Abstract

The on-axis two-frequency mutual coherence function (MCF) for beam waves propagating along a horizontal path in strong anisotropic atmospheric turbulence is theoretically formulated by making use of the extended Huygens-Fresnel principle. Based on this formulation, a new closed-form expression for the mean square temporal width of Gaussian-beam-wave pulses passing horizontally through strong anisotropic atmospheric turbulence is developed. With the help of this expression, the increments of mean square temporal pulse width due to strong anisotropic atmospheric turbulence under various conditions are further calculated. Results show that the increment of mean square temporal pulse width due to strong anisotropic atmospheric turbulence is basically proportional to the effective anisotropic factor in most situations of interest, with the possible exception of cases in which both the Fresnel ratio and spectral index become relatively small; increasing the effective anisotropic factor can reduce the number of the said exceptions; the turbulence-induced increment of mean square temporal pulse width enlarges as the spectral index increases with a fixed value of the nondimensional turbulence-strength parameter. It is also illustrated that a significant enlargement in the turbulence-induced increment of mean square temporal pulse width occurs by changing the Fresnel ratio from a large to a tiny value if both the effective anisotropic factor and spectral index are relatively small.

© 2015 Optical Society of America

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References

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  1. C. H. Liu and K. C. Yeh, “Propagation of pulsed beam waves through turbulence, cloud, rain, or fog,” J. Opt. Soc. Am. 67(9), 1261–1266 (1977).
    [Crossref]
  2. I. Sreenivasiah and A. Ishimaru, “Beam wave two-frequency mutual-coherence function and pulse propagation in random media: and analytic solution,” Appl. Opt. 18(10), 1613–1618 (1979).
    [Crossref] [PubMed]
  3. C. H. Liu and K. C. Yeh, “Statistics of pulse arrival time in turbulent media,” J. Opt. Soc. Am. 70(2), 168–172 (1980).
    [Crossref]
  4. C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 37(33), 7655–7660 (1998).
    [Crossref]
  5. J. Oz and E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: beam waves,” Waves Random Media 8(2), 159–174 (1998).
    [Crossref]
  6. D. E. T. T. S. Kelly and L. C. Andrews, “Temporal broadening and scintillations of ultrashort optical pulses,” Waves Random Media 9(3), 307–325 (1999).
    [Crossref]
  7. C. Y. Young, “Broadening of ultra-short optical pulses in moderate to strong turbulence,” Proc. SPIE 4821, 74–81 (2002).
    [Crossref]
  8. G. Samelsohn and V. Freilikher, “Two-frequency mutual coherence function and pulse propagation in random media,” Phys. Rev. E 65(4), 046617 (2002).
    [Crossref]
  9. Z. Xu and J. Wu, “On the mutual coherence function and mean arrival time of radio propagation through the turbulent ionosphere,” IEEE Trans. Antennas Propag. 56(8), 2622–2629 (2008).
    [Crossref]
  10. C. Chen, H. Yang, Y. Lou, S. Tong, and R. Liu, “Temporal broadening of optical pulses propagating through non-Kolmogorov turbulence,” Opt. Express 20(7), 7749–7757 (2012).
    [Crossref] [PubMed]
  11. V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low frequency range,” in Proceedings of International Geoscience and Remote Sensing Symposium, 1996. Remote Sensing for a Sustainable Future (IEEE, 1996), Vol. 1, pp. 22–24.
  12. M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
    [Crossref]
  13. C. Robert, J. Conan, V. Michau, J. Renard, C. Robert, and F. Dalaudier, “Retrieving parameters of the anisotropic refractive index fluctuations spectrum in the stratosphere from balloon-borne observations of stellar scintillation,” J. Opt. Soc. Am. A 25, (2)379–393 (2008).
    [Crossref]
  14. M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.
  15. R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the earth,” IEEE Trans. Antennas Propag. AP-34(2), 258–261 (1986).
    [Crossref]
  16. A. D. Wheelon, Electromagnetic Scintillation I: Geometrical Optics (Cambridge University, 2001).
    [Crossref]
  17. A. D. Wheelon, Electromagnetic Scintillation II: Weak Scattering (Cambridge University, 2003).
    [Crossref]
  18. A. Consortini, L. Ronchi, and L. Stefanutti, “Investigation of atmospheric turbulence by narrow laser beams,” Appl. Opt. 9(11), 2543–2547 (1970).
    [Crossref] [PubMed]
  19. A. S. Gurvich and M. S. Belenkii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12, (11)2517–2522 (1995).
    [Crossref]
  20. A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularities,” Waves Random Media 4(3), 297–306 (1994).
    [Crossref]
  21. V. S. RaoGudimetla, R. B. Holmes, C. Smith, and G. Needham, “Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence,” J. Opt. Soc. Am. A 29, (5)832–841 (2012).
    [Crossref]
  22. V. S. RaoGudimetla, R. B. Holmes, and J. F. Riker, “Analytical expressions for the log-amplitude correlation function for plane wave propagation in anisotropic non-Kolmogorov refractive turbulence,” J. Opt. Soc. Am. A 29, (12)2622–2627 (2012).
    [Crossref]
  23. I. Toselli, B. Agrawal, and S. Restaino, “Light propagation through anisotropic turbulence,” J. Opt. Soc. Am. A 28, (3)483–488 (2011).
    [Crossref]
  24. L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
    [Crossref]
  25. Y. Baykal and M. A. Plonus, “Two-source, two-frequency spherical wave structure functions in atmospheric turbulence,” J. Opt. Soc. Am. 70(10), 1278–1279 (1980).
    [Crossref]
  26. R. L. Fante, “Two-position, two-frequency mutual-coherence function in turbulence,” J. Opt. Soc. Am. 71(12), 1446–1451 (1981).
    [Crossref]
  27. H. T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. 11(6), 1399–1406 (1972).
    [Crossref] [PubMed]
  28. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2. (SPIE, 2005).
    [Crossref]
  29. I. Toselli, “Introducing the concept of anisotropy at different scales for modeling optical turbulence,” J. Opt. Soc. Am. A 31, (8)1868–1875 (2014).
    [Crossref]
  30. C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
    [Crossref]
  31. M. Charnotskii, “Common omissions and misconceptions of wave propagation in turbulence: discussion,” J. Opt. Soc. Am. A 29, (5)711–721 (2012).
    [Crossref]

