Abstract

Minimization of the on-axis scintillation index of sinusoidal Gaussian beams is investigated by using the modified Rytov method in weak atmospheric turbulence for uplink/downlink of aerial vehicle-satellite laser communications. Among the focused cosh-Gaussian (cosh-G), cos-Gaussian (cos-G), annular, and Gaussian beams, a suitable displacement parameter for a cosh-G beam is determined that will minimize the scintillation index in uplink and downlink configurations. Then, for both uplink and downlink, the variations of the scintillation index against the propagation distance, source size, and zenith angle are examined and compared among themselves to show the optimum beam that possesses the minimum scintillation index. Sinusoidal Gaussian beams that are focused at the receiver and obtained by employing the appropriate displacement parameter, which we name the optimum beams, are recommended to obtain smaller intensity fluctuations in atmospheric wireless optical communication systems operating in vertical links in weak turbulence.

© 2021 Optical Society of America

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References

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  1. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  2. M. A. Krainak, “Inter-satellite communications optoelectronics research at the Goddard Space Flight Center,” IEEE Aerosp. Electron. Syst. Mag. 7(9), 44–47 (1992).
    [Crossref]
  3. H. Willerbrand and B. Ghuman, “Fiber optics without the fiber,” IEEE Spectrum 38(8), 40–45 (2001).
    [Crossref]
  4. D. Kedar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
    [Crossref]
  5. Y. Baykal, C. F. Ouyang, and M. A. Plonus, “Scintillation index for a temporally partially coherent spherical wave light source in weak turbulence,” Radio Sci. 16, 343–345 (1981).
    [Crossref]
  6. L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian-beam wave,” Wave Random Media 11, 271–291 (2001).
    [Crossref]
  7. A. Peleg and J. V. Moloney, “Scintillation index for two Gaussian laser beams with different wavelengths in weak atmospheric turbulence,” J. Opt. Soc. Am. A 23, 3114–3122 (2006).
    [Crossref]
  8. H. T. Eyyuboğlu and Y. Baykal, “Scintillations of cos–Gaussian and annular beams,” J. Opt. Soc. Am. A 24, 156–162 (2007).
    [Crossref]
  9. S. A. Arpali, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of higher order cos- Gaussian, cosh-Gaussian and annular beams,” J. Mod. Opt. 55, 227–239 (2008).
    [Crossref]
  10. H. Gerçekcioğlu and Y. Baykal, “Annular beam scintillations in non-Kolmogorov weak turbulence,” Appl. Phys. B 106, 933–937 (2012).
    [Crossref]
  11. Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped Gaussian beams,” Appl. Opt. 45, 3793–3797 (2006).
    [Crossref]
  12. H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
    [Crossref]
  13. D. C. Cowan and L. C. Andrews, “Effects of atmospheric turbulence on the scintillation and fade probability of flattened Gaussian beams,” Opt. Eng. 47, 026001 (2008).
    [Crossref]
  14. H. Gerçekcioğlu and Y. Baykal, “BER of annular and flat-topped beams in non-Kolmogorov weak turbulence,” Opt. Commun. 286, 30–33 (2013).
    [Crossref]
  15. H. T. Eyyuboğlu and Y. Baykal, “Scintillation characteristics of cosh-Gaussian beams,” Appl. Opt. 46, 1099–1106 (2007).
    [Crossref]
  16. Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. 32, 2405–2407 (2007).
    [Crossref]
  17. Y. Baykal, “Scintillation index for a multimode laser incidence in weak atmospheric turbulence,” Opt. Commun. 62, 295–299 (1987).
    [Crossref]
  18. H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillations of laser array beams,” Appl. Phys. B 91, 265–271 (2008).
    [Crossref]
  19. H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of laser array beams in non-Kolmogorov turbulence,” IEEE J. Sel. Areas Commun. 33, 1877–1882 (2015).
    [Crossref]
  20. A. M. Aly, H. A. Fayed, N. E. Ismail, and M. H. Aly, “Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions,” Opt. Quantum Electron. 51, 94 (2019).
    [Crossref]
  21. I. Toselli and O. Korotkova, “Optical turbulence with anisotropy at different scales and its effect on laser beam propagation along vertical paths,” Proc. SPIE 9465, 94650P (2015).
    [Crossref]
  22. V. A. Banakh and I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Ocean. Opt. 5, 233–237 (1992).
  23. X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122, 221 (2016).
    [Crossref]
  24. L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45, 076001 (2006).
    [Crossref]
  25. Y. Baykal, “Coherence length in non-Kolmogorov satellite links,” Opt. Commun. 308, 105–108 (2013).
    [Crossref]
  26. H. Chen, X. Ji, G. Ji, and H. Zhang, “Scintillation characteristics of annular beams propagating through atmospheric turbulence along a slanted path,” J. Opt. 17, 085605 (2015).
    [Crossref]
  27. M. Charnotskii, “Beam scintillations for ground-to-space propagation. Part I: Path integrals and analytic techniques,” J. Opt. Soc. Am. A 27, 2169–2179 (2010).
    [Crossref]
  28. M. Toyoshima, T. Sasaki, H. Takenaka, and Y. Takayama, “Scintillation model of laser beam propagation in satellite-to-ground bidirectional atmospheric channels,” Opt. Commun. 80, 58–64 (2012).
    [Crossref]
  29. H. Gerçekcioğlu, “M-pulse amplitude modulation of flat-topped beam for aeronautical laser communications,” J. Opt. Soc. Am. A 35, 1560–1566 (2018).
    [Crossref]
  30. H. Gerçekcioğlu, “Performance of annular beams in weak atmospheric turbulence for satellite laser communications,” Opt. Commun. 439, 233–238 (2019).
    [Crossref]
  31. Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications,” Opt. Commun. 458, 124735 (2020).
    [Crossref]
  32. Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Multimode laser beam scintillations in weak atmospheric turbulence for vertical link laser communications,” Waves Random Complex Media 30, 118–129 (2020).
    [Crossref]
  33. H. T. Eyyuboğlu, H. Gerçekcioğlu, and Y. Baykal, “Minimization of scintillation index against displacement parameters,” Opt. Commun. 281, 4224–4229 (2008).
    [Crossref]
  34. H. Gerçekcioğlu and Y. Baykal, “Minimization effects on scintillations of sinusoidal Gaussian beams in strong turbulence,” J. Opt. A 13, 115705 (2011).
    [Crossref]
  35. H. T. Eyyuboğlu and Y. Baykal, “Analysis of reciprocity of cos- Gaussian and cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Express 12, 4659–4674 (2004).
    [Crossref]
  36. Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 889–893 (2006).
    [Crossref]

