Abstract

The analytical expressions for the spectral degree of coherence, the effective radius of curvature and the propagation factor of the Bessel-Gaussian Schell-model (BGSM) beam in turbulent atmosphere are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The evolution properties of BGSM beams propagating in non-Kolmogorov turbulence are investigated by a set of numerical examples. It is demonstrated that the spectral degree of coherence of the BGSM beam evolves into Gaussian profile twice with the increasing of the propagation distance. The turbulence-induced degradation can be remarkably reduced by using the BGSM beam with the proper source parameters. The effects that the generalized refractive-index structure constant, outer and inner scales, and the spectral index of spatial power spectrum of atmospheric turbulence have on the evolution properties of BGSM beams are also discussed in detail.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence

Hua-Feng Xu, Zhou Zhang, Jun Qu, and Wei Huang
Opt. Express 22(19) 22479-22489 (2014)

Propagation factors of multi-sinc Schell-model beams in non-Kolmogorov turbulence

Zhenzhen Song, Zhengjun Liu, Keya Zhou, Qiongge Sun, and Shutian Liu
Opt. Express 24(2) 1804-1813 (2016)

Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence

Jiayi Yu, Yahong Chen, Lin Liu, Xianlong Liu, and Yangjian Cai
Opt. Express 23(10) 13467-13481 (2015)

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
    [Crossref]
  2. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
    [Crossref]
  3. H. T. Eyyuboğlu, Ç. Arpali, and Y. Baykal, “Flat topped beams and their characteristics in turbulent media,” Opt. Express 14(10), 4196–4207 (2006).
    [Crossref]
  4. Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14(4), 1353–1367 (2006).
    [Crossref] [PubMed]
  5. Y. Cai and S. He, “Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere,” Opt. Lett. 31(5), 568–570 (2006).
    [Crossref] [PubMed]
  6. Z. Zang, “High-Power (> 110 mW) Superluminescent Diodes by Using Active Multimode Interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
    [Crossref]
  7. Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
    [Crossref]
  8. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19(9), 1794–1802 (2002).
    [Crossref]
  9. J. C. Ricklin and F. M. Davidson, “Atmospheric optical communication with a Gaussian Schell beam,” J. Opt. Soc. Am. A 20(5), 856–866 (2003).
    [Crossref]
  10. A. Dogariu and S. Amarande, “Propagation of partially coherent beams: turbulence-induced degradation,” Opt. Lett. 28(1), 10–12 (2003).
    [Crossref] [PubMed]
  11. M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216(4–6), 261–265 (2003).
    [Crossref]
  12. O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
    [Crossref]
  13. 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]
  14. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
    [Crossref] [PubMed]
  15. 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]
  16. L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
    [Crossref]
  17. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
    [Crossref] [PubMed]
  18. Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
    [Crossref]
  19. Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
    [Crossref] [PubMed]
  20. H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express 21(1), 190–195 (2013).
    [Crossref] [PubMed]
  21. S. Cui, Z. Chen, L. Zhang, and J. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
    [Crossref] [PubMed]
  22. Z. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39(2), 347–350 (2014).
    [Crossref] [PubMed]
  23. Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
    [Crossref] [PubMed]
  24. Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
    [Crossref] [PubMed]
  25. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
    [Crossref]
  26. S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
    [Crossref]
  27. Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
    [Crossref]
  28. O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
    [Crossref]
  29. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
    [Crossref] [PubMed]
  30. 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]
  31. 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]
  32. Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).
    [Crossref]
  33. Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
    [Crossref] [PubMed]
  34. F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
    [Crossref] [PubMed]
  35. Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
    [Crossref] [PubMed]
  36. Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
    [Crossref] [PubMed]
  37. Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
    [Crossref] [PubMed]
  38. J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
    [Crossref]
  39. 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]
  40. Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
    [Crossref] [PubMed]
  41. 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]
  42. H. Xu, Z. Zhang, J. Qu, and W. Huang, “Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 22(19), 22479–22489 (2014).
    [Crossref] [PubMed]
  43. Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
    [Crossref] [PubMed]
  44. L. Pan, C. Ding, and H. Wang, “Diffraction of cosine-Gaussian-correlated Schell-model beams,” Opt. Express 22(10), 11670–11679 (2014).
    [Crossref] [PubMed]
  45. 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]
  46. Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
    [Crossref] [PubMed]
  47. Z. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39(14), 4188–4191 (2014).
    [Crossref] [PubMed]
  48. Z. Mei and Y. Mao, “Electromagnetic sinc Schell-model beams and their statistical properties,” Opt. Express 22(19), 22534–22546 (2014).
    [Crossref] [PubMed]
  49. Y. Chen, F. Wang, L. Liu, C. Zhao, Y. 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]
  50. Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008).
    [Crossref] [PubMed]
  51. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
    [Crossref] [PubMed]
  52. G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35(5), 715–717 (2010).
    [Crossref] [PubMed]
  53. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).
  54. R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 2000).
  55. H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99(4), 801–807 (2010).
    [Crossref]
  56. X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).
    [Crossref] [PubMed]
  57. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, and P. Vahimaa, “Spreading properties of beams radiated by partially coherent Schell-model sources,” J. Opt. Soc. Am. A 16(1), 106–112 (1999).
    [Crossref]
  58. M. Charnotskii, “Common omissions and misconceptions of wave propagation in turbulence: discussion,” J. Opt. Soc. Am. A 29, 711–721 (2012).
    [Crossref]
  59. M. Charnotskii, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence: comment,” J. Opt. Soc. Am. A 29, 1838–1840 (2012).
    [Crossref]
  60. C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
    [Crossref]

