基于广义惠更斯-菲涅耳衍射积分公式，推导了双曲正弦-高斯光束通过像散透镜聚焦的场分布解析表达式，并用数值计算研究了双曲正弦-高斯光束在像散透镜焦平面上或焦平面附近的光强分布与相位特性。理论分析与数值计算结果表明，选择适当的光束参数与像散透镜结构参数，可以使双曲正弦-高斯光束经像散透镜后转换为具有涡旋的暗空心光束，其拓扑荷指数为1。此外，还对影响场强度分布与相位分布的光束参数与透镜参数进行了分析讨论。特别地，透镜的像散是双曲正弦-高斯光束经像散透镜聚焦产生暗空心涡旋光束的关键控制因素，利用合适的像散透镜可获得相当长度的理想暗空心光管。

Based on the generalized Huygens-Fresnel diffraction integral formula, field distribution expression of sinh-Gaussian beams passing through astigmatic lens is derived. The intensity distribution and the phase characteristic of sinh-Gaussian beam on focal plane or near focal plane of astigmatic lens are numerically calculated. Theoretical analysis and numerical calculation results indicate that the appropriate beam parameters and astigmatic lens structure parameters can make sinh-Gaussian beam passing through astigmatic lens transform into dark hollow beam with vortex. Its topological charge index is 1. Besides, the beam parameters and the lens coefficients affecting the field intensity distribution and phase distribution are discussed. It is found that the astigmatism of lens plays a critical role in converting sinh-Gaussian beam into a dark hollow beam with vortex through focusing of astigmatism lens, and a super-long dark hollow beam can be obtained with the astigmatic lens.