2020 (2)

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications,” Opt. Commun. 458, 124735 (2020).
[Crossref]

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Multimode laser beam scintillations in weak atmospheric turbulence for vertical link laser communications,” Waves Random Complex Media 30, 118–129 (2020).
[Crossref]

2019 (2)

H. Gerçekcioğlu, “Performance of annular beams in weak atmospheric turbulence for satellite laser communications,” Opt. Commun. 439, 233–238 (2019).
[Crossref]

A. M. Aly, H. A. Fayed, N. E. Ismail, and M. H. Aly, “Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions,” Opt. Quantum Electron. 51, 94 (2019).
[Crossref]

2018 (1)

2016 (1)

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122, 221 (2016).
[Crossref]

2015 (3)

H. Chen, X. Ji, G. Ji, and H. Zhang, “Scintillation characteristics of annular beams propagating through atmospheric turbulence along a slanted path,” J. Opt. 17, 085605 (2015).
[Crossref]

I. Toselli and O. Korotkova, “Optical turbulence with anisotropy at different scales and its effect on laser beam propagation along vertical paths,” Proc. SPIE 9465, 94650P (2015).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of laser array beams in non-Kolmogorov turbulence,” IEEE J. Sel. Areas Commun. 33, 1877–1882 (2015).
[Crossref]

