利用薛定谔方程，理论分析了自由空间中无衍射艾里光束的自弯曲性质.研究了控制该性质的因素，并与实际物理量联系，提出采用梯度折射率材料实现控制艾里光束自弯曲性质的方法.数值模拟了一维和二维艾里光束在传播时出现的自弯曲效应，以及经过控制的艾里光束沿直线无衍射传播和反向弯曲传播的强度分布情况，讨论了艾里光束在梯度折射率材料中沿直线近似无衍射传播的距离与指数衰减因子、光束的主瓣宽度及波长之间的关系.结果显示：在艾里光束的中心波瓣强度衰减为最大强度18%的传播距离内，艾里光束能够保持近似无衍射传播；在实际应用中可以根据艾里光束近似无衍射传播距离的具体要求，通过衰减因子、主瓣宽度和波长三者分别与近似无衍射传播距离之间的关系曲线，综合考虑选取合适的参数值和梯度折射率材料，实现对艾里光束的最佳控制.

Freespace selfbending of nondiffracting Airy beams was theoretically investigated with Schrodinger's equation, the factors influencing selfbending were analyzed, which were linked to actual physical quantities, and the method of acceleration control of Airy beams with gradientindex material was given. The selfbending property appearing during propagation of one and twodimensional Airy beams was numerical simulated. Moreover, the numerical simulation results that the deflection of Airy beams can be compensated and reversed with proper control. The relationship between the propagation length of compensated finite Airy beam in a gradientindex material and the decay factor was discussed. The results show that the compensated finite Airy beam can keep nondiffracting propagation when intensity of the central lobe decays from maximum to eighteen percent of the maximal value. The relationship between the propagation length of compensated finite Airy beam in a gradientindex material and the central lobe width as well as the wavelength was also studied, respectively. In practical application, three appropriate parameter values and a right gradient refractive index material can be selected through the dependent relationship between the decay factor, the central lobe width as well as wavelength and the propagation length of compensated finite Airy beam at the instance of the propagation length of compensated finite Airy beam, and optimal control of Airy beam can be realized.