In this paper, we investigate the focusing properties of a vortex-cosh-Gaussian (vChG) beam passing through a converging thin lens. Based on the Huygens–Fresnel diffraction integral, we derived the analytical propagation equation as well as the beam width expression of a focused vChGB. It is shown that the focusing properties including the focal shift of the focused vChGB are crucially dependent on the incident beam parameters namely the decentered parameter and the topological charge in addition to the Gaussian Fresnel number \(N_{F}\). From typical numerical examples, it is found that the focused vChGB is transformed into a multi-lobes structure shape at the real focus plane, and the principal maximum intensity of the beam is located away from the axis. The amount of focal shift, which is determined from the minimum spot size criterion, is strongly dependent on the Fresnel number, the decentered parameter and the vortex charge m. The obtained results may be useful for the applications of the vChGBs in beam shaping and beam focusing.

在本文中，我们研究了通过会聚薄透镜的涡旋 - 柯什 - 高斯 (vChG) 光束的聚焦特性。基于惠更斯-菲涅耳衍射积分，我们推导出了解析传播方程以及聚焦 vChGB 的光束宽度表达式。结果表明，除了高斯菲涅尔数\(N_{F}\)之外，包括聚焦 vChGB 的焦移在内的聚焦特性还取决于入射光束参数，即偏心参数和拓扑电荷. 从典型的数值例子中发现，聚焦的vChGB在真实焦平面上转化为多瓣结构形状，光束的主最大强度位于远离轴的位置。由最小光斑尺寸标准确定的焦移量很大程度上取决于菲涅耳数、偏心参数和涡流电荷m。获得的结果可能有助于 vChGBs 在光束整形和光束聚焦中的应用。