2014 (2)

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

I. Toselli, “Introducing the concept of anisotropy at different scales for modeling optical turbulence,” J. Opt. Soc. Am. A 31, (8)1868–1875 (2014).
[Crossref]

2013 (1)

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

2012 (4)

2011 (1)

2008 (2)

2002 (2)

C. Y. Young, “Broadening of ultra-short optical pulses in moderate to strong turbulence,” Proc. SPIE 4821, 74–81 (2002).
[Crossref]

G. Samelsohn and V. Freilikher, “Two-frequency mutual coherence function and pulse propagation in random media,” Phys. Rev. E 65(4), 046617 (2002).
[Crossref]

1999 (2)

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

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

1998 (2)

J. Oz and E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: beam waves,” Waves Random Media 8(2), 159–174 (1998).
[Crossref]

C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 37(33), 7655–7660 (1998).
[Crossref]

1995 (1)

1994 (1)

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularities,” Waves Random Media 4(3), 297–306 (1994).
[Crossref]

1986 (1)

R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the earth,” IEEE Trans. Antennas Propag. AP-34(2), 258–261 (1986).
[Crossref]

1981 (1)

1980 (2)

1979 (1)

1977 (1)

1972 (1)

1970 (1)

Agrawal, B.

Andrews, L. C.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

D. E. T. 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, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. 37(33), 7655–7660 (1998).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2. (SPIE, 2005).
[Crossref]

Barchers, J. D.

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Baykal, Y.

Belenkii, M. S.

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

A. S. Gurvich and M. S. Belenkii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12, (11)2517–2522 (1995).
[Crossref]

Beresnev, L. A.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Brown, J. M.

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Carhart, G. W.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Charnotskii, M.

Chen, C.

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

C. Chen, H. Yang, Y. Lou, S. Tong, and R. Liu, “Temporal broadening of optical pulses propagating through non-Kolmogorov turbulence,” Opt. Express 20(7), 7749–7757 (2012).
[Crossref] [PubMed]

Conan, J.

