Abstract

It has already been found that, in turbulent atmosphere, many partially coherent electromagnetic beams with uniform source polarization distributions can regain these distribution patterns in the far field. However, the far-zone polarization properties of beams with non-uniform source polarization distributions are not sufficiently studied and the condition for an electromagnetic beam to reconstruct its source polarization distribution in the far zone is not established. Using a type of electromagnetic anisotropic Gaussian Schell-model (GSM) beams which can have non-uniform polarization distributions on the source plane, we find that, under the influence of turbulent atmosphere, the transverse polarization distribution will finally become uniform starting with a non-uniform source polarization distribution, and the far-field degree of polarization is affected by the source intensity parameters, but not by the source spatial coherence parameters. We also find that, electromagnetic anisotropic GSM beams can regain their source polarization patterns in the far field when propagating through atmospheric turbulence if and only if, the two intensity distributions corresponding to the two orthogonal field components on the source plane are the same, or are different only for a constant parameter. The validity of this condition is unaffected by the intensity and spatial coherence profiles on the source plane.

© 2012 OSA

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    [CrossRef] [PubMed]
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2011 (2)

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102(4), 937–944 (2011).
[CrossRef]

B. Ghafary and M. Alavinejad, “Changes in the state of polarization of partially coherent flat-topped beams in turbulent atmosphere for different source conditions,” Appl. Phys. B 102(4), 945–952 (2011).
[CrossRef]

2009 (7)

X. Ji and Z. Pu, “Effects of atmospheric turbulence on the polarization of apertured electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 11(4), 045701 (2009).
[CrossRef]

X. Ji and X. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite-Gaussian beams in turbulence,” Opt. Laser Technol. 41(2), 165–171 (2009).
[CrossRef]

F. D. Kashani, M. Alavinejad, and B. Ghafary, “Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere,” Opt. Commun. 282(20), 4029–4034 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41(6), 714–722 (2009).
[CrossRef]

H. T. Eyyuboğlu, “Comparison of wave structure functions for intensity profiles,” Appl. Phys. B 94(3), 489–497 (2009).
[CrossRef]

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

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere,” Opt. Express 17(13), 11130–11139 (2009).
[CrossRef] [PubMed]

2008 (7)

2007 (5)

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87(3), 547–552 (2007).
[CrossRef]

X. Ji, E. Zhang, and B. Lü, “Changes in spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275(2), 292–300 (2007).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Degree of polarization for partially coherent general beams in turbulent atmosphere,” Appl. Phys. B 89(1), 91–97 (2007).
[CrossRef]

X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
[CrossRef] [PubMed]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation,” Opt. Lett. 32(15), 2215–2217 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (7)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15(3), 353–364 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[CrossRef]

H. T. Eyyuboglu, “Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Commun. 245(1-6), 37–47 (2005).
[CrossRef]

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, 1611–1618 (2005).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44(6), 976–983 (2005).
[CrossRef] [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).
[CrossRef] [PubMed]

H. T. Eyyuboğlu and Y. Baykal, “Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere,” J. Opt. Soc. Am. A 22(12), 2709–2718 (2005).
[CrossRef] [PubMed]

2004 (4)

H. T. Eyyuboğlu and Y. Baykal, “Analysis of reciprocity of cos-Gaussian and cosh- Gaussian laser beams in a turbulent atmosphere,” Opt. Express 12(20), 4659–4674 (2004).
[CrossRef] [PubMed]

J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A 21(11), 2205–2215 (2004).
[CrossRef] [PubMed]

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

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 (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

2000 (1)

1994 (1)

1982 (1)

1979 (1)

1978 (1)

1971 (1)

Agrawal, G. P.

Alavinejad, M.

B. Ghafary and M. Alavinejad, “Changes in the state of polarization of partially coherent flat-topped beams in turbulent atmosphere for different source conditions,” Appl. Phys. B 102(4), 945–952 (2011).
[CrossRef]

F. D. Kashani, M. Alavinejad, and B. Ghafary, “Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere,” Opt. Commun. 282(20), 4029–4034 (2009).
[CrossRef]

Baykal, Y.

