Abstract

Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express 23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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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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2015 (7)

2014 (12)

Z. Chen, S. Cui, L. Zhang, C. Sun, M. Xiong, and J. Pu, “Measuring the intensity fluctuation of partially coherent radially polarized beams in atmospheric turbulence,” Opt. Express 22(15), 18278–18283 (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]

S. Zhu, F. Wang, Y. Chen, Z. Li, and Y. Cai, “Statistical properties in Young’s interference pattern formed with a radially polarized beam with controllable spatial coherence,” Opt. Express 22(23), 28697–28710 (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]

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. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
[Crossref] [PubMed]

Y. Cai and S. Zhu, “Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain,” Opt. Lett. 39(7), 1968–1971 (2014).
[Crossref] [PubMed]

I. Toselli, “Introducing the concept of anisotropy at different scales for modeling optical turbulence,” J. Opt. Soc. Am. A 31(8), 1868–1875 (2014).
[Crossref] [PubMed]

M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
[Crossref] [PubMed]

G. Gbur and E. Wolf, “Partially coherent beam propagation in atmospheric turbulence [invited],” J. Opt. Soc. Am. A 31(9), 2038–2045 (2014).
[Crossref] [PubMed]

2013 (6)

2012 (4)

2011 (3)

2010 (3)

2009 (5)

2008 (1)

2007 (2)

2005 (1)

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52(11), 1611–1618 (2005).
[Crossref]

2004 (2)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

2003 (5)

2002 (1)

2001 (1)

1994 (1)

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularity,” Waves Random Complex Media 4(3), 297–306 (1994).
[Crossref]

1991 (1)

1972 (2)

H. T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. 11(6), 1399–1406 (1972).
[Crossref] [PubMed]

A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 15(10), 1187–1192 (1972).
[Crossref]

Agrawal, B.

Amarande, S.

Baykal, Y.

Bogatyryova, G. V.

Cada, M.

Cai, Y.

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

J. Yu, Y. Chen, L. Liu, X. Liu, and Y. Cai, “Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23(10), 13467–13481 (2015).
[Crossref] [PubMed]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

S. Zhu, F. Wang, Y. Chen, Z. Li, and Y. Cai, “Statistical properties in Young’s interference pattern formed with a radially polarized beam with controllable spatial coherence,” Opt. Express 22(23), 28697–28710 (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]

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. Cai and S. Zhu, “Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain,” Opt. Lett. 39(7), 1968–1971 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21(23), 27682–27696 (2013).
[Crossref] [PubMed]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

S. Zhu and Y. Cai, “M2-factor of a truncated electromagnetic Gaussian Schell-model beam,” Appl. Phys. B 103(4), 971–984 (2011).
[Crossref]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010).
[Crossref] [PubMed]

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt. 48(10), 1943–1954 (2009).
[Crossref] [PubMed]

H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, O. Korotkova, and Y. Cai, “Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media,” J. Opt. Soc. Am. A 26(2), 387–394 (2009).
[Crossref] [PubMed]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
[Crossref] [PubMed]

Charnotskii, M.

Chen, R.

Chen, Y.

Chen, Z.

Chu, X.

Cui, S.

Ding, C.

Dogariu, A.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

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

Dong, Y.

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Eyyuboglu, H. T.

Fel’de, C. V.

Friberg, A.

Friberg, A. T.

Gbur, G.

Gori, F.

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

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

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(1), 013823 (2015).
[Crossref]

Gu, Y.

Huang, W.

Ji, G.

Ji, X.

Jia, X.

Kon, A. I.

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularity,” Waves Random Complex Media 4(3), 297–306 (1994).
[Crossref]

A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 15(10), 1187–1192 (1972).
[Crossref]

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]

M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
[Crossref] [PubMed]

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

Z. Mei, E. Schchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (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]

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

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010).
[Crossref] [PubMed]

Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. 34(15), 2261–2263 (2009).
[Crossref] [PubMed]

H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, O. Korotkova, and Y. Cai, “Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media,” J. Opt. Soc. Am. A 26(2), 387–394 (2009).
[Crossref] [PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

Lajunen, H.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Li, Z.