Consortini, A.

Crabbs, R.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Dalaudier, F.

Fante, R. L.

Freilikher, V.

G. Samelsohn and V. Freilikher, “Two-frequency mutual coherence function and pulse propagation in random media,” Phys. Rev. E 65(4), 046617 (2002).
[Crossref]

Fugate, R. Q.

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Gudimetla, V. S. R.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Gurvich, A. S.

Heyman, E.

J. Oz and E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: beam waves,” Waves Random Media 8(2), 159–174 (1998).
[Crossref]

Holmes, R. B.

Ishimaru, A.

Karis, S. J.

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Kavehrad, M.

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

Kelly, D. E. T. T. S.

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

Kon, A. I.

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularities,” Waves Random Media 4(3), 297–306 (1994).
[Crossref]

Lachinova, S. L.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Leclerc, T.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Li, Y.

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

Liu, C. H.

Liu, J.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Liu, R.

Lou, Y.

Lukin, V. P.

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low frequency range,” in Proceedings of International Geoscience and Remote Sensing Symposium, 1996. Remote Sensing for a Sustainable Future (IEEE, 1996), Vol. 1, pp. 22–24.

Manning, R. M.

R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the earth,” IEEE Trans. Antennas Propag. AP-34(2), 258–261 (1986).
[Crossref]

Michau, V.

Needham, G.

Osmon, C. L.

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

Oz, J.

J. Oz and E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: beam waves,” Waves Random Media 8(2), 159–174 (1998).
[Crossref]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2. (SPIE, 2005).
[Crossref]

Plonus, M. A.

RaoGudimetla, V. S.

Rehder, K.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Renard, J.

Restaino, S.

Riker, J. F.

V. S. RaoGudimetla, R. B. Holmes, and J. F. Riker, “Analytical expressions for the log-amplitude correlation function for plane wave propagation in anisotropic non-Kolmogorov refractive turbulence,” J. Opt. Soc. Am. A 29, (12)2622–2627 (2012).
[Crossref]

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Robert, C.

Ronchi, L.

Samelsohn, G.

G. Samelsohn and V. Freilikher, “Two-frequency mutual coherence function and pulse propagation in random media,” Phys. Rev. E 65(4), 046617 (2002).
[Crossref]

Smith, C.

Sreenivasiah, I.

Stefanutti, L.

Stevenson, E.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Tong, S.

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

C. Chen, H. Yang, Y. Lou, S. Tong, and R. Liu, “Temporal broadening of optical pulses propagating through non-Kolmogorov turbulence,” Opt. Express 20(7), 7749–7757 (2012).
[Crossref] [PubMed]

Toselli, I.

Vorontsov, M.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Weyrauch, T.

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

Wheelon, A. D.

A. D. Wheelon, Electromagnetic Scintillation I: Geometrical Optics (Cambridge University, 2001).
[Crossref]

A. D. Wheelon, Electromagnetic Scintillation II: Weak Scattering (Cambridge University, 2003).
[Crossref]

Wu, J.

Z. Xu and J. Wu, “On the mutual coherence function and mean arrival time of radio propagation through the turbulent ionosphere,” IEEE Trans. Antennas Propag. 56(8), 2622–2629 (2008).
[Crossref]

Xu, Z.

Z. Xu and J. Wu, “On the mutual coherence function and mean arrival time of radio propagation through the turbulent ionosphere,” IEEE Trans. Antennas Propag. 56(8), 2622–2629 (2008).
[Crossref]

Yang, H.

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

C. Chen, H. Yang, Y. Lou, S. Tong, and R. Liu, “Temporal broadening of optical pulses propagating through non-Kolmogorov turbulence,” Opt. Express 20(7), 7749–7757 (2012).
[Crossref] [PubMed]

Yeh, K. C.

Young, C. Y.

Yura, H. T.

