Abstract

A closed set of three simultaneous partial differential equations is derived for the solution of the average irradiance and the irradiance variance of focused laser beams in turbulence. The equations are uniformly valid for arbitrary scintillation levels. Examples of solutions calculated by finite difference techniques are shown to fit typical atmospheric and laboratory data well. Analytic solutions derived for asymptotic conditions are in good agreement with the related classic perturbation results. The model also provides interesting physical insight into the phenomena of saturation and supersaturation.

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  1. J. W. Strohbehn, ed., Laser Beam Propagation in the Atmosphere, Volume 25 of Topics in Applied Physics (Springer-Verlag, New York, 1978).
  2. J. W. Strohbehn, "Line-of-sight wave propagation through the turbulent atmosphere," Proc. IEEE 56, 1301–1318 (1968).
  3. R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).
  4. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).
  5. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).
  6. R. L. Fante, "Electromagnetic beam propagation in turbulent media: an update," Proc. IEEE 68, 1424–1442 (1980).
  7. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).
  8. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).
  9. R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652–1658 (1971).
  10. L. R. Bissonnette, "Angle of arrival and irradiance statistics of laser beams in turbulence," DREV Rep. 4213/81, July 1981 Accession No. 81-03113 (Director of Scientific Information Services, Ottawa, Canada).
  11. L. R. Bissonnette, "Focused laser beams in turbulent media," DREV Rep. 4178/80, December 1980 Accession No. 81-00157 (Director of Scientific Information Services, Ottawa, Canada).
  12. L. R. Bissonnette, "Modelling of laser beam propagation in atmospheric turbulence," in Proceedings of the Second International Symposium on Gas Flow and Chemical Lasers, J. F. Wendt, ed. (Hemisphere, Washington, D.C., 1979), pp. 73–94.
  13. J. L. Lumley, "Computational modeling of turbulent flows," in Advances in Applied Mechanics (Academic, New York, 1978), Vol. 18.
  14. P. Bradshaw, ed., Turbulence, Volume 12 of Topics in Applied Physics (Springer-Verlag, New York, 1976), Chaps. 1, 5, and 6.
  15. J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1975), Chaps. 1 and 5.
  16. L. R. Bissonnette and P. L. Wizinowich, "Probability distribution of turbulent irradiance in a saturation regime," Appl. Opt. 18, 1590–1599 (1979).
  17. L. R. Bissonnette, "Atmospheric scintillation of optical and infrared waves: a laboratory simulation," Appl. Opt. 16, 2242–2251 (1977).
  18. W. P. Brown, Jr., "Second moment of a wave propagating in a random medium," J. Opt. Soc. Am. 61, 1051–1059 (1971).
  19. H. T. Yura, "Atmospheric turbulence induced beam spread," Appl. Opt. 10, 2771–2773 (1971).
  20. J. A. Dowling and P. M. Livingston, "Behavior of focused beams in atmospheric turbulence: measurements and comments on the theory," J. Opt. Soc. Am. 63, 846–858 (1973).
  21. L. R. Bissonnette, "Log-normal probability distribution in strong irradiance fluctuations: an asymptotic analysis," in AGARD Conference Proceedings No. 183 on Optical Propagation in the Atmosphere (National Technical Information Service, Springfield, Va., 1976).
  22. L. R. Bissonnette, "Propagation of adaptively corrected laser beams through a turbulent atmosphere," J. Phys. (Paris) 41, C9/415–427 (1980).
  23. L. R. Bissonnette, "Propagation model of adaptively corrected laser beams in turbulence," DREV Rep. 4200/81, October 1981 Accession No. 82-00524 (Director of Scientific Information Services, Ottawa, Canada).
  24. S. F. Clifford, G. R. Ochs, and R. S. Lawrence, "Saturation of optical scintillation by strong turbulence," J. Opt. Soc. Am. 64, 148–154 (1974).
  25. R. J. Hill and S. F. Clifford, "Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra," J. Opt. Soc. Am. 71, 675–686 (1981).
  26. R. J. Hill, "Theory of saturation of optical scintillation by strong turbulence: plane-wave variance and covariance and spherical- wave covariance," J. Opt. Soc. Am. 72, 212–222 (1982).

1982

1981

1980

L. R. Bissonnette, "Propagation of adaptively corrected laser beams through a turbulent atmosphere," J. Phys. (Paris) 41, C9/415–427 (1980).

1979

1977

1974

1973

1971

Bissonnette, L. R.

L. R. Bissonnette, "Propagation of adaptively corrected laser beams through a turbulent atmosphere," J. Phys. (Paris) 41, C9/415–427 (1980).

L. R. Bissonnette and P. L. Wizinowich, "Probability distribution of turbulent irradiance in a saturation regime," Appl. Opt. 18, 1590–1599 (1979).

