Abstract

The thermal blooming effect of laser beams propagating through seawater is studied in detail by using the numerical simulation method. It is found that an increase of the salinity in the seawater causes the more severe thermal blooming. As compared with the wavelength, the absorption coefficient is the main factor that dominates the thermal blooming because the absorption coefficient is very high in the seawater. In the seawater the thermal blooming becomes more severe for the wavelength corresponding to the higher absorption coefficient. Furthermore, both the behavior of the thermal blooming effect and the main factor dominating the thermal blooming effect in the shallow sea region are different from those in the deep sea region. In the shallow sea region, the dependence of the thermal blooming on the depth is not monotonic as the time increases. However, in the deep sea region, the thermal blooming effect becomes more severe monotonously as the depth increases. The physical explanations for the main results obtained in this paper are presented.

© 2017 Optical Society of America

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References

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2016 (1)

H. Pu and X. Ji, “Oceanic turbulence effects on long-exposure and short-exposure imaging,” J. Opt. 18(10), 105704 (2016).
[Crossref]

2014 (2)

2013 (5)

2012 (3)

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22(2), 260–266 (2012).
[Crossref]

W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt. 51(14), 2678–2686 (2012).
[Crossref] [PubMed]

2011 (1)

W. Liu, T. Liao, and Q. Gao, “Numerical simulation of thermal blooming effect of laser propagation in atmosphere,” Proc. SPIE 8192, 81924 (2011).
[Crossref]

2009 (4)

2008 (2)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep-Sea Res. 55(1), 50–72 (2008).
[Crossref]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).
[Crossref]

2006 (1)

W. Lu, L. Liu, and J. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

2003 (1)

R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
[Crossref]

1999 (2)

D. Kovsh, D. Hagan, and E. Van Stryland, “Numerical modeling of thermal refraction inliquids in the transient regime,” Opt. Express 4(8), 315–327 (1999).
[Crossref] [PubMed]

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE 3706, 361–367 (1999).
[Crossref]

1995 (1)

1993 (1)

W. S. Pegau and J. R. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[Crossref]

1992 (2)

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24(9), S1027–S1049 (1992).
[Crossref]

1990 (1)

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE 1221, 2–25 (1990).
[Crossref]

1983 (1)

N. P. Fofonoff and R. C. Millard, “Algorithms for computation of fundamental properties of seawater,” Paris: UNESCO Tech. Pap. Mar. Sci. 44, 31–37 (1983).

1981 (1)

1980 (2)

A. Poisson, C. Brunet, and J. C. Brun-Cottan, “Density of standard seawater solutions at atmospheric pressure,” Deep-Sea Res. 27(12), 1013–1028 (1980).
[Crossref]

E. Wild and M. Maier, “Thermal blooming in liquid N2 during high repetition rate stimulated Raman Scattering,” J. Appl. Phys. 51(6), 3078–3080 (1980).
[Crossref]

1977 (2)

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE 65(12), 1679–1714 (1977).
[Crossref]

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16(2), 129–139 (1977).
[Crossref]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

1972 (1)

1971 (1)

F. G. Gebhardt and D. C. Smith, “Self-Induced Thermal Distortion in the Near Field for a Laser Beam in a Moving Medium,” IEEE J. Quantum Electron. 7(2), 63–73 (1971).
[Crossref]

1970 (1)

A. Bradshaw and K. E. Schleicher, “Direct measurement of thermal expansion of sea water under pressure,” Deep-Sea Res. 17(4), 691–698 (1970).

1963 (1)

S. A. Sullivan, “Experimental study of the absorption in distilled water, artificial sea water, and heavy water in the visible region of the spectrum,” JOSA 53(8), 962–968 (1963).
[Crossref]

1939 (1)

G. L. Clarke and H. R. James, “Laboratory analysis of the selective absorption of light by sea water,” JOSA 29(2), 43–53 (1939).
[Crossref]

Arnon, S.