Appl. Opt. (4)

IEEE Trans. Antennas Propag. (2)

R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the earth,” IEEE Trans. Antennas Propag. AP-34(2), 258–261 (1986).
[Crossref]

Z. Xu and J. Wu, “On the mutual coherence function and mean arrival time of radio propagation through the turbulent ionosphere,” IEEE Trans. Antennas Propag. 56(8), 2622–2629 (2008).
[Crossref]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

C. Chen, H. Yang, M. Kavehrad, S. Tong, and Y. Li, “Validity of quadratic two-source spherical wave structure functions in analysis of beam propagation through generalized atmospheric turbulence,” Opt. Commun. 332(23), 343–349 (2014).
[Crossref]

Opt. Express (1)

Phys. Rev. E (1)

G. Samelsohn and V. Freilikher, “Two-frequency mutual coherence function and pulse propagation in random media,” Phys. Rev. E 65(4), 046617 (2002).
[Crossref]

Proc. SPIE (3)

C. Y. Young, “Broadening of ultra-short optical pulses in moderate to strong turbulence,” Proc. SPIE 4821, 74–81 (2002).
[Crossref]

M. S. Belenkii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999).
[Crossref]

L. C. Andrews, R. L. Phillips, R. Crabbs, and T. Leclerc, “Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence,” Proc. SPIE 8874, 887402 (2013).
[Crossref]

Waves Random Media (3)

J. Oz and E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media: beam waves,” Waves Random Media 8(2), 159–174 (1998).
[Crossref]

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

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularities,” Waves Random Media 4(3), 297–306 (1994).
[Crossref]

Other (5)

M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low frequency range,” in Proceedings of International Geoscience and Remote Sensing Symposium, 1996. Remote Sensing for a Sustainable Future (IEEE, 1996), Vol. 1, pp. 22–24.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2. (SPIE, 2005).
[Crossref]

A. D. Wheelon, Electromagnetic Scintillation I: Geometrical Optics (Cambridge University, 2001).
[Crossref]

A. D. Wheelon, Electromagnetic Scintillation II: Weak Scattering (Cambridge University, 2003).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Scaled turbulence-induced increment of mean square temporal pulse width as a function of the effective anisotropic factor ζe with T0 = 100 fs.
Fig. 2
Fig. 2 Scaled turbulence-induced increment of mean square temporal pulse width in terms of the Fresnel ratio Λ0 with T0 = 100 fs.
Fig. 3
Fig. 3 Variation of |Γturb(k12)|/Γturb(0) with k12, where k ˜ 12 = k ¯. (a) α = 3.3; (b) α = 11/3; (c) α = 3.8. The horizontal black dashed line denotes |Γturb(k12)|/Γturb(0) ≡ e−1.
Fig. 4
Fig. 4 Ratio of σ turb 2 ( α , ζ e , Λ 0 ) to σ turb 2 ( α , 1 , Λ 0 ) in terms of α. (a) ζe = 5; (b) ζe = 10.
Fig. 5
Fig. 5 Contours of log 10 [ σ t , 2 2 ( α , ζ e , Λ 0 ) / σ t , 1 2 ( α , ζ e ) ] as functions of α and Λ0. (a) ζe = 1; (b) ζe = 5; (c) ζe = 10; (d) ζe = 15.

Equations (36)

