、相位分布、质心、束斑尺寸和输出光束的光束传播因子的影响。实验结果与说明高斯涡旋光束艾里变换特性的理论结果相当吻合。