Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt. 50(21), 4174–4179 (2011).

[PubMed]

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).

[PubMed]

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).

[PubMed]

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).

[PubMed]

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

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

C. Li and J. Pu, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).

X. Ji and X. Li, “Directionality of Gaussian array beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 26(2), 236–243 (2009).

[PubMed]

X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009).

[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).

[PubMed]

D. Deng and Q. Guo, “Exact nonparaxial propagation of a hollow Gaussian beam,” J. Opt. Soc. Am. B 26, 2044–2049 (2009).

G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25(1), 225–230 (2008).

[PubMed]

Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A 25(3), 537–542 (2008).

[PubMed]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008).

[PubMed]

Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008).

[PubMed]

T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng. 47, 036002 (2008).

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not change on propagation,” Opt. Commun. 281, 3067–3070 (2008).

H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40, 156–166 (2008).

G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun. 281, 5653–5658 (2008).

J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056610 (2007).

[PubMed]

A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, “Definitions of the degree of polarization of a light beam,” Opt. Lett. 32(9), 1015–1016 (2007).

[PubMed]

Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32(15), 2076–2078 (2007).

[PubMed]

H. Ma, H. Cheng, W. Zhang, L. Liu, and Y. Wang, “Generation of a hollow laser beam by a multimode fiber,” Chin. Opt. Lett. 5, 460–462 (2007).

H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22(8), 1527–1535 (2005).

[PubMed]

Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A 22(9), 1898–1902 (2005).

[PubMed]

D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M2 factor of hollow Gaussian beams,” Appl. Opt. 44(33), 7187–7190 (2005).

[PubMed]

Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt. 7, 147–153 (2005).

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004).

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

C. Paterson and R. Smith, “High-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).

[PubMed]

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).

[PubMed]

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

V. I. Balykin and V. S. Letokhov, “The possibility of deep laser focusing of an atom beam into the A region,” Opt. Commun. 64, 151–156 (1987).

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

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).

[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).

[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).

[PubMed]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008).

[PubMed]

Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14(4), 1353–1367 (2006).

[PubMed]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).

[PubMed]

T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng. 47, 036002 (2008).

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).

[PubMed]

G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun. 281, 5653–5658 (2008).

D. Deng and Q. Guo, “Exact nonparaxial propagation of a hollow Gaussian beam,” J. Opt. Soc. Am. B 26, 2044–2049 (2009).

D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M2 factor of hollow Gaussian beams,” Appl. Opt. 44(33), 7187–7190 (2005).

[PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004).

Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt. 7, 147–153 (2005).

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).

[PubMed]

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

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).

[PubMed]

H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40, 156–166 (2008).

H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22(8), 1527–1535 (2005).

[PubMed]

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).

[PubMed]

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

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

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).

[PubMed]

X. Ji and X. Li, “Directionality of Gaussian array beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 26(2), 236–243 (2009).

[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).

[PubMed]

A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, “Definitions of the degree of polarization of a light beam,” Opt. Lett. 32(9), 1015–1016 (2007).

[PubMed]

J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056610 (2007).

[PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004).

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).

[PubMed]

V. I. Balykin and V. S. Letokhov, “The possibility of deep laser focusing of an atom beam into the A region,” Opt. Commun. 64, 151–156 (1987).

C. Li and J. Pu, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).

Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt. 50(21), 4174–4179 (2011).

[PubMed]

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).

[PubMed]

X. Ji and X. Li, “Directionality of Gaussian array beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 26(2), 236–243 (2009).

[PubMed]

Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt. 7, 147–153 (2005).

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).

[PubMed]

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32(15), 2076–2078 (2007).

[PubMed]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008).

[PubMed]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).

[PubMed]

Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt. 50(21), 4174–4179 (2011).

[PubMed]

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

H. Ma, H. Cheng, W. Zhang, L. Liu, and Y. Wang, “Generation of a hollow laser beam by a multimode fiber,” Chin. Opt. Lett. 5, 460–462 (2007).

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).

[PubMed]

C. Paterson and R. Smith, “High-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).

[PubMed]

C. Li and J. Pu, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).

T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng. 47, 036002 (2008).

J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056610 (2007).

[PubMed]

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).

[PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004).

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).

[PubMed]

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

C. Paterson and R. Smith, “High-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).

[PubMed]

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng. 47, 036002 (2008).

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).

[PubMed]

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

X. Wang and M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18(10), 767–768 (1993).

[PubMed]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008).