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Γ 2 ( r 1 , r 2 ; k 1 , k 2 ) = k 1 k 2 ( 2 π L ) 2 d 2 s 1 d 2 s 2 Γ 2 ( 0 ) ( s 1 , s 2 ; k 1 k 2 ) × exp [ i ( k 1 k 2 ) L + i k 1 2 L | r 1 s 1 | 2 i k 2 2 L | r 2 s 2 | 2 ] × exp [ 1 2 D ψ ( s 1 , r 1 , s 2 , r 2 ; k 1 , k 2 ) ] ,
D ψ ( s 1 , r 1 , s 2 , r 2 ; k 1 , k 2 ) = E 1 ( k 1 , k 2 ) + E 2 ( k 1 , k 2 )
E 1 ( k 1 , k 2 ) = 2 π ( k 1 2 + k 2 2 ) L d 2 K Φ n ( K ) ,
E 2 ( k 1 , k 2 ) = 4 π k 1 k 2 L d 2 K Φ n ( K ) 0 1 d ξ exp { i [ ( 1 ξ ) s d K + ξ r d K ] } ,
Φ n ( K ) = A ( α ) C ˜ n 2 ζ e 2 ( ζ e 2 κ x 2 + κ y 2 + ζ e 2 κ z 2 + κ 0 2 ) α / 2 exp ( ζ e 2 κ x 2 + κ y 2 + ζ e 2 κ z 2 κ m 2 ) ,
D ψ ( s 1 , r 1 , s 2 , r 2 ; k 1 , k 2 ) = ( 2 π 2 ) A ( α ) C ˜ n 2 ζ e L [ ( k 1 k 2 ) 2 Q 1 + 2 k 1 k 2 Q 2 ]
Q 2 = κ m 4 α 2 0 1 d ξ { κ 0 4 α κ m 4 α Γ ( α / 2 2 ) | ξ I a r d + ( 1 ξ ) I a s d | 2 4 Γ ( α / 2 ) + κ m 2 × Γ ( 1 α 2 ) [ 1 1 F 1 ( 1 α 2 ; 1 ; κ m 2 | ξ I a r d + ( 1 ξ ) I a s d | 2 4 ) ] } ,
I a = [ ζ e 1 0 0 1 ] .
Q 2 κ m 4 α 24 Γ ( 2 α 2 ) | I a s d | 2
Γ 2 ( 0 , 0 ; k ˜ 12 , k 12 ) = χ ( k 12 ) υ ( k 12 ) Γ ˜ 2 ( 0 , 0 ; k ˜ 12 , k 12 ) ,
χ ( k 12 ) k ˜ 12 2 ( 2 π L ) 2 exp ( i k 12 L k 12 2 δ ) ,
υ ( k 12 ) = π 2 T 0 2 exp [ 8 1 c 2 T 0 2 ( k 12 2 + 4 k ˜ 12 2 8 k ˜ 12 k ¯ + 4 k ¯ 2 ) ] ,
Γ ˜ 2 ( 0 , 0 ; k ˜ 12 , k 12 ) = 4 π [ γ ( 1 ) γ ( ζ e ) ] 1 / 2 ,
γ ( x ) k ˜ 12 2 L 2 + 4 w 0 4 2 i k 12 w 0 2 L + 8 w 0 2 ρ 0 2 x 2 2 i k 12 ρ 0 2 L x 2 ,
δ = 2 π 2 A ( α ) C ˜ n 2 ζ e L Q 1 , ρ 0 k ˜ 12 1 β ,
β = [ 6 1 π 2 A ( α ) C ˜ n 2 ζ e L κ m 4 α Γ ( 2 α / 2 ) 1 / 2 ] .
M ( n ) ( r , L ) = ( i ) n 2 π c n 1 d k ˜ 12 [ n k 12 n Γ 2 ( 0 , 0 ; k ˜ 12 , k 12 ) ] k 12 = 0 ,
σ t a 2 = M ( 2 ) ( r , L ) M ( 0 ) ( r , L ) ( M ( 1 ) ( r , L ) M ( 0 ) ( r , L ) ) 2 .
σ t a 2 T 0 2 4 + 2 δ c 2 + Δ c 2 ,
Δ = 2 ( 1 w 0 2 L + k ¯ 2 β 2 L ) 2 ( k ¯ 2 L 2 + 4 w 0 4 + 8 k ¯ 2 w 0 2 β 2 ) 2 + 2 ( 1 w 0 2 L + k ¯ 2 β 2 L ζ e 2 ) 2 ( k ¯ 2 L 2 + 4 w 0 4 + 8 k ¯ 2 w 0 2 β 2 ζ e 2 ) 2 .
Γ turb ( k 12 ) = π Γ 2 ( 0 , 0 ; k ˜ 12 , k 12 ) υ ( k 12 ) = k ˜ 12 2 exp ( i k 12 L k 12 2 δ ) L 2 γ ( 1 ) γ ( ζ e ) .
