Abstract

Enhanced backscattering of polarized light by disordered media composed of independently scattering particles of arbitrary size and shape is studied theoretically. Rigorous relations between the cyclical and the ladder parts of the backscattering matrix in exactly the backscattering direction are derived for three commonly used representations of polarization, and the corresponding polarization backscattering enhancement factors are introduced. The ladder part of the Stokes-backscattering matrix is calculated by solving Chandrasekhar’s vector radiative transfer equation [ Radiative Transfer ( Clarendon, London, 1950)]. The general properties of the enhancement factors are studied, and the results of numerical computations are reported for finite and semi-infinite homogeneous slabs composed of spherical and randomly oriented nonspherical particles. It is shown that the enhancement factors depend strongly on the direction of light incidence, the optical thickness of the medium, the true absorption, and the particle size and shape.

© 1992 Optical Society of America

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References

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  1. P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).
  2. M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990).
  3. A. Ishimaru, L. Tsang, “Backscattering enhancement of random discrete scatters of moderate sizes,” J. Opt. Soc. Am. A 5, 228–236 (1988).
    [Crossref]
  4. M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
    [Crossref]
  5. Y. N. Barabanenkov, V. D. Ozrin, “Diffusion approximation for coherent amplification of backscattered radiation in a randomly inhomogeneous medium,” Zh. Eksp. Teor. Fiz. 94(6), 56–64 (1938).
  6. E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
    [Crossref]
  7. E. E. Gorodnichev, S. L. Dudarev, D. B. Rogozkin, “Coherent wave backscattering by random medium. Exact solution of the albedo problem,” Phys. Lett. A 144, 48–54 (1990).
    [Crossref]
  8. Y. Kuga, L. Tsang, A. Ishimaru, “Depolarization effects of the enhanced retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 2, 616–618 (1985).
    [Crossref]
  9. M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
    [Crossref]
  10. F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
    [Crossref]
  11. M. P. van Albada, A. Lagendijk, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2356 (1987).
    [Crossref]
  12. C. E. Mandt, L. Tsang, A. Ishimaru, “Copolarized and depolarized backscattering enhancement of random discrete scatterers of large size based on second-order ladder and cyclical theory,” J. Opt. Soc. Am. A 7, 585–592 (1990).
    [Crossref]
  13. A. Ishimaru, C. W. Yeh, “Matrix representations of the vector radiative-transfer theory for randomly distributed nonspherical particles,” J. Opt. Soc. Am. A 1, 359–364 (1984).
    [Crossref]
  14. D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
    [Crossref]
  15. J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).
  16. A. P. Prishivalko, V. A. Babenko, V. N. Kuz’min, Scattering and Absorption of Light by Inhomogeneous and Anisotropic Spherical Particles (Nauka i Tekhnika, Minsk, Byelorussia, 1984).
  17. B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry,”IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
    [Crossref]
  18. S. Chandrasekhar, Radiative Transfer (Clarendon, London, 1950).
  19. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [Crossref]
  20. V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, Oxford, 1975).
  21. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  22. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
  23. J. Lenoble, ed., Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, Hampton, Va., 1985).
  24. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  25. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  26. W. A. de Rooij, “Reflection and transmission of polarized light by planetary atmospheres,” Ph.D. dissertation (Free University, Amsterdam, 1985).
  27. M. I. Mishchenko, “The fast invariant imbedding method for polarized light: computational aspects and numerical results for Rayleigh scattering,”J. Quant. Spectrosc. Radiat. Transfer 43, 163–171 (1990).
    [Crossref]
  28. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [Crossref]
  29. M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,”J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
    [Crossref]
  30. P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
    [Crossref]
  31. M. P. van Albada, M. B. van der Mark, A. Lagendijk, “Polarization effects in weak localization of light,”J. Phys. D 21, S28–S31 (1988).
    [Crossref]
  32. S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
    [Crossref] [PubMed]

