Abstract

Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere have been studied based on numerical solution of the parabolic wave equation for the complex spectral amplitude of the wave field by the split-step method. It has been shown that under conditions of strong optical turbulence, the relative variance of energy density fluctuations of pulsed radiation of femtosecond duration becomes much less than the relative variance of intensity fluctuations of continuous-wave radiation. The spatial structure of fluctuations of the energy density with a decrease of the pulse duration becomes more large-scale and homogeneous. For shorter pulses the maximal value of the probability density distribution of energy density fluctuations tends to the mean value of the energy density.

© 2014 Optical Society of America

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References

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  8. S. A. Shlyonov, V. Yu. Fedorov, and V. P. Kandidov, “Filamentation of phase-modulated femtosecond laser pulse on kilometer-long paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 20(4), 275–283 (2007).
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    [Crossref]
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    [Crossref]
  14. C. Y. Young, L. C. Andrews, and A. Ishimaru, “Broadening of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 37, 7655–7660 (1998).
    [Crossref] [PubMed]
  15. D. E. Tjin, T. S. Kelly, and L. C. Andrews, “Temporal broadening and scintillations of ultrashort optical pulses,” Waves Random Media 9(3), 307–325 (1999).
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  19. I. P. Christov, “Propagation of partially coherent light pulses,” Opt. Acta (Lond.) 33(1), 63–72 (1986).
    [Crossref]
  20. I. V. Zaloznaya and A. V. Falits, “Diffraction contraction of short pulses,” Atmos. Oceanic Opt. 22(6), 590–594 (2009).
    [Crossref]
  21. V. A. Banakh, “Diffraction-free propagation of a focused delta-pulsed beam,” Opt. Lett. 36(23), 4539–4541 (2011).
    [Crossref] [PubMed]
  22. L. O. Gerasimova and I. V. Zaloznaya, “Spatial and temporal coherence of short pulses (in Russian),” Atmos. Oceanic Opt. 24(3), 185–189 (2011).
  23. V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
    [Crossref]
  24. V. A. Banakh and L. O. Gerasimova, “Propagation of broadband pulsed optical beams (in Russian),” Atmos. Oceanic Opt. 26(1), 5–10 (2013).
  25. S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 1–20 (2010).
    [Crossref]
  26. 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]
  27. V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Phys. Usp. 39(12), 1243–1272 (1996).
    [Crossref]
  28. V. A. Banakh and I. N. Smalikho, Coherent Doppler Wind Lidars in a Turbulent Atmosphere (Artech House, Boston-London, 2013), Chap. 2.
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  30. V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
    [Crossref]
  31. A. S. Gurvich and V. Kan, “Fluctuations of the radiation intensity from two wave sources in a turbulent medium,” Radiophys. Quant. Electr. 22(7), 843–847 (1979).
  32. V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).
  33. V. A. Banakh and V. M. Buldakov, “Effect of the initial degree of spatial coherence of a light beam on intensity fluctuations in a turbulent atmosphere,” Opt. Spectrosc. 55(4), 423–426 (1983).
  34. V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Oceanic Opt. 24(5), 457–465 (2011).
    [Crossref]
  35. I. N. Smalikho, “Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation,” Atmos. Oceanic Opt. 26(2), 135–139 (2013).
    [Crossref]

2013 (3)

V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
[Crossref]

V. A. Banakh and L. O. Gerasimova, “Propagation of broadband pulsed optical beams (in Russian),” Atmos. Oceanic Opt. 26(1), 5–10 (2013).

I. N. Smalikho, “Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation,” Atmos. Oceanic Opt. 26(2), 135–139 (2013).
[Crossref]

2012 (2)

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

V. P. Kandidov and S. A. Shlyonov, “Thermal self-action of laser beams and filamentation of pulses in turbulent atmosphere,” Atmos. Oceanic Opt. 25(3), 192–198 (2012).
[Crossref]

2011 (3)

L. O. Gerasimova and I. V. Zaloznaya, “Spatial and temporal coherence of short pulses (in Russian),” Atmos. Oceanic Opt. 24(3), 185–189 (2011).