Borghi, R.

Cai, Y.

Chen, X.

X. Ji and X. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite-Gaussian beams in turbulence,” Opt. Laser Technol. 41(2), 165–171 (2009).
[CrossRef]

X. Ji, X. Chen, and B. Lü, “Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A 25(1), 21–28 (2008).
[CrossRef] [PubMed]

Chu, X.

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87(3), 547–552 (2007).
[CrossRef]

Cui, Z.

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102(4), 937–944 (2011).
[CrossRef]

Dogariu, A.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15(3), 353–364 (2005).
[CrossRef]

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

Du, X.

Eyyuboglu, H. T.

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere,” Opt. Express 17(13), 11130–11139 (2009).
[CrossRef] [PubMed]

H. T. Eyyuboğlu, “Comparison of wave structure functions for intensity profiles,” Appl. Phys. B 94(3), 489–497 (2009).
[CrossRef]

Y. Cai, H. T. Eyyuboglu, and Y. Baykal, “Propagation properties of anomalous hollow beams in a turbulent atmosphere,” Opt. Commun. 281(21), 5291–5297 (2008).
[CrossRef]

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]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Degree of polarization for partially coherent general beams in turbulent atmosphere,” Appl. Phys. B 89(1), 91–97 (2007).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere,” J. Opt. Soc. Am. A 22(12), 2709–2718 (2005).
[CrossRef] [PubMed]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44(6), 976–983 (2005).
[CrossRef] [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).
[CrossRef] [PubMed]

H. T. Eyyuboglu, “Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Commun. 245(1-6), 37–47 (2005).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Analysis of reciprocity of cos-Gaussian and cosh- Gaussian laser beams in a turbulent atmosphere,” Opt. Express 12(20), 4659–4674 (2004).
[CrossRef] [PubMed]

Friberg, A. T.

Ghafary, B.

B. Ghafary and M. Alavinejad, “Changes in the state of polarization of partially coherent flat-topped beams in turbulent atmosphere for different source conditions,” Appl. Phys. B 102(4), 945–952 (2011).
[CrossRef]

F. D. Kashani, M. Alavinejad, and B. Ghafary, “Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere,” Opt. Commun. 282(20), 4029–4034 (2009).
[CrossRef]

Gori, F.

He, S.

James, D. F. V.

Ji, G.

Ji, X.

X. Ji and X. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite-Gaussian beams in turbulence,” Opt. Laser Technol. 41(2), 165–171 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41(6), 714–722 (2009).
[CrossRef]

X. Ji and Z. Pu, “Effects of atmospheric turbulence on the polarization of apertured electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 11(4), 045701 (2009).
[CrossRef]

X. Ji, X. Chen, and B. Lü, “Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A 25(1), 21–28 (2008).
[CrossRef] [PubMed]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16(12), 8366–8380 (2008).
[CrossRef] [PubMed]

X. Ji and G. Ji, “Effect of turbulence on the beam quality of apertured partially coherent beams,” J. Opt. Soc. Am. A 25(6), 1246–1252 (2008).
[CrossRef] [PubMed]

X. Ji, E. Zhang, and B. Lü, “Changes in spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275(2), 292–300 (2007).
[CrossRef]

Kashani, F. D.

F. D. Kashani, M. Alavinejad, and B. Ghafary, “Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere,” Opt. Commun. 282(20), 4029–4034 (2009).
[CrossRef]

Korotkova, O.

X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15(3), 353–364 (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 Complex Media 14, 513–523 (2004).

Leader, J. C.

Li, Y.

Lin, Q.

Lü, B.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41(6), 714–722 (2009).
[CrossRef]

X. Ji, X. Chen, and B. Lü, “Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A 25(1), 21–28 (2008).
[CrossRef] [PubMed]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16(12), 8366–8380 (2008).
[CrossRef] [PubMed]

X. Ji, E. Zhang, and B. Lü, “Changes in spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275(2), 292–300 (2007).
[CrossRef]

Lutomirski, R. F.

Ni, Y.

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87(3), 547–552 (2007).
[CrossRef]

Plonus, M. A.

Ponomarenko, S. A.

