In free space optical communication, the type and quality of the light source are very important. In this paper, we introduce a vortex class of partially coherent sources of Schell type with a Laguerre–Gaussian Schell-model vortex (LGSMV) beam, which is the product of the dark hollow Laguerre–Gaussian Schell-model beam (2013 Opt. Lett. 38 91) passing through a spiral phase modulator. We study the characteristics of the intensity distribution of the LGSMV beam in the far-field plane. The analytical expression of the cross-spectral density function of a LGSMV beam in the far-field plane is derived. We demonstrate an implicit rule that the number of phase singularities of an LGSMV beam is equal to the original topological charge, when the order p increases to a certain extent. This novel rule provides an effective method for detecting the topological charge of an LGSMV beam in applications such as free space optical communication and optical manipulation.

中文翻译：

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Laguerre-Gaussian Schell模型涡旋光束的相位奇异性演变

在自由空间光通信中，光源的类型和质量非常重要。在本文中，我们介绍了带有Laguerre–Gaussian Schell模型涡旋（LGSMV）光束的Schell型部分相干源的涡流类别，该光束是暗空心Laguerre–Gaussian Schell模型光束的产物（2013年，Lett。 38.91）通过螺旋相位调制器。我们研究了LGSMV光束在远场平面上的强度分布特征。推导了LGSMV光束在远场平面上的交叉谱密度函数的解析表达式。我们证明了一个隐含的规则，即当阶数p增大到一定程度时，LGSMV光束的相奇点数等于原始拓扑电荷。