Abstract

We formulate a quantitative description of backscattered linearly polarized light with an extended photon diffusion formalism taking explicitly into account the scattering anisotropy parameter g of the medium. From diffusing wave spectroscopy measurements, the characteristic depolarization length for linearly polarized light, lp, is deduced. We investigate the dependence of this length on the scattering anisotropy parameter g spanning an extended range from -1 (backscattering) to 1 (forward scattering). Good agreement is found with Monte Carlo simulations of multiply scattered light.

© 2004 Optical Society of America

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  1. D. A. Weitz, D. J. Pine, in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16, pp. 652–720.
  2. G. Maret, P. E. Wolf, “Multiple light-scattering from disordered media—the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–431 (1987).
    [CrossRef]
  3. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  4. R. Lenke, G. Maret, in Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, Reading, UK, 2000), pp. 1–72.
  5. 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]
  6. E. E. Gorodnichev, A. I. Kuzovlev, D. B. Rogozkin, “Diffusion of circularly polarized light in a disordered medium with large-scale inhomogeneities,” JETP Lett. 68, 22–28 (1998).
    [CrossRef]
  7. F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
    [CrossRef]
  8. F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383–2406 (1989).
    [CrossRef]
  9. D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
    [CrossRef]
  10. V. L. Kuzmin, V. P. Romanov, “Multiply scattered light correlations in an expanded temporal range,” Phys. Rev. E 56, 6008 (1997).
    [CrossRef]
  11. D. Lacoste, V. Rossetto, F. Jaillon, H. Saint-Jalmes, “Geometric depolarization in patterns formed by backscattered light” Opt. Lett. (to be published).
  12. D. A. Zimnyakov, Y. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
    [CrossRef]
  13. A. D. Kim, J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003).
    [CrossRef]
  14. M. Moscoso, J. B. Keller, G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18, 948–960 (2001).
    [CrossRef]
  15. P. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, Dordrecht, The Netherlands, 2001).
  16. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  17. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  18. L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Saenz, P. Schurtenberger, F. Scheffold, “Photonic properties of strongly correlated colloidal liquids” Phys. Rev. Lett. (to be published). We note that in the present work we did not study concentrations above Φ=7.4%on account of a slow and streched long-time decay observed in this supercooled or glassy state. Note that these effects show up much more pronounced in backscattering DWS as compared with the transmission geometry studied previously.
  19. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  20. A. Lagendijk, R. Vreeker, P. DeVries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
    [CrossRef]
  21. J. X. Zhu, D. J. Pine, D. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
    [CrossRef] [PubMed]
  22. R. Lenke, G. Maret, “Magnetic field effects on coherent backscattering of light,” Eur. Phys. J. B 17, 171–185 (2000).
    [CrossRef]
  23. R. Lenke, R. Tweer, G. Maret, “Coherent backscattering of turbid samples containing large Mie spheres,” Pure Appl. Opt. 4, 293–298 (2002).
    [CrossRef]
  24. A. C. Maggs, V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett. 87, 253901 (2001).
    [CrossRef] [PubMed]
  25. A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Express1, 441–453 (1997); www.opticsexpress.org .
    [CrossRef] [PubMed]
  26. A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy—high resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
    [CrossRef]
  27. L. F. Rojas-Ochoa, S. Romer, F. Scheffold, P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
    [CrossRef]
  28. M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
    [PubMed]
  29. I. Freund, M. Kaveh, “Comment on ‘Polarization memory of multiply scattered light’,” Phys. Rev. B 45, 8162–8163 (1992).
  30. F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Reply to ‘Comment on “Polarization memory of multiply scattered light”’,” Phys. Rev. B 45, 8165 (1992).
  31. F. Scheffold, “Particle sizing with diffusing wave spectroscopy,” J. Dispersion Sci. Technol. 23, 591–599 (2002).

