## Partially coherent beam propagation in atmospheric turbulence [Invited] |

JOSA A, Vol. 31, Issue 9, pp. 2038-2045 (2014)

http://dx.doi.org/10.1364/JOSAA.31.002038

Acrobat PDF (373 KB)

### Abstract

Partially coherent beams hold much promise in free-space optical communications for their resistance to the deleterious effects of atmospheric turbulence. We describe the basic theoretical and computational tools used to investigate these effects, and review the research to date.

© 2014 Optical Society of America

## 1. INTRODUCTION

## 2. HISTORICAL OVERVIEW

3. R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulence media,” J. Opt. Soc. Am. **54**, 52–61 (1964). [CrossRef]

4. M. J. Beran, “Propagation of the mutual coherence function through random media,” J. Opt. Soc. Am. **56**, 1475–1480 (1966). [CrossRef]

5. L. S. Taylor, “Decay of mutual coherence in turbulent media,” J. Opt. Soc. Am. **57**, 304–308 (1967). [CrossRef]

6. R. F. Lutomirski and H. T. Yura, “Propagation of a finite optical beam in an inhomogeneous medium,” Appl. Opt. **10**, 1652–1658 (1971). [CrossRef]

*extended Huygens–Fresnel*(

*eHF*)

*principle*(to be discussed in Section 3), that can be used to derive propagation results over a broader range of circumstances and for more general fields. Yura [7

7. H. T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. **11**, 1399–1406 (1972). [CrossRef]

8. Z. I. Feizulin and Y. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. **10**, 33–35 (1967). [CrossRef]

9. A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. **15**, 1187–1192 (1972). [CrossRef]

*et al.*[10

10. M. S. Belen’kii, A. I. Kon, and V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. **7**, 287–290 (1977). [CrossRef]

11. J. C. Leader, “Atmospheric propagation of partially coherent radiation,” J. Opt. Soc. Am. **68**, 175–185 (1978). [CrossRef]

12. R. L. Fante, “Two-position, two-frequency mutual-coherence function in turbulence,” J. Opt. Soc. Am. **71**, 1446–1451 (1981). [CrossRef]

13. J. C. Leader, “Intensity fluctuations resulting from partially coherent light propagating through atmospheric turbulence,” J. Opt. Soc. Am. **69**, 73–84 (1979). [CrossRef]

14. R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium; effect of source coherence,” Opt. Acta **28**, 1203–1207 (1981). [CrossRef]

*et al.*[15], and Banakh and Buldakov [16] studied the fluctuations of intensity over different receiver response times, noting dramatic differences between a “fast” and a “slow” detector. Fante [17

17. R. L. Fante, “The effect of source temporal coherence on light scintillations in weak turbulence,” J. Opt. Soc. Am. **69**, 71–73 (1979). [CrossRef]

18. J. Wu, “Propagation of a Gaussian-Schell beam through turbulent media,” J. Mod. Opt. **37**, 671–684 (1990). [CrossRef]

19. J. Wu and A. D. Boardman, “Coherence length of a Gaussian-Schell beam and atmospheric turbulence,” J. Mod. Opt. **38**, 1355–1363 (1991). [CrossRef]

20. G. Gbur and E. Wolf, “Spreading of partially coherent beams in random media,” J. Opt. Soc. Am. A **19**, 1592–1598 (2002). [CrossRef]

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

*et al.*[22

22. S. A. Ponomarenko, J. J. Greffet, and E. Wolf, “The diffusion of partially coherent beams in turbulent media,” Opt. Commun. **208**, 1–8 (2002). [CrossRef]

*et al.*[23

23. T. Shirai, A. Dogariu, and E. Wolf, “Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A **20**, 1094–1102 (2003). [CrossRef]

24. Y. Baykal, “Average transmittance in turbulence for partially coherent sources,” Opt. Commun. **231**, 129–136 (2004). [CrossRef]

25. 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**, 1794–1802 (2002). [CrossRef]

