中文摘要：

空间相位调制一直是设计新型自加速光束的重要方法．参照类贝塞尔光束产生的思路，从理论上提出了一种新型的自加速无衍射类贝塞尔-厄米-高斯光束，并从数值模拟和实验两个方面研究此光束沿不同轨道的演化．理论上通过对厄米．高斯光束进行相位调制，产生了不同模式的自加速类贝塞尔-厄米-高斯光束．采用分步傅里叶算法模拟了（0，1），（1，0），（1，1）和（1，2）阶类贝塞尔-厄米．高斯光束沿预设轨道的传输过程．采用计算全息和空间光调制技术在实验中观察了类贝塞尔-厄米-高斯光束沿预设轨道的传输，例如抛物、双曲、双曲正割和三维轨道．实验观察与理论结果符合得很好．实验验证了不同阶类贝塞尔-厄米-高斯光束的奇特光斑结构，验证了光束的非衍射特性及传输轨道的可控性，且理论模拟验证了光束的自修复特性．作为此前研究的类贝塞尔光束的一般形式，本文所得到的光束可用于构造出更加新型实用的光束．

英文摘要：

Phase modulation is an important method of designing accelerating optical beams. In this paper, we present new self-accelerating non-diffracting Bessel-like Hermite-Gaussian beams based on our previous research on Bessel-like beams. The evolutions of the beams along different trajectories are studied numerically and experimentally. These beams are designed by modulating the phase of the initial Hermite-Gaussian beams. With the split-step beam propagation method, we show numerically that （0,1）, （1,0）, （1,1） and （1,2） modes of the Bessel-like Hermite-Gaussian beams can propagate along different predesigned trajectories. With the computer-generated hologram and spatial light modulator, we observe the propagating behaviors of the Bessel-like Hermite-Gaussian beams along different trajectories, including parabolic, hyperbolic, hyperbolic secant and 3D trajectories. Experimental results show good agreement with the theoretical prediction. It is also demonstrated that the peculiar profile of Bessel-like Hermite-Gaussian beams exhibits nondiffracting and self-healing properties propagating along the tunable trajectories. These beams generalize the concept of Bessel-like beams, suggesting that more exotic optical beams can be obtained.