2014 (16)

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

O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
[Crossref]

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]

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

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

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

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

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]

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]

Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
[Crossref] [PubMed]

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

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

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. 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]

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

C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

2013 (12)

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

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Z. Mei, 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]

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]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

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

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

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

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

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

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

2012 (9)

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
[Crossref]

Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
[Crossref] [PubMed]

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

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

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]

M. Charnotskii, “Common omissions and misconceptions of wave propagation in turbulence: discussion,” J. Opt. Soc. Am. A 29, 711–721 (2012).
[Crossref]

M. Charnotskii, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence: comment,” J. Opt. Soc. Am. A 29, 1838–1840 (2012).
[Crossref]

2011 (1)

2010 (4)

Z. Zang, “High-Power (> 110 mW) Superluminescent Diodes by Using Active Multimode Interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[Crossref]

G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35(5), 715–717 (2010).
[Crossref] [PubMed]

H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99(4), 801–807 (2010).
[Crossref]

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (1)

2007 (1)

2006 (3)

2004 (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

2003 (3)

2002 (1)

1999 (1)

Amarande, S.

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

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

Arpali, Ç.

Baykal, Y.

Borghi, R.

Bracewell, R. N.

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

Cai, Y.

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

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

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]

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]

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

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

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

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]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

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

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

Cang, J.

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Charnotskii, M.

Chen, C.

C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Chen, R.

Chen, Y.

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

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

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

Chen, Z.

Cincotti, G.

Cui, S.

Dan, Y.

Davidson, F. M.

Ding, C.

Dogariu, A.

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

M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216(4–6), 261–265 (2003).
[Crossref]

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Duelk, M.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

Eyyuboglu, H. T.

Fleischer, J. W.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Gbur, G.

Gori, F.

Gradshteyn, I. S.

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

Gu, Y.

Guo, H.

Hamamoto, K.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

He, S.

Huang, W.

Ji, X.

H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99(4), 801–807 (2010).
[Crossref]

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).
[Crossref] [PubMed]

Kavehrad, M.

C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Korotkova, O.

O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. 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. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

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

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

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

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
[Crossref]

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

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]

Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
[Crossref] [PubMed]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Lajunen, H.

Liang, C.

Liu, L.

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

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

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. 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]

Liu, X.

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]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

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

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Lou, Y.

C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Luo, B.

Mandel, L.

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

Mao, Y.

Mei, Z.

