Abstract

A recently introduced class of scalar cosine-Gaussian Schell-Model [CGSM] beams is generalized to electromagnetic theory. The realizability conditions and the beam conditions on the source parameters are derived. Analytical formulas for the cross-spectral density matrix elements of the electromagnetic cosine-Gaussian Schell-model [EM CGSM] beams propagating in isotropic random medium are derived. It is found that the EM CGSM beams possess single-ring or double-ring intensity profiles, depending of source parameters. As two examples, the statistical characteristics of the EM CGSM beams propagating in free space and non-Kolmogorov turbulent atmosphere are studied numerically. The effects of the fractal constant of the atmospheric spectrum and the refractive-index structure constant on such characteristics are analyzed in detail.

© 2013 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun.64(4), 311–316 (1987).
    [CrossRef]
  3. F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett.33(16), 1857–1859 (2008).
    [CrossRef] [PubMed]
  4. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett.36(20), 4104–4106 (2011).
    [CrossRef] [PubMed]
  5. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett.37(14), 2970–2972 (2012).
    [CrossRef] [PubMed]
  6. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A29(10), 2159–2164 (2012).
    [CrossRef] [PubMed]
  7. Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett.38(2), 91–93 (2013).
    [CrossRef] [PubMed]
  8. O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett.29(11), 1173–1175 (2004).
    [CrossRef] [PubMed]
  9. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun.249(4–6), 379–385 (2005).
    [CrossRef]
  10. F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt.11(8), 085706 (2009).
    [CrossRef]
  11. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
    [CrossRef]
  12. 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]
  13. X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express15(25), 16909–16915 (2007).
    [CrossRef] [PubMed]
  14. Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt.15(2), 025705 (2013).
    [CrossRef]
  15. Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A29(10), 2154–2158 (2012).
    [CrossRef] [PubMed]
  16. Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express20(24), 26458–26463 (2012).
    [CrossRef] [PubMed]
  17. G. Gbur and T. D. Visser, “Can spatial coherence effects produce a local minimum of intensity at focus,” Opt. Lett.28(18), 1627–1629 (2003).
    [CrossRef] [PubMed]
  18. Y. Cai and F. Wang, “Partially coherent anomalous hollow beam and its paraxial propagation,” Phys. Lett. A372(25), 4654–4660 (2008).
    [CrossRef]
  19. M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
    [CrossRef]
  20. Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett.38(14), 2578–2580 (2013).
    [CrossRef] [PubMed]
  21. Z. Mei, E. Shchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express21(15), 17512–17519 (2013).
    [CrossRef] [PubMed]
  22. H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun.278(1), 17–22 (2007).
    [CrossRef]
  23. G. Zhou and X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express17(13), 10529–10534 (2009).
    [CrossRef] [PubMed]
  24. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010).
    [CrossRef]
  25. E. Wolf, Introduction to the Theories of Coherence and Polarization of Light (Cambridge University, 2007).
  26. X. Du and D. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express17(6), 4257–4262 (2009).
    [CrossRef] [PubMed]
  27. 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. SPIE6551(65510E), 65510E (2007).
    [CrossRef]
  28. E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express18(10), 10650–10658 (2010).
    [CrossRef] [PubMed]
  29. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003 (2008).
    [CrossRef]
  30. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.7(5), 232–237 (2005).
    [CrossRef]

2013 (5)

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

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt.15(2), 025705 (2013).
[CrossRef]

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
[CrossRef]

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

Z. Mei, E. Shchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express21(15), 17512–17519 (2013).
[CrossRef] [PubMed]

2012 (4)

2011 (1)

2010 (2)

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010).
[CrossRef]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express18(10), 10650–10658 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (3)

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett.33(16), 1857–1859 (2008).
[CrossRef] [PubMed]

Y. Cai and F. Wang, “Partially coherent anomalous hollow beam and its paraxial propagation,” Phys. Lett. A372(25), 4654–4660 (2008).
[CrossRef]

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

2007 (3)

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. SPIE6551(65510E), 65510E (2007).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun.278(1), 17–22 (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. Express15(25), 16909–16915 (2007).
[CrossRef] [PubMed]

2005 (3)

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. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun.249(4–6), 379–385 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.7(5), 232–237 (2005).
[CrossRef]

2004 (1)

2003 (1)

2001 (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

Alavinejad, M.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
[CrossRef]

Andrews, L. C.