1991 (2)

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[Crossref]

M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,”J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
[Crossref]

1990 (4)

C. E. Mandt, L. Tsang, A. Ishimaru, “Copolarized and depolarized backscattering enhancement of random discrete scatterers of large size based on second-order ladder and cyclical theory,” J. Opt. Soc. Am. A 7, 585–592 (1990).
[Crossref]

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry,”IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[Crossref]

E. E. Gorodnichev, S. L. Dudarev, D. B. Rogozkin, “Coherent wave backscattering by random medium. Exact solution of the albedo problem,” Phys. Lett. A 144, 48–54 (1990).
[Crossref]

M. I. Mishchenko, “The fast invariant imbedding method for polarized light: computational aspects and numerical results for Rayleigh scattering,”J. Quant. Spectrosc. Radiat. Transfer 43, 163–171 (1990).
[Crossref]

1988 (6)

A. Ishimaru, L. Tsang, “Backscattering enhancement of random discrete scatters of moderate sizes,” J. Opt. Soc. Am. A 5, 228–236 (1988).
[Crossref]

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[Crossref]

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
[Crossref]

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[Crossref]

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

M. P. van Albada, M. B. van der Mark, A. Lagendijk, “Polarization effects in weak localization of light,”J. Phys. D 21, S28–S31 (1988).
[Crossref]

1987 (2)

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

M. P. van Albada, A. Lagendijk, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2356 (1987).
[Crossref]

1986 (1)

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[Crossref]

1985 (1)

1984 (1)

1983 (1)

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

1974 (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

1955 (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[Crossref]

1938 (1)

Y. N. Barabanenkov, V. D. Ozrin, “Diffusion approximation for coherent amplification of backscattered radiation in a randomly inhomogeneous medium,” Zh. Eksp. Teor. Fiz. 94(6), 56–64 (1938).

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
[Crossref]

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Andrejco, M. J.

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

Babenko, V. A.

A. P. Prishivalko, V. A. Babenko, V. N. Kuz’min, Scattering and Absorption of Light by Inhomogeneous and Anisotropic Spherical Particles (Nauka i Tekhnika, Minsk, Byelorussia, 1984).

Barabanenkov, Y. N.

Y. N. Barabanenkov, V. D. Ozrin, “Diffusion approximation for coherent amplification of backscattered radiation in a randomly inhomogeneous medium,” Zh. Eksp. Teor. Fiz. 94(6), 56–64 (1938).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Clarendon, London, 1950).

Cwilich, G.

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[Crossref]

de Rooij, W. A.

W. A. de Rooij, “Reflection and transmission of polarized light by planetary atmospheres,” Ph.D. dissertation (Free University, Amsterdam, 1985).

Dudarev, S. L.

E. E. Gorodnichev, S. L. Dudarev, D. B. Rogozkin, “Coherent wave backscattering by random medium. Exact solution of the albedo problem,” Phys. Lett. A 144, 48–54 (1990).
[Crossref]

Etemad, S.

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

Gorodnichev, E. E.

E. E. Gorodnichev, S. L. Dudarev, D. B. Rogozkin, “Coherent wave backscattering by random medium. Exact solution of the albedo problem,” Phys. Lett. A 144, 48–54 (1990).
[Crossref]

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Hovenier, J. W.

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

John, S.

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[Crossref]

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

Kuga, Y.

Kuz’min, V. N.

A. P. Prishivalko, V. A. Babenko, V. N. Kuz’min, Scattering and Absorption of Light by Inhomogeneous and Anisotropic Spherical Particles (Nauka i Tekhnika, Minsk, Byelorussia, 1984).

Lagendijk, A.

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[Crossref]

M. P. van Albada, M. B. van der Mark, A. Lagendijk, “Polarization effects in weak localization of light,”J. Phys. D 21, S28–S31 (1988).
[Crossref]

M. P. van Albada, A. Lagendijk, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2356 (1987).
[Crossref]

MacKintosh, F. C.

