Abstract

In this paper, we theoretically analyze the beam wander variance for the Gaussian beam propagation through weak oceanic turbulence. Particularly, we consider the effect of the eddy diffusivity ratio of salinity to temperature as well as the outer scale on the beam wander. To get to the tractable theoretical results, we first develop an approximate oceanic refractive-index spectrum with the outer scale and variable eddy diffusivity ratio. Based on this spectrum in weak turbulence, we then derive the closed-form expression for the beam wander variance. We present numerical results to show that the beam wander is either overestimated or underestimated as compared to the previous analyses which set the eddy diffusivity ratio to one. In addition, the finite outer scale of turbulence can significantly reduce the beam wander for Gaussian beams.

© 2019 Optical Society of America

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References

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  1. S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).
  2. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).
  3. R. Esposito, “Power scintillations due to the wandering of the laser beam,” Proc. IEEE 55, 1533–1534 (1967).
    [Crossref]
  4. M. Tamir, U. Halavee, and E. Azoulay, “Power fluctuations caused by laser beam wandering and shift,” Appl. Opt. 20, 734–735 (1981).
    [Crossref]
  5. C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
    [Crossref]
  6. J. H. Churnside and R. J. Lataitis, “Wander of an optical beam in the turbulent atmosphere,” Appl. Opt. 29, 926–930 (1990).
    [Crossref]
  7. J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46, 086002 (2007).
    [Crossref]
  8. D. H. Tofsted, “Outer-scale effects on beam-wander and angle-of-arrival variances,” Appl. Opt. 31, 5865–5870 (1992).
    [Crossref]
  9. L. C. Andrews, R. L. Phillips, and R. Parenti, “Beam wander effects on the scintillation index of a focused beam,” Proc. SPIE 5793, 28–38 (2005).
    [Crossref]
  10. V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).
    [Crossref]
  11. X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
    [Crossref]
  12. C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
    [Crossref]
  13. Q. Wang, Y. Zhu, and Y. Zhang, “Precision wander model of beam wave in the weak to strong turbulence of atmosphere,” Opt. Lett. 42, 3213–3216 (2017).
    [Crossref]
  14. G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
    [Crossref]
  15. 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, 6385–6391 (2008).
    [Crossref]
  16. W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
    [Crossref]
  17. L. Cui and L. Cao, “Theoretical expressions of long term beam spread and beam wander for Gaussian wave propagating through generalized atmospheric turbulence,” Optik 126, 4704–4707 (2015).
    [Crossref]
  18. Y. Huang, A. Zeng, Z. Gao, and B. Zhang, “Beam wander of partially coherent array beams through non-Kolmogorov turbulence,” Opt. Lett. 40, 1619–1622 (2015).
    [Crossref]
  19. S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, “Beam wander of electromagnetic Gaussian-Schell model beams propagating in atmospheric turbulence,” Appl. Opt. 51, 7581–7585 (2012).
    [Crossref]
  20. 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]
  21. B. E. Stribling and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [Crossref]
  22. Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
    [Crossref]
  23. L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
    [Crossref]
  24. V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the seawater refraction index,” Fluid Mech. Res. 27, 82–98(2000).
    [Crossref]
  25. J. Yao, Y. Zhang, R. Wang, Y. Wang, and X. Wang, “Practical approximation of the oceanic refractive index spectrum,” Opt. Express 25, 23283–23292 (2017).
    [Crossref]
  26. G. Einsele, Sedimentary Basins: Evolution, Facies, and Sediment Budget (Springer, 2000).
  27. M. Elamassie, M. Uysal, Y. Baykal, M. Abdallah, and K. Qaraqe, “Effect of eddy diffusivity ratio on underwater optical scintillation index,” J. Opt. Soc. Am. A 34, 1969–1973 (2017).
    [Crossref]
  28. K. N. Fedorov, The Thermohaline Finestructure of the Ocean (Pergamon, 1978), Vol. 77, pp. 165–167.
  29. P. R. Jackson and C. R. Rehmann, “Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow,” J. Phys. Oceanogr. 33, 1592–1603 (2003).
    [Crossref]
  30. E. Kunze, “A review of oceanic salt-fingering theory,” Prog. Oceanogr. 56, 399–417 (2003).
    [Crossref]
  31. L. Lu, P. F. Zhang, C. Y. Fan, and C. H. Qiao, “Influence of oceanic turbulence on propagation of a radial Gaussian beam array,” Opt. Express 23, 2827–2836 (2015).
    [Crossref]