V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Oceanic Opt. 24(5), 457–465 (2011).
[Crossref]

V. A. Banakh, “Diffraction-free propagation of a focused delta-pulsed beam,” Opt. Lett. 36(23), 4539–4541 (2011).
[Crossref] [PubMed]

2010 (1)

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 1–20 (2010).
[Crossref]

2009 (1)

I. V. Zaloznaya and A. V. Falits, “Diffraction contraction of short pulses,” Atmos. Oceanic Opt. 22(6), 590–594 (2009).
[Crossref]

2007 (1)

S. A. Shlyonov, V. Yu. Fedorov, and V. P. Kandidov, “Filamentation of phase-modulated femtosecond laser pulse on kilometer-long paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 20(4), 275–283 (2007).

2000 (1)

1999 (2)

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

D. E. Tjin, T. S. Kelly, and L. C. Andrews, “Temporal broadening and scintillations of ultrashort optical pulses,” Waves Random Media 9(3), 307–325 (1999).
[Crossref]

1998 (1)

1996 (1)

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Phys. Usp. 39(12), 1243–1272 (1996).
[Crossref]

1986 (1)

I. P. Christov, “Propagation of partially coherent light pulses,” Opt. Acta (Lond.) 33(1), 63–72 (1986).
[Crossref]

1985 (1)

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53(6), 364–366 (1985).
[Crossref]

1983 (2)

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

V. A. Banakh and V. M. Buldakov, “Effect of the initial degree of spatial coherence of a light beam on intensity fluctuations in a turbulent atmosphere,” Opt. Spectrosc. 55(4), 423–426 (1983).

1981 (1)

V. U. Zavorotnyi, “Frequency correlation of strong intensity fluctuations in a turbulent medium,” Radiophys. Quant. Electr. 24(5), 601–608 (1981).
[Crossref]

1980 (1)

C.-H. Lui and K. C. Yeh, “Statistics of pulse arrival time in turbulent media,” J. Opt. Soc. Am. A 70(2), 168–172 (1980).
[Crossref]

1979 (2)

C.-H. Lui and K. C. Yeh, “Pulse spreading and wandering in random media,” Radio Sci. 14(5), 925–931 (1979).
[Crossref]

A. S. Gurvich and V. Kan, “Fluctuations of the radiation intensity from two wave sources in a turbulent medium,” Radiophys. Quant. Electr. 22(7), 843–847 (1979).

1977 (2)

C.-H. Lui and K. C. Yeh, “Pulse propagation in random media,” IEEE Trans. Antenn. Propag. 26, 561–566 (1977).

C.-H. Lui and K. C. Yeh, “Propagation of pulsed beam waves through turbulence, cloud, rain or fog,” J. Opt. Soc. Am. A 67(9), 1261–1266 (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]

Akturk, S.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 1–20 (2010).
[Crossref]

Andrews, L. C.

D. E. Tjin, T. S. Kelly, and L. C. Andrews, “Temporal broadening and scintillations of ultrashort optical pulses,” Waves Random Media 9(3), 307–325 (1999).
[Crossref]

C. Y. Young, L. C. Andrews, and A. Ishimaru, “Broadening of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 37, 7655–7660 (1998).
[Crossref] [PubMed]

Banakh, V. A.

V. A. Banakh and L. O. Gerasimova, “Propagation of broadband pulsed optical beams (in Russian),” Atmos. Oceanic Opt. 26(1), 5–10 (2013).

V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
[Crossref]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Oceanic Opt. 24(5), 457–465 (2011).
[Crossref]

V. A. Banakh, “Diffraction-free propagation of a focused delta-pulsed beam,” Opt. Lett. 36(23), 4539–4541 (2011).
[Crossref] [PubMed]

V. A. Banakh and V. M. Buldakov, “Effect of the initial degree of spatial coherence of a light beam on intensity fluctuations in a turbulent atmosphere,” Opt. Spectrosc. 55(4), 423–426 (1983).

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

Bowlan, P.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 1–20 (2010).
[Crossref]

Brodeur, A.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Buldakov, V. M.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

V. A. Banakh and V. M. Buldakov, “Effect of the initial degree of spatial coherence of a light beam on intensity fluctuations in a turbulent atmosphere,” Opt. Spectrosc. 55(4), 423–426 (1983).

Chin, S. L.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Christov, I. P.

I. P. Christov, “Propagation of partially coherent light pulses,” Opt. Acta (Lond.) 33(1), 63–72 (1986).
[Crossref]

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53(6), 364–366 (1985).
[Crossref]

Falits, A. V.

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

I. V. Zaloznaya and A. V. Falits, “Diffraction contraction of short pulses,” Atmos. Oceanic Opt. 22(6), 590–594 (2009).
[Crossref]

Fedorov, V. Yu.