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[Crossref]

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

Mandt, C. E.

Maret, G.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
[Crossref]

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
[Crossref]

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,”J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
[Crossref]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[Crossref]

M. I. Mishchenko, “The fast invariant imbedding method for polarized light: computational aspects and numerical results for Rayleigh scattering,”J. Quant. Spectrosc. Radiat. Transfer 43, 163–171 (1990).
[Crossref]

Ozrin, V. D.

Y. N. Barabanenkov, V. D. Ozrin, “Diffusion approximation for coherent amplification of backscattered radiation in a randomly inhomogeneous medium,” Zh. Eksp. Teor. Fiz. 94(6), 56–64 (1938).

Prishivalko, A. P.

A. P. Prishivalko, V. A. Babenko, V. N. Kuz’min, Scattering and Absorption of Light by Inhomogeneous and Anisotropic Spherical Particles (Nauka i Tekhnika, Minsk, Byelorussia, 1984).

Rogozkin, D. B.

E. E. Gorodnichev, S. L. Dudarev, D. B. Rogozkin, “Coherent wave backscattering by random medium. Exact solution of the albedo problem,” Phys. Lett. A 144, 48–54 (1990).
[Crossref]

Saxon, D. S.

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[Crossref]

Sobolev, V. V.

V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, Oxford, 1975).

Stephen, M. J.

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[Crossref]

Thompson, R.

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

Travis, L. D.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Tsang, L.

van Albada, M. P.

M. P. van Albada, M. B. van der Mark, A. Lagendijk, “Polarization effects in weak localization of light,”J. Phys. D 21, S28–S31 (1988).
[Crossref]

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[Crossref]

M. P. van Albada, A. Lagendijk, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2356 (1987).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

van der Mark, M. B.

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[Crossref]

M. P. van Albada, M. B. van der Mark, A. Lagendijk, “Polarization effects in weak localization of light,”J. Phys. D 21, S28–S31 (1988).
[Crossref]

van der Mee, C. V. M.

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Wen, B.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry,”IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[Crossref]

Winebrenner, D. P.

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry,”IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[Crossref]

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
[Crossref]

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Yeh, C. W.

Astron. Astrophys. (1)

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

IEEE Trans. Geosci. Remote Sens. (1)

B. Wen, L. Tsang, D. P. Winebrenner, A. Ishimaru, “Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry,”IEEE Trans. Geosci. Remote Sens. 28, 46–59 (1990).
[Crossref]

J. Opt. Soc. Am. A (5)

J. Phys. (Paris) (2)

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,”J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,”J. Phys. (Paris) 49, 77–98 (1988).
[Crossref]

J. Phys. D (1)

M. P. van Albada, M. B. van der Mark, A. Lagendijk, “Polarization effects in weak localization of light,”J. Phys. D 21, S28–S31 (1988).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (2)

M. I. Mishchenko, “The fast invariant imbedding method for polarized light: computational aspects and numerical results for Rayleigh scattering,”J. Quant. Spectrosc. Radiat. Transfer 43, 163–171 (1990).
[Crossref]

M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,”J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
[Crossref]

Phys. Lett. A (1)

E. E. Gorodnichev, S. L. Dudarev, D. B. Rogozkin, “Coherent wave backscattering by random medium. Exact solution of the albedo problem,” Phys. Lett. A 144, 48–54 (1990).
[Crossref]

Phys. Rev. (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[Crossref]

Phys. Rev. B (4)

M. J. Stephen, G. Cwilich, “Rayleigh scattering and weak localization: effects of polarization,” Phys. Rev. B 34, 7564–7572 (1986).
[Crossref]

F. C. MacKintosh, S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1988).
[Crossref]

M. P. van Albada, A. Lagendijk, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2356 (1987).
[Crossref]

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[Crossref]

Phys. Rev. Lett. (1)

S. Etemad, R. Thompson, M. J. Andrejco, S. John, F. C. MacKintosh, “Weak localization of photons: termination of coherent random walks by absorption and confined geometry,” Phys. Rev. Lett. 59, 1420–1423 (1987).
[Crossref] [PubMed]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

Y. N. Barabanenkov, V. D. Ozrin, “Diffusion approximation for coherent amplification of backscattered radiation in a randomly inhomogeneous medium,” Zh. Eksp. Teor. Fiz. 94(6), 56–64 (1938).