2013 (2)

Y. Baykal, “Coherence length in non-Kolmogorov satellite links,” Opt. Commun. 308, 105–108 (2013).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “BER of annular and flat-topped beams in non-Kolmogorov weak turbulence,” Opt. Commun. 286, 30–33 (2013).
[Crossref]

2012 (3)

H. Gerçekcioğlu and Y. Baykal, “Annular beam scintillations in non-Kolmogorov weak turbulence,” Appl. Phys. B 106, 933–937 (2012).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
[Crossref]

M. Toyoshima, T. Sasaki, H. Takenaka, and Y. Takayama, “Scintillation model of laser beam propagation in satellite-to-ground bidirectional atmospheric channels,” Opt. Commun. 80, 58–64 (2012).
[Crossref]

2011 (1)

H. Gerçekcioğlu and Y. Baykal, “Minimization effects on scintillations of sinusoidal Gaussian beams in strong turbulence,” J. Opt. A 13, 115705 (2011).
[Crossref]

2010 (1)

2008 (4)

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillations of laser array beams,” Appl. Phys. B 91, 265–271 (2008).
[Crossref]

H. T. Eyyuboğlu, H. Gerçekcioğlu, and Y. Baykal, “Minimization of scintillation index against displacement parameters,” Opt. Commun. 281, 4224–4229 (2008).
[Crossref]

D. C. Cowan and L. C. Andrews, “Effects of atmospheric turbulence on the scintillation and fade probability of flattened Gaussian beams,” Opt. Eng. 47, 026001 (2008).
[Crossref]

S. A. Arpali, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of higher order cos- Gaussian, cosh-Gaussian and annular beams,” J. Mod. Opt. 55, 227–239 (2008).
[Crossref]

2007 (3)

2006 (4)

2004 (2)

H. T. Eyyuboğlu and Y. Baykal, “Analysis of reciprocity of cos- Gaussian and cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Express 12, 4659–4674 (2004).
[Crossref]

D. Kedar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

2001 (2)

H. Willerbrand and B. Ghuman, “Fiber optics without the fiber,” IEEE Spectrum 38(8), 40–45 (2001).
[Crossref]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian-beam wave,” Wave Random Media 11, 271–291 (2001).
[Crossref]

1992 (2)

M. A. Krainak, “Inter-satellite communications optoelectronics research at the Goddard Space Flight Center,” IEEE Aerosp. Electron. Syst. Mag. 7(9), 44–47 (1992).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Ocean. Opt. 5, 233–237 (1992).

1987 (1)

Y. Baykal, “Scintillation index for a multimode laser incidence in weak atmospheric turbulence,” Opt. Commun. 62, 295–299 (1987).
[Crossref]

1981 (1)

Y. Baykal, C. F. Ouyang, and M. A. Plonus, “Scintillation index for a temporally partially coherent spherical wave light source in weak turbulence,” Radio Sci. 16, 343–345 (1981).
[Crossref]

Al-Habash, M. A.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian-beam wave,” Wave Random Media 11, 271–291 (2001).
[Crossref]

Aly, A. M.

A. M. Aly, H. A. Fayed, N. E. Ismail, and M. H. Aly, “Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions,” Opt. Quantum Electron. 51, 94 (2019).
[Crossref]

Aly, M. H.

A. M. Aly, H. A. Fayed, N. E. Ismail, and M. H. Aly, “Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions,” Opt. Quantum Electron. 51, 94 (2019).
[Crossref]

Andrews, L. C.

D. C. Cowan and L. C. Andrews, “Effects of atmospheric turbulence on the scintillation and fade probability of flattened Gaussian beams,” Opt. Eng. 47, 026001 (2008).
[Crossref]

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45, 076001 (2006).
[Crossref]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian-beam wave,” Wave Random Media 11, 271–291 (2001).
[Crossref]

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

Arnon, S.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

Arpali, S. A.