2017 (3)

2016 (2)

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

2015 (4)

L. Lu, P. F. Zhang, C. Y. Fan, and C. H. Qiao, “Influence of oceanic turbulence on propagation of a radial Gaussian beam array,” Opt. Express 23, 2827–2836 (2015).
[Crossref]

G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
[Crossref]

L. Cui and L. Cao, “Theoretical expressions of long term beam spread and beam wander for Gaussian wave propagating through generalized atmospheric turbulence,” Optik 126, 4704–4707 (2015).
[Crossref]

Y. Huang, A. Zeng, Z. Gao, and B. Zhang, “Beam wander of partially coherent array beams through non-Kolmogorov turbulence,” Opt. Lett. 40, 1619–1622 (2015).
[Crossref]

2014 (2)

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[Crossref]

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

2013 (1)

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).
[Crossref]

2012 (2)

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, “Beam wander of electromagnetic Gaussian-Schell model beams propagating in atmospheric turbulence,” Appl. Opt. 51, 7581–7585 (2012).
[Crossref]

2009 (1)

C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[Crossref]

2008 (1)

2007 (1)

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46, 086002 (2007).
[Crossref]

2005 (1)

L. C. Andrews, R. L. Phillips, and R. Parenti, “Beam wander effects on the scintillation index of a focused beam,” Proc. SPIE 5793, 28–38 (2005).
[Crossref]

2003 (2)

P. R. Jackson and C. R. Rehmann, “Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow,” J. Phys. Oceanogr. 33, 1592–1603 (2003).
[Crossref]

E. Kunze, “A review of oceanic salt-fingering theory,” Prog. Oceanogr. 56, 399–417 (2003).
[Crossref]

2000 (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the seawater refraction index,” Fluid Mech. Res. 27, 82–98(2000).
[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 and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

1992 (1)

1990 (1)

1981 (1)

1967 (1)

R. Esposito, “Power scintillations due to the wandering of the laser beam,” Proc. IEEE 55, 1533–1534 (1967).
[Crossref]

Abdallah, M.

Aksenov, V. P.

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).
[Crossref]

Andrews, L. C.

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46, 086002 (2007).
[Crossref]

L. C. Andrews, R. L. Phillips, and R. Parenti, “Beam wander effects on the scintillation index of a focused beam,” Proc. SPIE 5793, 28–38 (2005).
[Crossref]

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

Azoulay, E.

Baykal, Y.

M. Elamassie, M. Uysal, Y. Baykal, M. Abdallah, and K. Qaraqe, “Effect of eddy diffusivity ratio on underwater optical scintillation index,” J. Opt. Soc. Am. A 34, 1969–1973 (2017).
[Crossref]

C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[Crossref]

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]

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]

Cai, Y.

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[Crossref]

C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[Crossref]

Cao, L.

L. Cui and L. Cao, “Theoretical expressions of long term beam spread and beam wander for Gaussian wave propagating through generalized atmospheric turbulence,” Optik 126, 4704–4707 (2015).
[Crossref]

Chen, Z.

Churnside, J. H.

Cill, C. Z.

C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[Crossref]

Cui, L.

L. Cui and L. Cao, “Theoretical expressions of long term beam spread and beam wander for Gaussian wave propagating through generalized atmospheric turbulence,” Optik 126, 4704–4707 (2015).
[Crossref]

Cui, Q.

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Dai, W.

