Skip to main content
Log in

M 2-factor of a truncated electromagnetic Gaussian Schell-model beam

  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

Based on the extended Huygens–Fresnel integral and the second-order moments of the Wigner distribution function, analytical expression for the M 2-factor of a truncated electromagnetic Gaussian Schell-model (EGSM) beam in turbulent atmosphere is derived by expanding the hard-aperture function into a finite sum of complex Gaussian functions. It is found that the evolution properties of the normalized M 2-factor of a truncated EGSM beam are closely determined by the truncation parameter, the parameters of the source beam and the parameters of the turbulent atmosphere together. The advantage of the EGSM beam for overcoming the turbulence-induced degradation disappears gradually as the truncation parameter decreases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C.J.R. Sheppard, H.J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987)

    Article  ADS  Google Scholar 

  2. X. Chu, G. Zhou, Opt. Express 15, 7697 (2007)

    Article  ADS  Google Scholar 

  3. Y. Cai, L. Zhang, Appl. Opt. 45, 5758 (2006)

    Article  ADS  Google Scholar 

  4. Y. Cai, S. He, J. Opt. Soc. Am. A 23, 1410 (2006)

    Article  ADS  Google Scholar 

  5. Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981)

    Article  ADS  Google Scholar 

  6. Y. Li, J. Opt. Soc. Am. A 72, 770 (1982)

    Article  ADS  Google Scholar 

  7. X. Liu, J. Pu, Opt. Commun. 252, 262 (2005)

    Article  ADS  Google Scholar 

  8. F. Wang, Y. Cai, O. Korotkova, Opt. Commun. 282, 3408 (2009)

    Article  ADS  Google Scholar 

  9. J. Pu, H. Zhang, S. Nemoto, Opt. Commun. 162, 57 (1999)

    Article  ADS  Google Scholar 

  10. J.J. Wen, M.A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988)

    Article  ADS  Google Scholar 

  11. F. Wang, Y. Cai, Q. Lin, J. Opt. Soc. Am. A 25, 2001 (2008)

    Article  ADS  Google Scholar 

  12. Y. Cai, L. Hu, Opt. Lett. 31, 685 (2006)

    Article  ADS  Google Scholar 

  13. Y. Cai, S. He, Appl. Phys. B 84, 493 (2006)

    Article  ADS  Google Scholar 

  14. Y. Cai, D. Ge, Phys. Lett. A 357, 72 (2006)

    Article  ADS  MATH  Google Scholar 

  15. Y. Cai, X. Lu, H.T. Eyyuboğlu, Y. Baykal, Opt. Commun. 281, 3221 (2008)

    Article  ADS  Google Scholar 

  16. A.E. Siegman, Proc. SPIE 1224, 2 (1990)

    Article  ADS  Google Scholar 

  17. R. Martinez-Herrero, P.M. Mejias, Opt. Lett. 18, 1669 (1993)

    Article  ADS  Google Scholar 

  18. D.L. Shealy, J.A. Hoffnagel, Appl. Opt. 45, 5118 (2006)

    Article  ADS  Google Scholar 

  19. F.M. Dickey, S.C. Holswade, D.L. Shealy (eds.), Laser Beam Shaping Applications (CRC Press, Boca Raton, 2005)

    Google Scholar 

  20. F. Gori, M. Santarsiero, A. Sona, Opt. Commun. 82, 197 (1991)

    Article  ADS  Google Scholar 

  21. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, P. Vahimaa, J. Opt. Soc. Am. A 16, 106 (1999)

