In this paper, we have introduced a general formula of a new laser beam with a nearly Flattened-top profile. The propagation properties of this beam, called Generalized Flattened Hermite-cosh-Gaussian (GFHChG) beam are studied in detail. Based on the Huygens–Fresnel integral, an analytical expression of the intensity distribution for GFHChG passing through a paraxial ABCD optical system is developed. Several particular cases such as the propagation of the flattened Gaussian beam, the cosh-Gaussian beam, the higher and squared cosh-Gaussian beam and the Hermite-cosh-Gaussian beam are deduced from our result. Numerical simulations are also given in free space and through a circular thin lens in a free space to study the comportment of this beam during propagation.

中文翻译：

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一种新型广义扁平化 Hermite-cosh-Gaussian 光束的传播特性

在本文中，我们介绍了具有近平顶轮廓的新型激光束的一般公式。详细研究了该光束的传播特性，称为广义扁平 Hermite-cosh-Gaussian (GFHChG) 光束。基于惠更斯-菲涅耳积分，开发了 GFHChG 通过近轴 ABCD 光学系统的强度分布的解析表达式。从我们的结果中推导出了几种特殊情况，例如扁平高斯光束，cosh-Gaussian光束，更高和平方的cosh-Gaussian光束和Hermite-cosh-Gaussian光束的传播。数值模拟也在自由空间中给出，并通过自由空间中的圆形薄透镜来研究该光束在传播过程中的特性。