[PubMed]

H. Ma, H. Cheng, W. Zhang, L. Liu, and Y. Wang, “Generation of a hollow laser beam by a multimode fiber,” Chin. Opt. Lett. 5, 460–462 (2007).

J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).

Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt. 7, 147–153 (2005).

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not change on propagation,” Opt. Commun. 281, 3067–3070 (2008).

J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056610 (2007).

[PubMed]

A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, “Definitions of the degree of polarization of a light beam,” Opt. Lett. 32(9), 1015–1016 (2007).

[PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004).

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

M. Yan, J. Yin, and Y. Zhu, “Dark-hollow-beam guiding and splitting of a low-velocity atomic beam,” J. Opt. Soc. Am. B 17, 1817–1820 (2000).

J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).

X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009).

[PubMed]

Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008).

[PubMed]

Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A 25(3), 537–542 (2008).

[PubMed]

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not change on propagation,” Opt. Commun. 281, 3067–3070 (2008).

Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A 22(9), 1898–1902 (2005).

[PubMed]

G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun. 281, 5653–5658 (2008).

G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun. 281, 5653–5658 (2008).

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008).

[PubMed]

M. Yan, J. Yin, and Y. Zhu, “Dark-hollow-beam guiding and splitting of a low-velocity atomic beam,” J. Opt. Soc. Am. B 17, 1817–1820 (2000).

J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).

[PubMed]

Y. Nie, H. Ma, X. Li, W. Hu, and J. Yang, “Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator,” Appl. Opt. 50(21), 4174–4179 (2011).

[PubMed]

D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M2 factor of hollow Gaussian beams,” Appl. Opt. 44(33), 7187–7190 (2005).

[PubMed]

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

C. Li and J. Pu, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

P. Zhou, X. Wang, Y. Ma, H. Ma, X. Xu, and Z. Liu, “Average intensity and spreading of Lorentz beam propagating in a turbulent atmosphere,” J. Opt. 12, 01540–01549 (2010).

Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A, Pure Appl. Opt. 7, 147–153 (2005).

Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A 22(9), 1898–1902 (2005).

[PubMed]

X. Ji and X. Li, “Directionality of Gaussian array beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 26(2), 236–243 (2009).

[PubMed]

H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22(8), 1527–1535 (2005).

[PubMed]

G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25(1), 225–230 (2008).

[PubMed]

Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A 25(3), 537–542 (2008).

[PubMed]

H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).

D. Deng and Q. Guo, “Exact nonparaxial propagation of a hollow Gaussian beam,” J. Opt. Soc. Am. B 26, 2044–2049 (2009).

J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15, 25–33 (1998).

M. Yan, J. Yin, and Y. Zhu, “Dark-hollow-beam guiding and splitting of a low-velocity atomic beam,” J. Opt. Soc. Am. B 17, 1817–1820 (2000).

K. Zhu, H. Tang, X. Sun, X. Wang, and T. Liu, “Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams,” Opt. Commun. 207, 29–34 (2002).

V. I. Balykin and V. S. Letokhov, “The possibility of deep laser focusing of an atom beam into the A region,” Opt. Commun. 64, 151–156 (1987).

C. Paterson and R. Smith, “High-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).

G. Zhou, X. Chu, and J. Zheng, “Investigation in hollow Gaussian beam from vectorial structure,” Opt. Commun. 281, 5653–5658 (2008).

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not change on propagation,” Opt. Commun. 281, 3067–3070 (2008).

T. Wang, J. Pu, and Z. Chen, “Propagation of partially coherent vortex beams in a turbulent atmosphere,” Opt. Eng. 47, 036002 (2008).

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).

[PubMed]

X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009).

[PubMed]

Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16(22), 18437–18442 (2008).

[PubMed]

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).

[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).

[PubMed]

Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14(4), 1353–1367 (2006).

[PubMed]

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).

[PubMed]

H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40, 156–166 (2008).

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).

[PubMed]

X. Wang and M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18(10), 767–768 (1993).

[PubMed]

Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32(15), 2076–2078 (2007).

[PubMed]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008).

[PubMed]

A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, “Definitions of the degree of polarization of a light beam,” Opt. Lett. 32(9), 1015–1016 (2007).

[PubMed]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).

[PubMed]

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).

[PubMed]

J. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056610 (2007).

[PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in turbulent atmosphere,” Waves Random Media 14, 513–523 (2004).

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, San Diego, CA, 1980).

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