Abstract

We derive several analytical expressions for the root-mean-square (rms) angular width and the M2-factor of the multi-sinc Schell-model (MSSM) beams propagating in non-Kolmogorov turbulence with the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. Numerical results show that a MSSM beam with dark-hollow far fields in free space has advantage over the one with flat-topped or multi-rings far fields for reducing the turbulence-induced degradation, which will become more obvious with larger dark-hollow size. Beam quality of MSSM beams can be further improved with longer wavelength and larger beam width, or under the condition of weaker turbulence. We also demonstrate that the non-Kolmogorov turbulence has significantly less effect on the MSSM beams than the Gaussian Schell-model beam.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (1)

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

2015 (4)

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[Crossref]

X. Wang, M. Yao, Z. Qiu, X. Yi, and Z. Liu, “Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23(10), 12508–12523 (2015).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

Z. Mei and Y. Mao, “Multi-sinc Schell-model beams and the interaction with a linear random medium,” Laser Phys. Lett. 12, 095002 (2015).
[Crossref]

2014 (8)

2013 (7)

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express 21(1), 190–195 (2013).
[Crossref] [PubMed]

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

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[Crossref]

Y. Huang, Z. Gao, and B. Zhang, “Propagation properties based on second-order moments for correlated combination partially coherent Hermite-Gaussian linear array beams in non-Kolmogorov turbulence,” J. Mod. Opt. 60(10), 841–850 (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]

2012 (1)

2011 (1)

2010 (1)

2009 (3)

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, 026003 (2008).
[Crossref]

2007 (2)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

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

2006 (3)

2003 (3)

2002 (2)

1991 (1)

1986 (1)

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, 026003 (2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

Bastiaans, M. J.

Baykal, Y.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 2000).

Cai, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[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]

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]

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. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
[Crossref]

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

Y. Cai and S. He, “Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere,” Opt. Lett. 31(5), 568–570 (2006).
[Crossref] [PubMed]

Chen, R.

Chen, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[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]

Dan, Y.

Davidson, F. M.

Dogariu, A.

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, 026003 (2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Gao, Z.

Y. Huang, Z. Gao, and B. Zhang, “Propagation properties based on second-order moments for correlated combination partially coherent Hermite-Gaussian linear array beams in non-Kolmogorov turbulence,” J. Mod. Opt. 60(10), 841–850 (2013).
[Crossref]

Gbur, G.

Gori, F.

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

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

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).

Gu, J.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[Crossref]

He, S.

Huang, W.

Huang, Y.

Y. Huang, Z. Gao, and B. Zhang, “Propagation properties based on second-order moments for correlated combination partially coherent Hermite-Gaussian linear array beams in non-Kolmogorov turbulence,” J. Mod. Opt. 60(10), 841–850 (2013).
[Crossref]

Korotkova, O.

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[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]

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

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[Crossref]

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

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]

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.

Liu, S.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

Liu, X.

Liu, Z.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

X. Wang, M. Yao, Z. Qiu, X. Yi, and Z. Liu, “Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23(10), 12508–12523 (2015).
[Crossref] [PubMed]

Mandel, L.

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

Mao, Y.

Z. Mei and Y. Mao, “Multi-sinc Schell-model beams and the interaction with a linear random medium,” Laser Phys. Lett. 12, 095002 (2015).
[Crossref]

Z. Mei and Y. Mao, “Electromagnetic sinc Schell-model beams and their statistical properties,” Opt. Express 22(19), 22534–22546 (2014).
[Crossref] [PubMed]

Martínez-Herrero, R.

Mei, Z.

Z. Mei and Y. Mao, “Multi-sinc Schell-model beams and the interaction with a linear random medium,” Laser Phys. Lett. 12, 095002 (2015).
[Crossref]

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

Z. Mei and Y. Mao, “Electromagnetic sinc Schell-model beams and their statistical properties,” Opt. Express 22(19), 22534–22546 (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]

Z. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39(14), 4188–4191 (2014).
[Crossref] [PubMed]

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

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

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

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[Crossref]

Mejías, P. M.

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, 026003 (2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

Qiu, Z.

Qu, J.

Remríez-Sánchez, V.

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

Ricklin, J. C.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

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

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

Serna, J.

Shchepakina, E.

Shirai, T.

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

T. Shirai, A. Dogariu, and E. Wolf, “Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A 20(6), 1094–1102 (2003).
[Crossref]

Song, Z.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

Sun, Q.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

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, 026003 (2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Wang, F.

Wang, X.

Wolf, E.

Wu, G.