Other (11)

A. P. Prishivalko, V. A. Babenko, V. N. Kuz’min, Scattering and Absorption of Light by Inhomogeneous and Anisotropic Spherical Particles (Nauka i Tekhnika, Minsk, Byelorussia, 1984).

V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, Oxford, 1975).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

J. Lenoble, ed., Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, Hampton, Va., 1985).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

W. A. de Rooij, “Reflection and transmission of polarized light by planetary atmospheres,” Ph.D. dissertation (Free University, Amsterdam, 1985).

P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).

M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990).

S. Chandrasekhar, Radiative Transfer (Clarendon, London, 1950).

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Tables (5)

Tables Icon

Table 1 Backscattering Enhancement Factors for Semi-Infinite Slabs Composed of Spherical Particles with μ0 = 1 and m = 1.2

Tables Icon

Table 2 Backscattering Enhancement Factors for a Rayleigh-Scattering Slab with τ = ∞ and ω = 1

Tables Icon

Table 3 Backscattering Enhancement Factors for a Rayleigh-Scattering Slab with τ = ∞ and μ0 = 1

Tables Icon

Table 4 Backscattering Enhancement Factors for a Rayleigh-Scattering Slab with μ0 = 1 and ω = 0.99

Tables Icon

Table 5 Backscattering Enhancement Factors for a Semi-Infinite Slab Composed of Randomly Oriented Oblate Spheroids with m = 1.5, xev = 4, and a/b = 2

Equations (38)