26. J. C. Ricklin and F. M. Davidson, “Atmospheric optical communication with a Gaussian-Schell beam,” J. Opt. Soc. Am. A **20**, 856–866 (2003). [CrossRef]

*et al.*[27

27. 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**, 330–341 (2004). [CrossRef]

28. T. J. Schulz, “Iterative transform algorithm for the computation of optimal beams,” J. Opt. Soc. Am. A **21**, 1970–1974 (2004). [CrossRef]

29. T. J. Schulz, “Optimal beams for propagation through random media,” Opt. Lett. **30**, 1093–1095 (2005). [CrossRef]

## 3. ANALYTIC PROPAGATION MODELS

31. V. A. Banakh, G. M. Krekov, V. L. Mironov, S. S. Khmelevtsov, and R. S. Tsvik, “Focused-laser-beam scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. **64**, 516–518 (1974). [CrossRef]

32. V. A. Banakh and V. L. Mironov, “Phase approximation of the Huygens-Kirchhoff method in problems of laser-beam propagation in the turbulent atmosphere,” Opt. Lett. **1**, 172–174 (1977). [CrossRef]

*outer scale*. These large eddies undergo a process in which they break up continually into smaller and smaller sizes, eventually reaching a critical minimum size

*inner scale*, at which their energy is dissipated completely. The outer scale can range widely from meters to tens of meters, while the inner scale is typically of the order of millimeters.

*structure parameter*and is a measure of the overall turbulence strength. Its values range from

*coherent mode representation*, as first demonstrated by Wolf [36

36. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part 1: Spectra and cross-spectra of steady-state sources,” J. Opt. Soc. Am. **72**, 343–351 (1982). [CrossRef]

*scintillation index*, defined as where

*Rytov variance*. The Rytov variance is often used as a loose measure of the strength of atmospheric turbulence, with

14. R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium; effect of source coherence,” Opt. Acta **28**, 1203–1207 (1981). [CrossRef]

*higher*than that of a fully coherent beam.

38. S. M. Wandzura, “Meaning of quadratic structure functions,” J. Opt. Soc. Am. **70**, 745–747 (1980). [CrossRef]

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

## 4. COMPUTATIONAL PROPAGATION MODELS

40. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. **27**, 2111–2126 (1988). [CrossRef]

*parabolic approximation*to the wave equation.

42. R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media **2**, 209–224 (1992). [CrossRef]

44. J. Xiang, “Accurate compensation of the low-frequency components for the FFT-based turbulent phase screen,” Opt. Express **20**, 681–687 (2012). [CrossRef]

## 5. BEAM PROPAGATION IN TURBULENCE

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

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

47. Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. **53**, 537–578 (2003). [CrossRef]

48. G. A. Sililoglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. **99**, 213901 (2007). [CrossRef]

49. B.-S. Chen and J.-X. Pu, “Propagation of Gauss-Bessel beams in turbulent atmosphere,” Chin. Phys. B **18**, 1033–1039 (2009). [CrossRef]

50. X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. **36**, 2701–2703 (2011). [CrossRef]

*et al.*[51

51. C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of *J*_{0}- and *I*_{0}-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B **98**, 195–202 (2010). [CrossRef]

*et al.*[52

52. B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. **40**, 820–827 (2008). [CrossRef]

*et al.*[53

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

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

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

*et al.*[56

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

*et al.*[57

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

58. W. Gao, “Changes of polarization of light beams on propagation through tissue,” Opt. Commun. **260**, 749–754 (2006). [CrossRef]

59. W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. **270**, 474–478 (2007). [CrossRef]

60. Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express **16**, 7665–7673 (2008). [CrossRef]

61. W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express **17**, 17829–17836 (2009). [CrossRef]

62. G. Gbur and O. Korotkova, “Angular spectrum representation for the propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence,” J. Opt. Soc. Am. A **24**, 745–752 (2007). [CrossRef]