G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
[Crossref]

Du, W.

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Einsele, G.

G. Einsele, Sedimentary Basins: Evolution, Facies, and Sediment Budget (Springer, 2000).

Elamassie, M.

Esposito, R.

R. Esposito, “Power scintillations due to the wandering of the laser beam,” Proc. IEEE 55, 1533–1534 (1967).
[Crossref]

Eyyuboglu, H. T.

C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[Crossref]

Fan, C.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

Fan, C. Y.

Fedorov, K. N.

K. N. Fedorov, The Thermohaline Finestructure of the Ocean (Pergamon, 1978), Vol. 77, pp. 165–167.

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]

Gao, Z.

Golbraikh, E.

Gu, W.

Guo, H.

G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
[Crossref]

S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, “Beam wander of electromagnetic Gaussian-Schell model beams propagating in atmospheric turbulence,” Appl. Opt. 51, 7581–7585 (2012).
[Crossref]

Halavee, U.

Hu, Z.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Huang, Y.

Jackson, P. R.

P. R. Jackson and C. R. Rehmann, “Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow,” J. Phys. Oceanogr. 33, 1592–1603 (2003).
[Crossref]

Ji, X.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

Jia, J.

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

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]

Kolosov, V. V.

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).
[Crossref]

Kopeika, N. S.

Kunze, E.

E. Kunze, “A review of oceanic salt-fingering theory,” Prog. Oceanogr. 56, 399–417 (2003).
[Crossref]

Lataitis, R. J.

Li, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Liu, D.

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Liu, X.

Lu, J.

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Lu, L.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

L. Lu, P. F. Zhang, C. Y. Fan, and C. H. Qiao, “Influence of oceanic turbulence on propagation of a radial Gaussian beam array,” Opt. Express 23, 2827–2836 (2015).
[Crossref]

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the seawater refraction index,” Fluid Mech. Res. 27, 82–98(2000).
[Crossref]

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the seawater refraction index,” Fluid Mech. Res. 27, 82–98(2000).
[Crossref]

Parenti, R.

L. C. Andrews, R. L. Phillips, and R. Parenti, “Beam wander effects on the scintillation index of a focused beam,” Proc. SPIE 5793, 28–38 (2005).
[Crossref]

Phillips, R. L.

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46, 086002 (2007).
[Crossref]

L. C. Andrews, R. L. Phillips, and R. Parenti, “Beam wander effects on the scintillation index of a focused beam,” Proc. SPIE 5793, 28–38 (2005).
[Crossref]

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

Pogutsa, C. E.

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).
[Crossref]

Qaraqe, K.

Qiao, C.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

Qiao, C. H.

Recolons, J.

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46, 086002 (2007).
[Crossref]

Rehmann, C. R.

P. R. Jackson and C. R. Rehmann, “Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow,” J. Phys. Oceanogr. 33, 1592–1603 (2003).
[Crossref]

Roggemann, M. C.

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

Si, C.

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

Stribling, B. E.

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

Tamir, M.

Tang, H.

G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
[Crossref]

Thorpe, S. A.

S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).

Tofsted, D. H.

Uysal, M.

Wang, F.

Wang, J.

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

Wang, Q.

Wang, R.

Wang, T.

Wang, X.

Wang, Y.

J. Yao, Y. Zhang, R. Wang, Y. Wang, and X. Wang, “Practical approximation of the oceanic refractive index spectrum,” Opt. Express 25, 23283–23292 (2017).
[Crossref]

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

Wang, Z.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

Wei, C.

Wu, G.

G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
[Crossref]

S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, “Beam wander of electromagnetic Gaussian-Schell model beams propagating in atmospheric turbulence,” Appl. Opt. 51, 7581–7585 (2012).
[Crossref]

Wu, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Yang, J.

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Yao, J.

Yao, Z.

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Yu, S.

Zeng, A.

Zhang, B.

Zhang, J.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

Zhang, P.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

Zhang, P. F.

