Abstract

We review the general features of coherent multiple scattering of electromagnetic waves in random media. In particular, coherent backscattering and angular correlation functions of speckle patterns are studied in some detail. We present a general formalism based on a physically intuitive description that also permits us to derive quantitative expressions. Then, the notion of phase boxes describing the quantum crossings of diffusons is discussed. This notion permits us to understand the long-range correlations that are at the origin of most of the mesoscopic effects either for electrons or photons. Then, we turn to the problem of decoherence, namely, the washing out of interference effects. We use as an example the effect of a nondeterministic motion of the scatterers. We discuss some applications of these ideas to diffusive wave spectroscopy, including calculations of the intensity–time correlation function in the presence of quantum crossings.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. “Mesoscopic quantum physics,” in Proceedings of the Les Houches Summer School, Session LXI, E. Akkermans, G. Montambaux, J. L. Pichard, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1995).
  2. Y. Imry, “The physics of mesoscopic systems,” in Directions in Condensed Matter Physics, G. Grinstein and G. Mazenko, eds. (World Scientific, Singapore, 1986).
  3. Y. Imry, Introduction to Mesoscopic Physics (Mesoscopic Physics and Nanotechnology) 2nd ed. (Oxford University, Oxford, UK, 2002).
  4. S. Chakraverty and A. Schmid, “Weak-localization: the quasi-classical theory of electrons in a random potential,” Phys. Rep. 140, 193–236 (1986).
    [CrossRef]
  5. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (EDP Sciences-CNRS, Paris, 2004).
  6. Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990).
  7. E. Akkermans and G. Montambaux, “Coherent multiple scattering in disordered media,” http: //arxiv.org/abs/cond-mat/0104013.
  8. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999), Chap. X.
  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, UK, 1995).
  10. B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics (Wiley, New York, 1976).
  11. G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B: Condens. Matter 65, 409–414 (1987).
    [CrossRef]
  12. P. E. Wolf and G. Maret, “Dynamics of Brownian particles from strongly multiple light scattering,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990).
  13. G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
    [CrossRef]
  14. T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
    [CrossRef] [PubMed]
  15. A. A. Golubentsev, “Suppression of interference effects in multiple scattering of light,” Sov. Phys. JETP 59, 26–39 (1984).
  16. E. Akkermans and R. Maynard, “Weak localization of waves,” J. Phys. (France) Lett. 46, L1045–1053 (1985).
  17. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
    [CrossRef] [PubMed]
  18. E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
    [CrossRef]
  19. B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
    [CrossRef]
  20. P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  21. M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  22. D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
    [CrossRef] [PubMed]
  23. A precursor of this effect has been observed in L. Tsang and A. Ishimaru, “Backscattering enhancement of random discrete scatterers,” J. Opt. Soc. Am. A 1, 836–839 (1984).
    [CrossRef]
  24. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  25. B. Shapiro, “Large-intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
    [CrossRef]
  26. R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
    [CrossRef]
  27. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
    [CrossRef] [PubMed]
  28. S. Hikami, “Anderson localization in a nonlinear-σ-model representation,” Phys. Rev. B 24, 2671–2679 (1981).
    [CrossRef]
  29. M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
    [CrossRef]
  30. S. Feng and P. A. Lee, “Mesoscopic conductors and correlations in laser speckle patterns,” Science 251, 633–639 (1991).
    [CrossRef] [PubMed]
  31. S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
    [CrossRef] [PubMed]
  32. R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
    [CrossRef]
  33. S. Washburn, “Fluctuations in the extrinsic conductivity of disordered metals,” IBM J. Res. Dev. 32, 335–346 (1988).
    [CrossRef]
  34. B. L. Al’tshuler and B. Shklovskiĭ, “Repulsion of energy lev-els and conductivity of small metal samples,” Sov. Phys. JETP 64, 127–141 (1986).
  35. F. Scheffold and G. Maret, “Universal conductance of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
    [CrossRef]
  36. A. G. Aronov and Y. V. Sharvin, “Magnetic flux effects in disordered conductors,” Rev. Mod. Phys. 59, 755–779 (1987).
    [CrossRef]
  37. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  38. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
    [CrossRef]
  39. G. Maret, “Dynamic speckla correlations,” in NATO Advanced Study Institute on Waves and Imaging through Ran-dom Media, P. Sebbah, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 413–434.
  40. F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
    [CrossRef]
  41. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, UK, 1986).
  42. E. Akkermans, C. Miniatura, and C. A. Müller, “Phase coherence times in the multiple scattering of photons by cold atoms,” http://arxiv.org/abs/cond-mat/0206298.
  43. C. A. Müller and C. Miniatura, “Multiple scattering of light by atoms with internal degeneracy,” J. Phys. A 35, 10163–10188 (2002).
    [CrossRef]