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

γ = γ 1 + γ L + γ C γ 1 + 2 γ L ,
ζ ˜ = γ 1 + 2 γ L γ 1 + γ L 2 ,
[ E ϑ E φ ] F [ E ϑ E φ ] .
F ( - n ^ , - n ^ ) = Q F T ( n ^ , n ^ ) Q ,
J 0 = E 0 E 0 * T = [ E 0 ϑ E 0 ϑ * E 0 ϑ E 0 φ * E 0 φ E 0 ϑ * E 0 φ E 0 φ * ] ,
D G ( - n ^ 0 , n ^ 0 ) D 0 ,
D 0 = [ J 11 0 J 12 0 J 21 0 J 22 0 ] ,             D = [ J 11 J 12 J 21 J 22 ] .
J = J 1 + J L + J C ,
G = G 1 + G L + G C ,
P ( n , 1 ) = Q [ P ( 1 , n ) ] T Q .
P ( 1 , n ) = [ a b c d ] .
E ( 1 , n ) [ E ( 1 , n ) ] * T + E ( n , 1 ) [ E ( n , 1 ) ] * T ,
E ( 1 , n ) [ E ( n , 1 ) ] * T + E ( n , 1 ) [ E ( 1 , n ) ] * T .
[ 2 a a * a b * - a c * b a * - c a * b b * - c c * - a b * + a c * 2 a d * b c * + c b * b d * - c d * - b a * + c a * b c * + c b * 2 d a * d b * - d c * b b * + c c * - b d * + c d * - d b * + d c * 2 d d * ] ,
[ 2 a a * a b * - a c * b a * - c a * - b c * - c b * - a b * + a c * 2 a d * - b b * - c c * b d * - c d * - b a * + c a * - b b * - c c * 2 d a * d b * - d c * - b c * - c b * - b d * + c d * - d b * + d c * 2 d d * ]
G C = [ G 11 L G 12 L G 13 L - G 32 L G 21 L G 22 L - G 41 L G 24 L G 31 L - G 41 L G 33 L G 34 L - G 32 L G 42 L G 43 L G 44 L ] .
G C = [ G 11 L 0 0 - G 32 L 0 G 22 L - G 41 L 0 0 - G 41 L G 33 L 0 - G 32 L 0 0 G 44 L ] .
I = [ I Q U V ] = [ J 11 + J 22 J 11 - J 22 - i J 12 - i J 21 - i J 12 + i J 21 ] ,
I CP = 1 2 [ Q + i U I + V I - V Q - i U ] .
S C = [ S 11 C S 12 L 0 0 S 12 L S 22 C 0 0 0 0 S 33 C S 34 L 0 0 - S 34 L S 44 C ] ,
C C = [ C 11 L C 12 L C 13 L C 32 L C 21 L C 22 L C 41 L C 24 L C 31 L C 41 L C 33 L C 34 L C 32 L C 42 L C 43 L C 44 L ] ,
S 11 L = ½ [ S 11 L + S 22 L - S 33 L + S 44 L ] ,
S 22 C = ½ [ S 11 L + S 22 L + S 33 L - S 44 L ] ,
S 33 L = ½ [ - S 11 L + S 22 L + S 33 L + S 44 L ] ,
S 44 C = ½ [ S 11 L - S 22 L + S 33 L + S 44 L ] .
ζ = [ G 11 1 + G 11 L + G 11 C ] / [ G 11 1 + G 11 L ] = [ G 11 1 + 2 G 11 L ] / [ G 11 1 + G 11 L ] ,
ζ = [ G 41 1 + G 41 L + G 41 C ] / [ G 41 1 + G 41 L ] = [ G 41 1 + G 41 L - G 32 L ] / [ G 41 1 + G 41 L ] ,
ζ = [ S 11 1 + S 11 L + S 11 C ] / [ S 11 1 + S 11 L ] = [ S 11 1 + S 11 L + ½ ( S 11 L + S 22 L - S 33 L + S 44 L ) ] / [ S 11 1 + S 11 L ] ,
ζ hp = [ C 22 1 + C 22 L + C 22 C ] / [ C 22 1 + C 22 L ] = [ C 22 1 + 2 C 22 L ] / [ C 22 1 + C 22 L ] ,
ζ oh = [ C 32 1 + C 32 L + C 32 C ] / [ C 32 1 + C 32 L ] = [ C 32 1 + C 32 L + C 41 L ] / [ C 32 1 + C 32 L ] .
ζ = S 11 1 + S 22 1 + 2 S 11 L + 4 S 12 L + 2 S 22 L S 11 1 + S 22 1 + S 11 L + 2 S 12 L + S 22 L ,
ζ = S 11 1 - S 22 1 + S 11 L - S 22 L - S 33 L + S 44 L S 11 1 - S 22 1 + S 11 L - S 22 L ,
ζ hp = S 11 1 + S 44 1 + 2 S 11 L + 2 S 44 L S 11 1 + S 44 1 + S 11 L + S 44 L ,
ζ oh = S 11 1 - S 44 1 + S 11 L + S 22 L - S 33 L - S 44 L S 11 1 - S 44 1 + S 11 L - S 44 L .
F S ( θ ) = [ a 1 ( θ ) b 1 ( θ ) 0 0 b 1 ( θ ) a 2 ( θ ) 0 0 0 0 a 3 ( θ ) b 2 ( θ ) 0 0 - b 2 ( θ ) a 4 ( θ ) ] ,
S 11 1 = S 22 1 ,             S 11 1 = - S 44 1 .
lim μ 0 0 ξ = lim ω 0 ξ = lim τ 0 ξ = 1 ,
1 ζ 2 , 0 ζ 2 , 0 ζ 2 , 1 ζ hp 2 , 0 ζ oh 2.

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