S. A. Shlyonov, V. Yu. Fedorov, and V. P. Kandidov, “Filamentation of phase-modulated femtosecond laser pulse on kilometer-long paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 20(4), 275–283 (2007).

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]

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]

Frehlich, R.

Gerasimova, L. O.

V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
[Crossref]

V. A. Banakh and L. O. Gerasimova, “Propagation of broadband pulsed optical beams (in Russian),” Atmos. Oceanic Opt. 26(1), 5–10 (2013).

L. O. Gerasimova and I. V. Zaloznaya, “Spatial and temporal coherence of short pulses (in Russian),” Atmos. Oceanic Opt. 24(3), 185–189 (2011).

Gu, X.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 1–20 (2010).
[Crossref]

Gurvich, A. S.

A. S. Gurvich and V. Kan, “Fluctuations of the radiation intensity from two wave sources in a turbulent medium,” Radiophys. Quant. Electr. 22(7), 843–847 (1979).

Ishimaru, A.

Kan, V.

A. S. Gurvich and V. Kan, “Fluctuations of the radiation intensity from two wave sources in a turbulent medium,” Radiophys. Quant. Electr. 22(7), 843–847 (1979).

Kandidov, V. P.

V. P. Kandidov and S. A. Shlyonov, “Thermal self-action of laser beams and filamentation of pulses in turbulent atmosphere,” Atmos. Oceanic Opt. 25(3), 192–198 (2012).
[Crossref]

S. A. Shlyonov, V. Yu. Fedorov, and V. P. Kandidov, “Filamentation of phase-modulated femtosecond laser pulse on kilometer-long paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 20(4), 275–283 (2007).

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Phys. Usp. 39(12), 1243–1272 (1996).
[Crossref]

Kelly, T. S.

D. E. Tjin, T. S. Kelly, and L. C. Andrews, “Temporal broadening and scintillations of ultrashort optical pulses,” Waves Random Media 9(3), 307–325 (1999).
[Crossref]

Kosareva, O. G.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Lui, C.-H.

C.-H. Lui and K. C. Yeh, “Statistics of pulse arrival time in turbulent media,” J. Opt. Soc. Am. A 70(2), 168–172 (1980).
[Crossref]

C.-H. Lui and K. C. Yeh, “Pulse spreading and wandering in random media,” Radio Sci. 14(5), 925–931 (1979).
[Crossref]

C.-H. Lui and K. C. Yeh, “Pulse propagation in random media,” IEEE Trans. Antenn. Propag. 26, 561–566 (1977).

C.-H. Lui and K. C. Yeh, “Propagation of pulsed beam waves through turbulence, cloud, rain or fog,” J. Opt. Soc. Am. A 67(9), 1261–1266 (1977).
[Crossref]

Mironov, V. L.

V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity fluctuations of a partially coherent light beam in a turbulent atmosphere,” Opt. Spectrosc. 54, 626–629 (1983).

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]

Shlyonov, S. A.

V. P. Kandidov and S. A. Shlyonov, “Thermal self-action of laser beams and filamentation of pulses in turbulent atmosphere,” Atmos. Oceanic Opt. 25(3), 192–198 (2012).
[Crossref]

S. A. Shlyonov, V. Yu. Fedorov, and V. P. Kandidov, “Filamentation of phase-modulated femtosecond laser pulse on kilometer-long paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 20(4), 275–283 (2007).

Smalikho, I. N.

I. N. Smalikho, “Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation,” Atmos. Oceanic Opt. 26(2), 135–139 (2013).
[Crossref]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Oceanic Opt. 24(5), 457–465 (2011).
[Crossref]

Tamarov, M. P.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Tikhomirova, O. V.

V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
[Crossref]

Tjin, D. E.

D. E. Tjin, T. S. Kelly, and L. C. Andrews, “Temporal broadening and scintillations of ultrashort optical pulses,” Waves Random Media 9(3), 307–325 (1999).
[Crossref]

Trebino, R.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 1–20 (2010).
[Crossref]

Yeh, K. C.