2002 (2)

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

C. A. Müller and C. Miniatura, “Multiple scattering of light by atoms with internal degeneracy,” J. Phys. A 35, 10163–10188 (2002).
[CrossRef]

2000 (1)

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

1999 (2)

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[CrossRef]

1998 (1)

F. Scheffold and G. Maret, “Universal conductance of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

1997 (1)

F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[CrossRef]

1995 (1)

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
[CrossRef] [PubMed]

1994 (1)

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[CrossRef]

1991 (1)

S. Feng and P. A. Lee, “Mesoscopic conductors and correlations in laser speckle patterns,” Science 251, 633–639 (1991).
[CrossRef] [PubMed]

1989 (1)

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[CrossRef]

1988 (6)

S. Washburn, “Fluctuations in the extrinsic conductivity of disordered metals,” IBM J. Res. Dev. 32, 335–346 (1988).
[CrossRef]

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

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, R. Maynard, and 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 and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B: Condens. Matter 65, 409–414 (1987).
[CrossRef]

A. G. Aronov and Y. V. Sharvin, “Magnetic flux effects in disordered conductors,” Rev. Mod. Phys. 59, 755–779 (1987).
[CrossRef]

1986 (4)

B. L. Al’tshuler and B. Shklovskiĭ, “Repulsion of energy lev-els and conductivity of small metal samples,” Sov. Phys. JETP 64, 127–141 (1986).

B. Shapiro, “Large-intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef]

S. Chakraverty and A. Schmid, “Weak-localization: the quasi-classical theory of electrons in a random potential,” Phys. Rep. 140, 193–236 (1986).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

1985 (3)

E. Akkermans and R. Maynard, “Weak localization of waves,” J. Phys. (France) Lett. 46, L1045–1053 (1985).

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

1984 (2)

A precursor of this effect has been observed in L. Tsang and A. Ishimaru, “Backscattering enhancement of random discrete scatterers,” J. Opt. Soc. Am. A 1, 836–839 (1984).
[CrossRef]

A. A. Golubentsev, “Suppression of interference effects in multiple scattering of light,” Sov. Phys. JETP 59, 26–39 (1984).

1981 (1)

S. Hikami, “Anderson localization in a nonlinear-σ-model representation,” Phys. Rev. B 24, 2671–2679 (1981).
[CrossRef]

Ahmed, R. E.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Akkermans, E.

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

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

E. Akkermans and R. Maynard, “Weak localization of waves,” J. Phys. (France) Lett. 46, L1045–1053 (1985).

Al’tshuler, B. L.

B. L. Al’tshuler and B. Shklovskiĭ, “Repulsion of energy lev-els and conductivity of small metal samples,” Sov. Phys. JETP 64, 127–141 (1986).

Aronov, A. G.

A. G. Aronov and Y. V. Sharvin, “Magnetic flux effects in disordered conductors,” Rev. Mod. Phys. 59, 755–779 (1987).
[CrossRef]

Athey, B. D.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Berkovits, R.

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[CrossRef]

Bernard, J.-C.

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

Chaikin, P. M.

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

Chakraverty, S.

S. Chakraverty and A. Schmid, “Weak-localization: the quasi-classical theory of electrons in a random potential,” Phys. Rep. 140, 193–236 (1986).
[CrossRef]

de Tomasi, F.

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

Delande, D.

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

Deslauriers, L.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Dilworth, D. S.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Feng, S.

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[CrossRef]

S. Feng and P. A. Lee, “Mesoscopic conductors and correlations in laser speckle patterns,” Science 251, 633–639 (1991).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Golubentsev, A. A.

A. A. Golubentsev, “Suppression of interference effects in multiple scattering of light,” Sov. Phys. JETP 59, 26–39 (1984).