E 1 ( k 1 , k 2 ) = 2 π ( k 1 2 + k 2 2 ) L d κ x d κ y Φ n ( κ x , κ y , 0 ) ,
E 2 ( k 1 , k 2 ) = 4 π k 1 k 2 L d κ x d κ y Φ n ( κ x , κ y , 0 ) × 0 1 d ξ exp { i [ ( 1 ξ ) s d K ˜ + ξ r d K ˜ ] } ,
D ψ ( s 1 , r 1 , s 2 , r 2 ; k 1 , k 2 ) = 2 π A ( α ) C ˜ n 2 ζ e 2 L d κ x d κ y exp [ κ m 2 ( ζ e 2 κ x 2 + κ y 2 ) ] × ( ζ e 2 κ x 2 + κ y 2 + κ 0 2 ) α / 2 0 1 d ξ [ k 1 2 + k 2 2 2 k 1 k 2 × exp { i [ ( 1 ξ ) s d K ˜ + ξ r d K ˜ ] } ] .
D ψ ( s 1 , r 1 , s 2 , r 2 ; k 1 , k 2 ) = 2 π A ( α ) C ˜ n 2 ζ e L d κ x d κ x exp ( κ m 2 K ˜ 2 ) × ( K ˜ 2 + κ 0 2 ) α / 2 0 1 d ξ [ k 1 2 + k 2 2 2 k 1 k 2 × exp { i [ ( 1 ξ ) I a s d K ˜ + ξ I a r d K ˜ ] } ] ,
D ψ ( s 1 , r 1 , s 2 , r 2 ; k 1 , k 2 ) = ( 2 π ) 2 A ( α ) C ˜ n 2 ζ e l 0 d K ˜ exp ( κ m 2 K ˜ 2 ) × K ˜ ( K ˜ 2 + κ 0 2 ) α / 2 0 1 d ξ { k 1 2 + k 2 2 2 k 1 k 2 × J 0 [ | ( 1 ξ ) I a s d + ξ I a r d | K ˜ ] }
M ( 0 ) ( r , L ) = Q 3 , M ( 1 ) ( r , L ) = L c Q 3 i 2 π Q 4 ,
M ( 2 ) ( r , L ) = ( T 0 2 4 + 2 δ c 2 + L 2 c 2 ) Q 3 i L π c Q 4 Q 5 2 π c ,
Q 3 = c T 0 2 2 L 2 d k ˜ 12 f 1 ( k ˜ 12 ) exp [ c 2 T 0 2 2 ( k ˜ 12 k ¯ ) 2 ] ,
Q 4 = T 0 2 π L 2 d k ˜ 12 f 2 ( k ˜ 12 ) exp [ c 2 T 0 2 2 ( k ˜ 12 k ¯ ) 2 ] ,
Q 5 = T 0 2 π L 2 d k ˜ 12 f 3 ( k ˜ 12 ) exp [ c 2 T 0 2 2 ( k ˜ 12 k ¯ ) 2 ]
f 1 ( k ˜ 12 ) = k ˜ 12 2 μ ( k ˜ 12 , 1 / 2 , 1 / 2 ) ,
f 2 ( k ˜ 12 ) = k ˜ 12 2 [ μ ( k ˜ 12 , 3 2 , 1 2 ) ( i w 0 2 L + i k ˜ 12 2 β 2 L ) + μ ( k ˜ 12 , 1 2 , 3 2 ) ( i w 0 2 L + i k ˜ 12 2 β 2 L ζ e 2 ) ] ,
f 3 ( k ˜ 12 ) = k ˜ 12 2 [ 3 μ ( k ˜ 12 , 5 2 , 1 2 ) ( i w 0 2 L + i k ˜ 12 2 β 2 L ) 2 + 2 μ ( k ˜ 12 , 3 2 , 3 2 ) ( i w 0 2 L + i k ˜ 12 2 β 2 L ) × ( i w 0 2 L + i k ˜ 12 2 β 2 L ζ e 2 ) + 3 μ ( k ˜ 12 , 1 2 , 5 2 ) ( i w 0 2 L + i k ˜ 12 2 β 2 L ζ e 2 ) 2 ] ,
μ ( k ˜ 12 , a , b ) = ( k ˜ 12 2 L 2 + 4 w 0 4 + 8 k ˜ 12 2 w 0 2 β 2 ) a ( k ˜ 12 2 L 2 + 4 w 0 4 + 8 k ˜ 12 2 w 0 2 β 2 ζ e 2 ) b .
σ t a 2 = T 0 2 4 + 2 δ c 2 + Q 4 2 4 π 2 Q 3 2 Q 5 2 π c Q 3 .

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