Abstract

In an atmospheric medium that shows a non-Kolmogorov turbulence behavior, the variation of the on-axis scintillation index is evaluated when higher-order laser modes are used as the excitation. The Rytov method is employed together with the equivalent structure constant, which makes our results valid in weak turbulence. In the limiting case, our solution correctly reduces to the known scintillation index of the Gaussian beam in Kolmogorov turbulence. For all the higher-order even modes, increase in the power law exponent, α of the non-Kolmogorov spectrum is found to increase the scintillations. When the source size of the higher-order modes is large, higher-order even modes attain almost the same scintillation index values for all α. However, for small source sizes, being valid for any realization of the non-Kolmogorov spectrum, the scintillations decrease as the mode order becomes large. The changes in the propagation distance, structure constant, and the wavelength do not vary these trends.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. Chu, C. Qiao, and X. Feng, Opt. Laser Technol. 43, 1150 (2011).
    [CrossRef]
  2. H. Xu, Z. Cui, and J. Qu, Opt. Express 19, 21163 (2011).
    [CrossRef]
  3. X. Chu, C. Qiao, and X. Feng, Opt. Commun. 283, 3398 (2010).
    [CrossRef]
  4. B. E. Stribling, B. M. Welsh, and M. C. Roggeman, Proc. SPIE 2471, 181 (1995).
  5. E. Shchepakina and O. Korotkova, Opt. Express 18, 10650 (2010).
    [CrossRef]
  6. G. Wu, H. Guo, S. Yu, and B. Luo, Opt. Lett. 35, 715 (2010).
    [CrossRef]
  7. P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, Opt. Lett. 35, 1043 (2010).
    [CrossRef]
  8. H. Tang, B. Ou, B. Luo, H. Guo, and A. Dang, J. Opt. Soc. Am. A 28, 1016 (2011).
    [CrossRef]
  9. L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, Opt. Express 18, 451 (2010).
    [CrossRef]
  10. C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
    [CrossRef]
  11. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).
  12. W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
    [CrossRef]
  13. B. Xue, L. Cui, W. Xue, X. Bai, and F. Zhou, Opt. Express 19, 8433 (2011).
    [CrossRef]
  14. L. Cui, B. Xue, X. Cao, J. Dong, and J. Wang, Opt. Express 18, 21269 (2010).
    [CrossRef]
  15. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).
  16. L. Cui, B. Xue, L. Cao, S. Zheng, W. Xue, X. Bai, X. Cao, and F. Zhou, Opt. Express 19, 16872 (2011).
    [CrossRef]
  17. P. Deng, X. Yuan, and D. Huang, Opt. Commun. 285, 880 (2012).
    [CrossRef]
  18. H. Gerçekcioğlu and Y. Baykal, J. Opt. Soc. Am. A 29, 169 (2012).
    [CrossRef]
  19. H. Gerçekcioğlu and Y. Baykal, Appl. Phys. B 106, 933 (2012).
    [CrossRef]
  20. H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 320, 1 (2014).
    [CrossRef]
  21. H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 286, 30 (2013).
    [CrossRef]
  22. Y. Ata, Y. Baykal, and H. Gerçekcioğlu, Opt. Commun. 305, 126 (2013).
    [CrossRef]
  23. A. Zilberman, E. Golbraikh, and N. S. Kopeika, Opt. Commun. 283, 1229 (2010).
    [CrossRef]
  24. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
    [CrossRef]
  25. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
    [CrossRef]
  26. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).
  27. Y. Baykal and H. Gerçekcioğlu, Opt. Lett. 36, 4554 (2011).
    [CrossRef]
  28. Y. Baykal and H. Gerçekcioğlu, Opt. Commun. 310, 109 (2014).
    [CrossRef]
  29. H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, Opt. Eng. 45, 038002 (2006).
    [CrossRef]
  30. Y. Baykal, Opt. Commun. 57, 311 (1986).
    [CrossRef]
  31. H. T. Eyyuboğlu, S. Altay, and Y. Baykal, Opt. Commun. 264, 25 (2006).
    [CrossRef]
  32. Y. Baykal, J. Opt. Soc. Am. A 23, 889 (2006).
    [CrossRef]
  33. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

2014 (2)

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 320, 1 (2014).
[CrossRef]

Y. Baykal and H. Gerçekcioğlu, Opt. Commun. 310, 109 (2014).
[CrossRef]

2013 (2)

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 286, 30 (2013).
[CrossRef]

Y. Ata, Y. Baykal, and H. Gerçekcioğlu, Opt. Commun. 305, 126 (2013).
[CrossRef]

2012 (3)

P. Deng, X. Yuan, and D. Huang, Opt. Commun. 285, 880 (2012).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Appl. Phys. B 106, 933 (2012).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, J. Opt. Soc. Am. A 29, 169 (2012).
[CrossRef]

2011 (6)

2010 (7)

2009 (2)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

2008 (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

2007 (3)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).