Mukai, K.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

Navaretti, P.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

Pan, L.

Phillips, R. L.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

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

Pu, J.

Qu, J.

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]

Ricklin, J. C.

Ryzhik, I. M.

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

Saastamoinen, T.

Sahin, S.

Salem, M.

M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216(4–6), 261–265 (2003).
[Crossref]

Santarsiero, M.

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]

M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216(4–6), 261–265 (2003).
[Crossref]

Situ, G.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Tong, Z.

Vahimaa, P.

Velez, C.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

Waller, L.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Wang, F.

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]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

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

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

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Wang, H.

Wolf, E.

M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216(4–6), 261–265 (2003).
[Crossref]

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

Wu, G.

Xiu, P.

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

Xu, H.

Yang, H.

C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Yu, S.

Yuan, Y.

Zang, Z.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

Z. Zang, “High-Power (> 110 mW) Superluminescent Diodes by Using Active Multimode Interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[Crossref]

Zhang, B.

Zhang, L.

Zhang, Y.

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

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]

Zhang, Z.

Zhao, C.

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

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. 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. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

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

Zhao, D.

Zhu, S.

Appl. Opt. (1)

Appl. Phys. B (1)

H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99(4), 801–807 (2010).
[Crossref]

Appl. Phys. Lett. (1)

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100(3), 031108 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Z. Zang, “High-Power (> 110 mW) Superluminescent Diodes by Using Active Multimode Interferometer,” IEEE Photon. Technol. Lett. 22(10), 721–723 (2010).
[Crossref]

J. Opt. (1)

O. Korotkova and E. Shchepakina, “Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence,” J. Opt. 16(4), 045704 (2014).
[Crossref]

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

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]

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

Nat. Photonics (1)

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

Opt. Commun. (2)

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

M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216(4–6), 261–265 (2003).
[Crossref]

Opt. Eng. (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Opt. Express (18)

Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
[Crossref] [PubMed]

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

H. T. Eyyuboğlu, Ç. Arpali, and Y. Baykal, “Flat topped beams and their characteristics in turbulent media,” Opt. Express 14(10), 4196–4207 (2006).
[Crossref]

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

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

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Z. Mei, 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]

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

Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008).
[Crossref] [PubMed]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

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

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre-Gaussian correlated Schell-model beam,” Opt. Express 22(11), 13975–13987 (2014).
[Crossref] [PubMed]

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. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
[Crossref] [PubMed]

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

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18(7), 6922–6928 (2010).
[Crossref] [PubMed]

Opt. Laser Technol. (3)

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[Crossref]

C. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Opt. Lett. (16)

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[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. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

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

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

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

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

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

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

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

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

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

G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35(5), 715–717 (2010).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

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

Phys. Lett. A (1)

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

Phys. Rev. A (1)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. 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 (4)

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

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

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

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Modulus of the transverse spectral degree of coherence of the BGSM beam as a function of ρ1x at several propagation distances in non-Kolmogorov turbulence for different values of parameter β.
Fig. 2
Fig. 2 Modulus of the transverse spectral degree of coherence of the BGSM beam with β = 5 as a function of ρ1x at propagation distance z = 2 km in non-Kolmogorov turbulence for different values of spectral index α and generalized Rytov variance σ R 2.
Fig. 3
Fig. 3 Normalized propagation factor of the BGSM beam for different values of parameter β versus propagation distance z in non-Kolmogorov turbulence with different values of generalized refractive-index structure constant C ˜ n 2.
Fig. 4
Fig. 4 Normalized propagation factor of the BGSM beam versus propagation distance z in non-Kolmogorov turbulence for different values of parameter β and beam width σ.
Fig. 5
Fig. 5 Normalized propagation factor of the BGSM beam with β = 2.5 as a function of propagation distance z in non-Kolmogorov turbulence for different values of (a) outer scale L0 and (b) inner scale l0.
Fig. 6
Fig. 6 Normalized propagation factor of the BGSM beam versus parameter β at propagation distance z = 10 km in non-Kolmogorov turbulence for different values of (a) spatial coherence width δ and (b) wavelength λ.
Fig. 7
Fig. 7 Normalized propagation factor of the BGSM beam versus spatial coherence width δ at propagation distance z = 10 km in non-Kolmogorov turbulence for different values of parameter β.
Fig. 8
Fig. 8 Normalized propagation factor of the BGSM beam versus spectral index α at propagation distance z = 1 km in non-Kolmogorov turbulence with σ R 2 = 0.2 for different values of parameter β.
Fig. 9
Fig. 9 Effective radius of curvature of the BGSM beam propagating in non-Kolmogorov turbulence for different values of parameter β and generalized refractive-index structure constant C ˜ n 2.