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, 1611–1618 (2005).
[CrossRef]

Pu, Z.

X. Ji and Z. Pu, “Effects of atmospheric turbulence on the polarization of apertured electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 11(4), 045701 (2009).
[CrossRef]

Qu, J.

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102(4), 937–944 (2011).
[CrossRef]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, and Y. Baykal, “Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere,” Opt. Express 17(13), 11130–11139 (2009).
[CrossRef] [PubMed]

Ramírez-Sánchez, V.

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, 1611–1618 (2005).
[CrossRef]

Salem, M.

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33(11), 1180–1182 (2008).
[CrossRef] [PubMed]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15(3), 353–364 (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 Complex Media 14, 513–523 (2004).

Santarsiero, M.

Setälä, T.

Shi, J.

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102(4), 937–944 (2011).
[CrossRef]

Tervo, J.

Wang, H.

Wang, S. C. H.

Wang, X.

Wolf, E.

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33(11), 1180–1182 (2008).
[CrossRef] [PubMed]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15(3), 353–364 (2005).
[CrossRef]

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, 1611–1618 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (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 Complex Media 14, 513–523 (2004).

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17(11), 2019–2023 (2000).
[CrossRef] [PubMed]

Y. Li and E. Wolf, “Radiation from anisotropic Gaussian Schell-model sources,” Opt. Lett. 7(6), 256–258 (1982).
[CrossRef] [PubMed]

Yang, A.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41(6), 714–722 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16(12), 8366–8380 (2008).
[CrossRef] [PubMed]

Yang, K.

Yuan, Y.

Yura, H. T.

Zeng, A.

Zhang, E.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41(6), 714–722 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16(12), 8366–8380 (2008).
[CrossRef] [PubMed]

X. Ji, E. Zhang, and B. Lü, “Changes in spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275(2), 292–300 (2007).
[CrossRef]

Zhao, D.

Zhong, Y.

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102(4), 937–944 (2011).
[CrossRef]

Zhou, G.

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87(3), 547–552 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (5)

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87(3), 547–552 (2007).
[CrossRef]

Y. Zhong, Z. Cui, J. Shi, and J. Qu, “Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere,” Appl. Phys. B 102(4), 937–944 (2011).
[CrossRef]

B. Ghafary and M. Alavinejad, “Changes in the state of polarization of partially coherent flat-topped beams in turbulent atmosphere for different source conditions,” Appl. Phys. B 102(4), 945–952 (2011).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Degree of polarization for partially coherent general beams in turbulent atmosphere,” Appl. Phys. B 89(1), 91–97 (2007).
[CrossRef]

H. T. Eyyuboğlu, “Comparison of wave structure functions for intensity profiles,” Appl. Phys. B 94(3), 489–497 (2009).
[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, 1611–1618 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

X. Ji and Z. Pu, “Effects of atmospheric turbulence on the polarization of apertured electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 11(4), 045701 (2009).
[CrossRef]

Y. Cai, “Propagation of various flat-topped beams in a turbulent atmosphere,” J. Opt. A, Pure Appl. Opt. 8(6), 537–545 (2006).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Commun. (6)

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[CrossRef]

X. Ji, E. Zhang, and B. Lü, “Changes in spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275(2), 292–300 (2007).
[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]

F. D. Kashani, M. Alavinejad, and B. Ghafary, “Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere,” Opt. Commun. 282(20), 4029–4034 (2009).
[CrossRef]

H. T. Eyyuboglu, “Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Commun. 245(1-6), 37–47 (2005).
[CrossRef]

Y. Cai, H. T. Eyyuboglu, and Y. Baykal, “Propagation properties of anomalous hollow beams in a turbulent atmosphere,” Opt. Commun. 281(21), 5291–5297 (2008).
[CrossRef]

Opt. Express (7)

Opt. Laser Technol. (2)

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41(6), 714–722 (2009).
[CrossRef]

X. Ji and X. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite-Gaussian beams in turbulence,” Opt. Laser Technol. 41(2), 165–171 (2009).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

Waves Random Complex Media (2)

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

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15(3), 353–364 (2005).
[CrossRef]