Liang, C.

Lin, Q.

Liu, L.

Liu, X.

Liu, Z.

Ma, L.

Ma, Y.

Martínez-Herrero, R.

Mei, Z.

Pan, L.

Polyanskii, P. V.

Ponomarenko, S. A.

Prado, F.

Pu, J.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Ramírez-Sánchez, V.

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

Restaino, S.

Roychowdhury, H.

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52(11), 1611–1618 (2005).
[Crossref]

Saastamoinen, T.

Sahin, S.

Salem, M.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

Santarsiero, M.

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

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

Schchepakina, E.

Sermutlu, E.

Setälä, T.

Shirai, T.

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

Soskin, M. S.

Sun, C.

Tatarskii, V. I.

A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 15(10), 1187–1192 (1972).
[Crossref]

Tervo, J.

Tong, Z.

Toselli, I.

Turunen, J.

Vasara, A.

Visser, T.

G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1-6), 117–125 (2003).
[Crossref]

Wang, F.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (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]

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]

S. Zhu, F. Wang, Y. Chen, Z. Li, and Y. Cai, “Statistical properties in Young’s interference pattern formed with a radially polarized beam with controllable spatial coherence,” Opt. Express 22(23), 28697–28710 (2014).
[Crossref] [PubMed]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21(23), 27682–27696 (2013).
[Crossref] [PubMed]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Wang, H.

Wang, J.

Wang, X.

Wolf, E.

G. Gbur and E. Wolf, “Partially coherent beam propagation in atmospheric turbulence [invited],” J. Opt. Soc. Am. A 31(9), 2038–2045 (2014).
[Crossref] [PubMed]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52(11), 1611–1618 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28(11), 878–880 (2003).
[Crossref] [PubMed]

S. A. Ponomarenko and E. Wolf, “Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light,” Opt. Lett. 27(20), 1770–1772 (2002).
[Crossref] [PubMed]

Wu, G.

Xiong, M.

Yao, M.

Yu, J.

Yuan, Y.

Yura, H. T.

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Zhang, L.

Zhang, Y.

Zhao, D.

Zhao, H.

Zhou, G.

Zhou, P.

Zhu, S.

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

S. Zhu, F. Wang, Y. Chen, Z. Li, and Y. Cai, “Statistical properties in Young’s interference pattern formed with a radially polarized beam with controllable spatial coherence,” Opt. Express 22(23), 28697–28710 (2014).
[Crossref] [PubMed]

Y. Cai and S. Zhu, “Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain,” Opt. Lett. 39(7), 1968–1971 (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]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21(23), 27682–27696 (2013).
[Crossref] [PubMed]

S. Zhu and Y. Cai, “M2-factor of a truncated electromagnetic Gaussian Schell-model beam,” Appl. Phys. B 103(4), 971–984 (2011).
[Crossref]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010).
[Crossref] [PubMed]

Zhu, X.

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (2)

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu and Y. Cai, “M2-factor of a truncated electromagnetic Gaussian Schell-model beam,” Appl. Phys. B 103(4), 971–984 (2011).
[Crossref]

Appl. Phys. Lett. (1)

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

J. Mod. Opt. (1)

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52(11), 1611–1618 (2005).
[Crossref]

J. Opt. A (1)

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

J. Opt. Soc. Am. A (8)

Opt. Commun. (2)

G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1-6), 117–125 (2003).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[Crossref]

Opt. Express (18)

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
[Crossref] [PubMed]

G. Zhou and X. Chu, “Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere,” Opt. Express 18(2), 726–731 (2010).
[Crossref] [PubMed]

