[1] Zhu K C, Zhou G Q, Li X G et al. Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere[J]. Optics Express, 16, 21315-21320(2008).

[2] Gu Y L. Statistics of optical vortex wander on propagation through atmospheric turbulence[J]. Journal of the Optical Society of America A, 30, 708-716(2013).

[3] Gbur G, Tyson R K. Vortex beam propagation through atmospheric turbulence and topological charge conservation[J]. Journal of the Optical Society of America A, 25, 225-230(2008).

[4] Lukin V P, Konyaev P A, Sennikov V A. Beam spreading of vortex beams propagating in turbulent atmosphere[J]. Applied Optics, 51, C84-C87(2012).

[5] Ge X L, Wang B Y, Guo C S. Beam broadening of vortex beams propagating in turbulent atmosphere[J]. Acta Optica Sinica, 36, 0301002(2016).

[6] Ke X Z, Wang C Z. Intensity distribution of partially coherent off-axis vortex beam propagating in atmospheric turbulence[J]. Acta Optica Sinica, 37, 0101005(2017).

[7] Zhong Y L, Cui Z F, Shi J P et al. Propagation properties of partially coherent Laguerre-Gaussian beams in turbulent atmosphere[J]. Optics & Laser Technology, 43, 741-747(2011).

[8] Xu H F, Zhang Z, Qu J et al. Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence[J]. Optics Express, 22, 22479-22489(2014).

[9] Xiao Q Y, Zhang R Z. Propagation characteristics of super-Gaussian beams with vortex wave-front[J]. High Power Laser and Particle Beams, 26, 121015(2014).

[10] Fleck J A. Jr., Morris J R, Feit M D. Time-dependent propagation of high energy laser beams through the atmosphere[J]. Applied Physics, 10, 129-160(1976).

[11] Frehlich R. Simulation of laser propagation in a turbulent atmosphere[J]. Applied Optics, 39, 393-397(2000).

[12] Nie J Y, Xiao Q Y, Liu G D et al. Propagation characteristics of ultra-short Gaussian vortex beams[J]. Optik, 141, 99-104(2017).