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

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. SPIE6551(65510E), 65510E (2007).
[CrossRef]

Baykal, Y.

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun.278(1), 17–22 (2007).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett.33(16), 1857–1859 (2008).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

Cai, Y.

Y. Cai and F. Wang, “Partially coherent anomalous hollow beam and its paraxial propagation,” Phys. Lett. A372(25), 4654–4660 (2008).
[CrossRef]

Chu, X.

Du, X.

Eyyuboglu, H. T.

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun.278(1), 17–22 (2007).
[CrossRef]

Ferrero, V.

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

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. SPIE6551(65510E), 65510E (2007).
[CrossRef]

Gbur, G.

Ghafary, B.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
[CrossRef]

Golbraikh, E.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010).
[CrossRef]

Gori, F.

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

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett.33(16), 1857–1859 (2008).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

Hadilou, N.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
[CrossRef]

Kopeika, N. S.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010).
[CrossRef]

Korotkova, O.

Z. Mei, E. Shchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express21(15), 17512–17519 (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(2), 025705 (2013).
[CrossRef]

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

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A29(10), 2159–2164 (2012).
[CrossRef] [PubMed]

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A29(10), 2154–2158 (2012).
[CrossRef] [PubMed]

Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express20(24), 26458–26463 (2012).
[CrossRef] [PubMed]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express18(10), 10650–10658 (2010).
[CrossRef] [PubMed]

X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express15(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]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun.249(4–6), 379–385 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.7(5), 232–237 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett.29(11), 1173–1175 (2004).
[CrossRef] [PubMed]

Lajunen, H.

Mei, Z.

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

Phillips, R. L.

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

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. SPIE6551(65510E), 65510E (2007).
[CrossRef]

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

Ramírez-Sánchez, V.

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

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun.249(4–6), 379–385 (2005).
[CrossRef]

Saastamoinen, T.

Sahin, S.

Salem, M.

Santarsiero, M.

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

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett.33(16), 1857–1859 (2008).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

Shchepakina, E.

Shirai, T.

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

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.7(5), 232–237 (2005).
[CrossRef]

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

Taherabadi, G.

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
[CrossRef]

Tong, Z.

Toselli, I.

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

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. SPIE6551(65510E), 65510E (2007).
[CrossRef]

Visser, T. D.

Wang, F.

Y. Cai and F. Wang, “Partially coherent anomalous hollow beam and its paraxial propagation,” Phys. Lett. A372(25), 4654–4660 (2008).
[CrossRef]

Wolf, E.

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]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.7(5), 232–237 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett.29(11), 1173–1175 (2004).
[CrossRef] [PubMed]

Zhao, D.

Zhou, G.

Zilberman, A.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010).
[CrossRef]

J. Opt. (1)

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt.15(2), 025705 (2013).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (3)

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

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.3(1), 1–9 (2001).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt.7(5), 232–237 (2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (6)

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun.249(4–6), 379–385 (2005).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun.64(4), 311–316 (1987).
[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]

M. Alavinejad, G. Taherabadi, N. Hadilou, and B. Ghafary, “Changes in the coherence properties of partially coherent dark hollow beam propagating through atmospheric turbulence,” Opt. Commun.288, 1–6 (2013).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun.278(1), 17–22 (2007).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010).
[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(2), 026003 (2008).
[CrossRef]

Opt. Express (6)

Opt. Lett. (7)

Phys. Lett. A (1)

Y. Cai and F. Wang, “Partially coherent anomalous hollow beam and its paraxial propagation,” Phys. Lett. A372(25), 4654–4660 (2008).
[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. SPIE6551(65510E), 65510E (2007).
[CrossRef]

Other (2)

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

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

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Figures (7)

Fig. 1
Fig. 1

Three-dimensional transverse distributions and corresponding contour graphs of the spectral density of an EM CGSM beam with n = 2 at several different propagation distances in free space. (a) z = 0 m; (b) z = 100 m; (c) z = 250 m; (d) z = 400 m.