Zhang, Y.

J. Yao, Y. Zhang, R. Wang, Y. Wang, and X. Wang, “Practical approximation of the oceanic refractive index spectrum,” Opt. Express 25, 23283–23292 (2017).
[Crossref]

Q. Wang, Y. Zhu, and Y. Zhang, “Precision wander model of beam wave in the weak to strong turbulence of atmosphere,” Opt. Lett. 42, 3213–3216 (2017).
[Crossref]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

Zhu, Y.

Zilberman, A.

Appl. Opt. (5)

Appl. Phys. B (1)

C. Z. Cill, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[Crossref]

Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulence fluctuations of the seawater refraction index,” Fluid Mech. Res. 27, 82–98(2000).
[Crossref]

J. Opt. (1)

V. P. Aksenov, V. V. Kolosov, and C. E. Pogutsa, “The influence of the vortex phase on the random wandering of a Laguerre-Gaussian beam propagating in a turbulent atmosphere: a numerical experiment,” J. Opt. 15, 044007 (2013).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. Oceanogr. (1)

P. R. Jackson and C. R. Rehmann, “Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow,” J. Phys. Oceanogr. 33, 1592–1603 (2003).
[Crossref]

J. Russ. Laser Res. (1)

W. Du, J. Yang, Z. Yao, J. Lu, D. Liu, and Q. Cui, “Wander of a Gaussian-beam wave propagated through a non-Kolmogorov turbulent atmosphere,” J. Russ. Laser Res. 35, 416–423 (2014).
[Crossref]

Opt. Commun. (2)

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

G. Wu, W. Dai, H. Tang, and H. Guo, “Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence,” Opt. Commun. 336, 55–58 (2015).
[Crossref]

Opt. Eng. (1)

J. Recolons, L. C. Andrews, and R. L. Phillips, “Analysis of beam wander effects for a horizontal-path propagating Gaussian-beam wave: focused beam case,” Opt. Eng. 46, 086002 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optik (3)

C. Si, Y. Zhang, Y. Wang, J. Wang, and J. Jia, “Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors,” Optik 123, 1–5 (2012).
[Crossref]

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, C. Fan, and C. Qiao, “Beam wander of laser beam propagating through oceanic turbulence,” Optik 127, 5341–5346 (2016).
[Crossref]

L. Cui and L. Cao, “Theoretical expressions of long term beam spread and beam wander for Gaussian wave propagating through generalized atmospheric turbulence,” Optik 126, 4704–4707 (2015).
[Crossref]

Proc. IEEE (1)

R. Esposito, “Power scintillations due to the wandering of the laser beam,” Proc. IEEE 55, 1533–1534 (1967).
[Crossref]

Proc. SPIE (3)

L. C. Andrews, R. L. Phillips, and R. Parenti, “Beam wander effects on the scintillation index of a focused beam,” Proc. SPIE 5793, 28–38 (2005).
[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]

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

Prog. Oceanogr. (1)

E. Kunze, “A review of oceanic salt-fingering theory,” Prog. Oceanogr. 56, 399–417 (2003).
[Crossref]

Other (4)

G. Einsele, Sedimentary Basins: Evolution, Facies, and Sediment Budget (Springer, 2000).

K. N. Fedorov, The Thermohaline Finestructure of the Ocean (Pergamon, 1978), Vol. 77, pp. 165–167.

S. A. Thorpe, The Turbulent Ocean (Cambridge University, 2005).

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

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Figures (4)

Fig. 1.
Fig. 1. Beam wander variance of collimated and focused beams versus L 0 with various ω and d r . (a) Collimated beam and (b) focused beam.
Fig. 2.
Fig. 2. Beam wander variance versus ω with various d r and L 0 . (a) Collimated beam and (b) focused beam.
Fig. 3.
Fig. 3. Dimensionless quantity B W for collimated beam and focused beam versus (a)  χ T , (b)  ε , and (c)  ω .
Fig. 4.
Fig. 4. Ratio of beam wander variance with a finite outer scale to that with an infinite outer scale.

