Abstract

In a recent publication [Opt. Lett. 42, 1512 (2017) [CrossRef]  ], a novel class of partially coherent sources with circular coherence was introduced. In this paper, we examine the propagation behavior of the spectral density and the spectral degree of spatial coherence of a beam generated by such a source in free space and in oceanic turbulent media. It is found that the beam exhibits self-focusing, which is dependent on the initial coherence and the parameters of oceanic turbulence. The self-focusing phenomenon disappears when the initial coherence is high enough or the oceanic turbulence is strong. The area of high coherence appears in the center and along two diagonal lines. With increasing turbulence, the coherence area reduces gradually along one diagonal line and is retained along the other one. A physical interpretation of the self-focusing phenomenon is presented, and potential applications in optical underwater communication and beam shaping are considered.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Tight focusing properties of a circular partially coherent Gaussian beam

Huichuan Lin, Xiaoming Zhou, Ziyang Chen, Osami Sasaki, Yan Li, and Jixiong Pu
J. Opt. Soc. Am. A 35(12) 1974-1980 (2018)

Statistical properties of rectangular cusped random beams propagating in oceanic turbulence

Chuanyi Lu and Daomu Zhao
Appl. Opt. 56(23) 6572-6576 (2017)

Average intensity and directionality of partially coherent model beams propagating in turbulent ocean

Yuqian Wu, Yixin Zhang, and Yun Zhu
J. Opt. Soc. Am. A 33(8) 1451-1458 (2016)

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  3. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  4. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  5. F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
    [Crossref]
  6. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36, 4104–4106 (2011).
    [Crossref]
  7. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
    [Crossref]
  8. Z. R. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39, 4188–4191 (2014).
    [Crossref]
  9. Z. R. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38, 91–93 (2013).
    [Crossref]
  10. O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39, 64–67 (2014).
    [Crossref]
  11. Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review,” J. Opt. Soc. Am. A 31, 2083–2096 (2014).
    [Crossref]
  12. F. Wang and O. Korotkova, “Random sources for beams with azimuthal intensity variation,” Opt. Lett. 41, 516–519 (2016).
    [Crossref]
  13. J. Li, F. Wang, and O. Korotkova, “Random sources for cusped beams,” Opt. Express 24, 17779–17791 (2016).
    [Crossref]
  14. Z. R. Mei and O. Korotkova, “Random sources for rotating spectral densities,” Opt. Lett. 42, 255–258 (2017).
    [Crossref]
  15. S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, “Experimental generation of ring-shaped beams with random sources,” Opt. Lett. 38, 4441–4444 (2013).
    [Crossref]
  16. S. W. Cui, Z. Y. Chen, L. Zhang, and J. X. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38, 4821–4824 (2013).
    [Crossref]
  17. F. Wang, C. H. Liang, Y. S. Yuan, and Y. J. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22, 23456–23464 (2014).
    [Crossref]
  18. 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, 5826–5838 (2014).
    [Crossref]
  19. 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, 013801 (2014).
    [Crossref]
  20. Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
    [Crossref]
  21. Y. H. Chen, J. X. Gu, F. Wang, and Y. J. Cai, “Self-splitting properties of a Hermite–Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
    [Crossref]
  22. W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
    [Crossref]
  23. Y. H. Chen, S. A. Ponomarenko, and Y. J. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7, 39957 (2017).
    [Crossref]
  24. Y. L. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38, 1395–1397 (2013).
    [Crossref]
  25. Z. R. Mei, “Light sources generating self-focusing beams of variable focal length,” Opt. Lett. 39, 347–350 (2014).
    [Crossref]
  26. R. Chen, L. Liu, S. J. Zhu, G. F. Wu, F. Wang, and Y. J. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (2014).
    [Crossref]
  27. H. F. Xu, Z. Zhang, J. Qu, and W. Huang, “Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 22, 22479–22489 (2014).
    [Crossref]
  28. X. Y. Wang, M. W. Yao, Z. L. Qiu, X. Yi, and Z. J. Liu, “Evolution properties of Bessel–Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23, 12508–12523 (2015).
    [Crossref]
  29. J. Yu, Y. H. Chen, L. Liu, X. L. Liu, and Y. J. Cai, “Splitting and combining properties of an elegant Hermite–Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23, 13467–13481 (2015).
    [Crossref]
  30. J. Wang, S. J. Zhu, H. Y. Wang, Y. J. Cai, and Z. H. Li, “Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence,” Opt. Express 24, 11626–11639 (2016).
    [Crossref]
  31. F. Wang and O. Korotkova, “Circularly symmetric cusped random beams in free space and atmospheric turbulence,” Opt. Express 25, 5057–5067 (2017).
    [Crossref]
  32. V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
    [Crossref]
  33. S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).
  34. L. J. Johnson, R. J. Green, and M. S. Leeson, “Underwater optical wireless communications: depth-dependent beam refraction,” Appl. Opt. 53, 7273–7277 (2014).
    [Crossref]
  35. W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A 8, 1052–1058 (2006).
    [Crossref]
  36. E. Shchepakina, N. Farwell, and O. Korotkova, “Spectral changes in stochastic light beams propagating in turbulent ocean,” Appl. Phys. B 105, 415–420 (2011).
    [Crossref]
  37. M. Tang and D. Zhao, “Spectral changes in stochastic anisotropic electromagnetic beams propagating through turbulent ocean,” Opt. Commun. 312, 89–93 (2014).
    [Crossref]
  38. Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
    [Crossref]
  39. L. Lu, X. L. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22, 27112–27122 (2014).
    [Crossref]
  40. Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
    [Crossref]
  41. D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence,” Appl. Opt. 54, 10510–10516 (2015).
    [Crossref]
  42. C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
    [Crossref]
  43. Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
    [Crossref]
  44. X. Peng, L. Liu, Y. Cai, and Y. Baykal, “Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium,” J. Opt. Soc. Am. A 34, 133–139 (2017).
    [Crossref]
  45. Y. Baykal, “Higher order mode laser beam intensity fluctuations in strong oceanic turbulence,” Opt. Commun. 390, 72–75 (2017).
    [Crossref]
  46. M. Santarsiero, R. Martínez-Herrero, D. Maluenda, J. C. G. de Sande, G. Piquero, and F. Gori, “Partially coherent sources with circular coherence,” Opt. Lett. 42, 1512–1515 (2017).
    [Crossref]
  47. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3533 (2007).
    [Crossref]
  48. F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988).
    [Crossref]
  49. H. Partanen, N. Sharmin, J. Tervo, and J. Turunen, “Specular and antispecular light beams,” Opt. Express 23, 28718–28727 (2015).
    [Crossref]

2017 (6)

2016 (4)

2015 (8)

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

W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
[Crossref]

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[Crossref]

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

X. Y. Wang, M. W. Yao, Z. L. Qiu, X. Yi, and Z. J. Liu, “Evolution properties of Bessel–Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23, 12508–12523 (2015).
[Crossref]

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

H. Partanen, N. Sharmin, J. Tervo, and J. Turunen, “Specular and antispecular light beams,” Opt. Express 23, 28718–28727 (2015).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence,” Appl. Opt. 54, 10510–10516 (2015).
[Crossref]

2014 (14)

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

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

R. Chen, L. Liu, S. J. Zhu, G. F. Wu, F. Wang, and Y. J. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (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, 5826–5838 (2014).
[Crossref]

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

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

Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

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

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

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

L. J. Johnson, R. J. Green, and M. S. Leeson, “Underwater optical wireless communications: depth-dependent beam refraction,” Appl. Opt. 53, 7273–7277 (2014).
[Crossref]

L. Lu, X. L. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22, 27112–27122 (2014).
[Crossref]

M. Tang and D. Zhao, “Spectral changes in stochastic anisotropic electromagnetic beams propagating through turbulent ocean,” Opt. Commun. 312, 89–93 (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, 013801 (2014).
[Crossref]

2013 (4)

2012 (1)

2011 (2)

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

E. Shchepakina, N. Farwell, and O. Korotkova, “Spectral changes in stochastic light beams propagating in turbulent ocean,” Appl. Phys. B 105, 415–420 (2011).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A 8, 1052–1058 (2006).
[Crossref]

2000 (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

1988 (1)

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Baykal, Y.

Borghi, R.

Born, M.

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

Cai, Y.

Cai, Y. J.

Y. H. Chen, S. A. Ponomarenko, and Y. J. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7, 39957 (2017).
[Crossref]

J. Wang, S. J. Zhu, H. Y. Wang, Y. J. Cai, and Z. H. Li, “Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence,” Opt. Express 24, 11626–11639 (2016).
[Crossref]

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

Y. H. Chen, J. X. Gu, F. Wang, and Y. J. Cai, “Self-splitting properties of a Hermite–Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[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, 013801 (2014).
[Crossref]

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

R. Chen, L. Liu, S. J. Zhu, G. F. Wu, F. Wang, and Y. J. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (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, 5826–5838 (2014).
[Crossref]

Chen, R.

Chen, Y.

Chen, Y. H.

