[1] Allen L, Beijersbergen M W. Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 45, 8185-8189(1992).

[2] Xu Q, Pan F, Huang L et al. Analysis of vectorial far-field characteristics of Laguerre-Gaussian beams by angular-spectrum method[J]. Chinese Journal of Lasers, 44, 0805001(2017).

[3] Gibson G, Courtial J, Padgett M J et al. Free-space information transfer using light beams carrying orbital angular momentum[J]. Optics Express, 12, 5448-5456(2004). http://www.ncbi.nlm.nih.gov/pubmed/19484105

[4] Wang J, Yang J Y, Fazal I M et al. Terabit free-space data transmission employing orbital angular momentum multiplexing[J]. Nature Photonics, 6, 488-496(2012). http://www.nature.com/nphoton/journal/v6/n7/abs/nphoton.2012.138.html

[5] Ke X Z, Wang C Z. Intensity distribution of the partially coherent vortex beams propagating in atmospheric turbulence[J]. Laser & Optoelectronics Progress, 53, 110604(2016).

[6] Toselli I, Andrews L C, Phillips R L et al. Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence[J]. Proceedings of SPIE, 6551, 65510E(2007). http://proceedings.spiedigitallibrary.org/mobile/proceeding.aspx?articleid=1302206

[7] Eyyuboglu H T, Baykal Y, Ji X. Scintillations of Laguerre Gaussian beams[J]. Applied Physics B, 98, 857-863(2009). http://link.springer.com/article/10.1007/s00340-009-3702-x

[8] Zhang G Q, Tang H, Wu G H. Study on scintillation of four Laguerre-Gauss beams propagating through the atmospheric turbulence[J]. Semiconductor Optoelectronics, 38, 382-385, 391(2017).

[9] Ke X Z, Chen J, Yang Y M. Study of orbital angular momentum of Laguerre Gaussian beam propagating in atmospheric turbulence in slant path[J]. Acta Physica Sinica, 63, 150301(2014).

[10] Noll R J. Zernike polynomials and atmospheric turbulence[J]. Journal of the Optical Society of America, 66, 207-211(1976). http://mnras.oxfordjournals.org/external-ref?access_num=10.1364/JOSA.66.000207&link_type=DOI

[11] Wu H L, Yan H X, Li X Y et al. Generation of rectangular turbulence phase screens based on fractal characteristics of distorted wavefront[J]. Acta Optica Sinica, 29, 114-119(2009).

[12] Long M H. Transmission characteristics and correlated imaging with partially coherent light through turbulent atmosphere Xi'an:[D]. Xidian University, 25-27(2014).

[13] Torner L, Torres J P, Carrasco S. Digital spiral imaging[J]. Optics Express, 13, 873-881(2005).

[14] Andrews L C, Phillips R L[M]. Laser beam propagation through random media(2005).

[15] 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).

[16] Ding P F, Pu J X. Propagation of Laguerre-Gaussian vortex beam[J]. Acta Physica Sinica, 60, 094204(2011).