Skip to main content
SpringerLink
Log in

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.A. Arnaud, H. Kogelink, Appl. Opt. 8, 1687 (1969)

    Article  ADS  Google Scholar 

  2. S. Medhekar, S. Konar, M.S. Sodha, Opt. Lett. 20, 2192 (1995)

    Article  ADS  Google Scholar 

  3. C.R. Giuliano, J.H. Marburger, A. Yariv, Appl. Phys. Lett. 21, 57 (1972)

    Article  ADS  Google Scholar 

  4. W. Zhang, J. Tian, Z. Liu, W. Zhou, C. Zhang, G. Zhang, Appl. Opt. 42, 2219 (2003)

    Article  ADS  Google Scholar 

  5. J. Courtial, K. Dholakia, L. Allen, M.J. Padgett, Opt. Commun. 144, 210 (1997)

    Article  ADS  Google Scholar 

  6. J.A. Arnaud, Hamiltonian theory of beam mode propagation, in Progress in Optics, vol. XI, ed. by E. Wolf (North-Holland, Amsterdam, 1973), pp. 247–304

    Google Scholar 

  7. Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990)

    Google Scholar 

  8. Q. Lin, Y. Cai, Opt. Lett. 27, 216 (2002)

    Article  ADS  Google Scholar 

  9. Y. Cai, Q. Lin, Appl. Opt. 41, 4336 (2002)

    Article  ADS  Google Scholar 

  10. Y. Cai, Q. Lin, J. Opt. A: Pure Appl. Opt. 6, 390 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. S.R. Seshadri, J. Opt. Soc. Am. A 20, 1818 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  15. Y. Cai, Q. Lin, Opt. Laser Technol. 34, 415 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Y. Cai, S. He, Opt. Lett. 31, 568 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Z.I. Feizulin, Y.A. Kravtsov, Radiophys. Quantum Electron. 10, 33 (1967)

    Article  ADS  Google Scholar 

  20. H.T. Yura, Appl. Opt. 11, 1399 (1972)

    Article  ADS  Google Scholar 

  21. V.A. Banakh, V.L. Mironov, Opt. Lett. 1, 172 (1977)

    Article  ADS  Google Scholar 

  22. V.A. Banakh, V.L. Mironov, Opt. Lett. 4, 259 (1979)

    Article  ADS  Google Scholar 

  23. S.C.H. Wang, M.A. Plonus, J. Opt. Soc. Am. 69, 1297 (1979)

    Article  ADS  Google Scholar 

  24. H.T. Eyyuboğlu, Y. Baykal, Opt. Express 12, 4659 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Y. Cai, J. Opt. A: Pure Appl. Opt. 8, 537 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Y. Chen, Y. Chen, H.T. Eyyuboğlu, Y. Baykal, Appl. Phys. B 90, 87 (2008)

    Article  ADS  Google Scholar 

  29. Y. Cai, D. Ge, Opt. Commun. 271, 509 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Y. Cai, J. Opt. A: Pure Appl. Opt. 10, 075003 (2008)

    Article  ADS  Google Scholar 

  32. Y. Cai, Q. Lin, H.T. Eyyuboğlu, Y. Baykal, Opt. Express 16, 7665 (2008)

    Article  ADS  Google Scholar 

  33. H.T. Eyyuboğlu, Y. Baykal, Y. Cai, J. Opt. Soc. Am. A 24, 2891 (2007)

    Article  ADS  Google Scholar 

  34. H.T. Eyyuboğlu, Y. Baykal, Y. Cai, Appl. Phys. B 89, 91 (2007)

    Article  ADS  Google Scholar 

  35. H.T. Yura, S.G. Hanson, J. Opt. Soc. Am. A 4, 1931 (1987)

    Article  ADS  Google Scholar 

  36. H.T. Yura, S.G. Hanson, J. Opt. Soc. Am. A 6, 564 (1989)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. R.K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkely, 1964), Chap. 4

    Google Scholar 

  39. H.T. Eyyuboğlu, S. Altay, Y. Baykal, Opt. Commun. 264, 25 (2006)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  41. W. Wang, P.X. Wang, Y.K. Ho, Q. Kong, Z. Chen, Y. Gu, S.J. Wang, Europhys. Lett. 73, 211 (2006)

    Article  ADS  Google Scholar 

  42. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984)

    Article  ADS  Google Scholar 

  43. D.W. Coutts, IEEE J. Quantum Electron. 38, 1217 (2002)

    Article  ADS  Google Scholar 

  44. H.T. Eyyuboğlu, A. Arpali, Y. Baykal, Opt. Express 14, 4196 (2006)

    Article  ADS  Google Scholar 

  45. Y. Baykal, H.T. Eyyuboğlu, Appl. Opt. 45, 3793 (2006)

    Article  ADS  Google Scholar 

  46. M.S. Bowers, Opt. Lett. 19, 1319 (1992)

    Article  ADS  Google Scholar 

  47. F. Gori, Opt. Commun. 107, 335 (1994)

    Article  ADS  Google Scholar 

  48. V. Bagini, R. Borghi, F. Gori, A.M. Pacileo, M. Santarsiero, J. Opt. Soc. Am. A 13, 1385 (1996)

    Article  ADS  Google Scholar 

  49. Y. Li, Opt. Lett. 27, 1007 (2002)

    Article  ADS  Google Scholar 

  50. Y. Li, J. Mod. Opt. 50, 1957 (2003)

    Article  ADS  Google Scholar 

  51. Y. Cai, Q. Lin, J. Opt. A: Pure Appl. Opt. 5, 272 (2003)

    Article  ADS  Google Scholar 

  52. Y. Cai, S. He, J. Opt. Soc. Am. A 23, 2623 (2006)

    Article  ADS  Google Scholar 

  53. X. Lu, Y. Cai, Opt. Commun. 269, 39 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  55. F. Wang, Y. Cai, Opt. Lett. 33, 1795 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physical Science and Technology, Suzhou University, Suzhou, 215006, China

    Yangjian Cai

  2. Max-Planck-Research-Group, Institute of Optics, Information and Photonics, University of Erlangen, Staudtstr. 7/B2, 91058, Erlangen, Germany

    Yangjian Cai

  3. Institute of Optics, Department of Physics, Zhejiang University, Hangzhou, 310027, China

    Q. Lin

  4. Department of Electronic and Communication Engineering, Çankaya University, Öğretmenler Cad. 14, Yüzüncüyıl, 06530, Balgat Ankara, Turkey

    H. T. Eyyuboğlu & Y. Baykal

Authors
  1. Yangjian Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Q. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. T. Eyyuboğlu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Baykal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yangjian Cai.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cai, Y., Lin, Q., Eyyuboğlu, H.T. et al. Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere. Appl. Phys. B 94, 319–325 (2009). https://doi.org/10.1007/s00340-008-3339-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00340-008-3339-1

PACS

Search

Navigation