We present in this work the propagation properties of Generalized Humbert-Gaussian beams (GHGBs) passing through a paraxial ABCD optical system. Based on the extended Huygens-Fresnel integral, the analytical expression of the intensity distribution for GHGBs is derived and some numerical simulations are performed for particular cases in free space, thin lens in a free space and graded refractive index system. Our results show that the comportment of several particular cases of these beams during the propagation is influenced by the beam orders and the characteristic parameters of the system.

中文翻译：

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一些环形激光束通过近轴 ABCD 光学系统的传播分析

我们在这项工作中介绍了通过近轴 ABCD 光学系统的广义 Humbert-Gaussian 光束 (GHGB) 的传播特性。基于扩展的惠更斯-菲涅耳积分，推导出了GHGBs强度分布的解析表达式，并对自由空间中的特殊情况、自由空间中的薄透镜和渐变折射率系统进行了一些数值模拟。我们的结果表明，这些光束在传播过程中的几种特殊情况的组合受光束阶数和系统特征参数的影响。