2006 (3)

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, Opt. Eng. 45, 038002 (2006).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, Opt. Commun. 264, 25 (2006).
[CrossRef]

Y. Baykal, J. Opt. Soc. Am. A 23, 889 (2006).
[CrossRef]

2000 (1)

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

1995 (1)

B. E. Stribling, B. M. Welsh, and M. C. Roggeman, Proc. SPIE 2471, 181 (1995).

1986 (1)

Y. Baykal, Opt. Commun. 57, 311 (1986).
[CrossRef]

Altay, S.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, Opt. Commun. 264, 25 (2006).
[CrossRef]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).

Ata, Y.

Y. Ata, Y. Baykal, and H. Gerçekcioğlu, Opt. Commun. 305, 126 (2013).
[CrossRef]

Bai, X.

Baykal, Y.

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 320, 1 (2014).
[CrossRef]

Y. Baykal and H. Gerçekcioğlu, Opt. Commun. 310, 109 (2014).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 286, 30 (2013).
[CrossRef]

Y. Ata, Y. Baykal, and H. Gerçekcioğlu, Opt. Commun. 305, 126 (2013).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Appl. Phys. B 106, 933 (2012).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, J. Opt. Soc. Am. A 29, 169 (2012).
[CrossRef]

Y. Baykal and H. Gerçekcioğlu, Opt. Lett. 36, 4554 (2011).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, Opt. Commun. 264, 25 (2006).
[CrossRef]

Y. Baykal, J. Opt. Soc. Am. A 23, 889 (2006).
[CrossRef]

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, Opt. Eng. 45, 038002 (2006).
[CrossRef]

Y. Baykal, Opt. Commun. 57, 311 (1986).
[CrossRef]

Cao, L.

Cao, X.

Chu, X.

X. Chu, C. Qiao, and X. Feng, Opt. Laser Technol. 43, 1150 (2011).
[CrossRef]

X. Chu, C. Qiao, and X. Feng, Opt. Commun. 283, 3398 (2010).
[CrossRef]

Cui, L.

Cui, Z.

Dang, A.

Deng, P.

P. Deng, X. Yuan, and D. Huang, Opt. Commun. 285, 880 (2012).
[CrossRef]

Dong, J.

Du, W.

L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, Opt. Express 18, 451 (2010).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, Opt. Commun. 264, 25 (2006).
[CrossRef]

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, Opt. Eng. 45, 038002 (2006).
[CrossRef]

Feng, X.

X. Chu, C. Qiao, and X. Feng, Opt. Laser Technol. 43, 1150 (2011).
[CrossRef]

X. Chu, C. Qiao, and X. Feng, Opt. Commun. 283, 3398 (2010).
[CrossRef]

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).

Gerçekcioglu, H.

Y. Baykal and H. Gerçekcioğlu, Opt. Commun. 310, 109 (2014).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 320, 1 (2014).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 286, 30 (2013).
[CrossRef]

Y. Ata, Y. Baykal, and H. Gerçekcioğlu, Opt. Commun. 305, 126 (2013).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Appl. Phys. B 106, 933 (2012).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, J. Opt. Soc. Am. A 29, 169 (2012).
[CrossRef]

Y. Baykal and H. Gerçekcioğlu, Opt. Lett. 36, 4554 (2011).
[CrossRef]

Golbraikh, E.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Opt. Commun. 283, 1229 (2010).
[CrossRef]

Guo, H.

Han, Q.

Huang, D.

P. Deng, X. Yuan, and D. Huang, Opt. Commun. 285, 880 (2012).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

Jiang, W.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

Jiang, Y.

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

Kopeika, N. S.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Opt. Commun. 283, 1229 (2010).
[CrossRef]

Korotkova, O.

Ling, N.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

Liu, Z.

Luo, B.

Ma, J.

L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, Opt. Express 18, 451 (2010).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

Ma, Y.

Ou, B.

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).

Qiao, C.