C.-H. Lui and K. C. Yeh, “Statistics of pulse arrival time in turbulent media,” J. Opt. Soc. Am. A 70(2), 168–172 (1980).
[Crossref]

C.-H. Lui and K. C. Yeh, “Pulse spreading and wandering in random media,” Radio Sci. 14(5), 925–931 (1979).
[Crossref]

C.-H. Lui and K. C. Yeh, “Propagation of pulsed beam waves through turbulence, cloud, rain or fog,” J. Opt. Soc. Am. A 67(9), 1261–1266 (1977).
[Crossref]

C.-H. Lui and K. C. Yeh, “Pulse propagation in random media,” IEEE Trans. Antenn. Propag. 26, 561–566 (1977).

Young, C. Y.

Zaloznaya, I. V.

V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
[Crossref]

L. O. Gerasimova and I. V. Zaloznaya, “Spatial and temporal coherence of short pulses (in Russian),” Atmos. Oceanic Opt. 24(3), 185–189 (2011).

I. V. Zaloznaya and A. V. Falits, “Diffraction contraction of short pulses,” Atmos. Oceanic Opt. 22(6), 590–594 (2009).
[Crossref]

Zavorotnyi, V. U.

V. U. Zavorotnyi, “Frequency correlation of strong intensity fluctuations in a turbulent medium,” Radiophys. Quant. Electr. 24(5), 601–608 (1981).
[Crossref]

Appl. Opt. (2)

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]

Atmos. Oceanic Opt. (9)

L. O. Gerasimova and I. V. Zaloznaya, “Spatial and temporal coherence of short pulses (in Russian),” Atmos. Oceanic Opt. 24(3), 185–189 (2011).

V. A. Banakh, L. O. Gerasimova, I. V. Zaloznaya, and O. V. Tikhomirova, “Diffraction of broadband pulsed light beams,” Atmos. Oceanic Opt. 26(3), 178–184 (2013).
[Crossref]

V. A. Banakh and L. O. Gerasimova, “Propagation of broadband pulsed optical beams (in Russian),” Atmos. Oceanic Opt. 26(1), 5–10 (2013).

S. A. Shlyonov, V. Yu. Fedorov, and V. P. Kandidov, “Filamentation of phase-modulated femtosecond laser pulse on kilometer-long paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 20(4), 275–283 (2007).

V. P. Kandidov and S. A. Shlyonov, “Thermal self-action of laser beams and filamentation of pulses in turbulent atmosphere,” Atmos. Oceanic Opt. 25(3), 192–198 (2012).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Oceanic Opt. 24(5), 457–465 (2011).
[Crossref]

I. N. Smalikho, “Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation,” Atmos. Oceanic Opt. 26(2), 135–139 (2013).
[Crossref]

I. V. Zaloznaya and A. V. Falits, “Diffraction contraction of short pulses,” Atmos. Oceanic Opt. 22(6), 590–594 (2009).
[Crossref]

V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the subharmonic method in problems of computer simulation of laser beam propagation in a turbulent atmosphere,” Atmos. Oceanic Opt. 25(2), 106–109 (2012).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

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[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Two-dimensional (а, c) and one-dimensional (b, d) random realizations of the normalized energy density of cw (а, b) and pulsed (c, d) radiation at C n 2 = 10−12 m-2/3.
Fig. 2
Fig. 2 Standard deviation of relative energy density fluctuations of cw (curve 1)and pulsed (curves 2-6) radiation as a function of the parameter β 0 .Curves 2–6 correspond to pulse durations of 50 (2), 20 (3), 10 (4), 5 (5), and 3 fs
Fig. 3
Fig. 3 Normalized correlation function of energy density fluctuations of cw (curve 1) and pulsed (curves 2-6) radiation at β 0 2 33. Curves 2–6 correspond to pulse durations of 50 (2), 20 (3), 10 (4), 5 (5), and 3 fs (6).
Fig. 4
Fig. 4 Normalized probability density distribution of energy density fluctuations of cw (curve 1) and pulsed (curves 2-6) radiation at β 0 2 33. Curves 2–6 correspond to pulse durations of 50 (2), 20 (3), 10 (4), 5 (5), and 3 fs (6). Dashed curve shows the exponential distribution of the probability density.

