Abstract

Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov’s power spectrum on the propagation factor are also analyzed in detailed.

© 2014 Optical Society of America

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References

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2014 (11)

Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014).
[Crossref] [PubMed]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[Crossref]

O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
[Crossref]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

L. Pan, C. Ding, and H. Wang, “Diffraction of cosine-Gaussian-correlated Schell-model beams,” Opt. Express 22(10), 11670–11679 (2014).
[Crossref] [PubMed]

Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

2013 (9)

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
[Crossref] [PubMed]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

S. Cui, Z. Chen, L. Zhang, and J. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (4)

2010 (4)

2009 (6)

2008 (2)

Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008).
[Crossref] [PubMed]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[Crossref]

2007 (1)

2005 (1)

Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056607 (2005).
[Crossref] [PubMed]

2004 (1)

O. Korotkova, R. L. Phillips, and L. C. Andrews, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

2003 (2)

2002 (1)

1999 (1)

1990 (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).

Amarande, S.

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[Crossref]

O. Korotkova, R. L. Phillips, and L. C. Andrews, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Baykal, Y.

Borghi, R.

Cai, Y.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[Crossref]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19(7), 5979–5992 (2011).
[Crossref] [PubMed]

C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam,” Opt. Lett. 36(12), 2251–2253 (2011).
[Crossref] [PubMed]

C. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express 17(3), 1753–1765 (2009).
[Crossref] [PubMed]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056607 (2005).
[Crossref] [PubMed]

Cang, J.

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Chen, R.

Chen, Y.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Chen, Z.

Cheng, W.

Chu, X.

G. Zhou and X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express 17(13), 10529–10534 (2009).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere,” Opt. Lasers Eng. 47(11), 1254–1258 (2009).
[Crossref]

Cincotti, G.

Cui, S.

Cui, Z.

Dan, Y.

Davidson, F. M.

Ding, C.

Dogariu, A.

Dong, Y.

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Eyyuboglu, H. T.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[Crossref]

Fischer, D. G.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104(17), 173902 (2010).
[Crossref] [PubMed]

Gbur, G.

Gori, F.

Gu, Y.

Guo, H.

Haus, J. W.

Korotkova, O.

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
[Crossref]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
[Crossref] [PubMed]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
[Crossref] [PubMed]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
[Crossref] [PubMed]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

O. Korotkova, R. L. Phillips, and L. C. Andrews, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Lajunen, H.

Liang, C.

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Liu, L.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[Crossref]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

Liu, X.

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Liu, Z.

P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, “Average spreading of a Gaussian beam array in non-Kolmogorov turbulence,” Opt. Lett. 35(7), 1043–1045 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere,” Opt. Lasers Eng. 47(11), 1254–1258 (2009).
[Crossref]

Lu, X.

Luo, B.

Ma, Y.

Mei, Z.

Pan, L.

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[Crossref]

O. Korotkova, R. L. Phillips, and L. C. Andrews, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Pu, J.

Qu, J.

Ramírez-Sánchez, V.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

Ricklin, J. C.

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Shchepakina, E.

Shirai, T.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

T. Shirai, A. Dogariu, and E. Wolf, “Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence,” Opt. Lett. 28(8), 610–612 (2003).
[Crossref] [PubMed]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).

Tong, Z.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[Crossref]

Vahimaa, P.

Van Dijk, T.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104(17), 173902 (2010).
[Crossref] [PubMed]

Visser, T. D.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104(17), 173902 (2010).
[Crossref] [PubMed]

Wang, F.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

Wang, H.

Wang, X.

Wolf, E.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104(17), 173902 (2010).
[Crossref] [PubMed]

T. Shirai, A. Dogariu, and E. Wolf, “Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence,” Opt. Lett. 28(8), 610–612 (2003).
[Crossref] [PubMed]

Wu, G.

Xiu, P.

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Xu, H.

Xu, X.

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere,” Opt. Lasers Eng. 47(11), 1254–1258 (2009).
[Crossref]

Yao, M.

Yu, S.

Yuan, Y.

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

Zhan, Q.

Zhang, B.

Zhang, L.

Zhang, Y.

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[Crossref]

Zhao, C.

Zhao, H.

Zhou, G.

Zhou, P.

P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, “Average spreading of a Gaussian beam array in non-Kolmogorov turbulence,” Opt. Lett. 35(7), 1043–1045 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere,” Opt. Lasers Eng. 47(11), 1254–1258 (2009).
[Crossref]

Zhu, S.

Zhu, S. Y.

Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056607 (2005).
[Crossref] [PubMed]

J. Opt. (1)

O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Opt. Eng. (2)

O. Korotkova, R. L. Phillips, and L. C. Andrews, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026003 (2008).
[Crossref]

Opt. Express (14)

L. Pan, C. Ding, and H. Wang, “Diffraction of cosine-Gaussian-correlated Schell-model beams,” Opt. Express 22(10), 11670–11679 (2014).
[Crossref] [PubMed]

Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
[Crossref] [PubMed]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19(7), 5979–5992 (2011).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008).
[Crossref] [PubMed]

C. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express 17(3), 1753–1765 (2009).
[Crossref] [PubMed]

G. Zhou and X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express 17(13), 10529–10534 (2009).
[Crossref] [PubMed]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17(20), 17829–17836 (2009).
[Crossref] [PubMed]

H. Xu, Z. Cui, and J. Qu, “Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence,” Opt. Express 19(22), 21163–21173 (2011).
[Crossref] [PubMed]

Opt. Laser Technol. (2)

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Opt. Lasers Eng. (1)

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere,” Opt. Lasers Eng. 47(11), 1254–1258 (2009).
[Crossref]

Opt. Lett. (18)

A. Dogariu and S. Amarande, “Propagation of partially coherent beams: turbulence-induced degradation,” Opt. Lett. 28(1), 10–12 (2003).
[Crossref] [PubMed]

T. Shirai, A. Dogariu, and E. Wolf, “Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence,” Opt. Lett. 28(8), 610–612 (2003).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[Crossref] [PubMed]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[Crossref] [PubMed]

G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35(5), 715–717 (2010).
[Crossref] [PubMed]

P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, “Average spreading of a Gaussian beam array in non-Kolmogorov turbulence,” Opt. Lett. 35(7), 1043–1045 (2010).
[Crossref] [PubMed]

S. Cui, Z. Chen, L. Zhang, and J. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[Crossref] [PubMed]

Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014).
[Crossref] [PubMed]

C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam,” Opt. Lett. 36(12), 2251–2253 (2011).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
[Crossref] [PubMed]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Phys. Lett. A (1)

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[Crossref]

Phys. Rev. A (1)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056607 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104(17), 173902 (2010).
[Crossref] [PubMed]

Proc. SPIE (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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Figures (7)

Fig. 1
Fig. 1 Normalized rms angular width of the CGSM beams on propagation in non-Kolmogorov turbulence for different values of (a) parameter n with δ = 0.02 m and (b) spatial coherence δ with n = 2 , respectively.
Fig. 2
Fig. 2 Normalized propagation factor of CGSM beams versus the propagation distance in non-Kolmogorov turbulence for several values of parameter n and spatial coherence δ , respectively.
Fig. 3
Fig. 3 Normalized propagation factor of CGSM beams with parameter n = 2 versus the propagation distance in non-Kolmogorov turbulence for different values of (a) spatial coherence δ with σ = 0.01 m and (b) beam waist width σ with δ = 0.02 m , respectively.
Fig. 4
Fig. 4 The dependence of the normalized propagation factor of the CGSM beams for several values of parameter n on spatial coherence δ at propagation distance z = 5 k m in non-Kolmogorov turbulence.
Fig. 5
Fig. 5 Normalized propagation factor of CGSM beams with δ = 0.02 m for several values of parameter n versus the propagation distance in non-Kolmogorov turbulence with different structure constant C ˜ n 2 , respectively.
Fig. 6
Fig. 6 Normalized propagation factor of the CGSM beam with n = 2 and δ = 0.02 m versus the propagation distance in non-Kolmogorov turbulence for different values of slope-parameter α , inner scale l 0 , outer scale L 0 and structure constant C ˜ n 2 , respectively. The other turbulence parameters are shown in each figure.
Fig. 7
Fig. 7 The dependence of the normalized propagation factor of the CGSM beams on slope-parameter α at propagation distance z = 5 k m in non-Kolmogorov turbulence for several values of (a) parameter n with δ = 0.02 m and (b) spatial coherence δ with n = 2 .

