为了调控艾里光束的传播, 提出一种广义艾里光束.在传统立方相位基础上引入两个可变旋转角因子θ1和θ2,形成新改进的可调谐相位, 加载该相位的高斯光束经傅里叶变换后可以产生广义艾里光束.基于衍射突变理论, 分析讨论了该光束的双曲抛物线传播行为. 重点研究了当旋转角θ1=π/3和θ2=7π/6时, 该光束在传播距离0、3、6、10cm处的无衍射传播特性; 以及旋转因子θ1=3π/2和θ2=π/4时, 该光束在传播距离0、3、6、10cm处的自愈特性.理论研究表明该光束并非傍轴波动方程的特解, 但数值模拟及实验证实其在一定程度上拥有无衍射及自愈特性. 该光束不仅可沿任意指定的抛物线轨迹传播, 同时还具有与传统艾里光束明显不同的空间强度分布, 使其在光学操纵与生物医学等方面有潜在的应用.

In order to control the propagation trajectory of an Airy beam, generalized Airy beams are proposed theoretically. Such beams can be generated by modulating a Gaussian beam imposed on a tunable phase pattern, where two angle factors θ1 and θ2 are introduced in cubic phase. The hyperbolic parabola is investigated based on diffraction catastrophe theory. We focus on the nondiffracting property in the propagation distances of 0, 3, 6, 10cm in the case of θ1=π/3 andθ2=7π/6, and the selfhealing property in the case of θ1=3π/2 and θ2=π/4. The experiment and numerical simulations demonstrate that such beams still possess the nondiffracting, selfhealing properties to some extent, although the theory shows that they are not the solutions for paraxial wave equation. The generalized Airy beams can propagate along arbitrarily appointed parabolic trajectories and directions in free space, and their intensity distributions are different from that of traditional Airy beams, which make the generalized Airy beams have potential applications in optical trapping and biomedicine.