2003 (1)

2002 (3)

R. Lenke, R. Tweer, G. Maret, “Coherent backscattering of turbid samples containing large Mie spheres,” Pure Appl. Opt. 4, 293–298 (2002).
[CrossRef]

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

F. Scheffold, “Particle sizing with diffusing wave spectroscopy,” J. Dispersion Sci. Technol. 23, 591–599 (2002).

2001 (3)

A. C. Maggs, V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett. 87, 253901 (2001).
[CrossRef] [PubMed]

M. Moscoso, J. B. Keller, G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18, 948–960 (2001).
[CrossRef]

D. A. Zimnyakov, Y. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
[CrossRef]

2000 (1)

R. Lenke, G. Maret, “Magnetic field effects on coherent backscattering of light,” Eur. Phys. J. B 17, 171–185 (2000).
[CrossRef]

1998 (1)

E. E. Gorodnichev, A. I. Kuzovlev, D. B. Rogozkin, “Diffusion of circularly polarized light in a disordered medium with large-scale inhomogeneities,” JETP Lett. 68, 22–28 (1998).
[CrossRef]

1997 (1)

V. L. Kuzmin, V. P. Romanov, “Multiply scattered light correlations in an expanded temporal range,” Phys. Rev. E 56, 6008 (1997).
[CrossRef]

1994 (1)

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

1992 (2)

I. Freund, M. Kaveh, “Comment on ‘Polarization memory of multiply scattered light’,” Phys. Rev. B 45, 8162–8163 (1992).

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Reply to ‘Comment on “Polarization memory of multiply scattered light”’,” Phys. Rev. B 45, 8165 (1992).

1991 (1)

J. X. Zhu, D. J. Pine, D. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

1990 (1)

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy—high resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

1989 (3)

A. Lagendijk, R. Vreeker, P. DeVries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[CrossRef]

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

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

1988 (2)

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

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]

1987 (2)

G. Maret, P. E. Wolf, “Multiple light-scattering from disordered media—the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–431 (1987).
[CrossRef]

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[PubMed]

Agafonov, D. N.

D. A. Zimnyakov, Y. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
[CrossRef]

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]

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Bohren, C. F.

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

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

DeVries, P.

A. Lagendijk, R. Vreeker, P. DeVries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[CrossRef]

Freund, I.

I. Freund, M. Kaveh, “Comment on ‘Polarization memory of multiply scattered light’,” Phys. Rev. B 45, 8162–8163 (1992).

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[PubMed]

Gorodnichev, E. E.

E. E. Gorodnichev, A. I. Kuzovlev, D. B. Rogozkin, “Diffusion of circularly polarized light in a disordered medium with large-scale inhomogeneities,” JETP Lett. 68, 22–28 (1998).
[CrossRef]

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Hoshen, M.

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[PubMed]

Huffman, D. R.

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

Ishimaru, A.

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

Jaillon, F.

D. Lacoste, V. Rossetto, F. Jaillon, H. Saint-Jalmes, “Geometric depolarization in patterns formed by backscattered light” Opt. Lett. (to be published).

John, S.

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

Kaplan, P. D.

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy—high resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Kaveh, M.

I. Freund, M. Kaveh, “Comment on ‘Polarization memory of multiply scattered light’,” Phys. Rev. B 45, 8162–8163 (1992).

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[PubMed]

Keller, J. B.

Kim, A. D.

Kuzmin, V. L.

V. L. Kuzmin, V. P. Romanov, “Multiply scattered light correlations in an expanded temporal range,” Phys. Rev. E 56, 6008 (1997).
[CrossRef]

Kuzovlev, A. I.

E. E. Gorodnichev, A. I. Kuzovlev, D. B. Rogozkin, “Diffusion of circularly polarized light in a disordered medium with large-scale inhomogeneities,” JETP Lett. 68, 22–28 (1998).
[CrossRef]

Lacoste, D.

D. Lacoste, V. Rossetto, F. Jaillon, H. Saint-Jalmes, “Geometric depolarization in patterns formed by backscattered light” Opt. Lett. (to be published).

Lagendijk, A.

A. Lagendijk, R. Vreeker, P. DeVries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[CrossRef]

Lenke, R.

R. Lenke, R. Tweer, G. Maret, “Coherent backscattering of turbid samples containing large Mie spheres,” Pure Appl. Opt. 4, 293–298 (2002).
[CrossRef]

R. Lenke, G. Maret, “Magnetic field effects on coherent backscattering of light,” Eur. Phys. J. B 17, 171–185 (2000).
[CrossRef]

R. Lenke, G. Maret, in Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, Reading, UK, 2000), pp. 1–72.

MacKintosh, F. C.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Reply to ‘Comment on “Polarization memory of multiply scattered light”’,” Phys. Rev. B 45, 8165 (1992).

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

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Maggs, A. C.

A. C. Maggs, V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett. 87, 253901 (2001).
[CrossRef] [PubMed]

Maret, G.