Equations (21)

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ϕ n ( κ ) = ( 4 π ) 1 C 0 ε 1 / 3 κ 11 / 3 [ 1 + C 1 ( κ η ) 2 / 3 ] × [ α 2 χ T exp ( C 0 C 1 2 P r T 1 δ ) + β 2 χ S exp ( C 0 C 1 2 P r S 1 δ ) 2 α β χ T S exp ( C 0 C 1 2 P r T S 1 δ ) ] ,
χ S = d r ( α ω β ) 2 χ T ,
χ T S = ( 1 + d r ) α 2 β ω χ T ,
d r = | ω | R F ,
R F { | ω | | ω | ( | ω | 1 ) , | ω | 1 1 1.85 0.85 | ω | 1 , 0.5 | ω | 1 1 0.15 , | ω | < 0.5 .
ϕ n ( κ ) = α 2 ϕ T ( κ ) + β 2 ϕ S ( κ ) 2 α β ϕ T S ( κ ) ,
ϕ i ( κ ) = C i 2 ( κ 11 / 3 + C 1 i η 2 / 3 κ 3 ) exp [ ( κ η ) 2 / N i 2 ] , i = T , S , T S ,
C i 2 = ( 4 π ) 1 C 0 ε 1 / 3 χ i ,
N i = 3 Q 3 / 2 ( W i 1 3 + 1 9 W i ) 3 / 2 ,
W i = { [ ( 1 27 P r i Q 2 6 C 0 ) 2 1 729 ] 1 / 2 ( 1 27 P r i Q 2 6 C 0 ) } 1 / 3 ,
ϕ n ( κ ) = ( 4 π ) 1 C 0 ε 1 / 3 α 2 χ T ( κ 2 + κ 0 2 ) 11 / 6 × { [ 1 + C 1 T ( κ η ) 2 / 3 ] exp [ ( κ η ) 2 N T 2 ] + ω 2 d r [ 1 + C 1 S ( κ η ) 2 / 3 ] exp [ ( κ η ) 2 N S 2 ] ω 1 ( 1 + d r ) [ 1 + C 1 T S ( κ η ) 2 / 3 ] exp [ ( κ η ) 2 N T S 2 ] } .
r c 2 = W 2 T L S = 4 π 2 k 2 W 2 L 0 1 0 κ ϕ n ( κ ) H L S ( κ , ξ ) [ 1 exp ( Λ L κ 2 ξ 2 / k ) ] d ξ d κ ,
H L S ( κ , ξ ) = exp { κ 2 W 0 2 [ ( Θ 0 + Θ ¯ 0 ξ ) 2 + Λ 0 2 ( 1 ξ ) 2 ] } ,
1 exp ( Λ L κ 2 ξ 2 / k ) Λ L κ 2 ξ 2 / k , L κ 2 / k 1 .
r c 2 = π k W 2 L 2 Λ α 2 C 0 ε 1 / 3 χ T × 0 1 ξ 2 [ I T + ω 2 d r I S ω 1 ( 1 + d r ) I T S ] d ξ ,
I i = 0 κ 3 [ 1 + C 1 i ( κ η ) 2 / 3 ] ( κ 2 + κ 0 2 ) 11 / 6 × exp { κ 2 [ η 2 N i 2 + W 0 2 ( Θ 0 + Θ ¯ 0 ξ ) 2 ] } d κ , i = T , S , T S .
I i = 3.6 κ 0 1 / 3 2.243 C 1 i η 2 / 3 κ 0 + 0.886 C 1 i η 2 / 3 + 2.783 [ η 2 / N i 2 + W 0 2 ( Θ 0 + Θ ¯ 0 ξ ) 2 ] 1 / 3 [ η 2 / N i 2 + W 0 2 ( Θ 0 + Θ ¯ 0 ξ ) 2 ] 1 / 2 , i = T , S , T S .