Grannell, S. M.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Hartl, W.

F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[CrossRef]

Herbolzheimer, E.

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

Hikami, S.

S. Hikami, “Anderson localization in a nonlinear-σ-model representation,” Phys. Rev. B 24, 2671–2679 (1981).
[CrossRef]

Hoover, B. G.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Ishimaru, A.

Jonckheere, T.

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

Kaiser, R.

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Labeyrie, G.

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

Lagendijk, A.

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
[CrossRef] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Lee, P. A.

S. Feng and P. A. Lee, “Mesoscopic conductors and correlations in laser speckle patterns,” Science 251, 633–639 (1991).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Leith, E. N.

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Maret, G.

F. Scheffold and G. Maret, “Universal conductance of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[CrossRef]

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

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B: Condens. Matter 65, 409–414 (1987).
[CrossRef]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Matijevic, E.

F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[CrossRef]

Maynard, R.

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

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

E. Akkermans and R. Maynard, “Weak localization of waves,” J. Phys. (France) Lett. 46, L1045–1053 (1985).

Miniatura, C.

C. A. Müller and C. Miniatura, “Multiple scattering of light by atoms with internal degeneracy,” J. Phys. A 35, 10163–10188 (2002).
[CrossRef]

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

Müller, C. A.

C. A. Müller and C. Miniatura, “Multiple scattering of light by atoms with internal degeneracy,” J. Phys. A 35, 10163–10188 (2002).
[CrossRef]

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

Nieuwenhuizen, T. M.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[CrossRef]

Pine, D. J.

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

Pnini, R.

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[CrossRef]

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Scheffold, F.

F. Scheffold and G. Maret, “Universal conductance of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[CrossRef]

Schmid, A.

S. Chakraverty and A. Schmid, “Weak-localization: the quasi-classical theory of electrons in a random potential,” Phys. Rep. 140, 193–236 (1986).
[CrossRef]

Shapiro, B.

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[CrossRef]

B. Shapiro, “Large-intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef]

Sharvin, Y. V.

A. G. Aronov and Y. V. Sharvin, “Magnetic flux effects in disordered conductors,” Rev. Mod. Phys. 59, 755–779 (1987).
[CrossRef]

Shklovskii?, B.

B. L. Al’tshuler and B. Shklovskiĭ, “Repulsion of energy lev-els and conductivity of small metal samples,” Sov. Phys. JETP 64, 127–141 (1986).

Stephen, M. J.

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Tsang, L.

van Albada, M. P.

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
[CrossRef] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

van Rossum, M. C. W.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[CrossRef]

van Tiggelen, B. A.

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
[CrossRef] [PubMed]

Washburn, S.

S. Washburn, “Fluctuations in the extrinsic conductivity of disordered metals,” IBM J. Res. Dev. 32, 335–346 (1988).
[CrossRef]

Weitz, D. A.

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

Wiersma, D. S.

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
[CrossRef] [PubMed]

Wolf, P. E.

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

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B: Condens. Matter 65, 409–414 (1987).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

IBM J. Res. Dev. (1)

S. Washburn, “Fluctuations in the extrinsic conductivity of disordered metals,” IBM J. Res. Dev. 32, 335–346 (1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. (France) Lett. (1)

E. Akkermans and R. Maynard, “Weak localization of waves,” J. Phys. (France) Lett. 46, L1045–1053 (1985).

J. Phys. (Paris) (1)

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

J. Phys. A (1)

C. A. Müller and C. Miniatura, “Multiple scattering of light by atoms with internal degeneracy,” J. Phys. A 35, 10163–10188 (2002).
[CrossRef]

Phys. Rep. (2)

S. Chakraverty and A. Schmid, “Weak-localization: the quasi-classical theory of electrons in a random potential,” Phys. Rep. 140, 193–236 (1986).
[CrossRef]

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[CrossRef]

Phys. Rev. B (4)

S. Hikami, “Anderson localization in a nonlinear-σ-model representation,” Phys. Rev. B 24, 2671–2679 (1981).
[CrossRef]

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[CrossRef]

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

F. Scheffold, W. Hartl, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal–intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[CrossRef]

Phys. Rev. E (1)

