Abstract

The expression of spectral density of cosine-Gaussian-correlated Schell-model (CGSM) beams diffracted by an aperture is derived, and used to study the changes in the spectral density distribution of CGSM beams upon propagation, where the effect of aperture diffraction is emphasized. It is shown that, comparing with that of GSM beams, the spectral density distribution of CGSM beams diffracted by an aperture has dip and shows dark hollow intensity distribution when the order-parameter n is big enough. The central intensity increases with increasing truncation parameter of aperture. The comparative study of spectral density distributions of CGSM beams with aperture and that of without aperture is performed. Furthermore, the effect of order-parameter n and spatial coherence of CGSM beams on the spectral density distribution is discussed in detail. The results obtained may be useful in optical particulate manipulation.

© 2014 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light, 1st ed. (Cambridge University, 2007).
  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. C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1–3), 113–121 (1996).
    [CrossRef]
  5. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
    [CrossRef] [PubMed]
  6. Z. S. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
    [CrossRef] [PubMed]
  7. Z. R. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
    [CrossRef] [PubMed]
  8. Z. R. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
    [CrossRef] [PubMed]
  9. Z. Mei, E. Shchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (2013).
    [CrossRef] [PubMed]
  10. Z. R. 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]
  11. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
    [CrossRef] [PubMed]
  12. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
    [CrossRef] [PubMed]
  13. Y. Y. Zhang and D. M. Zhao, “Scattering of multi-Gaussian Schell-model beams on a random medium,” Opt. Express 21(21), 24781–24792 (2013).
    [CrossRef] [PubMed]
  14. Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
    [CrossRef]
  15. Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
    [CrossRef]
  16. Z. R. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014).
    [CrossRef] [PubMed]
  17. Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
    [CrossRef]
  18. S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
    [CrossRef] [PubMed]
  19. C. H. Liang, F. Wang, X. L. Liu, Y. J. 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]
  20. Y. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
    [CrossRef] [PubMed]
  21. O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
    [CrossRef] [PubMed]

2014 (6)

Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[CrossRef]

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

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[CrossRef] [PubMed]

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[CrossRef] [PubMed]

2013 (7)

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

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[CrossRef] [PubMed]

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

Z. R. 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. Express 21(15), 17512–17519 (2013).
[CrossRef] [PubMed]

Z. R. 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]

2012 (3)

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. A 29(10), 2159–2164 (2012).
[CrossRef] [PubMed]

Z. S. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[CrossRef] [PubMed]

2011 (1)

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

2008 (1)

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

1996 (1)

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1–3), 113–121 (1996).
[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]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1–3), 113–121 (1996).
[CrossRef]

Cai, Y. J.

Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[CrossRef]

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[CrossRef] [PubMed]

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Chen, Y. H.

Y. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[CrossRef] [PubMed]

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Chen, Z. Y.

S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[CrossRef] [PubMed]

Cincotti, G.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1–3), 113–121 (1996).
[CrossRef]

Cui, S. W.

S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[CrossRef] [PubMed]

Eyyuboglu, H. T.

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Gori, F.

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

Korotkova, O.

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[CrossRef] [PubMed]

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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. R. 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. Express 21(15), 17512–17519 (2013).
[CrossRef] [PubMed]

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

Z. S. 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]

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

Lajunen, H.

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

Liang, C. H.

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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]

Liu, L.

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[CrossRef]

Liu, X. L.

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Mei, Z.

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

Mei, Z. R.

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

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

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

Z. R. 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]

Palma, C.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1–3), 113–121 (1996).
[CrossRef]

Pu, J. X.

S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[CrossRef] [PubMed]

Qu, J.

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Saastamoinen, T.

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

Sahin, S.

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

Santarsiero, M.

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

Shchepakina, E.

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

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

Tong, Z. S.

Z. S. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[CrossRef] [PubMed]

Wang, F.

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[CrossRef] [PubMed]

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Yuan, Y. S.

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

Zhang, L.

S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[CrossRef] [PubMed]

Zhang, Y. T.

Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[CrossRef]

Zhang, Y. Y.

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

Zhao, C. L.

Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[CrossRef]

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

Y. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[CrossRef] [PubMed]

Zhao, D. M.

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

J. Opt. Soc. Am. A (1)

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

Opt. Commun. (2)

Y. S. Yuan, X. L. Liu, F. Wang, Y. H. Chen, Y. J. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305(0), 57–65 (2013).
[CrossRef]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125(1–3), 113–121 (1996).
[CrossRef]

Opt. Express (4)

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

Z. R. 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]

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

Y. H. Chen, F. Wang, C. L. Zhao, and Y. J. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[CrossRef] [PubMed]

Opt. Lett. (10)

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[CrossRef] [PubMed]

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

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

S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[CrossRef] [PubMed]

C. H. Liang, F. Wang, X. L. Liu, Y. J. 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. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (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]

Z. S. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[CrossRef] [PubMed]

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

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

Phys. Lett. A (1)

Y. T. Zhang, L. Liu, C. L. Zhao, and Y. J. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
[CrossRef]

Phys. Rev. A (1)

Y. H. Chen, F. Wang, L. Liu, C. L. Zhao, Y. J. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light, 1st ed. (Cambridge University, 2007).

