Abstract

Based on the generalized spectral model for non-Kolmogorov atmospheric turbulence, analytic expressions of the scintillation index (SI) are derived for plane, spherical optical waves and a partially coherent Gaussian beam propagating through non-Kolmogorov turbulence horizontally in the weak fluctuation regime. The new expressions relate the SI to the finite turbulence inner and outer scales, spatial coherence of the source and spectral power-law and then used to analyze the effects of atmospheric condition and link length on the performance of wireless optical communication links.

© 2011 OSA

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References

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  1. A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res. 2(4), 345–396 (2005).
    [CrossRef]
  2. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
    [CrossRef]
  3. H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
    [CrossRef]
  4. L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
    [CrossRef]
  5. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, 2005).
  6. 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(2), 330–341 (2004).
    [CrossRef]
  7. C. Y. Chen, H. M. Yang, X. Feng, and H. Wang, “Optimization criterion for initial coherence degree of lasers in free-space optical links through atmospheric turbulence,” Opt. Lett. 34(4), 419–421 (2009).
    [CrossRef] [PubMed]
  8. D. K. Borah and D. G. Voelz, “Spatially partially coherent beam parameter optimization for free space optical communications,” Opt. Express 18(20), 20746–20758 (2010).
    [CrossRef] [PubMed]
  9. 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(5), 715–717 (2010).
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    [CrossRef]
  12. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [CrossRef]
  13. M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
    [CrossRef]
  14. 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(34), 6385–6391 (2008).
    [CrossRef] [PubMed]
  15. N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
    [CrossRef]
  16. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
    [CrossRef]
  17. L. Y. Cui, B. D. Xue, X. G. Cao, J. K. Dong, and J. N. Wang, “Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(20), 21269–21283 (2010).
    [CrossRef] [PubMed]
  18. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
    [CrossRef]
  19. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
    [CrossRef]
  20. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
    [CrossRef]
  21. L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(2), 451–462 (2010).
    [CrossRef] [PubMed]
  22. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
    [CrossRef]
  23. B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence,” Opt. Express 19(9), 8433–8443 (2011).
    [CrossRef] [PubMed]
  24. B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Generalized modified atmospheric spectral model for optical wave propagating through non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 28(5), 912–916 (2011).
    [CrossRef] [PubMed]
  25. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11(10), 2719–2726 (1994).
    [CrossRef]
  26. L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE Optical Engineering Press, 1998).

2011 (2)

2010 (6)

2009 (4)

C. Y. Chen, H. M. Yang, X. Feng, and H. Wang, “Optimization criterion for initial coherence degree of lasers in free-space optical links through atmospheric turbulence,” Opt. Lett. 34(4), 419–421 (2009).
[CrossRef] [PubMed]

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
[CrossRef]

2008 (1)

2007 (3)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

2005 (1)

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res. 2(4), 345–396 (2005).
[CrossRef]

2004 (1)

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(2), 330–341 (2004).
[CrossRef]

2002 (1)

L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

1997 (1)

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

1995 (1)

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

1994 (2)

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11(10), 2719–2726 (1994).
[CrossRef]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

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(2), 330–341 (2004).
[CrossRef]

L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11(10), 2719–2726 (1994).
[CrossRef]

Bai, X. Z.

Belen’kii, M. S.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Bishop, K. P.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

Borah, D. K.

Brown, J. M.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Cao, X. G.

Chen, C. Y.

Cui, L. Y.

Dong, J. K.

Du, W.

Fafalios, M. E.

Feng, X.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

Fugate, R. Q.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Golbraikh, E.

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

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(34), 6385–6391 (2008).
[CrossRef] [PubMed]

Guo, H.

Han, Q.

Karagianni, E. A.

Karis, S. J.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Keating, D. B.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

Kopeika, N. S.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

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(34), 6385–6391 (2008).
[CrossRef] [PubMed]

Korotkova, O.

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(2), 330–341 (2004).
[CrossRef]

Kyrazis, D. T.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

Luo, B.

Ma, J.

Majumdar, A. K.

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res. 2(4), 345–396 (2005).
[CrossRef]

Miller, W. B.

Nistazakis, H. E.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
[CrossRef]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

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(2), 330–341 (2004).
[CrossRef]

L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

Preble, A. J.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

Ricklin, J. C.

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Tan, L.

Tombras, G. S.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
[CrossRef]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

Tsiftsis, T. A.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

Tsigopoulos, A. D.

Voelz, D. G.

Wang, H.

Wang, J. N.

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Wissler, J.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

Wu, G.