S. A. Arpali, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of higher order cos- Gaussian, cosh-Gaussian and annular beams,” J. Mod. Opt. 55, 227–239 (2008).
[Crossref]

Banakh, V. A.

V. A. Banakh and I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Ocean. Opt. 5, 233–237 (1992).

Baykal, Y.

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications,” Opt. Commun. 458, 124735 (2020).
[Crossref]

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Multimode laser beam scintillations in weak atmospheric turbulence for vertical link laser communications,” Waves Random Complex Media 30, 118–129 (2020).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of laser array beams in non-Kolmogorov turbulence,” IEEE J. Sel. Areas Commun. 33, 1877–1882 (2015).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “BER of annular and flat-topped beams in non-Kolmogorov weak turbulence,” Opt. Commun. 286, 30–33 (2013).
[Crossref]

Y. Baykal, “Coherence length in non-Kolmogorov satellite links,” Opt. Commun. 308, 105–108 (2013).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Annular beam scintillations in non-Kolmogorov weak turbulence,” Appl. Phys. B 106, 933–937 (2012).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Minimization effects on scintillations of sinusoidal Gaussian beams in strong turbulence,” J. Opt. A 13, 115705 (2011).
[Crossref]

H. T. Eyyuboğlu, H. Gerçekcioğlu, and Y. Baykal, “Minimization of scintillation index against displacement parameters,” Opt. Commun. 281, 4224–4229 (2008).
[Crossref]

S. A. Arpali, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of higher order cos- Gaussian, cosh-Gaussian and annular beams,” J. Mod. Opt. 55, 227–239 (2008).
[Crossref]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Scintillations of laser array beams,” Appl. Phys. B 91, 265–271 (2008).
[Crossref]

H. T. Eyyuboğlu and Y. Baykal, “Scintillations of cos–Gaussian and annular beams,” J. Opt. Soc. Am. A 24, 156–162 (2007).
[Crossref]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. 32, 2405–2407 (2007).
[Crossref]

H. T. Eyyuboğlu and Y. Baykal, “Scintillation characteristics of cosh-Gaussian beams,” Appl. Opt. 46, 1099–1106 (2007).
[Crossref]

Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped Gaussian beams,” Appl. Opt. 45, 3793–3797 (2006).
[Crossref]

Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 889–893 (2006).
[Crossref]

H. T. Eyyuboğlu and Y. Baykal, “Analysis of reciprocity of cos- Gaussian and cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Express 12, 4659–4674 (2004).
[Crossref]

Y. Baykal, “Scintillation index for a multimode laser incidence in weak atmospheric turbulence,” Opt. Commun. 62, 295–299 (1987).
[Crossref]

Y. Baykal, C. F. Ouyang, and M. A. Plonus, “Scintillation index for a temporally partially coherent spherical wave light source in weak turbulence,” Radio Sci. 16, 343–345 (1981).
[Crossref]

Cai, Y.

Charnotskii, M.

Chen, H.

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122, 221 (2016).
[Crossref]

H. Chen, X. Ji, G. Ji, and H. Zhang, “Scintillation characteristics of annular beams propagating through atmospheric turbulence along a slanted path,” J. Opt. 17, 085605 (2015).
[Crossref]

Chen, Y.

Cowan, D. C.

D. C. Cowan and L. C. Andrews, “Effects of atmospheric turbulence on the scintillation and fade probability of flattened Gaussian beams,” Opt. Eng. 47, 026001 (2008).
[Crossref]

Eyyuboglu, H. T.

Fayed, H. A.

A. M. Aly, H. A. Fayed, N. E. Ismail, and M. H. Aly, “Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions,” Opt. Quantum Electron. 51, 94 (2019).
[Crossref]

Gerçekcioglu, H.