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

W ( 0 ) ( r 1 , r 2 ) = exp ( | r 1 | 2 + | r 2 | 2 4 σ 2 ) cos [ n 2 π ( r 2 r 1 ) δ ] exp [ | r 2 r 1 | 2 2 δ 2 ]
μ ( 0 ) ( r 2 r 1 ) = W ( 0 ) ( r 1 , r 2 ) W ( 0 ) ( r 1 , r 1 ) W ( 0 ) ( r 2 , r 2 ) = exp [ | r 2 r 1 | 2 2 δ 2 ] cos [ n 2 π ( r 2 r 1 ) δ ]
1 4 σ 2 + 1 δ 2 2 π 2 λ 2
W ( ρ , ρ d , z ) = ( k / 2 π z ) 2 W ( 0 ) ( r , r d , 0 ) × exp [ i k z ( ρ r ) ( ρ d r d ) H ( ρ d , r d ; z ) ] d 2 r d 2 r d
r = ( r 1 + r 2 ) 2 , r d = r 1 r 2 , ρ = ( ρ 1 + ρ 2 ) 2 , ρ d = ρ 1 ρ 2 ,
W ( 0 ) ( r , r d , 0 ) = W ( 0 ) ( r 1 , r 2 , 0 ) = W ( 0 ) ( r + r d 2 , r r d 2 , 0 )
W ( 0 ) ( r ' , ρ d + z k κ d , 0 ) = exp [ 1 2 σ 2 r ' 2 ( 1 8 σ 2 + 1 2 δ 2 ) ( ρ d + z k κ d ) 2 ] cos [ n 2 π δ ( ρ d + z k κ d ) ]
W ( ρ , ρ d , z ) = ( 1 2 π ) 2 W ( 0 ) ( r ' , ρ d + z k κ d , 0 ) × exp [ i ρ κ d + i r ' κ d H ( ρ d , ρ d + z k κ d , z ) ] d 2 r ' d 2 κ d
H ( ρ d , ρ d + z k κ d ; z ) = π 2 k 2 z 3 ( 3 ρ d 2 + 3 z k ρ d κ d + z 2 k 2 κ d 2 ) 0 κ 3 Φ n ( κ ) d κ
Φ n ( κ , α ) = A ( α ) C ˜ n 2 exp [ ( κ 2 / κ m 2 ) ] / ( κ 2 + κ 0 2 ) α / 2 , 0 κ < , 3 < α < 4
c ( α ) = [ Γ ( 5 α / 2 ) A ( α ) 2 π / 3 ] [ 1 / ( α 5 ) ] , A ( α ) = Γ ( α 1 ) cos ( α π / 2 ) / ( 4 π 2 )
I = 0 κ 3 Φ n ( κ ) d κ = A ( α ) C ˜ n 2 2 ( α 2 ) [ κ m 2 α β exp ( κ 0 2 κ m 2 ) Γ ( 2 α 2 , κ 0 2 κ m 2 ) 2 κ 0 4 α ]
h ( ρ , θ ; z ) = ( k 2 π ) 2 W ( ρ , ρ d ; z ) exp ( i k θ ρ d ) d 2 ρ d
h ( ρ , θ , z ) = k 2 16 π 4 2 π σ 2 exp [ a ρ d 2 b κ d 2 c ρ d κ d i k θ ρ d i ρ κ d H ( ρ d , ρ d + z k κ d , z ) ] cos [ n 2 π δ ( ρ d + z k κ d ) ] d 2 ρ d d 2 κ d
1 ε 2 = 1 4 σ 2 + 1 δ 2 , a = 1 2 ε 2 , b = 1 2 ε 2 z 2 k 2 + σ 2 2 , c = 1 ε 2 z k
< x n 1 y n 2 θ x m 1 θ y m 2 > = 1 P x n 1 y n 2 θ x m 1 θ y m 2 h ( ρ , θ , z ) d 2 ρ d 2 θ
P = h ( ρ , θ , z ) d 2 ρ d 2 θ
< ρ 2 > = ( 2 ε 2 + 4 π n 2 δ 2 ) z 2 k 2 + 2 σ 2 + 4 3 π 2 z 3 I
< θ 2 > = 1 k 2 ( 2 ε 2 + 4 π n 2 δ 2 ) + 4 π 2 z I
< ρ θ > = ( 2 ε 2 + 4 π n 2 δ 2 ) z k 2 + 2 π 2 z 2 I
w N ( z ) ( < | ρ < ρ > | 2 > ) 1 / 2 = ( < ρ 2 > ) 1 / 2 = [ ( 2 ε 2 + 4 π n 2 δ 2 ) z 2 k 2 + 2 σ 2 + 4 3 π 2 z 3 I ] 1 / 2
θ N ( z ) ( < | θ < θ > | 2 > ) 1 / 2 = ( < θ 2 > ) 1 / 2 = [ 1 k 2 ( 2 ε 2 + 4 π n 2 δ 2 ) + 4 π 2 z I ] 1 / 2
θ r N ( z ) θ N ( z ) θ N ( 0 ) = [ 1 + 4 π 2 k 2 ( 2 ε 2 + 4 π n 2 δ 2 ) 1 z I ] 1 / 2
M 2 ( z ) = k ( < ρ 2 > < θ 2 > < ρ θ > 2 ) 1 / 2 = k [ ( < x 2 > + < y 2 > ) ( < θ x 2 > + < θ y 2 > ) ( < x θ x > + < y θ y > ) 2 ] 1 / 2
M 2 ( z ) = { [ ( 2 ε 2 + 4 π n 2 δ 2 ) z 2 k 2 + 2 σ 2 + 4 3 π 2 z 3 I ] ( 2 ε 2 + 4 π n 2 δ 2 + 4 π 2 k 2 z I ) [ ( 2 ε 2 + 4 π n 2 δ 2 ) z k + 2 π 2 k z 2 I ] 2 } 1 / 2
M 2 ( z ) = [ 1 + 4 σ 2 δ 2 ( 1 + 2 π n 2 ) ] 1 / 2
M 2 ( z ) = ( 1 + 4 σ 2 / δ 2 ) 1 / 2

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