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

W ( r 1 , r 2 , 0 ) = exp ( | r 1 | 2 + | r 2 | 2 4 σ 2 ) μ ( r 1 , r 2 , 0 )
μ ( r 1 , r 2 , 0 ) = exp [ | r 1 r 2 | 2 2 δ 2 ] J 0 ( β | r 1 r 2 | δ )
W ( ρ s , ρ d , z ) = ( k 2 π z ) 2 W ( r s , r d , 0 ) × exp [ i k z ( ρ s r s ) ( ρ d r d ) ] × exp [ H ( ρ d , r d , z ) ] d 2 r s d 2 r d
r s = r 1 + r 2 2 , r d = r 1 r 2
ρ s = ρ 1 + ρ 2 2 , ρ d = ρ 1 ρ 2
W ( r s , r d , 0 ) = W ( r 1 , r 2 , 0 ) = W ( r s + r d 2 , r s r d 2 , 0 )
H ( ρ d , r d , z ) = π 2 k 2 z T 3 [ r d 2 + r d ρ d + ρ d 2 ]
T = 0 κ 3 Φ n ( κ ) d κ
Φ n ( κ , α ) = A ( α ) C ˜ n 2 exp [ ( κ 2 / κ m 2 ) ] ( κ 2 + κ 0 2 ) α / 2 , 0 κ < , 3 < α < 4
c ( α ) = [ Γ ( 5 α 2 ) A ( α ) 2 π 3 ] 1 / ( α 5 )
A ( α ) = Γ ( α 1 ) cos ( α π / 2 ) 4 π 2
T = 0 κ 3 Φ n ( κ ) d κ = A ( α ) 2 ( α 2 ) C ˜ n 2 [ κ m 2 α μ exp ( κ 0 2 κ m 2 ) Γ ( 2 α 2 , κ 0 2 κ m 2 ) 2 κ 0 4 α ]
exp ( p 2 x 2 ± q x ) d x = π p exp ( q 2 4 p 2 ) , ( p > 0 )
W ( ρ s , ρ d , z ) = Q exp [ a r d 2 b ρ s r d + c ρ d r d ] J 0 ( β | r d | δ ) d 2 r d
Q = σ 2 k 2 2 π z 2 exp [ i k z ρ s ρ d ( π 2 k 2 z T 3 + σ 2 k 2 2 z 2 ) ρ d 2 ]
a = 1 8 σ 2 + 1 2 δ 2 + σ 2 k 2 2 z 2 + π 2 k 2 T z 3 , b = i k z , c = σ 2 k 2 z 2 π 2 k 2 T z 3
W ( ρ s , ρ d , z ) = Q 0 0 2 π exp [ a r d 2 | b ρ s c ρ d | r d cos φ ] J 0 ( β r d δ ) r d d r d d φ
0 2 π exp ( ± x cos φ ) d φ = 2 π I 0 ( x )
0 x exp ( γ x 2 ) I ν ( p x ) J ν ( q x ) d x = 1 2 γ exp ( p 2 q 2 4 γ ) J ν ( p q 2 γ ) , [ Re γ > 0 , Re ν > 1 ]
W ( ρ s , ρ d , z ) = σ 2 k 2 2 a z 2 exp [ | b ρ s c ρ d | 2 4 a + i k z ρ s ρ d ( π k 2 z T 3 + σ 2 k 2 2 z 2 ) ρ d 2 ] × exp ( β 2 4 a δ 2 ) J 0 ( β | b ρ s c ρ d | 2 a δ )