Tables (1)

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Table 1 Simulation Parameters

Equations (33)

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E ( 0 , ρ , t ) = E 0 exp ( ρ 2 2 a 0 2 t 2 2 τ 0 2 2 π i f 0 t + j ψ 0 ) ,
E ˜ ( z , ρ , f ) = + d t E ( z , ρ , t ) exp ( 2 π i f t )
2 E ˜ ( z , ρ , f ) z 2 + Δ E ˜ ( z , ρ , f ) + ( 2 π f c ) 2 n 2 ( z , ρ , f ) E ˜ ( z , ρ , f ) = 0.
E ˜ ( 0 , ρ , f ) = 2 π τ 0 E 0 exp [ ρ 2 2 a 0 2 ( f f 0 ) 2 2 σ f 2 + i ψ 0 ] ,
n ( z , ρ , f ) = 1 + 10 6 P a T ( z , ρ ) [ 77.6 + 0.584 λ 0 2 ( f f 0 ) 2 ] ,
n ( z , ρ , f ) = < n ( f ) > + n ( z , ρ , f ) ,
< n ( f ) > = 1 + 10 6 P a < T > [ 77.6 + 0.584 λ 0 2 ( f f 0 ) 2 ]
n ( z , ρ , f ) = [ 1 < n ( f ) > ] T ( z , ρ ) / < T >
n 2 ( z , ρ , f ) = < n ( f ) > 2 [ 1 + 2 n ( z , ρ , f ) / < n ( f ) > ] .
E ˜ ( z , ρ , f ) = E ˜ ( 0 , ρ , f ) exp [ 2 π i f < n ( f ) > z / c ] .
E ( z , ρ , t ) = + d f E ˜ ( z , ρ , f ) exp ( 2 π i t f ) .
P ( z , t ) = 2 ( π τ 0 a 0 E 0 ) 2 | + d f exp { ( f f 0 ) 2 2 σ f 2 2 π i [ t < n ( f ) > z / c ] f } | 2 .
τ P ( z ) = 2 ln 2 τ 0 1 + ( 3 π μ z c τ 0 2 f 0 ) 2 ,
μ = 10 6 P a < T > 0.584 λ 0 2 .
E ˜ ( z , ρ , f ) = U ( z , ρ , f ) exp ( 2 π i f < n ( f ) > z / c ) .
i 4 π f c U ( z , ρ , f ) z + Δ U ( z , ρ , f ) + 2 ( 2 π f c ) 2 n ( z , ρ ) U ( z , ρ , f ) = 0.
U 1 ( z j 1 , ρ , f ) = U ( z j 1 , ρ , f ) .
U 1 ( z j , ρ , f ) = U ( z j 1 , ρ , f ) exp [ i Ψ j ( ρ , f ) ] ,
Ψ j ( ρ , f ) = ( 2 π f / c ) 0 Δ z d z n ˜ ( z j 1 + z , ρ )
U 2 ( z j 1 , ρ , f ) = U 1 ( z j , ρ , f ) .
U ˜ 2 ( z , κ , f ) = + d 2 ρ U 2 ( z , ρ , f ) exp ( 2 π i κ ρ ) ,
U ˜ 2 ( z j , κ , f ) = U ˜ 2 ( z j 1 , κ , f ) exp ( i π κ 2 Δ z c / f ) ,
U ˜ 2 ( z j 1 , κ , f ) = + d 2 ρ U 1 ( z j , ρ , f ) exp ( 2 π i κ ρ ) .
U ( z j , ρ , f ) = + d 2 κ U ˜ 2 ( z j , κ , f ) exp ( 2 π i κ ρ ) .
D Ψ ( r , f ) = < [ Ψ j ( ρ + r , f ) Ψ j ( ρ , f ) ] 2 > = 2 + d 2 κ S Ψ ( κ , f ) [ 1 exp ( 2 π i κ ρ ) ] ,
S Ψ ( κ , f ) = 0.382 C n 2 Δ z ( f / c ) 2 | κ | 11 / 3 ,
D Ψ ( r , f ) = 2.92 C n 2 Δ z ( 2 π f / c ) 2 | r | 5 3 .
S I ( L , ρ , f ) = | U ( L , ρ , f ) | 2 ,
S P ( L , f ) = + d 2 ρ S I ( L , ρ , f ) ,
W ( L , ρ ) = + d t I ( L , ρ , t ) = + d t | E ( L , ρ , t ) | 2 .
W ( L , ρ ) = + d f S I ( L , ρ , f ) .
σ W 2 ( L , ρ ) = < W 2 ( L , ρ ) > / < W ( L , ρ ) > 2 1 ,
σ W 2 ( z j ) = ( π τ 0 E 0 2 ) 2 + d f 1 + d f 2 < S I ( f 1 ) > < S I ( f 2 ) > K s ( z j , f 1 , f 2 )

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