Xue, B. D.

Xue, W. F.

Yang, H. M.

Yu, S.

Zhou, F. G.

Zilberman, A.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

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(34), 6385–6391 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE Trans. Antenn. Propag. (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. 57(6), 1783–1788 (2009).
[CrossRef]

IET Commun. (1)

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Fiber Commun. Res. (1)

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res. 2(4), 345–396 (2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. 283(7), 1229–1235 (2010).
[CrossRef]

Opt. Eng. (1)

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(2), 330–341 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Proc. SPIE (8)

L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[CrossRef]

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[CrossRef]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Other (3)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, 2005).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Trans. NOAA by Israel Program for Scientific Translations, 1971).

L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE Optical Engineering Press, 1998).

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Figures (6)

Fig. 1
Fig. 1

Scintillation index as a function of inner scale for different link lengths and spectral indices.

Fig. 2
Fig. 2

Scintillation index as a function of alpha for different link lengths and inner scales.

Fig. 3
Fig. 3

Outage probability as a function of normalized average SNR for different spectral indices.

Fig. 4
Fig. 4

Outage probability as a function of normalized average SNR for different spectral indices and inner scales.

Fig. 5
Fig. 5

Mean BER as a function of SNR for different alpha values.

Fig. 6
Fig. 6

Mean BER as a function of SNR for different spectral indices and inner scale values.

Equations (22)