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Multimode laser beam scintillations in weak atmospheric turbulence for vertical link laser communications,” Waves Random Complex Media 30, 118–129 (2020).
[Crossref]

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications,” Opt. Commun. 458, 124735 (2020).
[Crossref]

H. Gerçekcioğlu, “Performance of annular beams in weak atmospheric turbulence for satellite laser communications,” Opt. Commun. 439, 233–238 (2019).
[Crossref]

H. Gerçekcioğlu, “M-pulse amplitude modulation of flat-topped beam for aeronautical laser communications,” J. Opt. Soc. Am. A 35, 1560–1566 (2018).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of laser array beams in non-Kolmogorov turbulence,” IEEE J. Sel. Areas Commun. 33, 1877–1882 (2015).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “BER of annular and flat-topped beams in non-Kolmogorov weak turbulence,” Opt. Commun. 286, 30–33 (2013).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Annular beam scintillations in non-Kolmogorov weak turbulence,” Appl. Phys. B 106, 933–937 (2012).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Minimization effects on scintillations of sinusoidal Gaussian beams in strong turbulence,” J. Opt. A 13, 115705 (2011).
[Crossref]

H. T. Eyyuboğlu, H. Gerçekcioğlu, and Y. Baykal, “Minimization of scintillation index against displacement parameters,” Opt. Commun. 281, 4224–4229 (2008).
[Crossref]

Ghuman, B.

H. Willerbrand and B. Ghuman, “Fiber optics without the fiber,” IEEE Spectrum 38(8), 40–45 (2001).
[Crossref]

Hopen, C. Y.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian-beam wave,” Wave Random Media 11, 271–291 (2001).
[Crossref]

Ismail, N. E.

A. M. Aly, H. A. Fayed, N. E. Ismail, and M. H. Aly, “Gaussian beam scintillation index for slant path in weak turbulence: closed form expressions,” Opt. Quantum Electron. 51, 94 (2019).
[Crossref]

Ji, G.

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122, 221 (2016).
[Crossref]

H. Chen, X. Ji, G. Ji, and H. Zhang, “Scintillation characteristics of annular beams propagating through atmospheric turbulence along a slanted path,” J. Opt. 17, 085605 (2015).
[Crossref]

Ji, X.

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122, 221 (2016).
[Crossref]

H. Chen, X. Ji, G. Ji, and H. Zhang, “Scintillation characteristics of annular beams propagating through atmospheric turbulence along a slanted path,” J. Opt. 17, 085605 (2015).
[Crossref]

Kedar, D.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

Korotkova, O.

I. Toselli and O. Korotkova, “Optical turbulence with anisotropy at different scales and its effect on laser beam propagation along vertical paths,” Proc. SPIE 9465, 94650P (2015).
[Crossref]

Krainak, M. A.

M. A. Krainak, “Inter-satellite communications optoelectronics research at the Goddard Space Flight Center,” IEEE Aerosp. Electron. Syst. Mag. 7(9), 44–47 (1992).
[Crossref]

Moloney, J. V.

Ouyang, C. F.

Y. Baykal, C. F. Ouyang, and M. A. Plonus, “Scintillation index for a temporally partially coherent spherical wave light source in weak turbulence,” Radio Sci. 16, 343–345 (1981).
[Crossref]

Parenti, R. R.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45, 076001 (2006).
[Crossref]

Peleg, A.

Phillips, R. L.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45, 076001 (2006).
[Crossref]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian-beam wave,” Wave Random Media 11, 271–291 (2001).
[Crossref]

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

Plonus, M. A.

Y. Baykal, C. F. Ouyang, and M. A. Plonus, “Scintillation index for a temporally partially coherent spherical wave light source in weak turbulence,” Radio Sci. 16, 343–345 (1981).
[Crossref]

Sasaki, T.