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of CGSM beams diffracted by an aperture.

Fig. 2
Fig. 2

Normalized spectral density distribution S(u,z)/S(0,0) of CGSM beams as a function of propagation distance z and relative coordinate u for different values of order-parameter n (a) n = 0, (b) n = 1, (c) n = 2, (d) n = 4 and (e), (f), (g), (h) the color-coded plot corresponding to (a), (b), (c), (d) respectively. The other parameters are δ = 0.4, σ/w0 = 0.5.

Fig. 3
Fig. 3

Normalized transverse spectral density distribution S(u,z)/S(0,0) of CGSM beams for different values of propagation distance (a) z/z0 = 0.2, (b) z/z0 = 0.3, (c) z/z0 = 0.4, (d) z/z0→∞. The other parameters are δ = 0.4, σ/w0 = 0.5, n = 2.

Fig. 4
Fig. 4

Normalized transverse spectral density distribution S(u,z)/S(0,0) of CGSM beams for different values of truncation parameter. The other parameters are σ/w0 = 0.5, n = 2, (a) z/z0 = 0.3, (b) z/z0 = 0.4.

Fig. 5
Fig. 5

Normalized transverse spectral density distribution S(u,z)/S(0,0) of CGSM beams for different values of order-parameter n. The other parameters are σ/w0 = 0.5, δ = 0.4, (a) z/z0 = 0.3, (b) z/z0→∞.

Fig. 6
Fig. 6

Normalized transverse spectral density distribution S(u,z)/S(0,0) of CGSM beams for different values of coherence parameter σ/w0. The other parameters are n = 2, δ = 0.4, (a) z/z0 = 0.3, (b) z/z0→∞.

Equations (11)

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W ( 0 ) ( x 1 , x 2 )=exp[ x 1 2 + x 2 2 w 0 2 ]cos[ n 2π ( x 2 x 1 ) σ ]exp[ ( x 2 x 1 ) 2 2 σ 2 ],
S(x,z)=W(x,x,z)= k 2πz a a a a W (0) ( x 1 , x 2 ,z=0) ×exp{ ik 2z [ ( x 1 2 x 2 2 )2x( x 1 x 2 ) ] }d x 1 d x 2 2 .
S(u,z)= i 4 π Q 2 z 0 z × δ δ exp{ 1 4 (σ/ w 0 ) 4 Q 2 [ 4π 2π nu z 0 z ( σ w 0 ) 3 4 π 2 u 2 ( z 0 z ) 2 ( σ w 0 ) 4 2π n 2 ( σ w 0 ) 2 +2i( n 2π σ w 0 +2πu z 0 z ( σ w 0 ) 2 +4πu z 0 z Q 2 ( σ w 0 ) 4 ) u +( 14 Q 1 Q 2 ( σ w 0 ) 4 ) u 2 ] } ×{ H 1 exp[ in 2π (σ/ w 0 ) 3 Q 2 u ]+ H 2 exp[ 2 2 n π 3/2 ( z 0 /z) (σ/ w 0 ) Q 2 u ] }d u ,
H 1 =[ cos( u 2π u σ/ w 0 )+isin( u 2π u σ/ w 0 ) ]×{ Erf[ i u + σ w 0 ( 2π n2πu z 0 z σ w 0 )2iδ Q 2 ( σ w 0 ) 2 2 ( σ/ w 0 ) 2 Q 2 ] Erf[ i u + σ w 0 ( 2π n2πu z 0 z σ w 0 )+2iδ Q 2 ( σ w 0 ) 2 2 ( σ/ w 0 ) 2 Q 2 ] },
H 2 =[ cos( u 2π u σ/ w 0 )isin( u 2π u σ/ w 0 ) ]×{ Erf[ i u + σ w 0 ( 2π n+2πu z 0 z σ w 0 )2iδ Q 2 ( σ w 0 ) 2 2 ( σ/ w 0 ) 2 Q 2 ] Erf[ i u + σ w 0 ( 2π n+2πu z 0 z σ w 0 )+2iδ Q 2 ( σ w 0 ) 2 2 ( σ/ w 0 ) 2 Q 2 ] },
δ= a w 0 , ( truncation parameter )
z 0 = w 0 2 λ ,
u = x w 0 ,( relative transversal coordinate at z=0 plane )
u= x w 0 , ( relative transversal coordinate at z plane )
Q 1 =1 1 2 (σ/ w 0 ) 2 iπ z 0 z ,
Q 2 =1 1 2 (σ/ w 0 ) 2 +iπ z 0 z ,

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