63. O. Korotkova and G. Gbur, “Angular spectrum representation for propagation of random electromagnetic beams in turbulent atmosphere,” J. Opt. Soc. Am. A **24**, 2728–2736 (2007). [CrossRef]

64. S. A. Ponomarenko and E. Wolf, “Solution for the inverse scattering problem for strongly fluctuating media,” Opt. Lett. **27**, 1770–1772 (2002). [CrossRef]

*et al.*[65

65. J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, “Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source,” Opt. Lett. **25**, 4–6 (2000). [CrossRef]

*variable coherence tomography*was introduced in [66

66. E. Baleine and A. Dogariu, “Variable-coherence tomography for inverse scattering problems,” J. Opt. Soc. Am. A **21**, 1917–1923 (2004). [CrossRef]

67. E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. **95**, 193904 (2005). [CrossRef]

68. J. S. Tyo and T. S. Turner, “Sensing polarization with variable coherence tomography,” J. Opt. Soc. Am. A **25**, 2383–2389 (2008). [CrossRef]

69. Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. **283**, 1209–1212 (2010). [CrossRef]

## 6. SCINTILLATION EFFECTS IN TURBULENCE

70. F. E. Strömqvist Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE **5160**, 86–97 (2004). [CrossRef]

71. Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A **22**, 672–679 (2005). [CrossRef]

*et al.*[72

72. Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. **32**, 2405–2407 (2007). [CrossRef]

*et al.*[73

73. H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, and Y. Cai, “Scintillation advantages of lowest order Bessel-Gaussian beams,” Appl. Phys. B **92**, 229–235 (2008). [CrossRef]

74. H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, O. Korotkova, and Y. Cai, “Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media,” J. Opt. Soc. Am. A **26**, 387–394 (2009). [CrossRef]

75. H. Gerçekcioğlu and Y. Baykal, “Scintillation index of flat-topped Gaussian laser beam in strongly turbulent medium,” J. Opt. Soc. Am. A **28**, 1540–1544 (2011). [CrossRef]

*et al.*[76

76. G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, “Suppression of intensity fluctuations in free space high-speed optical communication based on spectral encoding of a partially coherent beam,” Opt. Commun. **280**, 264–270 (2007). [CrossRef]

*et al.*[77

77. Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt. **48**, 1943–1954 (2009). [CrossRef]

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

79. K. Kiasaleh, “On the scintillation index of a multiwavelength Gaussian beam in a turbulent free-space optical communications channel,” J. Opt. Soc. Am. A **23**, 557–566 (2006). [CrossRef]

83. A. Peleg and J. V. Moloney, “Scintillation index for two Gaussian laser beams with different wavelengths in weak atmospheric turbulence,” J. Opt. Soc. Am. A **23**, 3114–3122 (2006). [CrossRef]

84. A. Peleg and J. V. Moloney, “Scintillation reduction by use of multiple Gaussian laser beams with different wavelengths,” IEEE Photon. Technol. Lett. **19**, 883–885 (2007). [CrossRef]

85. P. Polynki, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. **32**, 885–887 (2007). [CrossRef]

86. O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. **281**, 2342–2348 (2008). [CrossRef]

87. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express **16**, 15834–15846 (2008). [CrossRef]

88. O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B **94**, 681–690 (2009). [CrossRef]

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

*et al.*[90

90. Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. **34**, 2261–2263 (2009). [CrossRef]

91. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express **18**, 10777–10785 (2010). [CrossRef]

92. Y. Gu and G. Gbur, “Reduction of turbulence-induced scintillation by nonuniformly polarized beam arrays,” Opt. Lett. **37**, 1553–1555 (2012). [CrossRef]

## ACKNOWLEDGMENTS

## REFERENCES

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2. | L. A. Chernov, |

3. | R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulence media,” J. Opt. Soc. Am. |

4. | M. J. Beran, “Propagation of the mutual coherence function through random media,” J. Opt. Soc. Am. |

5. | L. S. Taylor, “Decay of mutual coherence in turbulent media,” J. Opt. Soc. Am. |