Ata, Y.

Baker, K. S.

Barchers, J. D.

Baykal, Y.

Bradford, L. W.

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).
[Crossref]

Bradshaw, A.

A. Bradshaw and K. E. Schleicher, “Direct measurement of thermal expansion of sea water under pressure,” Deep-Sea Res. 17(4), 691–698 (1970).

Brun-Cottan, J. C.

A. Poisson, C. Brunet, and J. C. Brun-Cottan, “Density of standard seawater solutions at atmospheric pressure,” Deep-Sea Res. 27(12), 1013–1028 (1980).
[Crossref]

Brunet, C.

A. Poisson, C. Brunet, and J. C. Brun-Cottan, “Density of standard seawater solutions at atmospheric pressure,” Deep-Sea Res. 27(12), 1013–1028 (1980).
[Crossref]

Christou, J. C.

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).
[Crossref]

Clarke, G. L.

G. L. Clarke and H. R. James, “Laboratory analysis of the selective absorption of light by sea water,” JOSA 29(2), 43–53 (1939).
[Crossref]

Eyyuboglu, H. T.

Farwell, N.

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22(2), 260–266 (2012).
[Crossref]

Feistel, R.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep-Sea Res. 55(1), 50–72 (2008).
[Crossref]

R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
[Crossref]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Fiorino, S. T.

Fischer, R.

P. Sprangle, A. Ting, J. Penano, R. Fischer, and B. Hafizi, “Incoherent combining and atmosphere propagation of high-power fiber lasers for directed-energy applications,” IEEE J. Quantum Electron. 45(2), 138–148 (2009).
[Crossref]

Flatley, J. P.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Fofonoff, N. P.

N. P. Fofonoff and R. C. Millard, “Algorithms for computation of fundamental properties of seawater,” Paris: UNESCO Tech. Pap. Mar. Sci. 44, 31–37 (1983).

Fortes, B. V.

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE 3706, 361–367 (1999).
[Crossref]

Freeman, D. E.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Fry, E. S.

Gao, Q.

W. Liu, T. Liao, and Q. Gao, “Numerical simulation of thermal blooming effect of laser propagation in atmosphere,” Proc. SPIE 8192, 81924 (2011).
[Crossref]

Gebhardt, F. G.

F. G. Gebhardt, “Twenty-five years of thermal blooming: an overview,” Proc. SPIE 1221, 2–25 (1990).
[Crossref]

F. G. Gebhardt and D. C. Smith, “Self-Induced Thermal Distortion in the Near Field for a Laser Beam in a Moving Medium,” IEEE J. Quantum Electron. 7(2), 63–73 (1971).
[Crossref]

Gladysz, S.

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).
[Crossref]

Goode, W.

Hafizi, B.

P. Sprangle, A. Ting, J. Penano, R. Fischer, and B. Hafizi, “Incoherent combining and atmosphere propagation of high-power fiber lasers for directed-energy applications,” IEEE J. Quantum Electron. 45(2), 138–148 (2009).
[Crossref]

Hagan, D.

Hayes, J. N.

Hou, W.

James, H. R.

G. L. Clarke and H. R. James, “Laboratory analysis of the selective absorption of light by sea water,” JOSA 29(2), 43–53 (1939).
[Crossref]

Jarosz, E.

Ji, G.

Ji, X.

Jia, X.

Kedar, D.

Keefer, K. J.

Korotkova, O.

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
[Crossref]

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22(2), 260–266 (2012).
[Crossref]

Kovsh, D.

Landry, M. A.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Liao, T.

W. Liu, T. Liao, and Q. Gao, “Numerical simulation of thermal blooming effect of laser propagation in atmosphere,” Proc. SPIE 8192, 81924 (2011).
[Crossref]

Lindstrom, C. E.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Liu, B. Q.

