Abstract

The intensity temporal profiles of diffusive light propagation in highly concentrated (up to volume fraction ϕ0.55) dispersions measured by 100-fs laser pulses showed an increase in transport scattering mean free path above a critical concentration. This observation confirms the previous theoretical predictions of enhanced transmission at high particle concentrations due to correlated scattering. The correlation effects are accounted for by incorporating a hard sphere Percus–Yevick static structure factor into the prediction of transport mean free path.

© 1998 Optical Society of America

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References

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  1. C. I. Beard, T. H. Kays, V. Twersky, “Scattering by random distribution of spheres vs. concentration,” IEEE Trans. Antennas Propag. AP-15, 99–118 (1967).
    [CrossRef]
  2. V. Twersky, “Transparency of pair correlated, random distribution of small scatterers with applications to the cornea,” J. Opt. Soc. Am. 65, 524–530 (1975).
    [CrossRef] [PubMed]
  3. A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
    [CrossRef]
  4. P. F. Jacobs, Rapid Prototyping and Manufacturing—Fundamentals of Stereolithography (Society of Manufacturing Engineers, Dearborn, Mich., 1992).
  5. L. Feng, K. M. Yoo, R. R. Alfano, “Ultrafast laser pulse transmission and imaging through biological tissues,” Appl. Opt. 32, 554–558 (1993).
    [CrossRef]
  6. P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621–2623 (1990).
    [CrossRef]
  7. M. Fraden, G. Maret, “Multiple scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
    [CrossRef] [PubMed]
  8. F. C. MacKintosh, J. Sajeev, “Diffusion wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
    [CrossRef]
  9. D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.
  10. P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
    [CrossRef] [PubMed]
  11. P. D. Kaplan, “Optical studies of the structure and dynamics of opaque colloids,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1993).
  12. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1 and 2, (Academic, New York, 1978), p. 175.
  13. M. Lax, V. Narayanamurti, R. C. Fulton, “Classical diffusive photon transport in a slab,” in Proceedings of the Symposium on Laser Optics and Condensed Matter, Leningrad, June 1987, J. L. Birman, H. Z. Cumins, eds. (Plenum, New York, 1987), pp. 229–235.
  14. S.-C. Lee, “Dependent scattering by parallel fibers: effects of multiple scattering and wave interferences,” J. Thermophys. Heat Tr. 6, 589–595 (1990).
    [CrossRef]
  15. N. W. Ashcroff, J. Lekner, “Structure and resistivity of liquid metals,” Phys. Rev. 145, 83–90 (1966).
    [CrossRef]
  16. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 126.

1993 (1)

1992 (1)

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

1990 (3)

S.-C. Lee, “Dependent scattering by parallel fibers: effects of multiple scattering and wave interferences,” J. Thermophys. Heat Tr. 6, 589–595 (1990).
[CrossRef]

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621–2623 (1990).
[CrossRef]

M. Fraden, G. Maret, “Multiple scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

1989 (1)

F. C. MacKintosh, J. Sajeev, “Diffusion wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
[CrossRef]

1982 (1)

1975 (1)

1967 (1)

C. I. Beard, T. H. Kays, V. Twersky, “Scattering by random distribution of spheres vs. concentration,” IEEE Trans. Antennas Propag. AP-15, 99–118 (1967).
[CrossRef]

1966 (1)

N. W. Ashcroff, J. Lekner, “Structure and resistivity of liquid metals,” Phys. Rev. 145, 83–90 (1966).
[CrossRef]

Alfano, R. R.

Ashcroff, N. W.

N. W. Ashcroff, J. Lekner, “Structure and resistivity of liquid metals,” Phys. Rev. 145, 83–90 (1966).
[CrossRef]

Beard, C. I.

C. I. Beard, T. H. Kays, V. Twersky, “Scattering by random distribution of spheres vs. concentration,” IEEE Trans. Antennas Propag. AP-15, 99–118 (1967).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 126.

Chaikin, P. M.

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

Feng, L.

Fraden, M.

M. Fraden, G. Maret, “Multiple scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

Fulton, R. C.

M. Lax, V. Narayanamurti, R. C. Fulton, “Classical diffusive photon transport in a slab,” in Proceedings of the Symposium on Laser Optics and Condensed Matter, Leningrad, June 1987, J. L. Birman, H. Z. Cumins, eds. (Plenum, New York, 1987), pp. 229–235.

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 126.

Ishimaru, A.

A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1 and 2, (Academic, New York, 1978), p. 175.

Jacobs, P. F.

P. F. Jacobs, Rapid Prototyping and Manufacturing—Fundamentals of Stereolithography (Society of Manufacturing Engineers, Dearborn, Mich., 1992).

Kaplan, P. D.

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

P. D. Kaplan, “Optical studies of the structure and dynamics of opaque colloids,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1993).

Kays, T. H.

C. I. Beard, T. H. Kays, V. Twersky, “Scattering by random distribution of spheres vs. concentration,” IEEE Trans. Antennas Propag. AP-15, 99–118 (1967).
[CrossRef]

Kuga, Y.

Lax, M.