r c 2 = 2 3 π L 3 α 2 C 0 ε 1 / 3 χ T × [ 0.886 C 1 T η 2 / 3 + 2.783 ( η 2 / N T 2 + W 0 2 ) 1 / 3 ( η 2 / N T 2 + W 0 2 ) 1 / 2 + ω 2 d r 0.886 C 1 S η 2 / 3 + 2.783 ( η 2 / N S 2 + W 0 2 ) 1 / 3 ( η 2 / N S 2 + W 0 2 ) 1 / 2 ω 1 ( 1 + d r ) 0.886 C 1 T S η 2 / 3 + 2.783 ( η 2 / N T S 2 + W 0 2 ) 1 / 3 ( η 2 / N T S 2 + W 0 2 ) 1 / 2 ] .
r c 2 = 2 π L 3 α 2 C 0 ε 1 / 3 χ T 0 1 ξ 2 × [ 0.886 C 1 T η 2 / 3 + 2.783 ( η 2 / N T 2 + W 0 2 ξ 2 ) 1 / 3 ( η 2 / N T 2 + W 0 2 ξ 2 ) 1 / 2 + ω 2 d r 0.886 C 1 S η 2 / 3 + 2.783 ( η 2 / N S 2 + W 0 2 ξ 2 ) 1 / 3 ( η 2 / N S 2 + W 0 2 ξ 2 ) 1 / 2 ω 1 ( 1 + d r ) 0.886 C 1 T S η 2 / 3 + 2.783 ( η 2 / N T S 2 + W 0 2 ξ 2 ) 1 / 3 ( η 2 / N T S 2 + W 0 2 ξ 2 ) 1 / 2 ] d ξ .
r c 2 = 2 3 π L 3 α 2 C 0 ε 1 / 3 χ T × { [ 3.6 κ 0 1 / 3 2.243 C 1 T η 2 / 3 κ 0 + 0.886 C 1 T η 2 / 3 + 2.783 ( η 2 N T 2 + W 0 2 ) 1 / 3 ( η 2 N T 2 + W 0 2 ) 1 / 2 ] + d r ω 2 [ 3.6 κ 0 1 / 3 2.243 C 1 S η 2 / 3 κ 0 + 0.886 C 1 S η 2 / 3 + 2.783 ( η 2 N S 2 + W 0 2 ) 1 / 3 ( η 2 N S 2 + W 0 2 ) 1 / 2 ] 1 + d r ω [ 3.6 κ 0 1 / 3 2.243 C 1 T S η 2 / 3 κ 0 + 0.886 C 1 T S η 2 / 3 + 2.783 ( η 2 N T S 2 + W 0 2 ) 1 / 3 ( η 2 N T S 2 + W 0 2 ) 1 / 2 ] } .
r c 2 = 2 π L 3 α 2 C 0 ε 1 / 3 χ T 0 1 ξ 2 × { [ 3.6 κ 0 1 / 3 2.243 C 1 T η 2 / 3 κ 0 + 0.886 C 1 T η 2 / 3 + 2.783 ( η 2 N T 2 + W 0 2 ξ 2 ) 1 / 3 ( η 2 N T 2 + W 0 2 ξ 2 ) 1 / 2 ] + d r ω 2 [ 3.6 κ 0 1 / 3 2.243 C 1 S η 2 / 3 κ 0 + 0.886 C 1 S η 2 / 3 + 2.783 ( η 2 N S 2 + W 0 2 ξ 2 ) 1 / 3 ( η 2 N S 2 + W 0 2 ξ 2 ) 1 / 2 ] 1 + d r ω [ 3.6 κ 0 1 / 3 2.243 C 1 T S η 2 / 3 κ 0 + 0.886 C 1 T S η 2 / 3 + 2.783 ( η 2 N T S 2 + W 0 2 ξ 2 ) 1 / 3 ( η 2 N T S 2 + W 0 2 ξ 2 ) 1 / 2 ] } d ξ .

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