    Article  ADS  Google Scholar 

  22. F. Wang, Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007)

    Article  ADS  Google Scholar 

  23. B. Zhang, X. Chu, Q. Li, J. Opt. Soc. Am. A 19, 1370 (2002)

    Article  ADS  Google Scholar 

  24. X. Chu, B. Zhang, Q. Wen, Appl. Opt. 42, 4280 (2003)

    Article  ADS  Google Scholar 

  25. S. Zhu, Y. Cai, Opt. Express 18, 27567 (2010)

    Article  ADS  Google Scholar 

  26. Y. Cai, S. He, Appl. Phys. Lett. 89, 041117 (2006)

    Article  ADS  Google Scholar 

  27. Y. Cai, S. He, Opt. Express 14, 1353 (2006)

    Article  ADS  Google Scholar 

  28. X. Chu, Opt. Express 15, 17613 (2007)

    Article  ADS  Google Scholar 

  29. Y. Baykal, H.T. Eyyuboğlu, Appl. Opt. 46, 5044 (2007)

    Article  ADS  Google Scholar 

  30. Y. Cai, Y. Chen, H.T. Eyyuboğlu, Y. Baykal, Opt. Lett. 32, 2405 (2007)

    Article  ADS  Google Scholar 

  31. M. Alavinejad, M. Khatiri, B. Chafary, Opt. Commun. 282, 3541 (2009)

    Article  ADS  Google Scholar 

  32. Y. Cai, Q. Lin, H.T. Eyyuboğlu, Y. Baykal, Opt. Commun. 278, 157 (2007)

    Article  ADS  Google Scholar 

  33. Y. Cai, Y. Chen, H.T. Eyyuboğlu, Y. Baykal, Appl. Phys. B 88, 467 (2007)

    Article  ADS  Google Scholar 

  34. Y. Cai, Q. Lin, H.T. Eyyuboğlu, Y. Baykal, Appl. Phys. B 94, 319 (2009)

    Article  ADS  Google Scholar 

  35. Y. Yuan, Y. Cai, J. Qu, H.T. Eyyuboğlu, Y. Baykal, Opt. Express 17, 11130 (2009)

    Article  ADS  Google Scholar 

  36. O. Korotkova, M. Salem, E. Wolf, Opt. Commun. 233, 225 (2004)

    Article  ADS  Google Scholar 

  37. O. Korotkova, M. Salem, A. Dogariu, E. Wolf, Media Waves Random Complex 15, 353 (2005)

    Article  ADS  MATH  Google Scholar 

  38. Y. Cai, H.T. Eyyuboğlu, Y. Baykal, J. Opt. Soc. Am. A 25, 1497 (2008)

    Article  ADS  Google Scholar 

  39. Y. Cai, O. Korotkova, H.T. Eyyuboğlu, Y. Baykal, Opt. Express 16, 15834 (2008)

    Article  ADS  Google Scholar 

  40. F. Wang, Y. Cai, H.T. Eyyuboğlu, Y. Baykal, Prog. Electromagn. Res. 103, 33 (2010)

    Article  Google Scholar 

  41. O. Korotkova, Y. Cai, E. Watson, Appl. Phys. B 94, 681 (2009)

    Article  ADS  Google Scholar 

  42. O. Korotkova, Opt. Commun. 281, 2342 (2008)

    Article  ADS  Google Scholar 

  43. Y. Dan, B. Zhang, P. Pan, J. Opt. Soc. Am. A 25, 2223 (2008)

    Article  ADS  Google Scholar 

  44. Y. Dan, B. Zhang, Opt. Express 16, 15563 (2008)

    Article  ADS  Google Scholar 

  45. Y. Yuan, Y. Cai, J. Qu, H.T. Eyyuboğlu, Y. Baykal, O. Korotkova, Opt. Express 17, 17344 (2009)

    Article  ADS  Google Scholar 

  46. F. Wang, Y. Cai, Opt. Express 18, 24661 (2010)

    Article  ADS  Google Scholar 

  47. S. Zhu, Y. Cai, O. Korotkova, Opt. Express 18, 12587 (2010)

    Article  ADS  Google Scholar 

  48. F. Gori, Opt. Lett. 23, 241 (1998)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  50. F. Gori, M. Santarsiero, R. Borghi, V. Ramírez-Sánchez, J. Opt. Soc. Am. A 25, 1016 (2008)

    Article  ADS  Google Scholar 

  51. O. Korotkova, M. Salem, E. Wolf, Opt. Lett. 29, 1173 (2004)

    Article  ADS  Google Scholar 

  52. L.C. Andrews, R.L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere, 2nd edn. (SPIE Press, Bellington, 2005)

    Google Scholar 

  53. A. Erdelyi, W. Magnus, F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, New York, 1954)

    Google Scholar 

  54. M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions (Academic Press, San Diego, 2000)

    Google Scholar 

  55. T.L. Ho, J. Opt. Soc. Am. A 60, 667 (1970)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Y. Cai.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, S., Cai, Y. M 2-factor of a truncated electromagnetic Gaussian Schell-model beam. Appl. Phys. B 103, 971–984 (2011). https://doi.org/10.1007/s00340-011-4417-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00340-011-4417-3

Keywords

Navigation