R. Lenke, R. Tweer, G. Maret, “Coherent backscattering of turbid samples containing large Mie spheres,” Pure Appl. Opt. 4, 293–298 (2002).
[CrossRef]

R. Lenke, G. Maret, “Magnetic field effects on coherent backscattering of light,” Eur. Phys. J. B 17, 171–185 (2000).
[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]

G. Maret, P. E. Wolf, “Multiple light-scattering from disordered media—the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–431 (1987).
[CrossRef]

R. Lenke, G. Maret, in Multiple Scattering of Light: Coherent Backscattering and Transmission, W. Brown, ed. (Gordon & Breach, Reading, UK, 2000), pp. 1–72.

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[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]

Mendez-Alcaraz, J. M.

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Saenz, P. Schurtenberger, F. Scheffold, “Photonic properties of strongly correlated colloidal liquids” Phys. Rev. Lett. (to be published). We note that in the present work we did not study concentrations above Φ=7.4%on account of a slow and streched long-time decay observed in this supercooled or glassy state. Note that these effects show up much more pronounced in backscattering DWS as compared with the transmission geometry studied previously.

Moscoso, M.

Papanicolaou, G.

Pine, D. J.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Reply to ‘Comment on “Polarization memory of multiply scattered light”’,” Phys. Rev. B 45, 8165 (1992).

J. X. Zhu, D. J. Pine, D. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy—high resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16, pp. 652–720.

Rogozkin, D. B.

E. E. Gorodnichev, A. I. Kuzovlev, D. B. Rogozkin, “Diffusion of circularly polarized light in a disordered medium with large-scale inhomogeneities,” JETP Lett. 68, 22–28 (1998).
[CrossRef]

Rojas-Ochoa, L. F.

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Saenz, P. Schurtenberger, F. Scheffold, “Photonic properties of strongly correlated colloidal liquids” Phys. Rev. Lett. (to be published). We note that in the present work we did not study concentrations above Φ=7.4%on account of a slow and streched long-time decay observed in this supercooled or glassy state. Note that these effects show up much more pronounced in backscattering DWS as compared with the transmission geometry studied previously.

Romanov, V. P.

V. L. Kuzmin, V. P. Romanov, “Multiply scattered light correlations in an expanded temporal range,” Phys. Rev. E 56, 6008 (1997).
[CrossRef]

Romer, S.

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

Rosenbluh, M.

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[PubMed]

Rossetto, V.

A. C. Maggs, V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett. 87, 253901 (2001).
[CrossRef] [PubMed]

D. Lacoste, V. Rossetto, F. Jaillon, H. Saint-Jalmes, “Geometric depolarization in patterns formed by backscattered light” Opt. Lett. (to be published).

Saenz, J. J.

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Saenz, P. Schurtenberger, F. Scheffold, “Photonic properties of strongly correlated colloidal liquids” Phys. Rev. Lett. (to be published). We note that in the present work we did not study concentrations above Φ=7.4%on account of a slow and streched long-time decay observed in this supercooled or glassy state. Note that these effects show up much more pronounced in backscattering DWS as compared with the transmission geometry studied previously.

Saint-Jalmes, H.

D. Lacoste, V. Rossetto, F. Jaillon, H. Saint-Jalmes, “Geometric depolarization in patterns formed by backscattered light” Opt. Lett. (to be published).

Scheffold, F.

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

F. Scheffold, “Particle sizing with diffusing wave spectroscopy,” J. Dispersion Sci. Technol. 23, 591–599 (2002).

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Saenz, P. Schurtenberger, F. Scheffold, “Photonic properties of strongly correlated colloidal liquids” Phys. Rev. Lett. (to be published). We note that in the present work we did not study concentrations above Φ=7.4%on account of a slow and streched long-time decay observed in this supercooled or glassy state. Note that these effects show up much more pronounced in backscattering DWS as compared with the transmission geometry studied previously.

Schmitt, J. M.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Schurtenberger, P.

L. F. Rojas-Ochoa, S. Romer, F. Scheffold, P. Schurtenberger, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403 (2002).
[CrossRef]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Saenz, P. Schurtenberger, F. Scheffold, “Photonic properties of strongly correlated colloidal liquids” Phys. Rev. Lett. (to be published). We note that in the present work we did not study concentrations above Φ=7.4%on account of a slow and streched long-time decay observed in this supercooled or glassy state. Note that these effects show up much more pronounced in backscattering DWS as compared with the transmission geometry studied previously.

Sebbah, P.

P. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, Dordrecht, The Netherlands, 2001).

Sinichkin, Y. P.

