OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 21 — Jul. 20, 2011
  • pp: 3871–3878

Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model

Xiuxiang Chu, Chunhong Qiao, Xiaoxing Feng, and Ruipin Chen  »View Author Affiliations

Applied Optics, Vol. 50, Issue 21, pp. 3871-3878 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (622 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian–Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.

© 2011 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: December 20, 2010
Revised Manuscript: March 24, 2011
Manuscript Accepted: May 20, 2011
Published: July 12, 2011

Xiuxiang Chu, Chunhong Qiao, Xiaoxing Feng, and Ruipin Chen, "Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model," Appl. Opt. 50, 3871-3878 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Dayton, B. Pierson, B. Spielbusch, and J. Gonglewski, “Atmospheric structure function measurement with a Shack–Hartmann wavefront sensor,” Opt. Lett. 17, 1737–1739 (1992). [CrossRef] [PubMed]
  2. E. Golbraikh and S. S. Moiseev, “Different spectra formation in the presence of helical transfer,” Phys. Lett. A 305, 173–175(2002). [CrossRef]
  3. C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000). [CrossRef]
  4. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995). [CrossRef]
  5. G. D. Boreman and C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 13, 517–522(1996). [CrossRef]
  6. C. Rao, W. Jiang, and N. Ling, “Adaptive-optics compensation by distributed beacons for non-Kolmogorov turbulence,” Appl. Opt. 40, 3441–3449 (2001). [CrossRef]
  7. E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004). [CrossRef] [PubMed]
  8. E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlin. Proc. Geoph. 13, 297–301 (2006). [CrossRef]
  9. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008). [CrossRef]
  10. D. G. Pérez and L. Zunino, “Generalized wavefront phase for non-Kolmogorov turbulence,” Opt. Lett. 33, 572–574 (2008). [CrossRef] [PubMed]
  11. A. S. Gurvich and M. S. Belen’kii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12, 2517–2522 (1995). [CrossRef]
  12. M. S. Belen’kii, “Effect of the stratospheric turbulence on star image motion,” Opt. Lett. 20, 1359–1361 (1995). [CrossRef] [PubMed]
  13. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47, 6385–6391 (2008). [CrossRef] [PubMed]
  14. R. F. Lutomirski and H. T. Yura, “Propagation of a finite optical beam in an inhomogeneous medium,” Appl. Opt. 10, 1652–1658 (1971). [CrossRef] [PubMed]
  15. S. C. H. Wang and M. A. Plonus, “Optical beam propagation for a partially coherent source in the turbulent atmosphere,” J. Opt. Soc. Am. 69, 1297–1304 (1979). [CrossRef]
  16. 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] [PubMed]
  17. R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980). [CrossRef]
  18. L. C. Andrews, C. Y. Young, and W. B. Miller, “Coherence properties of a reflected optical wave in atmospheric turbulence,” J. Opt. Soc. Am. A 13, 851–861 (1996). [CrossRef]
  19. O. Korotkova and G. Gbur, “Angular spectrum representation for propagation of random electromagnetic beams in a turbulent atmosphere,” J. Opt. Soc. Am. A 24, 2728–2736(2007). [CrossRef]
  20. H. T. Eyyuboğlu and Y. Baykal, “Reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Express 12, 4659–4674 (2004). [CrossRef] [PubMed]
  21. Y. Cai and S. He, “Propagation of various dark hollow beams in turbulent atmosphere,” Opt. Express 14, 1353–1367 (2006). [CrossRef] [PubMed]
  22. H. T. Eyyuboğlu, C. Arpali, and Y. Baykal, “Flat topped beams and their characteristics in turbulent media,” Opt. Express 14, 4196–4207 (2006). [CrossRef] [PubMed]
  23. X. Chu, “Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere,” Opt. Express 15, 17613–17618 (2007). [CrossRef] [PubMed]
  24. X. Chu, Z. Liu, and Y. Wu, “Propagation of a general multi-Gaussian beam in turbulent atmosphere in a slant path,” J. Opt. Soc. Am. A 25, 74–79 (2008). [CrossRef]
  25. Y. Zhu, D. Zhao, and X. Du, “Propagation of stochastic Gaussian–Schell model array beams in turbulent atmosphere,” Opt. Express 16, 18437–18442 (2008). [CrossRef] [PubMed]
  26. X. Chu and Z. Liu, “Comparison between quadratic approximation and δ expansion in studying the spreading of multi-Gaussian beams in turbulent atmosphere,” Appl. Opt. 49, 204–212 (2010). [CrossRef] [PubMed]
  27. S. M. Wandzura, “Systematic corrections to quadratic approximations for power-law structure functions: the delta expansion,” J. Opt. Soc. Am. 71, 321–326 (1981). [CrossRef]
  28. X. Chu, C. Qiao, and X. Feng, “The effect of non-Kolmogorov turbulence on the propagation of cosh-Gaussian beam,” Opt. Commun. 283, 3398–3403 (2010). [CrossRef]
  29. Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16, 15563–15575 (2008). [CrossRef] [PubMed]
  30. Y. Dan and B. Zhang, “Second moments of partially coherent beams in atmospheric turbulence,” Opt. Lett. 34, 563–565(2009). [CrossRef] [PubMed]
  31. P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, “Average spreading of a Gaussian beam array in non-Kolmogorov turbulence,” Opt. Lett. 35, 1043–1045 (2010). [CrossRef] [PubMed]
  32. 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, 715–717 (2010). [CrossRef] [PubMed]
  33. S. G. Hanson and H. T. Yura, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). [CrossRef]
  34. M. Salem, T. Shirai, A. Dogariu, and E. Wolf, “Long-distance propagation of partially coherent beams through atmospheric turbulence,” Opt. Commun. 216, 261–265 (2003). [CrossRef]
  35. ITU-R. Document 3J/31-E, “On propagation data and prediction methods required for the design of space-to-earth and earth-to-space optical communication systems,” Radiocommunication Study Group Meeting, Budapest, July 2001.
  36. M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999). [CrossRef]
  37. M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 6304OU (2006). [CrossRef]
  38. G. Piquero, P. M. Mejias, and R. Martinez-Herrero, “On the propagation of the kurtosis parameter of general beams,” in Proceedings of the Workshop on Laser Beam Characterization, P.M.Mejias, H.Weber, R. Martinez-Herrero, and A.Gonzalez-Urena, eds. (SEDO, 1993), pp. 141–154.
  39. B. Lü and S. Luo, “Analytical expression for the kurtosis parameter of flattened Gaussian beams propagating through ABCD optical systems,” J. Mod. Opt. 49, 1731–1738(2002). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited