We investigate the propagation characteristics of partially coherent multi-Gaussian Schell-model (MGSM) and modified Bessel-correlated (MBc) vortex beams traveling in a turbulent plasma. Based on the extended Huygens-Fresnel principle, the cross-spectral density expressions for partially coherent MGSM and MBc vortex beams propagating through turbulent plasma were derived. The results show that the dark spot at the center of the partially coherent MGSM beams disappears in the low-coherence states and remains in the high-coherence states only. In contrast, the intensity of partially coherent MBc vortex beams exists in low- and high-coherence states and does not change during propagation in a weak turbulent plasma.

The propagation properties of partially coherent circular flat-topped (FT) vortex hollow/nonvortex beams are studied in anisotropic turbulent plasma. The analytical expression of the optical intensity of these beams is obtained by employing the extended Huygens–Fresnel integral. The effects of the source and turbulent plasma parameters on the intensity distribution of partially coherent circular FT vortex hollow/nonvortex beams are analyzed numerically. The results show that partially coherent circular FT vortex hollow/nonvortex beams will finally converge into a Gaussian intensity profile at increasing propagation distances. The results also showed that the partially coherent FT vortex hollow/nonvortex beams with higher coherence are less affected by anisotropic turbulent plasma than the less coherent beams.

Based on the extended Huygens-Fresnel principle, the analytical expressions for partially coherent four-petal Gaussian (FPG) vortex beams propagating in turbulent plasma are obtained, the influence of the turbulent plasma parameters on beam profile and coherence of the beams is discussed in detail using numerical examples. It is found that a four-petal Gaussian-shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent plasma. Meanwhile, turbulent plasma parameters will also influence the coherence characterizations of the beams.

The propagation of a partially Lorentz–Gauss beam in a uniform-intensity diffractive axicon is studied according to the Huygens–Fresnel principle, the Hermite–Gaussian expansion of a Lorentz function, and using the stationary phase method. We have derived the intensity equation of a partially coherent Lorentz-Gauss beams propagating through uniform-intensity diffractive axicon, and we proved mathematically that it is the superposition of Bessel beams of various orders after emerging from axicon, using Hermite’s function series and the Bessel function integral formulas. The results show that the intensity distribution of the diffracted beam is the intensity pattern evolved from a Lorentz–Gauss shaped spot into a Gaussian-shaped spot at any position on the focal length of the axicon, and the intensity distribution of a partially Lorentz–Gauss beam generated by an axicon becomes uniform by increasing the beam width and more uniform and constant with the larger coherence width.