Y. H. Yan, B. Q. Liu, B. Zhou, and D. S. Wu, “Studies of energy Strehl ratio of a collimated Gaussian beam in turbulent atmosphere,” Proc. SPIE 8906, 89062H1 (2013).
[Crossref]

Liu, L.

W. Lu, L. Liu, and J. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

Liu, W.

W. Liu, T. Liao, and Q. Gao, “Numerical simulation of thermal blooming effect of laser propagation in atmosphere,” Proc. SPIE 8192, 81924 (2011).
[Crossref]

Longacre, J. R.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Lu, L.

Lu, W.

W. Lu, L. Liu, and J. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

Lukin, V. P.

B. V. Fortes and V. P. Lukin, “Estimation of turbulent and thermal blooming degradation and required characterization of adaptive system,” Proc. SPIE 3706, 361–367 (1999).
[Crossref]

Maier, M.

E. Wild and M. Maier, “Thermal blooming in liquid N2 during high repetition rate stimulated Raman Scattering,” J. Appl. Phys. 51(6), 3078–3080 (1980).
[Crossref]

McDougall, T. J.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep-Sea Res. 55(1), 50–72 (2008).
[Crossref]

McNeil, G. T.

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16(2), 129–139 (1977).
[Crossref]

Millard, R. C.

N. P. Fofonoff and R. C. Millard, “Algorithms for computation of fundamental properties of seawater,” Paris: UNESCO Tech. Pap. Mar. Sci. 44, 31–37 (1983).

Millero, F. J.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep-Sea Res. 55(1), 50–72 (2008).
[Crossref]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Pegau, W. S.

W. S. Pegau and J. R. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[Crossref]

Penano, J.

P. Sprangle, A. Ting, J. Penano, R. Fischer, and B. Hafizi, “Incoherent combining and atmosphere propagation of high-power fiber lasers for directed-energy applications,” IEEE J. Quantum Electron. 45(2), 138–148 (2009).
[Crossref]

Poisson, A.

A. Poisson, C. Brunet, and J. C. Brun-Cottan, “Density of standard seawater solutions at atmospheric pressure,” Deep-Sea Res. 27(12), 1013–1028 (1980).
[Crossref]

Pu, H.

H. Pu and X. Ji, “Oceanic turbulence effects on long-exposure and short-exposure imaging,” J. Opt. 18(10), 105704 (2016).
[Crossref]

Quan, X.

Roberts, L. C.

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).
[Crossref]

Schleicher, K. E.

A. Bradshaw and K. E. Schleicher, “Direct measurement of thermal expansion of sea water under pressure,” Deep-Sea Res. 17(4), 691–698 (1970).

Schwartz, J. A.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Shchepakina, E.

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22(2), 260–266 (2012).
[Crossref]

Smith, D. C.

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE 65(12), 1679–1714 (1977).
[Crossref]

F. G. Gebhardt and D. C. Smith, “Self-Induced Thermal Distortion in the Near Field for a Laser Beam in a Moving Medium,” IEEE J. Quantum Electron. 7(2), 63–73 (1971).
[Crossref]

Smith, R. C.

Snow, J. B.

J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
[Crossref]

Sprangle, P.

P. Sprangle, A. Ting, J. Penano, R. Fischer, and B. Hafizi, “Incoherent combining and atmosphere propagation of high-power fiber lasers for directed-energy applications,” IEEE J. Quantum Electron. 45(2), 138–148 (2009).
[Crossref]

Sullivan, S. A.

S. A. Sullivan, “Experimental study of the absorption in distilled water, artificial sea water, and heavy water in the visible region of the spectrum,” JOSA 53(8), 962–968 (1963).
[Crossref]

Sun, J.

W. Lu, L. Liu, and J. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
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Tang, M.

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111(4), 665–670 (2013).
[Crossref]

Ting, A.

P. Sprangle, A. Ting, J. Penano, R. Fischer, and B. Hafizi, “Incoherent combining and atmosphere propagation of high-power fiber lasers for directed-energy applications,” IEEE J. Quantum Electron. 45(2), 138–148 (2009).
[Crossref]

Van Stryland, E.