6. | R. F. Lutomirski and H. T. Yura, “Propagation of a finite optical beam in an inhomogeneous medium,” Appl. Opt. |

7. | H. T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. |

8. | Z. I. Feizulin and Y. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. |

9. | A. I. Kon and V. I. Tatarskii, “On the theory of the propagation of partially coherent light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. |

10. | M. S. Belen’kii, A. I. Kon, and V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. |

11. | J. C. Leader, “Atmospheric propagation of partially coherent radiation,” J. Opt. Soc. Am. |

12. | R. L. Fante, “Two-position, two-frequency mutual-coherence function in turbulence,” J. Opt. Soc. Am. |

13. | J. C. Leader, “Intensity fluctuations resulting from partially coherent light propagating through atmospheric turbulence,” J. Opt. Soc. Am. |

14. | R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium; effect of source coherence,” Opt. Acta |

15. | V. A. Banach, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. |

16. | V. A. Banakh and V. M. Buldakov, “Effect of the initial degree of spatial coherence of a light beam on intensity fluctuations in a turbulent atmosphere,” Opt. Spectrosc. |

17. | R. L. Fante, “The effect of source temporal coherence on light scintillations in weak turbulence,” J. Opt. Soc. Am. |

18. | J. Wu, “Propagation of a Gaussian-Schell beam through turbulent media,” J. Mod. Opt. |

19. | J. Wu and A. D. Boardman, “Coherence length of a Gaussian-Schell beam and atmospheric turbulence,” J. Mod. Opt. |

20. | G. Gbur and E. Wolf, “Spreading of partially coherent beams in random media,” J. Opt. Soc. Am. A |

21. | A. Dogariu and S. Amarande, “Propagation of partially coherent beams: turbulence-induced degradation,” Opt. Lett. |

22. | S. A. Ponomarenko, J. J. Greffet, and E. Wolf, “The diffusion of partially coherent beams in turbulent media,” Opt. Commun. |

23. | T. Shirai, A. Dogariu, and E. Wolf, “Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A |

24. | Y. Baykal, “Average transmittance in turbulence for partially coherent sources,” Opt. Commun. |

25. | 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 |

26. | J. C. Ricklin and F. M. Davidson, “Atmospheric optical communication with a Gaussian-Schell beam,” J. Opt. Soc. Am. A |

27. | 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. |

28. | T. J. Schulz, “Iterative transform algorithm for the computation of optimal beams,” J. Opt. Soc. Am. A |

29. | T. J. Schulz, “Optimal beams for propagation through random media,” Opt. Lett. |

30. | M. Born and E. Wolf, |

31. | V. A. Banakh, G. M. Krekov, V. L. Mironov, S. S. Khmelevtsov, and R. S. Tsvik, “Focused-laser-beam scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. |

32. | V. A. Banakh and V. L. Mironov, “Phase approximation of the Huygens-Kirchhoff method in problems of laser-beam propagation in the turbulent atmosphere,” Opt. Lett. |

33. | L. C. Andrews and R. L. Phillips, |

34. | H. Cramér, |

35. | E. Wolf, |

36. | E. Wolf, “New theory of partial coherence in the space-frequency domain. Part 1: Spectra and cross-spectra of steady-state sources,” J. Opt. Soc. Am. |

37. | G. Gbur, “Simulating fields of arbitrary spatial and temporal coherence,” Opt. Express |

38. | S. M. Wandzura, “Meaning of quadratic structure functions,” J. Opt. Soc. Am. |

39. | M. Charnotskii, “Common omissions and misconceptions of wave propagation in turbulence: discussion,” J. Opt. Soc. Am. A |

40. | J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. |

41. | D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE |

42. | R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media |

43. | J. Recolons and F. Dios, “Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence,” Proc. SPIE |

44. | J. Xiang, “Accurate compensation of the low-frequency components for the FFT-based turbulent phase screen,” Opt. Express |

45. | Y. Cai and S. He, “Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere,” Opt. Lett. |

46. | Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express |

47. | Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. |

48. | G. A. Sililoglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. |

49. | B.-S. Chen and J.-X. Pu, “Propagation of Gauss-Bessel beams in turbulent atmosphere,” Chin. Phys. B |

50. | X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. |

51. | C. Z. Çil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of |

52. | B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. |

53. | X. Ji, X. Chen, and B. Lü, “Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A |

54. | F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. |

55. | Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. |

56. | M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves Random Complex Media |

57. | O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media |

58. | W. Gao, “Changes of polarization of light beams on propagation through tissue,” Opt. Commun. |

59. | W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. |

60. | Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express |

61. | W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express |

62. | G. Gbur and O. Korotkova, “Angular spectrum representation for the propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence,” J. Opt. Soc. Am. A |

63. | O. Korotkova and G. Gbur, “Angular spectrum representation for propagation of random electromagnetic beams in turbulent atmosphere,” J. Opt. Soc. Am. A |

64. | S. A. Ponomarenko and E. Wolf, “Solution for the inverse scattering problem for strongly fluctuating media,” Opt. Lett. |

65. | J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, “Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source,” Opt. Lett. |

66. | E. Baleine and A. Dogariu, “Variable-coherence tomography for inverse scattering problems,” J. Opt. Soc. Am. A |

67. | E. Baleine and A. Dogariu, “Variable coherence scattering microscopy,” Phys. Rev. Lett. |

68. | J. S. Tyo and T. S. Turner, “Sensing polarization with variable coherence tomography,” J. Opt. Soc. Am. A |

69. | Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. |

70. | F. E. Strömqvist Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE |

71. | Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A |

72. | Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. |

73. | H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, and Y. Cai, “Scintillation advantages of lowest order Bessel-Gaussian beams,” Appl. Phys. B |

74. | H. T. Eyyuboğlu, Y. Baykal, E. Sermutlu, O. Korotkova, and Y. Cai, “Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media,” J. Opt. Soc. Am. A |

75. | H. Gerçekcioğlu and Y. Baykal, “Scintillation index of flat-topped Gaussian laser beam in strongly turbulent medium,” J. Opt. Soc. Am. A |

76. | G. P. Berman, A. R. Bishop, B. M. Chernobrod, D. C. Nguyen, and V. N. Gorshkov, “Suppression of intensity fluctuations in free space high-speed optical communication based on spectral encoding of a partially coherent beam,” Opt. Commun. |

77. | Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt. |

78. | Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. |

79. | K. Kiasaleh, “On the scintillation index of a multiwavelength Gaussian beam in a turbulent free-space optical communications channel,” J. Opt. Soc. Am. A |

80. | Y. Gu and G. Gbur, “Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence,” J. Opt. Soc. Am. A |

81. | Y. Gu and G. Gbur, “Scintillation of Airy beam arrays in atmospheric turbulence,” Opt. Lett. |

82. | D. Voelz and K. Fitzhenry, “Pseudo-partially coherent beam for free-space laser communication,” Proc. SPIE |

83. | A. Peleg and J. V. Moloney, “Scintillation index for two Gaussian laser beams with different wavelengths in weak atmospheric turbulence,” J. Opt. Soc. Am. A |

84. | A. Peleg and J. V. Moloney, “Scintillation reduction by use of multiple Gaussian laser beams with different wavelengths,” IEEE Photon. Technol. Lett. |

85. | P. Polynki, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. |

86. | O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. |

87. | Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express |

88. | O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B |

89. | Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express |

90. | Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. |

91. | A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express |

92. | Y. Gu and G. Gbur, “Reduction of turbulence-induced scintillation by nonuniformly polarized beam arrays,” Opt. Lett. |

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(030.7060) Coherence and statistical optics : Turbulence

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: July 16, 2014

Manuscript Accepted: July 18, 2014

Published: August 25, 2014

**Citation**

Greg Gbur, "Partially coherent beam propagation in atmospheric turbulence [Invited]," J. Opt. Soc. Am. A **31**, 2038-2045 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-9-2038

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