M. Toyoshima, T. Sasaki, H. Takenaka, and Y. Takayama, “Scintillation model of laser beam propagation in satellite-to-ground bidirectional atmospheric channels,” Opt. Commun. 80, 58–64 (2012).
[Crossref]

Sasiela, R. J.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, “Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects,” Opt. Eng. 45, 076001 (2006).
[Crossref]

Sayan, Ö. F.

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications,” Opt. Commun. 458, 124735 (2020).
[Crossref]

Ö. F. Sayan, H. Gerçekcioğlu, and Y. Baykal, “Multimode laser beam scintillations in weak atmospheric turbulence for vertical link laser communications,” Waves Random Complex Media 30, 118–129 (2020).
[Crossref]

Smalikho, I. N.

V. A. Banakh and I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Ocean. Opt. 5, 233–237 (1992).

Takayama, Y.

M. Toyoshima, T. Sasaki, H. Takenaka, and Y. Takayama, “Scintillation model of laser beam propagation in satellite-to-ground bidirectional atmospheric channels,” Opt. Commun. 80, 58–64 (2012).
[Crossref]

Takenaka, H.

M. Toyoshima, T. Sasaki, H. Takenaka, and Y. Takayama, “Scintillation model of laser beam propagation in satellite-to-ground bidirectional atmospheric channels,” Opt. Commun. 80, 58–64 (2012).
[Crossref]

Toselli, I.

I. Toselli and O. Korotkova, “Optical turbulence with anisotropy at different scales and its effect on laser beam propagation along vertical paths,” Proc. SPIE 9465, 94650P (2015).
[Crossref]

Toyoshima, M.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (11)

Fig. 1.
Fig. 1. Scintillation index versus propagation uplink distance from 0 to 25 km.
Fig. 2.
Fig. 2. Scintillation index versus propagation uplink distance from 25 to 700 km.
Fig. 3.
Fig. 3. Scintillation index versus source size for propagation uplink distance at $L = 20\;{\rm{km}}$ .
Fig. 4.
Fig. 4. Scintillation index versus source size for propagation uplink distance at $L = 700\;{\rm{km}}$ .
Fig. 5.
Fig. 5. Scintillation index versus zenith angle for propagation uplink distance at $L = 20\;{\rm{km}}$ .
Fig. 6.
Fig. 6. Scintillation index versus zenith angle for propagation uplink distance at $L = 700\;{\rm{km}}$ .
Fig. 7.
Fig. 7. Scintillation index versus propagation downlink distance.
Fig. 8.
Fig. 8. Scintillation index versus source size for propagation downlink distance at $L = 20\;{\rm{km}}$ .
Fig. 9.
Fig. 9. Scintillation index versus source size for propagation downlink distance at $L = 700\;{\rm{km}}$ .
Fig. 10.
Fig. 10. Scintillation index versus zenith angle for propagation downlink distance at $L = 20\;{\rm{km}}$ .
Fig. 11.
Fig. 11. Scintillation index versus zenith angle for propagation downlink distance at $L = 700\;{\rm{km}}$ .

Tables (5)

Tables Icon

Table 1. List of Samples of Displacement Parameters V x 1 and V y 1 at Different Propagation Lengths ( L ) for the Uplink for α s = 8 c m

Tables Icon

Table 2. List of Samples of Displacement Parameters V x 1 and V y 1 versus Source Size at Selected Propagation Lengths ( L ) for the Uplink

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Table 3. List of Samples of Displacement Parameters V x 1 and V y 1 versus Source Size at Selected Propagation Lengths ( L ) for the Uplink

Tables Icon

Table 4. List of Samples of Displacement Parameters V x 1 and V y 1 at Different Propagation Lengths ( L ) for Downlink for α s = 42 c m

Tables Icon

Table 5. List of Samples of Displacement Parameters V x 1 and V y 1 versus Source Size at Selected Propagation Lengths ( L ) for Downlink

Equations (11)