D. A. Zimnyakov, Y. P. Sinichkin, P. V. Zakharov, D. N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media 11, 395–412 (2001).
[CrossRef]

Tweer, R.

R. Lenke, R. Tweer, G. Maret, “Coherent backscattering of turbid samples containing large Mie spheres,” Pure Appl. Opt. 4, 293–298 (2002).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vreeker, R.

A. Lagendijk, R. Vreeker, P. DeVries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[CrossRef]

Weitz, D.

J. X. Zhu, D. J. Pine, D. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Weitz, D. A.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Reply to ‘Comment on “Polarization memory of multiply scattered light”’,” Phys. Rev. B 45, 8165 (1992).

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16, pp. 652–720.

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]

G. Maret, P. E. Wolf, “Multiple light-scattering from disordered media—the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–431 (1987).
[CrossRef]

Yodh, A. G.

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy—high resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Zakharov, P. V.

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D. A. Weitz, D. J. Pine, in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16, pp. 652–720.

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

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Figures (4)

Fig. 1
Fig. 1

Normalized path-length distribution P(s)×l for backscattered light from a semi-infinite medium. The symbols refer to Monte Carlo simulations, and the curves are calculations based on relation (2) with f(g)=3g/2 (solid) and f(g)0 (dashed). Inset: f(g) obtained from Eq. (1) adjusted to fit the simulation results. The wavelength is λ0=532 nm, and the refractive indices are np=1.59 of the particle and ns=1.332 of the solvent. Nonreflecting boundary conditions were used.

Fig. 2
Fig. 2

Depolarization of multiply scattered light: 2d(s)-1 from theory [Eq. (4), curves] and simulation (symbols). Excellent agreement is found for Rayleigh scatterers, while for larger particles the agreement becomes somewhat less good.

Fig. 3
Fig. 3

DWS autocorrelation function for different g values detecting polarized and depolarized light. The lines are calculations based on Eq. (12) with lp adjusted to fit the data best [(g=-0.78: l*/la=0.004, lp/l*=4.83), (g=0.32: l*/la=0.0064, lp/l*=2.21), (g=0.924: l*/la=0.016, lp/l*=0.713)].

Fig. 4
Fig. 4

(a), (b) Depolarization length lp from DWS measurements and Monte Carlo simulations: (squares) measurements for different particle sizes (random particle configuration S(q)1), (circles) strongly interacting charged particles,18 (triangles) hard-sphere data from Ref. 27, (Diamonds) Monte Carlo simulations. (c) Depolarization ratio directly obtained from the measured intensities. The curves are calculated from the linear fit to lp/l* shown in (a).4,22

Tables (1)

Tables Icon

Table 1 Diameter as Obtained from Dynamic Light Scattering, Volume Fraction Φ, and Scattering Anisotropy Parameter g

Equations (20)

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

P(s)=34πl*s3/2zpexp-34zp2l*s+(zp+2ze)exp-34(zp+2ze)2l*s,
Pcorr(s)P(s)[1-f(g)exp(-s/l*)].
P,(s)=d,(s)P(s),
d(s)=1+2 exp(-s/lp)2+exp(-s/lp),
d(s)=1-exp(-s/lp)2+exp(-s/lp),
P,(s)[12±34exp(-s/lp)]P(s).
g1(t)=0P(s)exp[-2(t/τ0)s/l*]ds.
6t/τ06t/τ0+3l*/la
g1(t)=exp(-γx),
γ=1+ze/l*=5/3.
g1(t)=0P(s)exp[-2(t/τ0)(s/l*)ds]P(s)ds,
g1(t)=0P(s)exp[-2(t/τ0)(s/l*)ds]0P(s)ds.
g1,(t)
=h[x1(t)]-32h[y1(t)]-3g2h[x2(t)]+9g4h[y2(t)]h[x1(0)]-32h[y1(0)]-3g2h[x2(0)]+9g4h[y2(0)],
g1,(t)
=h[x1(t)]+32h[y1(t)]-3g2h[x2(t)]-9g4h[y2(t)]h[x1(0)]+32h[y1(0)]-3g2h[x2(0)]-9g4h[y2(0)],
d=I-II+I.
d=0[P(s)-P(s)]ds0[P(s)+P(s)]ds032exp(-s/lp)P(s)ds,
d(s)32exp(-s/lp).
d=0P(s)d(s)ds34{exp[-γp(3l*/lp)1/2]+exp[-(γp+2γe)×(3l*/lp)1/2]}.

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