J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

S. Zhu, F. Wang, Y. Chen, Z. Li, and Y. Cai, “Statistical properties in Young’s interference pattern formed with a radially polarized beam with controllable spatial coherence,” Opt. Express 22(23), 28697–28710 (2014).
[Crossref] [PubMed]

X. Ji, H. T. Eyyuboğlu, G. Ji, and X. Jia, “Propagation of an Airy beam through the atmosphere,” Opt. Express 21(2), 2154–2164 (2013).
[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. Chen, S. Cui, L. Zhang, C. Sun, M. Xiong, and J. Pu, “Measuring the intensity fluctuation of partially coherent radially polarized beams in atmospheric turbulence,” Opt. Express 22(15), 18278–18283 (2014).
[Crossref] [PubMed]

Z. Mei, E. Schchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (2013).
[Crossref] [PubMed]

Y. Zhang and D. Zhao, “Scattering of multi-Gaussian Schell-model beams on a random medium,” Opt. Express 21(21), 24781–24792 (2013).
[Crossref] [PubMed]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21(23), 27682–27696 (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]

M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Free-space propagation of optical coherence lattices and periodicity reciprocity,” Opt. Express 23(2), 1848–1856 (2015).
[Crossref] [PubMed]

R. Martínez-Herrero and F. Prado, “Polarization evolution of radially polarized partially coherent vortex fields: role of Gouy phase of Laguerre-Gauss beams,” Opt. Express 23(4), 5043–5051 (2015).
[Crossref] [PubMed]

J. Yu, Y. Chen, L. Liu, X. Liu, and Y. Cai, “Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23(10), 13467–13481 (2015).
[Crossref] [PubMed]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010).
[Crossref] [PubMed]

Opt. Lett. (15)

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. Cai and S. Zhu, “Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain,” Opt. Lett. 39(7), 1968–1971 (2014).
[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]

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

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

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

L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
[Crossref] [PubMed]

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28(11), 878–880 (2003).
[Crossref] [PubMed]

S. A. Ponomarenko, W. Huang, and M. Cada, “Dark and antidark diffraction-free beams,” Opt. Lett. 32(17), 2508–2510 (2007).
[Crossref] [PubMed]

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

S. A. Ponomarenko and E. Wolf, “Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light,” Opt. Lett. 27(20), 1770–1772 (2002).
[Crossref] [PubMed]

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

Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. 34(15), 2261–2263 (2009).
[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(1), 013823 (2015).
[Crossref]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Prog. Electromagnetics Res. (1)

F. Wang, X. Liu, and Y. Cai, “Propagation of partially coherent beam in turbulent atmosphere: a review (Invited review),” Prog. Electromagnetics Res. 150, 123–143 (2015).
[Crossref]

Radiophys. Quantum Electron. (1)

A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 15(10), 1187–1192 (1972).
[Crossref]

Waves Random Complex Media (1)

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularity,” Waves Random Complex Media 4(3), 297–306 (1994).
[Crossref]

Waves Random Media (1)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Media 14(4), 513–523 (2004).
[Crossref]

Other (3)

A. Ishimaru, Wave Propagation and Scattering in Random Media, vol. 2 (Academic, 1978).

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (8)

Fig. 1
Fig. 1

Normalized average intensity distribution and the corresponding cross line of a radially polarized CGCSM beam at several different propagation distances for different values ofn.

Fig. 2
Fig. 2

Normalized average intensity distribution, composition components U xx (ρ,ρ) , U yy (ρ,ρ) and the corresponding cross lines of a radially polarized CGCSM beam at several different propagation distances with n=2 .

Fig. 3
Fig. 3

On-axis average intensity of a radially polarized CGCSM beam for different values ofn. (a1)-(a3) as a function of distance z and ζ eff , (b1)-(b3) as a function of α and ζ eff at z=10km .

Fig. 4
Fig. 4

The modulus of the spectral DOC μ( u,v,0cm,0cm ) distribution and the corresponding cross line of a radially polarized CGCSM beam at different propagation distances for different values ofn.

