An efficient tensor approach is used to simulate the propagation of partially coherent Hermite-sinh-Gaussian (H-ShG) beams through an ABCD optical system in a turbulent atmosphere. Analytical expressions for the average intensity are derived. The properties of the average intensity of the beam are studied numerically. It is found that the average intensity distribution of the beam is almost independent of the structure constant of turbulence when the spatial coherence length is very small and the beam with larger spatial coherence length is less affected by the turbulent atmosphere. Moreover, the transition from an H-ShG beam into a Gaussian beam becomes quicker with smaller beam order and smaller Sh parameters.

中文翻译：

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一种有效的张量方法，用于模拟部分相干的Hermite-sinh-Gaussian光束在湍流大气中通过ABCD光学系统的传播。

一种有效的张量方法用于模拟湍流中通过ABCD光学系统传播的部分相干Hermite-sinh-Gaussian（H-ShG）光束的传播。得出平均强度的解析表达式。对光束的平均强度特性进行了数值研究。研究发现，当空间相干长度很小时，光束的平均强度分布几乎与湍流的结构常数无关，而空间相干长度较大的光束受湍流大气的影响较小。此外，从H-ShG光束到高斯光束的过渡变得更快，且光束阶数较小，Sh参数较小。