Other (2)

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

L. C. Andrews and R. L. Philiphs, Laser Beam Propagation through Random Media, 2nd Edition (SPIE Press, 2005).

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Figures (2)

Fig. 1
Fig. 1

Comparison of the polarization curves calculated by the analytic formulas and by numerically evaluating the exact quadruple integrations, in x ( y=0 ) and y ( x=0 ) directions at three different propagation distances, of an anisotropic electromagnetic GSM beam propagating in turbulent atmosphere. The solid curves represent the results calculated by the analytic formulas, and the dotted curves represent the results calculated by exact numerical evaluations. For both beams in (a) and (b), the source intensity parameters are chosen as σ 0x (x) =0.02m , σ 0y (x) =0.03m , σ 0x (y) =0.09m , σ 0y (y) =0.006m . For the beam in (a), the source spatial coherence parameters are chosen as δ 0x (x) =0.002m , δ 0y (x) =0.004m , δ 0x (y) =0.006m , δ 0y (y) =0.001m , δ 0x (n) =0.0045m , δ 0y (n) =0.003m , and for the beam in (b), the source spatial coherence parameters are chosen as δ 0x (x) =0.003m , δ 0y (x) =0.004m , δ 0x (y) =0.001m , δ 0y (y) =0.002m , δ 0x (n) =0.0025m , δ 0y (n) =0.0035m .

Fig. 2
Fig. 2

Same as in Fig. 1, except that the source intensity parameters are chosen as σ 0x (x) = σ 0x (y) =0.04m , σ 0y (x) = σ 0y (y) =0.02m .

Equations (42)

