Airy transform of elegant Hermite-Gaussian beams is theoretically and experimentally investigated. The analytically general formula of the Airy transform of elegant Hermite-Gaussian beams is presented. The analytically general expressions of the centroid and the beam spot size of an elegant Hermite-Gaussian beam passing through an Airy transform optical system are derived. The effects of the Airy control parameters and the transverse mode numbers on the intensity distribution, the centroid, and the beam spot size of elegant Hermite-Gaussian beams passing through Airy transform optical systems are investigated, respectively. The experimental results coincide with the theoretical results. Also, the Airy transform of the elegant and the standard Hermite-Gaussian beams is compared. The analytical expression of the Airy transform of the elegant Hermite-Gaussian beam is more concise than that of the standard Hermite-Gaussian beam. Although the optical fields in the x-direction of the Airy transform of the elegant and the standard Hermite-Gaussian beams with transverse mode number m > 1 are both the sum of the zero-order derivative up to m^th-order derivative of the Airy function, the weight coefficient of the same order derivative of the Airy function is different for the elegant and the standard transformed Hermite-Gaussian beams. The centroids of the elegant and the standard Hermite-Gaussian beams passing through the same Airy transform optical system are the same. However, the beam spot size of the elegant transformed Hermite-Gaussian beam is less than or equal to that of the standard transformed Hermite-Gaussian beam. The meaning of elegance is also embodied in the Airy transform of the elegant optical beams. This research reveals the difference between the Airy transform of the elegant and the standard Hermite-Gaussian beams.

理论上和实验上研究了优雅的厄米-高斯光束的Airy变换。给出了优雅的厄米-高斯光束的艾里变换的解析通式。推导了通过艾里变换光学系统的优雅厄米-高斯光束的质心和束斑尺寸的解析一般表达式。研究了Airy控制参数和横向模数对通过Airy变换光学系统的优雅Hermite-Gaussian光束的强度分布，质心和束斑尺寸的影响。实验结果与理论结果吻合。而且，比较了优雅光束和标准埃尔米-高斯光束的Airy变换。优雅的Hermite-Gaussian光束的Airy变换的解析表达式比标准Hermite-Gaussian光束的解析表达式更简洁。虽然在横向模数为m  > 1的优雅光束和标准Hermite-Gaussian光束的Airy变换的x方向都是零阶导数之和，直至m ^th艾里函数的高阶导数，对于优雅和标准变换的厄米-高斯光束，艾里函数的同一阶导数的权重系数是不同的。穿过同一Airy变换光学系统的优雅光束和标准Hermite-Gaussian光束的质心相同。但是，优雅变换的厄米-高斯光束的束斑尺寸小于或等于标准变换的厄米-高斯光束的束斑尺寸。高雅的含义还体现在高雅光束的Airy变换中。这项研究揭示了高雅的艾里变换与标准的埃尔米-高斯光束之间的区别。