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u s ( s ) = u s ( s x , s y ) = = 1 2 A exp { [ k α ( s x 2 + s y 2 ) / 2 + j V x s x + j V y s y ] } ,
m 2 = 4 π Re { 0 L d η 0 κ d κ 0 2 π d θ × [ T G 1 ( L , η , κ , θ ) + T G 2 ( L , η , κ , θ ) ] Φ n ( κ ) 0 L } ,
T G 1 ( L , η , κ , θ ) = T G ( L , η , κ , θ ) T G ( L , η , κ , θ ) / D G 2 ( L ) ,
T G 2 ( L , η , κ , θ ) = T G ( L , η , κ , θ ) T G ( L , η , κ , θ ) / | D G ( L ) | 2 ,
T G ( L , η , κ , θ ) = n = 1 2 A n j k ( 1 + j α n L ) 1 exp { j [ 2 k ( 1 + j α n L ) ] 1 × [ ( V x n 2 + V y n 2 ) L 2 ( L η ) ( V x n cos θ + V y n sin θ ) κ + ( L η ) ( 1 + i α n η ) κ 2 ] } ,
D G ( L ) = n = 1 2 A n 1 ( 1 + j α n L ) × exp [ j ( V x n 2 + V y n 2 ) L 2 k ( 1 + j α n L ) ] ,
C ~ n 2 ( h ) = 5.94 × 10 53 ( w / 27 ) 2 h 10 exp ( h / 1000 ) + 2.7 × 10 16 exp ( h / 1500 ) + A exp ( h / 100 ) ,
m 2 = 1 .3028 k 2 Re { 0 L d η C ~ n 2 ( η ) × [ T G 1 ( L , η , V x 1 , V x 2 , V y 1 , V y 2 ) + T G 2 ( L , η , V x 1 , V x 2 , V y 1 , V y 2 ) ] 0 L } ,
T G 1 ( L , η , V x 1 , V x 2 , V y 1 , V y 2 ) = | D G ( L ) | 2 n 1 = 1 2 n 2 = 1 2 A n 1 A n 2 ( 1 + j α n 1 L ) ( 1 j α n 2 L ) × r = 0 ( 0.25 ) r Γ ( r 5 / 6 ) ( r ! ) 2 × [ j ( L η ) 2 k ( 1 + j α n 1 η 1 + j α n 1 L 1 j α n 2 η 1 j α n 2 L ) ] r + 5 / 6 × exp { j L 2 k [ V x n 1 2 + V y n 1 2 1 + j α n 1 L ( V x n 2 2 ) + ( V y n 2 2 ) 1 j α n 2 L ] } × { [ j ( L η ) k ( V x n 1 1 + j α n 1 L V y n 2 1 j α n 2 L ) ] 2 + [ j ( L η ) k ( V y n 1 1 + j α n 1 L V y n 2 1 j α n 2 L ) ] 2 } r ,
T G 2 ( L , η , V x 1 , V x 2 , V y 1 , V y 2 ) = D G ( L ) 2 n 1 = 1 2 n 2 = 1 2 A n 1 A n 2 ( 1 + j α n 1 L ) ( 1 + j α n 2 L ) × r = 0 ( 0.25 ) r Γ ( r 5 / 6 ) ( r ! ) 2 × [ j ( L η ) 2 k ( 1 + j α n 1 η 1 + j α n 1 L + 1 + j α n 2 η 1 + j α n 2 L ) ] r + 5 / 6 × exp [ j L 2 k ( V x n 1 2 + V y n 1 2 1 + j α n 1 L + V x n 2 2 + V y n 2 2 1 + j α n 2 L ) ] × { [ j ( L η ) k ( V x n 1 1 + j α n 1 L V x n 2 1 + j α n 2 L ) ] 2 + [ j ( L η ) k ( V y n 1 1 + j α n 1 L V y n 2 1 + j α n 2 L ) ] 2 } r .
d [ T G 1 ( V x n ) + T G 2 ( V x n ) ] d V x n = 0 , d [ T G 1 ( V y n ) + T G 2 ( V y n ) ] d V y n = 0 ,