The results show that the larger the real part of the wave number is, the farther the transmission of PCVBs with hollow distribution will be. The expression of partially coherent vortex beams passing through a gain/absorption medium is derived in this paper based on the generalized Huygens–Fresnel principle. The influences of the refractive index (related to the real part of the wave number) and the gain/absorption characteristics (related to the imaginary part of the wave number) on the transmission of partially coherence vortex beams are investigated. The results show that the larger the real part of the wave number is, the farther the transmission of PCVBs with hollow distribution will be. In gain media, the light power keeps increasing; on the other hand, in absorption media, the light power keeps decreasing. The diffraction effect of the media on the intensity distribution also is mentioned. We discover that, during the transmission, the evolutions of the spectral degree of coherence relate to the real and imaginary parts of the wave number, and the coherence vortices can split and generate. We believe the results of this study are important to the fields of singular optics and optical communications.

中文翻译：

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增益或吸收介质对部分相干涡旋光束传输的影响

结果表明，波数的实部越大，具有空心分布的PCVB的传输距离就越远。本文基于广义惠更斯-菲涅耳原理，推导了通过增益/吸收介质的部分相干涡旋光束的表达式。研究了折射率（与波的实部有关）和增益/吸收特性（与波的虚部有关）对部分相干涡旋光束的传输的影响。结果表明，波数的实部越大，具有空心分布的PCVB的传输距离就越远。在增益媒体中，光功率不断增加；另一方面，在吸收介质中，光功率持续降低。还提到了介质对强度分布的衍射作用。我们发现，在传输过程中，频谱相干度的演变与波数的实部和虚部有关，并且相干涡旋可以分裂并产生。我们相信这项研究的结果对单一光学和光通信领域很重要。