Fig. 5
Fig. 5

The modulus of the spectral DOC μ( 0cm,0cm,5cm,0cm ) of a radially polarized CGCSM beam for different values ofn. (a1)-(a3) as a function of distance z and ζ eff , (b1)-(b3) as a function of α and ζ eff at z=10km .

Fig. 6
Fig. 6

The spectral DOP distribution and the corresponding cross line of a radially polarized CGCSM beam at different propagation distances for different values ofn.

Fig. 7
Fig. 7

The spectral DOP of a radially polarized CGCSM beam for different values ofn at (5cm, 0cm). (a1)-(a3) as a function of distance z and ζ eff , (b1)-(b3) as a function of α and ζ eff at z=10km .

Fig. 8
Fig. 8

The SOP of a radially polarized CGCSM beam at different propagation distances for different values ofn.

Equations (21)

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E( r;ω )= E x ( r;ω ) e x + E y ( r;ω ) e y = x w 0 exp( r 2 w 0 2 ) e x + y w 0 exp( r 2 w 0 2 ) e y ,
U αβ ( r 1 , r 2 ;ω )= α 1 β 2 w 0 2 exp( r 1 2 + r 2 2 w 0 2 ) g αβ ( r 1 r 2 ;ω ), ( α=x,y;β=x,y ),
g αβ ( r 1 r 2 ;ω )=exp[ ( r 1 r 2 ) 2 2 σ 0 2 ]cos[ n π ( x 1 x 2 ) σ 0 ]cos[ n π ( y 1 y 2 ) σ 0 ],
U αβ ( ρ 1 , ρ 2 ;ω )= ( k 2πz ) 2 U αβ ( r 1 , r 2 ;ω ) exp[ ψ( r 1 , ρ 1 ;ω )+ ψ ( r 2 , ρ 2 ;ω ) ] ×exp[ ik 2z [ ( r 1 2 r 2 2 )2( r 1 ρ 1 r 2 ρ 2 )+( ρ 1 2 ρ 2 2 ) ] ] d 2 r 1 d 2 r 2 ,
exp[ ψ( r 1 , ρ 1 ;ω )+ ψ ( r 2 , ρ 2 ;ω ) ] =exp[ π 2 k 2 z 3 ( r Δ 2 + r Δ ρ Δ + ρ Δ 2 ) 0 κ 3 Φ n ( κ,α )dκ ],
Φ n ( κ,α )= A( α ) C ˜ n 2 ζ eff 2 ( ζ eff 2 κ xy 2 + κ z 2 + κ 0 2 ) α/2 exp( ζ eff 2 κ xy 2 + κ z 2 κ H 2 ),
κ= ζ eff 2 ( κ x 2 + κ y 2 )+ κ z 2 = ζ eff 2 κ xy 2 + κ z 2 , A( α )= Γ( α1 ) 4 π 2 cos( πα 2 ), 3<α<4,
C( α )= [ πA( α )Γ( 3 2 α 2 )( 3α 3 ) ] 1/ ( α5 ) , 3<α<4,
n(R)= n 0 + n 1 (R),
n 1 ( R 1 ) n 1 ( R 2 ) δ( z 1 z 2 ) Α n ( r 1 r 2 ).
C ˜ ¯ n 2 = 1 H h 0 h 0 H C ˜ n 2 ( h ) dh,