Van Zandt, N. R.

Weber, H.

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24(9), S1027–S1049 (1992).
[Crossref]

Weidemann, A.

Wild, E.

E. Wild and M. Maier, “Thermal blooming in liquid N2 during high repetition rate stimulated Raman Scattering,” J. Appl. Phys. 51(6), 3078–3080 (1980).
[Crossref]

Woods, S.

Wright, D. G.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep-Sea Res. 55(1), 50–72 (2008).
[Crossref]

Wu, D. S.

Y. H. Yan, B. Q. Liu, B. Zhou, and D. S. Wu, “Studies of energy Strehl ratio of a collimated Gaussian beam in turbulent atmosphere,” Proc. SPIE 8906, 89062H1 (2013).
[Crossref]

Yan, Y. H.

Y. H. Yan, B. Q. Liu, B. Zhou, and D. S. Wu, “Studies of energy Strehl ratio of a collimated Gaussian beam in turbulent atmosphere,” Proc. SPIE 8906, 89062H1 (2013).
[Crossref]

Zaneveld, J. R.

W. S. Pegau and J. R. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
[Crossref]

Zhao, D.

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111(4), 665–670 (2013).
[Crossref]

Zhou, B.

Y. H. Yan, B. Q. Liu, B. Zhou, and D. S. Wu, “Studies of energy Strehl ratio of a collimated Gaussian beam in turbulent atmosphere,” Proc. SPIE 8906, 89062H1 (2013).
[Crossref]

Appl. Opt. (4)

Appl. Phys. (Berl.) (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-Dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Appl. Phys. B (1)

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111(4), 665–670 (2013).
[Crossref]

Deep-Sea Res. (3)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep-Sea Res. 55(1), 50–72 (2008).
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[Crossref]

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F. G. Gebhardt and D. C. Smith, “Self-Induced Thermal Distortion in the Near Field for a Laser Beam in a Moving Medium,” IEEE J. Quantum Electron. 7(2), 63–73 (1971).
[Crossref]

P. Sprangle, A. Ting, J. Penano, R. Fischer, and B. Hafizi, “Incoherent combining and atmosphere propagation of high-power fiber lasers for directed-energy applications,” IEEE J. Quantum Electron. 45(2), 138–148 (2009).
[Crossref]

J. Appl. Phys. (1)

E. Wild and M. Maier, “Thermal blooming in liquid N2 during high repetition rate stimulated Raman Scattering,” J. Appl. Phys. 51(6), 3078–3080 (1980).
[Crossref]

J. Opt. (1)

H. Pu and X. Ji, “Oceanic turbulence effects on long-exposure and short-exposure imaging,” J. Opt. 18(10), 105704 (2016).
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J. Opt. A, Pure Appl. Opt. (1)

W. Lu, L. Liu, and J. Sun, “Influence of temperature and salinity fluctuations on propagation behavior of partially coherent beams in oceanic turbulence,” J. Opt. A, Pure Appl. Opt. 8(12), 1052–1058 (2006).
[Crossref]

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S. A. Sullivan, “Experimental study of the absorption in distilled water, artificial sea water, and heavy water in the visible region of the spectrum,” JOSA 53(8), 962–968 (1963).
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W. S. Pegau and J. R. Zaneveld, “Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum,” Limnol. Oceanogr. 38(1), 188–192 (1993).
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N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285(6), 872–875 (2012).
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H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24(9), S1027–S1049 (1992).
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D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE 65(12), 1679–1714 (1977).
[Crossref]

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J. B. Snow, J. P. Flatley, D. E. Freeman, M. A. Landry, C. E. Lindstrom, J. R. Longacre, and J. A. Schwartz, “Underwater propagation of high-data rate laser communications pulses,” Proc. SPIE 1750, 419–427 (1992).
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Y. H. Yan, B. Q. Liu, B. Zhou, and D. S. Wu, “Studies of energy Strehl ratio of a collimated Gaussian beam in turbulent atmosphere,” Proc. SPIE 8906, 89062H1 (2013).
[Crossref]