μ ( ρ 1 , ρ 2 , z ) = W ( ρ 1 + ρ 2 2 , ρ 1 ρ 2 , z ) S ( ρ 1 , z ) S ( ρ 2 , z )
W ( ρ s , ρ d , z ) = 1 ( 2 π ) 2 W ( r , ρ d + z k κ d , 0 ) × exp [ i ρ s κ d + i κ d r H ( ρ d , ρ d + z k κ d , z ) ] d 2 r d 2 κ d
W ( r , ρ d + z k κ d , 0 ) = exp [ 1 2 σ 2 r 2 ( 1 8 σ 2 + 1 2 δ 2 ) ( ρ d + z k κ d ) 2 ] × J 0 ( β δ | ρ d + z k κ d | )
H ( ρ d , ρ d + z k κ d , z ) = π 2 k 2 z T 3 [ 3 ρ d 2 + 3 z k κ d ρ d + z 2 k 2 κ d 2 ]
h ( ρ s , θ , z ) = ( k 2 π ) 2 W ( ρ s , ρ d , z ) exp ( i k θ ρ d ) d 2 ρ d
h ( ρ s , θ , z ) = k 2 σ 2 8 π 3 exp [ η 1 ρ d 2 η 2 κ d 2 η 3 ρ d κ d i ρ s κ d i k θ ρ d ] × exp [ H ( ρ d , ρ d + z k κ d , z ) ] J 0 ( β δ | ρ d + z k κ d | ) d 2 ρ d d 2 κ d
η 1 = 1 8 σ 2 + 1 2 δ 2 , η 2 = ( 1 8 σ 2 + 1 2 δ 2 ) z 2 k 2 + 1 2 σ 2 , η 3 = ( 1 4 σ 2 + 1 δ 2 ) z k
ρ s x n 1 ρ s y n 2 θ x m 1 θ y m 2 = 1 P ρ s x n 1 ρ s y n 2 θ x m 1 θ y m 2 h ( ρ s , θ , z ) d 2 ρ s d 2 θ
ρ s 2 = ρ s x 2 + ρ s y 2 = 2 σ 2 + ( 1 2 σ 2 + 2 + β 2 δ 2 ) z 2 k 2 + 4 3 π 2 T z 3
θ 2 = θ x 2 + θ x 2 = ( 1 2 σ 2 + 2 + β 2 δ 2 ) 1 k 2 + 4 π 2 T z
ρ s θ = ρ s x θ x + ρ s y θ y = ( 1 2 σ 2 + 2 + β 2 δ 2 ) z k 2 + 2 π 2 T z 2
J ν ( x ) = n = 0 ( 1 ) n ( x / 2 ) 2 n + ν n ! Γ ( n + ν + 1 ) , | x | <
δ ( p x ) = 1 | p | δ ( x )
δ ( n ) ( s ) = 1 2 π ( i x ) n exp ( i s x ) d x , ( n = 0 , 1 , 2 )
f ( x ) δ ( n ) ( x ) d x = ( 1 ) n f ( n ) ( 0 ) , ( n = 0 , 1 , 2 )
R ( z ) = ρ s 2 ρ s θ = 2 σ 2 + ( 1 2 σ 2 + 2 + β 2 δ 2 ) z 2 k 2 + 4 3 π 2 T z 3 ( 1 2 σ 2 + 2 + β 2 δ 2 ) z k 2 + 2 π 2 T z 2
M 2 ( z ) = k ( ρ s 2 θ 2 ρ s θ 2 ) 1 / 2
M 2 ( z ) = [ 2 σ 2 ( 1 2 σ 2 + 2 + β 2 δ 2 ) + 8 π 2 k 2 σ 2 T z + 4 3 π 2 ( 1 2 σ 2 + 2 + β 2 δ 2 ) T z 3 + 4 3 π 4 k 2 T 2 z 4 ] 1 2

Metrics