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W (0) ( s 1 , s 2 ,ω )=( W xx (0) ( s 1 , s 2 ,ω ) W xy (0) ( s 1 , s 2 ,ω ) W yx (0) ( s 1 , s 2 ,ω ) W yy (0) ( s 1 , s 2 ,ω ) ),
W ij (0) ( s 1 , s 2 ,ω)= S i ( s 1 ,ω) S j ( s 2 ,ω) μ ij ( s 1 s 2 ,ω),
S i (s,ω)= A i 2 exp( 1 2 s T σ ˜ i s ), μ ij ( s 1 s 2 ,ω)= B ij exp[ 1 2 ( s 1 s 2 ) T δ ˜ ij ( s 1 s 2 ) ],
σ ˜ x =[ [ σ 0x (x) ] 2 0 0 [ σ 0y (x) ] 2 ], σ ˜ y =[ [ σ 0x (y) ] 2 0 0 [ σ 0y (y) ] 2 ], δ ˜ xx =[ [ δ 0x (x) ] 2 0 0 [ δ 0y (x) ] 2 ], δ ˜ yy =[ [ δ 0x (y) ] 2 0 0 [ δ 0y (y) ] 2 ], δ ˜ yy =[ [ δ 0x (y) ] 2 0 0 [ δ 0y (y) ] 2 ], δ ˜ xy =[ [ δ 0x (n) ] 2 0 0 [ δ 0y (n) ] 2 ].
W xx (0) ( s 1 , s 2 ,ω)= A x 2 exp[ ξ 1 2 + ξ 2 2 4 σ 0x (x)2 η 1 2 + η 2 2 4 σ 0y (x)2 ( ξ 1 ξ 2 ) 2 2 δ 0x (x)2 ( η 1 η 2 ) 2 2 δ 0y (x)2 ],
W yy (0) ( s 1 , s 2 ,ω)= A y 2 exp[ ξ 1 2 + ξ 2 2 4 σ 0x (y)2 η 1 2 + η 2 2 4 σ 0y (y)2 ( ξ 1 ξ 2 ) 2 2 δ 0x (y)2 ( η 1 η 2 ) 2 2 δ 0y (y)2 ],
W xy (0) ( s 1 , s 2 ,ω)= A x A y B xy exp[ ξ 1 2 4 σ 0x (x)2 η 1 2 4 σ 0y (x)2 ]exp[ ξ 2 2 4 σ 0x (y)2 η 2 2 4 σ 0y (y)2 ] ×exp[ ( ξ 1 ξ 2 ) 2 2 δ 0x (n)2 ]exp[ ( η 1 η 2 ) 2 2 δ 0y (n)2 ],
W yx (0) ( s 1 , s 2 ,ω)= W xy (0)* ( s 2 , s 1 ,ω).
i=x,y j=x,y f i * ( s 1 ) f j ( s 2 ) W ij (0) ( s 1 , s 2 ,ω)d s 1 d s 2 0,
μ ˜ ij (η)= μ ij (ρ)exp(i2πη·ρ) d 2 ρ, (ρ s 1 s 2 ),
{ μ ˜ xx ( η x , η y )0 μ ˜ yy ( η x , η y )0 | μ ˜ xy ( η x , η y ) | μ ˜ xx ( η x , η y ) μ ˜ yy ( η x , η y ) .
| B xy | δ 0x (n) δ 0y (n) exp[ 2 π 2 ( δ 0x (n)2 η x 2 + δ 0y (n)2 η y 2 ) ] δ 0x (x) δ 0y (x) δ 0x (y) δ 0y (y) exp{ π 2 [ ( δ 0x (x)2 + δ 0x (y)2 ) η x 2 +( δ 0y (x)2 + δ 0y (y)2 ) η y 2 ] }.
{ | B xy | δ 0x (n) δ 0y (n) δ 0x (x) δ 0y (x) δ 0x (y) δ 0y (y) 2 δ 0x (n)2 ( δ 0x (x)2 + δ 0x (y)2 ) 2 δ 0y (n)2 ( δ 0y (x)2 + δ 0y (y)2 ) .
P(s)= 1 4detW(s,s,ω) [ TrW(s,s,ω) ] 2 ,
P(s)= 1 4( A x 2 / A y 2 )(1 | B xy | 2 ) { ( A x 2 / A y 2 )exp[ 1 4 ( 1 σ 0x (y)2 1 σ 0x (x)2 ) ξ 2 + 1 4 ( 1 σ 0y (y)2 1 σ 0y (x)2 ) η 2 ] +exp[ 1 4 ( 1 σ 0x (y)2 1 σ 0x (x)2 ) ξ 2 1 4 ( 1 σ 0y (y)2 1 σ 0y (x)2 ) η 2 ] } 2 .
{ 1 σ 0x (y)2 1 σ 0x (x)2 >0 1 σ 0y (y)2 1 σ 0y (x)2 >0 1 σ 0x (y)2 1 σ 0x (x)2 1 σ 0y (y)2 1 σ 0y (x)2 ,
{ 1 σ 0x (y)2 1 σ 0x (x)2 <0 1 σ 0y (y)2 1 σ 0y (x)2 <0 1 σ 0x (y)2 1 σ 0x (x)2 1 σ 0y (y)2 1 σ 0y (x)2 .
1 σ 0x (y)2 1 σ 0x (x)2 = 1 σ 0y (y)2 1 σ 0y (x)2 0.