Xu, H.

Yao, M.

Yi, X.

Yuan, Y.

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, 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]

Zhang, B.

Y. Huang, Z. Gao, and B. Zhang, “Propagation properties based on second-order moments for correlated combination partially coherent Hermite-Gaussian linear array beams in non-Kolmogorov turbulence,” J. Mod. Opt. 60(10), 841–850 (2013).
[Crossref]

Y. Dan and B. Zhang, “Second moments of partially coherent beams in atmospheric turbulence,” Opt. Lett. 34(5), 563–565 (2009).
[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]

Zhang, Z.

Zhao, C.

Zhou, K.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

Zhu, S.

Appl. Phys. Lett. (1)

Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
[Crossref]

J. Mod. Opt. (1)

Y. Huang, Z. Gao, and B. Zhang, “Propagation properties based on second-order moments for correlated combination partially coherent Hermite-Gaussian linear array beams in non-Kolmogorov turbulence,” J. Mod. Opt. 60(10), 841–850 (2013).
[Crossref]

J. Opt. (2)

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18, 015606 (2016).
[Crossref]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[Crossref]

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

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

J. Opt. Soc. Am. A (7)

Laser Phys. Lett. (1)

Z. Mei and Y. Mao, “Multi-sinc Schell-model beams and the interaction with a linear random medium,” Laser Phys. Lett. 12, 095002 (2015).
[Crossref]

Opt. Eng. (1)

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, 026003 (2008).
[Crossref]

Opt. Express (12)

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]

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express 21(1), 190–195 (2013).
[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]

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]

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]

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]

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]

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

H. Xu, Z. Zhang, J. Qu, and W. Huang, “Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 22(19), 22479–22489 (2014).
[Crossref] [PubMed]

Z. Mei and Y. Mao, “Electromagnetic sinc Schell-model beams and their statistical properties,” Opt. Express 22(19), 22534–22546 (2014).
[Crossref] [PubMed]

X. Wang, M. Yao, Z. Qiu, X. Yi, and Z. Liu, “Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23(10), 12508–12523 (2015).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

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]

Opt. Lett. (11)

Y. Cai and S. He, “Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere,” Opt. Lett. 31(5), 568–570 (2006).
[Crossref] [PubMed]

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

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

Z. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39(14), 4188–4191 (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]

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

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

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

Y. Dan and B. Zhang, “Second moments of partially coherent beams in atmospheric turbulence,” Opt. Lett. 34(5), 563–565 (2009).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

Phys. Rev. A (1)

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[Crossref]

Proc. SPIE (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Other (4)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[Crossref]

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 2000).

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

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Figures (7)

Fig. 1
Fig. 1 The cross line (ρy = 0) of the spectral intensity of MSSM beams for several values of parameters N and m at propagation distance z = 10km in free space.
Fig. 2
Fig. 2 Normalized rms angular width of MSSM beams propagating through non-Kolmogorov turbulence for several values of (a) parameter N and (b) parameter m, respectively.
Fig. 3
Fig. 3 Normalized M2-factor of MSSM beams at propagation distance z = 10km in non-Kolmogorov turbulence versus (a) wavelength λ and (b) beam width σ, respectively.
Fig. 4
Fig. 4 Normalized M2-factor of MSSM beams versus the power-law exponent α at propagation distance z = 10km in non-Kolmogorov turbulence.
Fig. 5
Fig. 5 Normalized M2-factor of MSSM beams for several values of parameters N and m versus the index-of-refraction structure constant C ˜ n 2 at propagation distance z = 10km in non-Kolmogorov turbulence.
Fig. 6
Fig. 6 Normalized M2-factor of the MSSM beams with N = 2 and m = 5 on propagation in non-Kolmogorov turbulence for different power-law exponent α, outer scale L0, and inner scale l0.
Fig. 7
Fig. 7 Normalized M2-factor of the MSSM beams for several values of parameters N and m on propagation in non-Kolmogorov turbulence compared with the case of GSM beam.