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

Φ n ( κ , α , l 0 , L 0 ) = A ( α ) C ˜ n 2 κ α f ( κ , l 0 , L 0 , α ) ( 0 κ < , 3< α <5),
f ( κ , l 0 , L 0 , α ) = [ 1 exp ( κ 2 κ 0 2 ) ] [ 1 + a 1 ( κ κ l ) b 1 ( κ κ l ) β ] exp ( κ 2 κ l 2 )
A ( α ) = Γ ( α 1 ) 4 π 2 sin [ ( α 3 ) π 2 ] c ( α ) = { π A ( α ) [ Γ ( α 2 + 3 2 ) ( 1 α 3 ) + a 1 Γ ( α 2 + 2 ) ( 4 α 3 ) b 1 Γ ( α + 3 + β 2 ) ( 3 + β α 3 ) ] } 1 α 5
Φ n ( κ , α ) = A ( α ) C ˜ n 2 κ α
σ I 2 ( ρ , L ) = σ I , l 2 ( L ) + σ I , r 2 ( ρ , L )
σ I , l 2 ( L ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ , α , l 0 , L 0 ) exp ( Λ e d L κ 2 ξ 2 / k ) × { 1 cos [ L κ 2 k ξ ( 1 Θ ¯ e d ξ ) ] } d κ d ξ
σ I , r 2 ( ρ , L ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ , α , l 0 , L 0 ) exp ( Λ e d L κ 2 ξ 2 / k ) × [ I 0 ( 2 Λ e d ρ ξ κ ) 1 ] d κ d ξ
σ I , l 2 ( L ) = g ( E 1 , H 1 ) + a 1 κ l g ( E 2 , H 1 ) b 1 κ l β g ( E 3 , H 1 ) g ( E 1 , H 2 ) a 1 κ l g ( E 2 , H 2 ) + b 1 κ l β g ( E 3 , H 2 )
g ( E i , H j ) = 4 π 2 k 2 L A ( α ) C ˜ n 2 Γ ( E i 2 + 1 ) ( L k ) E i 2 1 H j E i 2 + 1 { F 2 1 ( E i 2 + 1 , 1 2 ; 3 2 ; Λ e d H j ) Re [ n = 0 ( E i / 2 + 1 ) n ( 1 ) n n ! ( 2 ) n ( i H j ) n F 2 1 ( n , n + 1 ; n + 2 ; Θ ¯ e d + i Λ e d ) ] } , H j < 1
g ( E i , H j ) 4 π 2 k 2 L A ( α ) C ˜ n 2 Γ ( E i 2 + 1 ) ( L k ) E i 2 1 H j E i 2 + 1 × { F 2 1 ( E i 2 + 1 , 1 2 ; 3 2 ; Λ e d H j ) Re [ 1 + H j ( 2 Λ e d + i+2 Θ e d i ) / 3 ] E i 2 1 E i 2 H j [ 2 Λ e d + i(1+2 Θ e d ) ] / 3 } , | Θ ¯ e d + i Λ e d | < 1
σ I , r 2 ( L ) = f ( E 1 , H 1 ) + a 1 κ l f ( E 2 , H 1 ) b 1 κ l β f ( E 3 , H 1 ) f ( E 1 , H 2 ) a 1 κ l f ( E 2 , H 2 ) + b 1 κ l β f ( E 3 , H 2 )
f ( E i , H j ) = 4 π 2 k 2 L A ( α ) C ˜ n 2 Γ ( E i 2 + 1 ) ( L k ) E i 2 1 H j 1 E i 2 n = 1 ( E i / 2 + 1 ) n ( 1 / 2 ) n n ! ( 1 ) n ( 3 / 2 ) n × ( 2 ρ 2 W e d 2 ) n ( Λ e d H j ) n F 2 1 ( n + 1 E i 2 , n + 1 2 ; n + 3 2 ; Λ e d H j ) 4 π 2 k 2 L A ( α ) C ˜ n 2 Γ ( E i 2 + 1 ) ( L k ) E i 2 1 H j 1 E i 2 2 E i 3 × ( ρ 2 W e d 2 ) ( Λ e d H j ) F 2 1 ( 2 E i 2 , 3 2 ; 5 2 ; Λ e d H j ) , ρ / W e d < 1.
σ I , p l 2 ( L , α , l 0 , L 0 ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ , α , l 0 , L 0 ) [ 1 cos ( L κ 2 k ξ ) ] d κ d ξ = h p l ( E 1 , H 1 ) + a 1 κ l h p l ( E 2 , H 1 ) b 1 κ l β h p l ( E 3 , H 1 ) h p l ( E 1 , H 2 ) a 1 κ l h p l ( E 2 , H 2 ) + b 1 κ l β h p l ( E 3 , H 2 )
h p l ( E i , H j ) = 8 π 2 A ( α ) 1.23 E i Γ ( 1 E i 2 ) σ ˜ R 2 ( E i ) [ ( 1 + 1 H j 2 ) E i / 4 sin ( E i 2 tan 1 H j ) E i 2 H j E i 2 + 1 ]
σ I , s p 2 ( L , α , l 0 , L 0 ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ , α , l 0 , L 0 ) [ 1 cos ( L κ 2 k ξ ( 1 ξ ) ) ] d κ d ξ = h s p ( E 1 , H 1 ) + a 1 κ l h s p ( E 2 , H 1 ) b 1 κ l β h s p ( E 3 , H 1 ) h s p ( E 1 , H 2 ) a 1 κ l h s p ( E 2 , H 2 ) + b 1 κ l β h s p ( E 3 , H 2 )
h s p ( E i , H j ) = 4 π 2 A ( α ) 1.23 σ ˜ R 2 ( E i ) Γ ( E i 2 + 1 ) H j E i 2 + 1 × Re [ F 2 1 ( E i 2 + 1 , 1 ; 3 2 ; i H j 4 ) 1 ] = 4 π 2 A ( α ) 1.23 σ ˜ R 2 ( E i ) Γ ( E i 2 + 1 ) H j E i 2 + 1 × [ F 3 2 ( 1 , 2 E i 4 , 4 E i 4 ; 3 4 , 5 4 ; H j 2 16 ) 1 ]
p I ( I ) = 1 I σ I 2 π exp { [ ln ( I ) + σ I 2 / 2 ] 2 2 σ I 2 } , I > 0
p μ ( μ ) = 1 2 μ σ I 2 π exp { [ ln ( μ / μ ¯ ) + σ I 2 ] 2 8 σ I 2 } , I > 0
P o u t = Pr ( μ μ t h ) = 0 μ t h p μ ( μ ) d μ = 1 2 erfc [ ln ( μ ¯ / μ t h ) σ I 2 2 2 σ I ]
BER = 1 2 0 p I ( I ) e r f c ( I SNR 2 2 I ) d I = 1 2 0 p μ ( μ ) e r f c ( u SNR 2 2 ) d u
C = 0 B log 2 ( 1 + ( η I ) 2 N 0 ) p I ( I ) d I
C = B 2 σ I 2 π ln ( 2 ) 0 ln ( 1 + μ ) μ exp ( ( ln μ A ) 2 8 σ I 2 ) d μ = B exp ( A 2 / 8 σ I 2 ) 2 ln ( 2 ) m = 1 ( 1 ) m + 1 m [ erfcx ( 2 σ I m + A 2 2 σ I ) + erfcx ( 2 σ I m A 2 2 σ I ) ] + B exp ( A 2 / 8 σ I 2 ) 2 ln ( 2 ) [ 4 σ I 2 π + A exp ( A 2 8 σ I 2 ) erfc ( A 2 2 σ I ) ]

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