Fig. 2
Fig. 2

Free-space evolution of the normalized spectral density for different n and δ yy . Black solid curves (source plane, z = 0), red dashed curves (z = 100 m), blue dotted curves (z = 500 m) and green dash-dotted curves (z = 1 km).

Fig. 3
Fig. 3

Free-space evolution of degree of coherence for different n and δ yy . Black solid curves (source plane, z = 0), red dashed curves (z = 0.1 m), blue dotted curves (z = 100 m) and green dash-dotted curves (z = 500 m).

Fig. 4
Fig. 4

Transverse cross-sections of the spectral density (a) and three polarization properties: the degree of polarization (b), the orientation angle (c) and the degree of ellipticity (d) of the EM CGSM beams at the range 1 km from the source.

Fig. 5
Fig. 5

Transverse distribution of the spectral density of the same EM CGSM beam as in Fig. 1 propagating in the atmosphere at distance z = 10 km for different values of atmospheric parameters.

Fig. 6
Fig. 6

Modulus of the spectral degree of coherence of the same EM CGSM beam as in Fig. 1 on propagation in the atmosphere as a function | ρ d | . Black thick solid curves (source plane, z = 0), red dotted curves (100 m); blue dashed curves (500 m), green dash-dotted curves (2 km); black thin solid curves (z = 10 km).

Fig. 7
Fig. 7

Changes in the polarization ellipse associated with the polarized part of the EM CGSM beam with n = 4 for different parameters α and C ˜ n 2 at the plane z = 4 km in the non-Kolmogorov turbulence and free space (z = 0 and 4km). The background is the transverse distribution of the spectral density of the beam.

Tables (1)

Tables Icon

Table 1 Value interval of δ xy for different values of δ xx , δ yy , | B xy | and n.

Equations (34)