W. Liu, T. Liao, and Q. Gao, “Numerical simulation of thermal blooming effect of laser propagation in atmosphere,” Proc. SPIE 8192, 81924 (2011).
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R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
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S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).
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O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22(2), 260–266 (2012).
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Figures (16)

Fig. 1
Fig. 1 3D intensity distribution and contour lines for different values of the wavelength λ. t = 1 s, P = 3kW, z = 100m.
Fig. 2
Fig. 2 (a) SR and (b) SRE versus time t for different values of the wavelength λ. P = 3kW, z = 100m.
Fig. 3
Fig. 3 η versus (a) the propagation distance z and (b) time t for different values of the wavelength λ. P = 3kW.
Fig. 4
Fig. 4 x ¯ versus time t for different values of the wavelength λ. P = 3kW, z = 100m.
Fig. 5
Fig. 5 (a) SR and (b) SRE versus time t for different values of the salinity S. P = 200W, z = 1km.
Fig. 6
Fig. 6 (a) η and (b) x ¯ versus time t for different values of the salinity S. P = 200W, z = 1km.
Fig. 7
Fig. 7 Distortion parameter N versus the salinity S. P = 200W, z = 1km.
Fig. 8
Fig. 8 3D intensity distribution and contour lines for different values of the depth h within shallow sea region. t = 1 s, P = 200W, z = 1km.
Fig. 9
Fig. 9 (a) SR and (b) SRE versus time t for different values of the depth h within shallow sea region. P = 200W, z = 1km.
Fig. 10
Fig. 10 η versus time t for different values of the depth h within shallow sea region. P = 200W, z = 1km.
Fig. 11
Fig. 11 (a) wx, (b) wy and (c) wx / wy versus time t for different values of the depth h within shallow sea region. P = 200W, z = 1km.
Fig. 12
Fig. 12 3D intensity distribution and contour lines for different values of the temperature T. t = 1 s, P = 200W, z = 1km, h = 0.
Fig. 13
Fig. 13 Distortion parameter N versus the depth h within shallow sea region. P = 200W, z = 1km.
Fig. 14
Fig. 14 (a) SRE, (b) η and (c) x ¯ versus time t for different values of the depth h within deep sea region. P = 200W, z = 1km.
Fig. 15
Fig. 15 (a) nT, (b) C p versus the depth h within deep sea region. P = 200W, z = 1km.
Fig. 16
Fig. 16 Distortion parameter N versus the depth h within deep sea region. P = 200W, z = 1km.

Equations (12)

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

2ik E z = 2 E+ k 2 ( n 2 n 0 2 1)E,
n 2 n 0 2 1= ( n 0 2 1)( n 0 2 +2) 3 n 0 2 ρ 1 ρ 0 ,
( n 0 2 1)( n 0 2 +2) 3 n 0 2 2 n T β ,
ρ 1 t +v ρ 1 = βα C p I,
E= P π w 0 2 exp( x 2 + y 2 2 w 0 2 ),
E n+1 =exp( i 4k Δz 2 )exp(is)exp( i 4k Δz 2 ) E n ,
N=( 2 n T I 0 z n 0 ρ 0 C p v w 0 )[ 1 (1 e αz ) αz ],
S R = I max I 0max ,
S R E = x 2 + y 2 w 2 I(x,y,z)dxdy x 2 + y 2 w 2 I vacuum (x,y,z)dxdy ,
η= σ I(x,y,z)dxdy I(x,y,0)dxdy ,
j ¯ = jI(x,y,z)dxdy I(x,y,z)dxdy ,
w j 2 = 4 (j j ¯ ) 2 I(x,y,z)dxdy I(x,y,z)dxdy ,

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