In this paper, the propagation of partially coherent vortex beams in gain media was investigated based on the generalized Huygens-Fresnel principle. Our research focused on the influences of topological charge (m) and coherence length (σ₀) on light intensity distribution, phase and spectral degree of coherence during the propagation. The results show that partially coherent vortex beams can maintain their initial dark hollow intensity distributions for a longer distance with larger m and σ₀ as the gain and diffraction effects appear simultaneously. The decay of the maximum value of light intensity caused by diffraction is more obvious with a smaller σ₀. On the other hand, the larger σ₀ is, the more obvious the gain effect on the maximum value of light intensity is. We also observe that the coherence vortex with topological charge equals to m will split into m coherence vortices with topological charges are 1, and the coherence vortices with negative topological charge will generate at the same time. Some phenomena also appear with a larger coherence length, for example, a larger distance between coherence vortices with negative topological charge, a bigger splitting of the coherence vortices, and a slower damping of spectral degree of coherence, et al. This study can be used in the research and application of vortex beams in the materials field.

在本文中，基于广义惠更斯-菲涅耳原理研究了部分相干涡旋光束在增益介质中的传播。我们的研究重点是拓扑电荷 ( m ) 和相干长度 ( σ ₀ ) 对传播过程中光强分布、相位和光谱相干度的影响。结果表明，当增益和衍射效应同时出现时，部分相干涡旋光束可以在更长的距离内保持其初始暗空心强度分布，并具有更大的m和σ ₀。σ ₀越小，衍射引起的光强最大值衰减越明显. 另一方面，σ ₀越大，增益对光强最大值的影响越明显。我们还观察到与拓扑荷相干旋涡等于米分裂成米相干涡旋与拓扑收费1，并与负拓扑荷的相干涡旋会在同一时间产生。一些现象也伴随着较大的相干长度而出现，例如具有负拓扑电荷的相干涡之间的距离较大、相干涡分裂较大、谱相干度衰减较慢等。本研究可用于涡旋光束在材料领域的研究和应用。