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W ^ (0) ( ρ 1 , ρ 2 ;ω)=[ W xx (0) ( ρ 1 , ρ 2 ;ω) W xy (0) ( ρ 1 , ρ 2 ;ω) W yx (0) ( ρ 1 , ρ 2 ;ω) W yy (0) ( ρ 1 , ρ 2 ;ω) ].
W αβ (0) ( ρ 1 , ρ 2 ;ω)= E α ( ρ 1 ) E β ( ρ 2 ); (α=x,y;β=x,y),
W αβ (0) ( ρ 1 , ρ 2 )= p αβ (v) H α ( ρ 1 ,v ) H β ( ρ 2 ,v)dv,
H α ( ρ 1 ,v)= A α τ( ρ 1 )exp(2πiv ρ 1 ),
H β ( ρ 2 ,v)= A β τ( ρ 2 )exp(2πiv ρ 2 ),
p αβ (v)= 2π B αβ δ αβ cosh[n (2π) 3/2 δ αβ v]exp(2 π 2 δ αβ 2 v 2 2 n 2 π),
W αβ (0) ( ρ 1 , ρ 2 )= A α A β B αβ exp( ρ 1 2 + ρ 2 2 4 σ 2 )cos[ n 2π ( ρ 2 ρ 1 ) δ αβ ]exp[ ( ρ 2 ρ 1 ) 2 2 δ αβ 2 ].
B xx = B yy =1, | B xy |=| B yx |, δ xy = δ yx .
p xx (v) p yy (v) p xy (v) p yx (v)0,
δ xx 2 δ yy 2 cosh[n (2π) 3/2 δ xx v]cosh[n (2π) 3/2 δ yy v]exp[ v 2 ( δ xx 2 + δ yy 2 )/2 ] | B xy | 2 δ xy 4 { cosh[n (2π) 3/2 δ xy v } 2 exp( v 2 δ xy 2 ).
S (r)= (2πk/r) 2 cos 2 θ[ W ˜ xx (0) (k s ,k s )+ W ˜ yy (0) (k s ,k s ) ],
W ˜ αα (0) ( f 1 , f 2 )= 1 (2π) 4 W αα (0) ( ρ 1 , ρ 2 ) exp[i( f 1 ρ 1 + f 2 ρ 2 ) d 2 ρ 1 d 2 ρ 2 ,
S (r)= k 2 σ 2 cos 2 θ 2 r 2 [ A x 2 a xx exp( k 2 s 2 4 a xx n 2 π 2 a xx δ xx 2 )cosh( n 2π k s 2 a xx δ xx ) + A y 2 a yy exp( k 2 s 2 4 a yy n 2 π 2 a yy δ yy 2 )cosh( n 2π k s 2 a yy δ yy ) ],
exp( k 2 s 2 4 a xx )0, exp( k 2 s 2 4 a yy )0, unless s 2 1,
4 a xx k 2 , 4 a yy k 2 ,
1 4 σ 2 + 1 δ xx 2 2 π 2 λ 2 , 1 4 σ 2 + 1 δ yy 2 2 π 2 λ 2 .
W αβ ( ρ 1 , ρ 2 ,z)= ( k 2πz ) 2 d 2 ρ 1 d 2 ρ 2 W αβ (0) ( ρ 1 , ρ 2 ) ×exp{ ik 2z [ ( ρ 1 ρ 1 ) 2 ( ρ 2 ρ 2 ) 2 ] } exp[ ϕ ( ρ 1 , ρ 1 ,z)+ϕ( ρ 2 , ρ 2 ,z)] M .
exp[ ϕ ( ρ 1 , ρ 1 ,z)+ϕ( ρ 2 , ρ 2 ,z)] M = exp{ π 2 k 2 z 3 [ ( ρ 1 ρ 2 ) 2 +( ρ 1 ρ 2 )( ρ 1 ρ 2 )+ ( ρ 1 ρ 2 ) 2 ] 0 κ 3 Φ n (κ)dκ },
Φ n (κ)=A(α) C ˜ n 2 exp[( κ 2 / κ m 2 )]/ ( κ 2 + κ 0 2 ) α/2 , 0κ<, 3<α<4,
c(α)= [Γ(5 α 2 )A(α) 2π 3 ] 1/(α5) ,
A(α)=Γ(α1) cos(απ/2) 4 π 2 ,
0 κ 3 Φ n (κ)dκ = A(α) 2(α2) C ˜ n 2 [ κ m 2α βexp( κ 0 2 κ m 2 )Γ(2 α 2 , κ 0 2 κ m 2 )2 κ 0 4α ],
W αβ ( ρ 1 , ρ 2 ,z)= k 2 σ 2 A α A β B αβ 4 z 2 Δ αβ (z) exp[ ( ρ 1 ρ 2 ) 2 R(z) ]exp[ ik 2z ( ρ 1 2 ρ 2 2 ) ] ×[ exp( γ + 2 Δ αβ (z) )+exp( γ 2 Δ αβ (z) ) ],
1 R(z) = k 2 σ 2 2 z 2 + k 2 π 2 z 3 0 κ 3 Φ n (κ)dκ ,
Δ αβ (z)= 1 R(z) + 1 8 σ 2 + 1 2 δ αβ 2 ,
γ ± =( 3 k 2 σ 2 4 z 2 1 2R(z) )( ρ 1 ρ 2 )+ ik 4z ( ρ 1 + ρ 2 )± in 2π 2 δ αβ .
S(ρ,z)=Tr W ^ (ρ,ρ,z),
μ( ρ 1 , ρ 2 ,z)= Tr W ^ ( ρ 1 , ρ 2 ,z) Tr W ^ ( ρ 1 , ρ 1 ,z)Tr W ^ ( ρ 2 , ρ 2 ,z) ,
P(ρ,z)= 1 4Det W ^ (ρ,ρ,z) [ Tr W ^ (ρ,ρ,z) ] 2 ,
ϕ(ρ,z)=arctan{2[ W xy (ρ,z)]/[ W xx (ρ,z) W yy (ρ,z)]}/2,
ε ± (ρ,z)= A+B AB ,
A= [ W xx (ρ,z) W yy (ρ,z)] 2 +4| W xy (ρ,z) | 2 ,
B= [ W xx (ρ,z) W yy (ρ,z)] 2 +4|[ W xy (ρ,z)] | 2 ,
μ αβ (0) ( ρ 1 , ρ 2 )= B αβ cos[ n 2π ( ρ 2 ρ 1 ) δ αβ ]exp[ | ρ 2 ρ 1 | 2 2 δ αβ 2 ],

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