Y. H. Chen, S. A. Ponomarenko, and Y. J. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7, 39957 (2017).
[Crossref]

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

J. Yu, Y. H. Chen, L. Liu, X. L. Liu, and Y. J. Cai, “Splitting and combining properties of an elegant Hermite–Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23, 13467–13481 (2015).
[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, 5826–5838 (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, 013801 (2014).
[Crossref]

Chen, Z. Y.

Cui, S. W.

David, G. V.

W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
[Crossref]

de Sande, J. C. G.

Ding, C. L.

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Duan, Z.

Farwell, N.

E. Shchepakina, N. Farwell, and O. Korotkova, “Spectral changes in stochastic light beams propagating in turbulent ocean,” Appl. Phys. B 105, 415–420 (2011).
[Crossref]

Gao, Z.

Gbur, G.

Gori, F.

Green, R. J.

Gu, J. X.

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

Gu, Y. L.

Guattari, G.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988).
[Crossref]

Hu, Z.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Huang, P.

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[Crossref]

Huang, W.

Huang, Y.

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[Crossref]

Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

Ji, X. L.

Johnson, L. J.

Korotkova, O.

Kumar, A.

Lajunen, H.

Leeson, M. S.

Li, J.

Li, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Li, Z. H.

Liang, C. H.

Liao, L. M.

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Liu, D.

Liu, L.

Liu, L. R.

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A 8, 1052–1058 (2006).
[Crossref]

Liu, X. L.

Liu, Z. J.

Lu, L.

Lu, W.

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A 8, 1052–1058 (2006).
[Crossref]

Maluenda, D.

Mandel, L.

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

Martínez-Herrero, R.

Mei, Z. R.

Milo, W. H. I. V.

W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
[Crossref]

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

Padovani, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988).
[Crossref]

Palma, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988).
[Crossref]

Pan, L. Z.

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Partanen, H.

Peng, X.

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Piquero, G.

Ponomarenko, S. A.

Y. H. Chen, S. A. Ponomarenko, and Y. J. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7, 39957 (2017).
[Crossref]

Prabhakar, S.

Pu, J. X.

Qiu, Z. L.

Qu, J.

Reddy, S. G.

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Santasri, B.

W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
[Crossref]

Sharmin, N.

Shchepakina, E.

E. Shchepakina, N. Farwell, and O. Korotkova, “Spectral changes in stochastic light beams propagating in turbulent ocean,” Appl. Phys. B 105, 415–420 (2011).
[Crossref]

Singh, R. P.

Sun, J. F.

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A 8, 1052–1058 (2006).
[Crossref]

Tang, M.

M. Tang and D. Zhao, “Spectral changes in stochastic anisotropic electromagnetic beams propagating through turbulent ocean,” Opt. Commun. 312, 89–93 (2014).
[Crossref]

Tervo, J.

Thorpe, S. A.

S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).

Turunen, J.

Wang, F.

F. Wang and O. Korotkova, “Circularly symmetric cusped random beams in free space and atmospheric turbulence,” Opt. Express 25, 5057–5067 (2017).
[Crossref]

J. Li, F. Wang, and O. Korotkova, “Random sources for cusped beams,” Opt. Express 24, 17779–17791 (2016).
[Crossref]

F. Wang and O. Korotkova, “Random sources for beams with azimuthal intensity variation,” Opt. Lett. 41, 516–519 (2016).
[Crossref]

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

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[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, 013801 (2014).
[Crossref]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (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, 5826–5838 (2014).
[Crossref]

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

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

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

Wang, H. X.

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Wang, H. Y.

Wang, J.

Wang, X. Y.

Wang, Y.

Wolf, E.

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

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

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

Wu, G. F.

Wu, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Xifeng, X.

W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
[Crossref]

Xu, H. F.

Yao, M. W.

Yi, X.

Yin, H.

Yu, J.

Yuan, Y. S.

Zeng, A.

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[Crossref]

Zhang, B.

Zhang, L.

Zhang, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Zhang, Y. T.

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

Zhang, Z.

Zhao, C.

Zhao, C. L.

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, 5826–5838 (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, 013801 (2014).
[Crossref]

Zhao, D.

M. Tang and D. Zhao, “Spectral changes in stochastic anisotropic electromagnetic beams propagating through turbulent ocean,” Opt. Commun. 312, 89–93 (2014).
[Crossref]

Zhao, G.

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[Crossref]

Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

Zhu, S. J.