Equations (23)

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W 0 ( r 1 , r 2 , 0 ) = 1 C exp ( r 1 2 + r 2 2 2 σ 2 ) n = 1 N ( 1 ) n 1 B m n sinc ( r 1 r 2 B m n δ ) ,
W ( ρ 1 , ρ 2 , z ) = ( k 2 π z ) 2 W 0 ( r 1 , r 2 , 0 ) exp [ i k ( ρ 1 r 1 ) 2 ( ρ 2 r 2 ) 2 2 z ] × exp { k 2 z T 2 [ ( ρ 1 ρ 2 ) 2 + ( ρ 1 ρ 2 ) ( r 1 r 2 ) + ( r 1 r 2 ) 2 ] } d 2 r 1 d 2 r 2 ,
T = 2 π 2 3 0 κ 3 Φ ( κ , α ) d κ ,
S ( ρ , z ) = W ( ρ , ρ , z ) = δ σ 2 C ω 2 ( z ) exp [ ( ρ + 2 π z υ / k ) 2 ω 2 ( z ) ] n = 1 N ( 1 ) n 1 rect ( B m n δ υ ) d 2 υ ,
ω 2 ( z ) = σ 2 + z 2 / ( k 2 σ 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 ) ] × exp [ k 2 z T 2 ( ρ d 2 + ρ d r d + r d 2 ) ] d 2 r d 2 r d ,
W ( ρ , ρ d , z ) = ( 1 2 π ) 2 W 0 ( r , ρ d + z k κ d , 0 ) exp i r κ d i ρ κ d ) × exp [ k 2 z T 2 ( 3 ρ d 2 + 3 z k ρ d κ d + z 2 k 2 κ d 2 ) ] d 2 r d 2 κ d ,
W 0 ( r , ρ d + z k κ d , 0 ) = 1 C exp [ 1 σ 2 r 2 1 4 σ 2 ( ρ d + z k κ d ) 2 ] × n = 1 N ( 1 ) n 1 B m n sinc [ 1 B m n δ ( ρ d + z k κ d ) ] .
h ( ρ , θ , z ) = ( k 2 π ) 2 W ( ρ , ρ d , z ) exp ( i k θ ρ d ) d 2 ρ d ,
exp ( a x 2 ± b x ) d x = π a exp ( b 2 4 a ) , ( a > 0 ) ,
h ( ρ , θ , z ) = k 2 σ 2 16 π 3 C exp [ σ 2 κ d 2 4 1 4 σ 2 ( ρ d + z k κ d ) 2 ] × n = 1 N ( 1 ) n 1 B m n sinc [ 1 B m n δ ( ρ d + z k κ d ) ] exp ( i ρ κ d i k θ ρ d ) × exp [ k 2 z T 2 ( 3 ρ d 2 + 3 z k ρ d κ d + z 2 k 2 κ d 2 ) ] d 2 κ d d 2 ρ d .
ρ x n 1 ρ y n 2 θ x m 1 θ y m 2 = 1 P ρ x n 1 ρ y n 2 θ x m 1 θ y m 2 h ( ρ , θ , z ) d 2 ρ d 2 θ ,
ρ 2 = ρ 2 0 + θ 2 0 z 2 + 2 T z 3 ,
θ 2 = θ 2 0 + 6 T z ,
ρ θ = θ 2 0 z + 3 T z 2 ,
ρ 2 0 = σ 2 ,
θ 2 0 = 2 k 2 1 / ( 2 σ 2 ) + n = 1 N [ ( 1 ) n 1 π 2 ] / ( B m n 3 δ 2 ) n = 1 N ( 1 ) n 1 / B m n .
θ N ( z ) ( | θ θ | 2 ) 1 / 2 = ( θ 2 ) 1 / 2 = { 2 k 2 1 / ( 2 σ 2 ) + n = 1 N [ ( 1 ) n 1 π 2 ] / ( B m n 3 δ 2 ) n = 1 N ( 1 ) n 1 / B m n + 6 T z } 1 / 2 ,
M 2 ( z ) = k ( ρ 2 θ 2 ρ θ 2 ) 1 / 2 = { ( 2 σ 2 + 4 T z 3 ) 1 / ( 2 σ 2 ) + n = 1 N [ ( 1 ) n 1 π 2 ] / ( B m n 3 δ 2 ) n = 1 N ( 1 ) n 1 / B m n + 6 k 2 σ 2 T z + 3 k 2 T 2 z 4 } 1 / 2 .
M G 2 ( z ) = [ ( 2 σ 2 + 4 T z 3 ) ( 1 2 σ 2 + 2 δ 2 ) + 12 k 2 σ 2 T z ] 1 / 2 .
Φ ( 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 ,
Φ ( κ , 11 / 3 ) = 0.033 C n 2 κ 11 / 3 ,
T = π 2 3 ( α 2 ) A ( α ) C ˜ n 2 [ β κ m 2 α exp ( κ 0 2 κ m 2 ) Γ ( 2 α 2 , κ 0 2 κ m 2 ) 2 κ 0 ( 4 α ) ] ,

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