P. Zhou, X. L. Wang, Y. X. Ma, H. T. Ma, X. J. Xu, and Z. J. Liu, “Propagation property of a nonuniformly polarized beam array in turbulent atmosphere,” Appl. Opt. 50, 1234–1239 (2011).

[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).

[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).

[CrossRef]

Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).

[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).

[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).

[CrossRef]

X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).

[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).

[CrossRef]

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).

[CrossRef]

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).

[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).

[CrossRef]

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).

[CrossRef]

M. H. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008).

[CrossRef]

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).

[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).

[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).

[CrossRef]

R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).

[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).

[CrossRef]

Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).

[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).

[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).

[CrossRef]

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).

[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).

[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).

[CrossRef]

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).

[CrossRef]

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).

[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).

[CrossRef]

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).

[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).

[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).

[CrossRef]

X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).

[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).

[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).

[CrossRef]

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).

[CrossRef]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).

[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).

[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).

[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).

[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).

[CrossRef]

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).

[CrossRef]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).

[CrossRef]

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).

[CrossRef]

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).

[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).

[CrossRef]

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).

[CrossRef]

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” in Proceedings of IEEE Conference (IEEE, 1983), pp. 722–737.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).

[CrossRef]

M. H. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008).

[CrossRef]

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).

[CrossRef]

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).

[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).

[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).

[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).

[CrossRef]

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).

[CrossRef]

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).

[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).

[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).

[CrossRef]

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

S. S. Khmelertov, “Propagation of laser radian in a turbulent atmosphere,” Appl. Opt. 12, 2421–2433 (1973).

[CrossRef]

V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).

[CrossRef]

R. Frehlich, “Simulation of laser propagation in a turbulent atmosphere,” Appl. Opt. 39, 393–397 (2000).

[CrossRef]

J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).

[CrossRef]

A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39, 5426–5445 (2000).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).

[CrossRef]

P. Zhou, X. L. Wang, Y. X. Ma, H. T. Ma, X. J. Xu, and Z. J. Liu, “Propagation property of a nonuniformly polarized beam array in turbulent atmosphere,” Appl. Opt. 50, 1234–1239 (2011).

[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).

[CrossRef]

V. P. Lukin, P. A. Konyaev, and V. A. Sennikov, “Beam spreading of vortex beams propagating in turbulent atmosphere,” Appl. Opt. 51, C84–C87 (2012).

[CrossRef]

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).

[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).

[CrossRef]

R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).

[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).

[CrossRef]

M. H. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008).

[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).

[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).

[CrossRef]

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).

[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).

[CrossRef]

Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).

[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).

[CrossRef]

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).

[CrossRef]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).

[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).

[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).

[CrossRef]

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).

[CrossRef]

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” in Proceedings of IEEE Conference (IEEE, 1983), pp. 722–737.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).