M. Lax, V. Narayanamurti, R. C. Fulton, “Classical diffusive photon transport in a slab,” in Proceedings of the Symposium on Laser Optics and Condensed Matter, Leningrad, June 1987, J. L. Birman, H. Z. Cumins, eds. (Plenum, New York, 1987), pp. 229–235.

Lee, S.-C.

S.-C. Lee, “Dependent scattering by parallel fibers: effects of multiple scattering and wave interferences,” J. Thermophys. Heat Tr. 6, 589–595 (1990).
[CrossRef]

Lekner, J.

N. W. Ashcroff, J. Lekner, “Structure and resistivity of liquid metals,” Phys. Rev. 145, 83–90 (1966).
[CrossRef]

MacKintosh, F. C.

F. C. MacKintosh, J. Sajeev, “Diffusion wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
[CrossRef]

Maret, G.

M. Fraden, G. Maret, “Multiple scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

Narayanamurti, V.

M. Lax, V. Narayanamurti, R. C. Fulton, “Classical diffusive photon transport in a slab,” in Proceedings of the Symposium on Laser Optics and Condensed Matter, Leningrad, June 1987, J. L. Birman, H. Z. Cumins, eds. (Plenum, New York, 1987), pp. 229–235.

Pine, D. J.

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

Sajeev, J.

F. C. MacKintosh, J. Sajeev, “Diffusion wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
[CrossRef]

Saulnier, P. M.

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621–2623 (1990).
[CrossRef]

Twersky, V.

V. Twersky, “Transparency of pair correlated, random distribution of small scatterers with applications to the cornea,” J. Opt. Soc. Am. 65, 524–530 (1975).
[CrossRef] [PubMed]

C. I. Beard, T. H. Kays, V. Twersky, “Scattering by random distribution of spheres vs. concentration,” IEEE Trans. Antennas Propag. AP-15, 99–118 (1967).
[CrossRef]

Watson, G. H.

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621–2623 (1990).
[CrossRef]

Weitz, D. A.

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

Wolf, P. E.

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

Yodh, A. G.

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Yoo, K. M.

Zinkin, M. P.

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621–2623 (1990).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

C. I. Beard, T. H. Kays, V. Twersky, “Scattering by random distribution of spheres vs. concentration,” IEEE Trans. Antennas Propag. AP-15, 99–118 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Thermophys. Heat Tr. (1)

S.-C. Lee, “Dependent scattering by parallel fibers: effects of multiple scattering and wave interferences,” J. Thermophys. Heat Tr. 6, 589–595 (1990).
[CrossRef]

Phys. Rev. (1)

N. W. Ashcroff, J. Lekner, “Structure and resistivity of liquid metals,” Phys. Rev. 145, 83–90 (1966).
[CrossRef]

Phys. Rev. B (2)

P. M. Saulnier, M. P. Zinkin, G. H. Watson, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621–2623 (1990).
[CrossRef]

F. C. MacKintosh, J. Sajeev, “Diffusion wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
[CrossRef]

Phys. Rev. Lett. (2)

M. Fraden, G. Maret, “Multiple scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Other (6)

P. D. Kaplan, “Optical studies of the structure and dynamics of opaque colloids,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1993).

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1 and 2, (Academic, New York, 1978), p. 175.

M. Lax, V. Narayanamurti, R. C. Fulton, “Classical diffusive photon transport in a slab,” in Proceedings of the Symposium on Laser Optics and Condensed Matter, Leningrad, June 1987, J. L. Birman, H. Z. Cumins, eds. (Plenum, New York, 1987), pp. 229–235.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 126.

D. J. Pine, D. A. Weitz, G. Maret, P. E. Wolf, E. Herbolzheimer, P. M. Chaikin, “Dynamical correlations of multiply scattered light,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 312–371.

P. F. Jacobs, Rapid Prototyping and Manufacturing—Fundamentals of Stereolithography (Society of Manufacturing Engineers, Dearborn, Mich., 1992).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of experimental apparatus.

Fig. 2
Fig. 2

Transmitted temporal profiles for aqueous dispersion of 0.51-µm alumina particles obtained in 2-mm-thick scattering samples at the ϕ values indicated. The intensity scale is normalized to the same incident intensity.

Fig. 3
Fig. 3

Transmitted temporal profiles for aqueous dispersions of 0.32-µm alumina particles at the ϕ values indicated. The thickness of the scattering samples for ϕ values of 0.02, 0.05, and 0.1 was 2 mm and for 0.3, 0.35 and 0.5 was 1 mm.

Fig. 4
Fig. 4

Transport mean free path versus volume fraction of scattering particles on log–log scale. Solid curves are computed values without correlations and σtr from Mie theory; dashed curves, computed values obtained by using Eq. (3) and S(θ) from PY. Symbols represent transport lengths obtained from the experimental temporal profiles: squares, 0.51-µm alumina; circles, 0.32-µm alumina; triangles, 0.46-µm silica. The curve for 0.51-µm alumina has been shifted up by log (3) for clarity.

Equations (4)

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

t-D2+claI(r, t)=f(r, t),
Iz(t)=14d2tm=1m sin(mπz/d)×exp[-Dt(mπ/d)2]exp(-ct/la),
σtr= dσdΩ[1-cos(θ)]S(θ)dΩ,
S(q)=1+n[g(r)-1]exp(iqr)d3r,

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