Appl. Opt. (2)

Appl. Phys. B (1)

E. Shchepakina, N. Farwell, and O. Korotkova, “Spectral changes in stochastic light beams propagating in turbulent ocean,” Appl. Phys. B 105, 415–420 (2011).
[Crossref]

Int. J. Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

J. Appl. Phys. (1)

W. H. I. V. Milo, B. Santasri, G. V. David, and X. Xifeng, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118, 093102 (2015).
[Crossref]

J. Opt. (1)

C. L. Ding, L. M. Liao, H. X. Wang, Y. T. Zhang, and L. Z. Pan, “Effect of oceanic turbulence on the propagation of cosine-Gaussian-correlated Schell-model beams,” J. Opt. 17, 035615 (2015).
[Crossref]

J. Opt. A (1)

W. Lu, L. R. Liu, and J. F. Sun, “Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence,” J. Opt. A 8, 1052–1058 (2006).
[Crossref]

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

Opt. Commun. (5)

M. Tang and D. Zhao, “Spectral changes in stochastic anisotropic electromagnetic beams propagating through turbulent ocean,” Opt. Commun. 312, 89–93 (2014).
[Crossref]

Y. Baykal, “Higher order mode laser beam intensity fluctuations in strong oceanic turbulence,” Opt. Commun. 390, 72–75 (2017).
[Crossref]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988).
[Crossref]

Y. Huang, P. Huang, F. Wang, G. Zhao, and A. Zeng, “The influence of oceanic turbulence on the beam quality parameters of partially coherent Hermite–Gaussian linear array beams,” Opt. Commun. 336, 146–152 (2015).
[Crossref]

Opt. Express (13)

H. Partanen, N. Sharmin, J. Tervo, and J. Turunen, “Specular and antispecular light beams,” Opt. Express 23, 28718–28727 (2015).
[Crossref]

Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

L. Lu, X. L. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22, 27112–27122 (2014).
[Crossref]

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

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

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

X. Y. Wang, M. W. Yao, Z. L. Qiu, X. Yi, and Z. J. Liu, “Evolution properties of Bessel–Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23, 12508–12523 (2015).
[Crossref]

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

J. Wang, S. J. Zhu, H. Y. Wang, Y. J. Cai, and Z. H. Li, “Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence,” Opt. Express 24, 11626–11639 (2016).
[Crossref]

F. Wang and O. Korotkova, “Circularly symmetric cusped random beams in free space and atmospheric turbulence,” Opt. Express 25, 5057–5067 (2017).
[Crossref]

F. Wang, C. H. Liang, Y. S. Yuan, and Y. J. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22, 23456–23464 (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, 5826–5838 (2014).
[Crossref]

J. Li, F. Wang, and O. Korotkova, “Random sources for cusped beams,” Opt. Express 24, 17779–17791 (2016).
[Crossref]

Opt. Lett. (14)

Z. R. Mei and O. Korotkova, “Random sources for rotating spectral densities,” Opt. Lett. 42, 255–258 (2017).
[Crossref]

S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, “Experimental generation of ring-shaped beams with random sources,” Opt. Lett. 38, 4441–4444 (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, 4821–4824 (2013).
[Crossref]

F. Wang and O. Korotkova, “Random sources for beams with azimuthal intensity variation,” Opt. Lett. 41, 516–519 (2016).
[Crossref]

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

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

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

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

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

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

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

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

M. Santarsiero, R. Martínez-Herrero, D. Maluenda, J. C. G. de Sande, G. Piquero, and F. Gori, “Partially coherent sources with circular coherence,” Opt. Lett. 42, 1512–1515 (2017).
[Crossref]

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

Phys. Rev. A (2)

Y. H. Chen, J. X. Gu, F. Wang, and Y. J. Cai, “Self-splitting properties of a Hermite–Gaussian correlated Schell-model beam,” Phys. Rev. A 91, 013823 (2015).
[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, 013801 (2014).
[Crossref]

Sci. Rep. (1)

Y. H. Chen, S. A. Ponomarenko, and Y. J. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7, 39957 (2017).
[Crossref]

Other (5)

S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).

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

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

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

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

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 (7)

