1. Peleg, A. and J. V. Moloney, "Scintillation index for two Gaussian laser beams with different wavelengths in weak atmospheric turbulence ," J. Opt. Soc. Am. A Opt. Image. Sci. Vis., Vol. 23, 3114-3122, 2006.
doi:10.1364/JOSAA.23.003114

2. Ji, X. and G. Ji, "Spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence," Applied Physics B, Vol. 92, 111-118, 2008.
doi:10.1007/s00340-008-3050-2

3. Li, X., X. Chen, and X. Ji, "Influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian beams," Opt. Commun., Vol. 282, 7-13, 2009.
doi:10.1016/j.optcom.2008.09.063

4. Gu, Y. L. and G. Gbur, "Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence," J. Opt. Soc. Am. A, Vol. 27, 2621-2629, 2010.
doi:10.1364/JOSAA.27.002621

5. Zhou, G. Q. and X. X. Chu, "Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere," Opt. Express, Vol. 18, 726-731, 2010.
doi:10.1364/OE.18.000726

6. Wang, K. L. and C. H. Zhao, "Propagation properties of a radial phased-locked partially coherent anomalous hollow beam array in turbulent atmosphere," Opt. Laser Technol., Vol. 57, 44-51, 2014.
doi:10.1016/j.optlastec.2013.09.037

7. Tang, M. M. and D. M. Zhao, "Regions of spreading of Gaussian array beams propagating through oceanic turbulence," Appl. Optics, Vol. 54, 3407-3411, 2015.
doi:10.1364/AO.54.003407

8. Liu, D. J., L. Chen, Y. C. Wang, and H. M. Yin, "Intensity properties of four-petal Gaussian vortex beams propagating through atmospheric turbulence," Optik, Vol. 127, 3905-3911, 2016.
doi:10.1016/j.ijleo.2016.01.024

9. Yin, X. and L. C. Zhang, "Quantum polarization fluctuations of an Airy beam in turbulent atmosphere in a slant path," J. Opt. Soc. Am. A, Vol. 33, 1348-1352, 2016.
doi:10.1364/JOSAA.33.001348

10. Zhu, J., X. Li, H. Tang, and K. Zhu, "Propagation of multi-cosine-Laguerre-Gaussian correlated Schell-model beams in free space and atmospheric turbulence," Opt. Express, Vol. 25, 20071-20086, 2017.
doi:10.1364/OE.25.020071

11. Wang, F. and O. Korotkova, "Circularly symmetric cusped random beams in free space and atmospheric turbulence," Opt Express, Vol. 25, 5057-5067, 2017.
doi:10.1364/OE.25.005057

12. Tian, H. H., Y. G. Xu, T. Yang, Z. R. Ma, S. J. Wang, and Y. Q. Dan, "Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path ," J. Mod. Optic, Vol. 64, 422-429, 2017.
doi:10.1080/09500340.2016.1241441

13. Zheng, G., G., J. Wang, L. Wang, M. Zhou, Y. Chen, and M. Song, "Scintillation analysis of pseudo-Bessel-Gaussian Schell-mode beams propagating through atmospheric turbulence with wave optics simulation," Optics & Laser Technology, Vol. 100, 139-144, 2018.
doi:10.1016/j.optlastec.2017.10.002

14. Wang, F., X. L. Liu, and Y. J. Cai, "Propagation of partially coherent beam in turbulent atmosphere: A review," Progress In Electromagnetics Research, Vol. 150, 123-143, 2015.
doi:10.2528/PIER15010802

15. Wang, F., J. Li, G. Martinez-Piedra, and O. Korotkova, "Propagation dynamics of partially coherent crescent-like optical beams in free space and turbulent atmosphere," Opt. Express, Vol. 25, 26055-26066, 2017.
doi:10.1364/OE.25.026055

16. Liu, D., G. Wang, and Y. Wang, "Average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence," Optics & Laser Technology, Vol. 98, 309-317, 2018.
doi:10.1016/j.optlastec.2017.08.011

17. Liu, D. J., X. X. Luo, H. M. Yin, G. Q. Wang, and Y. C. Wang, "Effect of optical system and turbulent atmosphere on the average intensity of partially coherent flat-topped vortex hollow beam," Optik, Vol. 130, 227-236, 2017.
doi:10.1016/j.ijleo.2016.08.128

18. Banakh, V. A. and L. O. Gerasimova, "Strong scintillations of pulsed Laguerrian beams in a turbulent atmosphere," Opt. Express, Vol. 24, 19264-19277, 2016.
doi:10.1364/OE.24.019264

19. Liu, D. and Y. Wang, "Evolution properties of a radial phased-locked partially coherent Lorentz-Gauss array beam in oceanic turbulence," Optics & Laser Technology, Vol. 103, 33-41, 2018.
doi:10.1016/j.optlastec.2018.01.014

20. Golmohammady, S. and B. Ghafary, "Stokes parameters of phase-locked partially coherent flat-topped array laser beams propagating through turbulent atmosphere," Laser Phys., Vol. 26, 2016.
doi:10.1088/1054-660X/26/6/066201

21. Liu, D., H. Yin, G. Wang, and Y. Wang, "Propagation of partially coherent Lorentz-Gauss vortex beam through oceanic turbulence," Appl. Optics, Vol. 56, 8785-8792, 2017.
doi:10.1364/AO.56.008785

22. Liu, D. J., Y. C. Wang, and H. M. Yin, "Propagation properties of partially coherent four-petal Gaussian vortex beams in turbulent atmosphere," Opt. Laser Technol., Vol. 78, 95-100, 2016.
doi:10.1016/j.optlastec.2015.10.004

23. Zhi, D., R. M. Tao, P. Zhou, Y. X. Ma, W. M. Wu, X. L. Wang, and L. Si, "Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence," Opt. Commun., Vol. 387, 157-165, 2017.
doi:10.1016/j.optcom.2016.11.049

24. Liu, D., H. Zhong, G. Wang, and Y. Wang, "Model of a four-petal Lorentz-Gauss beam and its paraxial propagation ," Optik, Vol. 179, 492-498, 2019.
doi:10.1016/j.ijleo.2018.10.134

25. Liu, D., G. Wang, H. Zhong, H. Yin, A. Dong, and Y. Wang, "Properties of a four-petal Lorentz-Gauss beam propagating in uniaxial crystal orthogonal to the optical axis," Optik, Vol. 183, 257-265, 2019.
doi:10.1016/j.ijleo.2019.02.136

26. El Gawhary, O. and S. Severini, "Lorentz beams and symmetry properties in paraxial optics," J. Opt. A: Pure Appl. Opt., Vol. 8, 409-414, 2006.
doi:10.1088/1464-4258/8/5/007

27. Schmidt, P., "A method for the convolution of lineshapes which involve the Lorentz distribution," Journal of Physics B, Vol. 9, 2331-2339, 1976.
doi:10.1088/0022-3700/9/13/018

28. Jeffrey, H. D. A., Handbook of Mathematical Formulas and Integrals, 4th Ed., Academic Press Inc, 2008.