Based on the Huygens-Fresnel diffraction integral, a concise formula for the higher-order cosh-Gaussian beams (HOChGB) propagating through a paraxial ABCD optical system is derived. The propagation formula of the HOChGB is expressed as a superposition of cosh-Gaussian modes and in terms of the Gaussian beam-parameter q. The profile and the inter-lobe space of the beam at the initial plane are analyzed with the help of the maximum intensity criterion as a function of the decentered parameter and the beam order. It is shown that during propagation the HOChGB with appropriate parameters may progressively change profile, and in far-field the amplitude of the beam is expressed as a superposition of cosine functions modulated by a Gaussian envelope. Furthermore, it is found that the focal shift of the focused HOChGB increases with the decrease of the Fresnel number, the decentered parameter and the beam order.

基于惠更斯-菲涅耳衍射积分，推导出了通过近轴ABCD光学系统传播的高阶cosh-Gaussian光束(HOChGB)的简明公式。HOChGB 的传播公式表示为 cosh-Gaussian 模式的叠加和高斯光束参数 q。借助作为偏心参数和光束阶次的函数的最大强度准则，分析初始平面处光束的轮廓和叶间空间。结果表明，在传播过程中，具有适当参数的 HOChGB 可能会逐渐改变轮廓，并且在远场中，光束的幅度表示为由高斯包络调制的余弦函数的叠加。此外，