Fig. 1.
Fig. 1. Absolute value of the spectral degree of coherence, |μ0(ρ1,ρ2)|, of the PCSG source. (a) A plot across the source plane for ρ1=9  mm and σ=5  mm. (b) A plot as a function of ρ1 and ρ2, again with σ=5  mm.
Fig. 2.
Fig. 2. 3D density plot of the xz cross-section of the normalized spectral density for the PCSG beam upon propagation in free space.
Fig. 3.
Fig. 3. (a) Normalized on-axis spectral density distributions of free-space PCSG beams with different degrees of spatial coherence. (b) The same quantity plotted as a function of propagation distance z and coherence parameter σ.
Fig. 4.
Fig. 4. Absolute value of the spectral degree of coherence for free-space PCSG beams with different degrees of spatial coherence. Distributions at a distance z=100  m as a function of x1 and x2 with y1=y2=0 when (a) σ=15  mm, (b) σ=20  mm, (c) σ=30  mm, and (d) σ=40  mm. (e) Profiles as a function of x1 with x2=y1=y2=0.
Fig. 5.
Fig. 5. Normalized spectral density distributions of the PCSG beam with different values of oceanic turbulence parameter: (a) T=1015  m1, (b) T=1014  m1, (c) T=1013  m1 and (d) T=1012  m1 in the xz plane. (e) The on-axis distributions as a function of propagation distance z.
Fig. 6.
Fig. 6. Same as Fig. 4, but for propagation of a PCSG beam over a distance z=100  m in oceanic turbulence (a) T=1015  m1, (b) T=1014  m1, (c) T=1013  m1, and (d) T=1012  m1. (e) Profiles as a function of x1 with x2=y1=y2=0.
Fig. 7.
Fig. 7. Same as Fig. 1, but for the NUCPC source.

Equations (29)

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

W0(ρ1,ρ2,ω)=E0*(ρ1,ω)E0(ρ2,ω),
W0(ρ1,ρ2)=p(v)H0*(ρ1,v)H0(ρ2,v)dv,
H0(ρ,v)=τ(ρ)exp(2πivρ2),
W0(ρ1,ρ2)=τ*(ρ1)τ(ρ2)p˜(ρ12ρ22),
p(v)=σ2rect(σ2v)
τ(ρ)=exp(ρ22w02),
W0(ρ1,ρ2)=exp(ρ12+ρ222w02)sinc(ρ22ρ12σ2),
W0(x1,y1,x2,y2)=W0(x1,y1,x2,y2).
μ0(ρ1,ρ2)=W0(ρ1,ρ2)W0(ρ1,ρ1)W0(ρ2,ρ2)=sinc(ρ22ρ12σ2)=sinc(2ρ¯Δρσ2),
W(r1,r2,z)=(k2πz)2W0(ρ1,ρ2)×exp[ik(r1ρ1)2(r2ρ2)22z]×exp[ϕ(r1,ρ1,z)+ϕ*(r2,ρ2,z)]Md2ρ1d2ρ2,
exp[ϕ*(r1,ρ1,z)+ϕ(r2,ρ2,z)]M=exp{13π2k2zT[(r1r2)2+(r1r2)·(ρ1ρ2)+(ρ1ρ2)2]},
T=0κ3ϕn(κ)dκ,
ϕn(κ)=ϕ0ε1/3κ11/3χT[1+2.35(κη)2/3]×[exp(ATδ)+ϖ2exp(ASδ)2ϖ1exp(ATSδ)],
T=0.388×108ε1/3χT×(47.5708ϖ217.6701ϖ1+6.78335).
W(r1,r2,z)=p(v)H*(r1,v,z)H(r2,v,z)dv,
H*(r1,v,z)H(r2,v,z)=(k2πz)2H0*(ρ1,v)H0(ρ2,v)×exp[ik(r1ρ1)2(r2ρ2)22z]×exp{13π2k2zT[(r1r2)2+(r1r2)·(ρ1ρ2)+(ρ1ρ2)2]}d2ρ1d2ρ2.
H*(r1,v,z)H(r2,v,z)=w02w2(z)exp[ik2z(r22r12)]×exp{[k2w024z2+π2k2z3T](r2r1)2}×exp(1w2(z){r1+r22+i[kw022z(14πvzk)π2kz23]T(r2r1)}2),
w2(z)=w02(14πvzk)2+(zkw0)2+4π2z33T.
H*(r,v,z)H(r,v,z)=w02w2(z)exp[r2w2(z)].
S(r,z)=W(r,r,z)=p(v)H*(r,v,z)H(r,v,z)dv
μ(r1,r2,z)=W(r1,r2,z)S(r1,z)S(r2,z)
μ(ρ1,ρ2)=exp{[(ρ2ρ0)2(ρ1ρ0)2σ2]2},
w2(z)=az2+bz+c,
a=16π2v2w04+1k2w02,b=8πvw02k,c=w02.
zmin=4πkvw0416π2v2w04+1,
w2(z)=dz3+az2+bz+c,
ddzw2(z)=3dz2+2az+b=0,
4a212db=4(16π2v2w04+1k2w02)2+128π3Tvw02k
zmin=a+a23db3d=14π2T[(16π2v2w04+1k2w02)2+32π3Tvw02k16π2v2w04+1k2w02]

Metrics