X. Chu, C. Qiao, and X. Feng, Opt. Laser Technol. 43, 1150 (2011).
[CrossRef]

X. Chu, C. Qiao, and X. Feng, Opt. Commun. 283, 3398 (2010).
[CrossRef]

Qu, J.

Rao, C.

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

Roggeman, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggeman, Proc. SPIE 2471, 181 (1995).

Shchepakina, E.

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggeman, Proc. SPIE 2471, 181 (1995).

Tan, L.

L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, Opt. Express 18, 451 (2010).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

Tang, H.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).

Wang, J.

Wang, X.

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggeman, Proc. SPIE 2471, 181 (1995).

Wu, G.

Xie, W.

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

Xu, H.

Xue, B.

Xue, W.

Yenice, Y. E.

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, Opt. Eng. 45, 038002 (2006).
[CrossRef]

Yu, S.

Yuan, X.

P. Deng, X. Yuan, and D. Huang, Opt. Commun. 285, 880 (2012).
[CrossRef]

Zhao, H.

Zheng, S.

Zhou, F.

Zhou, P.

Zilberman, A.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Opt. Commun. 283, 1229 (2010).
[CrossRef]

Appl. Phys. B (1)

H. Gerçekcioğlu and Y. Baykal, Appl. Phys. B 106, 933 (2012).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, IEEE Trans. Antennas Propag. 57, 1783 (2009).
[CrossRef]

J. Mod. Opt. (1)

C. Rao, W. Jiang, and N. Ling, J. Mod. Opt. 47, 1111 (2000).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (10)

Y. Baykal, Opt. Commun. 57, 311 (1986).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, Opt. Commun. 264, 25 (2006).
[CrossRef]

X. Chu, C. Qiao, and X. Feng, Opt. Commun. 283, 3398 (2010).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, Opt. Commun. 282, 705 (2009).
[CrossRef]

P. Deng, X. Yuan, and D. Huang, Opt. Commun. 285, 880 (2012).
[CrossRef]

Y. Baykal and H. Gerçekcioğlu, Opt. Commun. 310, 109 (2014).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 320, 1 (2014).
[CrossRef]

H. Gerçekcioğlu and Y. Baykal, Opt. Commun. 286, 30 (2013).
[CrossRef]

Y. Ata, Y. Baykal, and H. Gerçekcioğlu, Opt. Commun. 305, 126 (2013).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, Opt. Commun. 283, 1229 (2010).
[CrossRef]

Opt. Eng. (2)

H. T. Eyyuboğlu, Y. E. Yenice, and Y. Baykal, Opt. Eng. 45, 038002 (2006).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Opt. Eng. 47, 026003 (2008).
[CrossRef]

Opt. Express (6)

Opt. Laser Technol. (1)

X. Chu, C. Qiao, and X. Feng, Opt. Laser Technol. 43, 1150 (2011).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (4)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6747, 67470B (2007).

B. E. Stribling, B. M. Welsh, and M. C. Roggeman, Proc. SPIE 2471, 181 (1995).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6551, 65510E (2007).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, Proc. SPIE 6457, 64570T (2007).

Other (1)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

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 (5)

Fig. 1.
Fig. 1.

Scintillation index of relatively small-sized higher-order even modes versus α.

Fig. 2.
Fig. 2.

Scintillation index of large-sized higher-order even modes versus α.

Fig. 3.
Fig. 3.

Scintillation index of higher-order even modes versus α for λ=1.55μm.

Fig. 4.
Fig. 4.

Scintillation index of higher-order even modes versus α for λ=0.63μm.

Fig. 5.
Fig. 5.

Normalized scintillation index versus α where the same parameters as in Fig. 3 are used.

Equations (6)

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

us=Hn(sx/αs)Hm(sy/αs)exp[0.5αs2(sx2+sy2)],
Φn(κ,α)=A(α)Cn2(α)κα,κ>0,3<α<4,
Φn(κ)=h(α)κα,0κ<,3<α<4,
h(α)=Γ(α)(k/L)α/211/6Cn28π2Γ(10.5α)[Γ(0.5α)]2sin(0.25πα),
m2=4π[Hn(0)Hm(0)]2Re{0Ldη0κdκ02πdθ[E(η,κ,θ,L)×E(η,κ,θ,L)+|E(η,κ,θ,L)|2]Φn(κ)},
E(η,κ,θ,L)=ikexp[0.5i(kξ)1(Lη)(kαs2+iη)κ2]×Hn[(ξ*)1αs(ηL)κcosθ]×Hm[(ξ*)1αs(ηL)κsinθ],

Metrics