L. R. Bissonnette, "Atmospheric scintillation of optical and infrared waves: a laboratory simulation," Appl. Opt. 16, 2242–2251 (1977).

L. R. Bissonnette, "Log-normal probability distribution in strong irradiance fluctuations: an asymptotic analysis," in AGARD Conference Proceedings No. 183 on Optical Propagation in the Atmosphere (National Technical Information Service, Springfield, Va., 1976).

L. R. Bissonnette, "Propagation model of adaptively corrected laser beams in turbulence," DREV Rep. 4200/81, October 1981 Accession No. 82-00524 (Director of Scientific Information Services, Ottawa, Canada).

L. R. Bissonnette, "Angle of arrival and irradiance statistics of laser beams in turbulence," DREV Rep. 4213/81, July 1981 Accession No. 81-03113 (Director of Scientific Information Services, Ottawa, Canada).

L. R. Bissonnette, "Modelling of laser beam propagation in atmospheric turbulence," in Proceedings of the Second International Symposium on Gas Flow and Chemical Lasers, J. F. Wendt, ed. (Hemisphere, Washington, D.C., 1979), pp. 73–94.

L. R. Bissonnette, "Focused laser beams in turbulent media," DREV Rep. 4178/80, December 1980 Accession No. 81-00157 (Director of Scientific Information Services, Ottawa, Canada).

Brown, Jr., W. P.

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).

Clifford, S. F.

Dowling, J. A.

Fante, R. L.

R. L. Fante, "Electromagnetic beam propagation in turbulent media: an update," Proc. IEEE 68, 1424–1442 (1980).

R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).

Hill, R. J.

Hinze, J. O.

J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1975), Chaps. 1 and 5.

Lawrence, R. S.

S. F. Clifford, G. R. Ochs, and R. S. Lawrence, "Saturation of optical scintillation by strong turbulence," J. Opt. Soc. Am. 64, 148–154 (1974).

R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).

Livingston, P. M.

Lumley, J. L.

J. L. Lumley, "Computational modeling of turbulent flows," in Advances in Applied Mechanics (Academic, New York, 1978), Vol. 18.

Lutomirski, R. F.

R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652–1658 (1971).

Ochs, G. R.

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).

Strohbehn, J. W.

R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).

J. W. Strohbehn, "Line-of-sight wave propagation through the turbulent atmosphere," Proc. IEEE 56, 1301–1318 (1968).

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).

Wizinowich, P. L.

Yura, H. T.

H. T. Yura, "Atmospheric turbulence induced beam spread," Appl. Opt. 10, 2771–2773 (1971).

R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652–1658 (1971).

Appl. Opt.

J. Opt. Soc. Am.

J. Phys.

L. R. Bissonnette, "Propagation of adaptively corrected laser beams through a turbulent atmosphere," J. Phys. (Paris) 41, C9/415–427 (1980).

Other

L. R. Bissonnette, "Propagation model of adaptively corrected laser beams in turbulence," DREV Rep. 4200/81, October 1981 Accession No. 82-00524 (Director of Scientific Information Services, Ottawa, Canada).

J. W. Strohbehn, ed., Laser Beam Propagation in the Atmosphere, Volume 25 of Topics in Applied Physics (Springer-Verlag, New York, 1978).

J. W. Strohbehn, "Line-of-sight wave propagation through the turbulent atmosphere," Proc. IEEE 56, 1301–1318 (1968).

R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).

R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).

R. L. Fante, "Electromagnetic beam propagation in turbulent media: an update," Proc. IEEE 68, 1424–1442 (1980).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).

R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652–1658 (1971).

L. R. Bissonnette, "Angle of arrival and irradiance statistics of laser beams in turbulence," DREV Rep. 4213/81, July 1981 Accession No. 81-03113 (Director of Scientific Information Services, Ottawa, Canada).

L. R. Bissonnette, "Focused laser beams in turbulent media," DREV Rep. 4178/80, December 1980 Accession No. 81-00157 (Director of Scientific Information Services, Ottawa, Canada).

L. R. Bissonnette, "Modelling of laser beam propagation in atmospheric turbulence," in Proceedings of the Second International Symposium on Gas Flow and Chemical Lasers, J. F. Wendt, ed. (Hemisphere, Washington, D.C., 1979), pp. 73–94.

J. L. Lumley, "Computational modeling of turbulent flows," in Advances in Applied Mechanics (Academic, New York, 1978), Vol. 18.

P. Bradshaw, ed., Turbulence, Volume 12 of Topics in Applied Physics (Springer-Verlag, New York, 1976), Chaps. 1, 5, and 6.

J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1975), Chaps. 1 and 5.

L. R. Bissonnette, "Log-normal probability distribution in strong irradiance fluctuations: an asymptotic analysis," in AGARD Conference Proceedings No. 183 on Optical Propagation in the Atmosphere (National Technical Information Service, Springfield, Va., 1976).

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