C ˜ n 2 ( h )=0.00594 ( v s 27 ) 2 ( 10 5 h ) 10 exp( h 1000 )+2.7× 10 16 exp( h 1500 )+ C ˜ n 2 exp( h 100 ),
T ani = π 2 k 2 z 3 0 Φ n ( κ,α ) κ 3 dκ = π 2 k 2 z ζ eff 2α 6( α2 ) A( α ) C ˜ ¯ n 2 [ κ ˜ H 2α βexp( κ 0 2 κ H 2 )Γ( 2 α 2 , κ 0 2 κ H 2 )2 κ ˜ 0 4α ],
U xx ( ρ 1 , ρ 2 ;ω )=V( ρ 1 , ρ 2 ;ω ){ exp[ γ v12 2 4 M 1 + Ω v22 2 4Π ]+exp[ γ v11 2 4 M 1 + Ω v21 2 4Π ] } ×{ ( Δ+ γ u11 Ω u21 + Δ 2Π Ω u21 2 )exp[ γ u11 2 4 M 1 + Ω u21 2 4Π ] ( Δ+ γ u12 Ω u22 + Δ 2Π Ω u22 2 )exp[ γ u12 2 4 M 1 + Ω u22 2 4Π ] + },
U yy ( ρ 1 , ρ 2 ;ω )=V( ρ 1 , ρ 2 ;ω ){ exp[ γ u12 2 4 M 1 + Ω u22 2 4Π ]+exp[ γ u11 2 4 M 1 + Ω u21 2 4Π ] } ×{ ( Δ+ γ v11 Ω v21 + Δ 2Π Ω v21 2 )exp[ γ v11 2 4 M 1 + Ω v21 2 4Π ] ( Δ+ γ v12 Ω v22 + Δ 2Π Ω v22 2 )exp[ γ v12 2 4 M 1 + Ω v22 2 4Π ] + },
U xy ( ρ 1 , ρ 2 ;ω )=V( ρ 1 , ρ 2 ;ω ){ Ω v22 exp[ γ v12 2 4 M 1 + Ω v22 2 4Π ]+ Ω v21 exp[ γ v11 2 4 M 1 + Ω v21 2 4Π ] } ×{ ( γ u11 + Δ 2Π Ω u21 )exp[ γ u11 2 4 M 1 + Ω u21 2 4Π ]+( γ u12 + Δ 2Π Ω u22 )exp[ γ u12 2 4 M 1 + Ω u22 2 4Π ] },
U yx ( ρ 1 , ρ 2 ;ω )= U xy * ( ρ 1 , ρ 2 ;ω ),
V( ρ 1 , ρ 2 ;ω )= k 2 64 z 2 w 0 2 M 1 2 Π 2 exp[ ik 2z ( ρ 1 2 ρ 2 2 ) T ani ρ Δ 2 ], a= n 2π / σ 0 , ξ u1 = ik u 1 z T ani u Δ , ξ u2 = ik u 2 z T ani u Δ , ξ v1 = ik v 1 z T ani v Δ , ξ v2 = ik v 2 z T ani v Δ , γ u11 = ξ u1 +ia, γ u12 = ξ u1 ia, γ u21 = ξ u2 +ia, γ u22 = ξ u2 ia, γ v11 = ξ v1 +ia, γ v12 = ξ v1 ia, γ v21 = ξ v2 +ia, γ v22 = ξ v2 ia, Ω u22 = Δ γ u12 2 M 1 γ u22 , Ω u21 = Δ γ u11 2 M 1 γ u21 , Ω v22 = Δ γ v12 2 M 1 γ v22 , Ω v21 = Δ γ v11 2 M 1 γ v21 , Δ= 1 σ 0 2 +2 T ani , M 1 = 1 w 0 2 + 1 2 σ 0 2 + ik 2z + T ani , Π= 1 w 0 2 + 1 2 σ 0 2 ik 2z Δ 2 4 M 1 + T ani .
I( ρ;ω )= U xx ( ρ,ρ;ω )+ U yy ( ρ,ρ;ω ),
P( ρ;ω )= 1 4Det[ U ( ρ,ρ;ω ) ] { Tr[ U ( ρ,ρ;ω ) ] } 2 ,
μ( ρ 1 , ρ 2 ;ω )= Tr U ( ρ 1 , ρ 2 ;ω ) Tr[ U ( ρ 1 , ρ 1 ;ω ) ]Tr[ U ( ρ 2 , ρ 2 ;ω ) ] .

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