{ 1 σ 0x (y)2 1 σ 0x (x)2 >0 1 σ 0y (y)2 1 σ 0y (x)2 <0 ,
{ 1 σ 0x (y)2 1 σ 0x (x)2 <0 1 σ 0y (y)2 1 σ 0y (x)2 >0 .
{ σ 0x (x) = σ 0x (y) σ 0y (x) = σ 0y (y) .
W ij (r,r,z,ω)= ( k 2πz ) 2 W ij (0) ( s 1 , s 2 ,ω)exp{ ik 2z [ (r s 1 ) 2 (r s 2 ) 2 ] } × exp[ψ(r, s 1 ,z)+ ψ * (r, s 2 ,z)] d s 1 d s 2 .
exp[ψ(r, s 1 ,z)+ ψ * (r, s 2 ,z)] =exp{ 4 π 2 k 2 z 0 1 0 κ Φ n (κ) [ 1 J 0 (κξ| Q |) ]dκdξ } =exp[ 1 2 D sp (| Q |,z) ],
D sp (| Q |,z)=1.09 C n 2 k 2 z Q 5/3 ,
exp[ψ(r, s 1 ,z)+ ψ * (r, s 2 ,z)] =exp( Q 2 ρ 0 2 ),
{ s 2 + s 1 =2 s 1 s 2 s 1 = s 2 ,
exp( z 1 t 2 )exp(i z 2 t)dt= π z 1 exp( z 2 2 4 z 1 ), (Re z 1 >0),
W xx (x,y,z,ω)= A x 2 M x (x) M y (x) exp( x 2 2 σ 0x (x)2 M x (x)2 )exp( y 2 2 σ 0y (x)2 M y (x)2 ),
[ M x (x) (z)] 2 =1+ z 2 k 2 σ 0x (x)2 ( 1 4 σ 0x (x)2 + 1 δ 0x (x)2 + 2 ρ 0 2 ), [ M y (x) (z)] 2 =1+ z 2 k 2 σ 0y (x)2 ( 1 4 σ 0y (x)2 + 1 δ 0y (x)2 + 2 ρ 0 2 ); W yy (x,y,z,ω)= A y 2 M x (y) M y (y) exp( x 2 2 σ 0x (y)2 M x (y)2 )exp( y 2 2 σ 0y (y)2 M y (y)2 ),
[ M x (y) (z)] 2 =1+ z 2 k 2 σ 0x (y)2 ( 1 4 σ 0x (y)2 + 1 δ 0x (y)2 + 2 ρ 0 2 ),
[ M y (y) (z)] 2 =1+ z 2 k 2 σ 0y (y)2 ( 1 4 σ 0y (y)2 + 1 δ 0y (y)2 + 2 ρ 0 2 );
W xy (x,y,z,ω)= W yx * (x,y,z,ω) = A x A y B xy M x (n) M y (n) exp[ x 2 2 σ x (n)2 M x (n) 2 ]exp[ y 2 2 σ y (n)2 M y (n) 2 ],
σ x (n)2 = 2 σ 0x (x)2 σ 0x (y)2 σ 0x (x)2 + σ 0x (y)2 ,
σ y (n)2 = 2 σ 0y (x)2 σ 0y (y)2 σ 0y (x)2 + σ 0y (y)2 ,
[ M x (n) (z)] 2 =1+ z 2 k 2 σ x (n)2 [ 1 2( σ 0x (x)2 + σ 0x (y)2 ) + 1 δ 0x (n)2 + 2 ρ 0 2 ] iz k σ 0x (y)2 σ 0x (x)2 2 σ 0x (x)2 σ 0x (y)2 ,
[ M y (n) (z)] 2 =1+ z 2 k 2 σ y (n)2 [ 1 2( σ 0y (x)2 + σ 0y (y)2 ) + 1 δ 0y (n)2 + 2 ρ 0 2 ] iz k σ 0y (y)2 σ 0y (x)2 2 σ 0y (x)2 σ 0y (y)2 .
W xx (ff) (r,z)= A x 2 k 2 σ 0x (x) σ 0y (x) 2 z 2 ρ 0 2 exp( k 2 r 2 4 z 2 ρ 0 2 ),
W yy (ff) (r,z)= A y 2 k 2 σ 0x (y) σ 0y (y) 2 z 2 ρ 0 2 exp( k 2 r 2 4 z 2 ρ 0 2 ),
W xy (ff) (r,z)= A x A y B xy k 2 σ x (n) σ y (n) 2 z 2 ρ 0 2 exp( k 2 r 2 4 z 2 ρ 0 2 ),
W yx (ff) (r,z)= A x A y B xy * k 2 σ x (n) σ y (n) 2 z 2 ρ 0 2 exp( k 2 r 2 4 z 2 ρ 0 2 ).
P (ff)2 =1 4( A x 2 / A y 2 )( σ 0x (x) σ 0y (x) σ 0x (y) σ 0y (y) | B xy | 2 σ x (n)2 σ y (n)2 ) [( A x 2 / A y 2 ) σ 0x (x) σ 0y (x) + σ 0x (y) σ 0y (y) ] 2 .
P (0) = 1 4 A x 2 / A y 2 (1 | B xy | 2 ) (1+ A x 2 / A y 2 ) 2 ;

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