B. G. Hoover, L. Deslauriers, S. M. Grannell, R. E. Ahmed, D. S. Dilworth, B. D. Athey, and E. N. Leith, “Correlations among angular wave component amplitudes in elastic, multiple-scattering random media,” Phys. Rev. E 65, 026614–026621 (2002).
[CrossRef]

Phys. Rev. Lett. (11)

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental evidence for recurrent multiple-scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, “Coherent backscattering of light by cold atoms,” Phys. Rev. Lett. 83, 5266–5269 (1999).
[CrossRef]

T. Jonckheere, C. A. Müller, R. Kaiser, C. Miniatura, and D. Delande, “Multiple scattering of light by atoms in the weak localization regime,” Phys. Rev. Lett. 85, 4269–4272 (2000).
[CrossRef] [PubMed]

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

F. Scheffold and G. Maret, “Universal conductance of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

B. Shapiro, “Large-intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[CrossRef]

A. G. Aronov and Y. V. Sharvin, “Magnetic flux effects in disordered conductors,” Rev. Mod. Phys. 59, 755–779 (1987).
[CrossRef]

Science (1)

S. Feng and P. A. Lee, “Mesoscopic conductors and correlations in laser speckle patterns,” Science 251, 633–639 (1991).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

B. L. Al’tshuler and B. Shklovskiĭ, “Repulsion of energy lev-els and conductivity of small metal samples,” Sov. Phys. JETP 64, 127–141 (1986).

A. A. Golubentsev, “Suppression of interference effects in multiple scattering of light,” Sov. Phys. JETP 59, 26–39 (1984).

Z. Phys. B: Condens. Matter (1)

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B: Condens. Matter 65, 409–414 (1987).
[CrossRef]

Other (14)

P. E. Wolf and G. Maret, “Dynamics of Brownian particles from strongly multiple light scattering,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990).

“Mesoscopic quantum physics,” in Proceedings of the Les Houches Summer School, Session LXI, E. Akkermans, G. Montambaux, J. L. Pichard, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1995).

Y. Imry, “The physics of mesoscopic systems,” in Directions in Condensed Matter Physics, G. Grinstein and G. Mazenko, eds. (World Scientific, Singapore, 1986).

Y. Imry, Introduction to Mesoscopic Physics (Mesoscopic Physics and Nanotechnology) 2nd ed. (Oxford University, Oxford, UK, 2002).

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (EDP Sciences-CNRS, Paris, 2004).

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

E. Akkermans and G. Montambaux, “Coherent multiple scattering in disordered media,” http: //arxiv.org/abs/cond-mat/0104013.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999), Chap. X.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, UK, 1995).

B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics (Wiley, New York, 1976).

G. Maret, “Dynamic speckla correlations,” in NATO Advanced Study Institute on Waves and Imaging through Ran-dom Media, P. Sebbah, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 413–434.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, UK, 1986).

E. Akkermans, C. Miniatura, and C. A. Müller, “Phase coherence times in the multiple scattering of photons by cold atoms,” http://arxiv.org/abs/cond-mat/0206298.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Geometry of a slab of width L and section S used for the measurement of the angular-correlation functions both in reflection and in transmission.

Fig. 2
Fig. 2

Multiple scattering trajectories that contribute both to the incoherent and the coherent intensity.

Fig. 3
Fig. 3

Multiple scattering trajectories that contribute to the classical probability.

Fig. 4
Fig. 4

Contribution of the diffuson to the average incoherent albedo.

Fig. 5
Fig. 5

Contribution of the cooperon to the average coherent albedo.

Fig. 6
Fig. 6

Angular-correlation function in transmission corresponding to four waves incident along the directions sˆa and sˆa and outgoing along the directions sˆb and sˆb. A nonzero contribution corresponds to the pairing of two amplitudes into a diffusion.

Fig. 7
Fig. 7

Two contributions to the product TabTab¯ that correspond, respectively, to the pairing C1=C2, C3=C4 and C1=C4, C2=C3. The first gives T¯abT¯ab. The second corresponds to the angular correlation function noted Cabab(1) in the text.

Fig. 8
Fig. 8

Contribution to δTabδTab¯ involving one crossing of the two diffusons. The different cases correspond to configurations of plane waves incident along sˆa and sˆa and outgoing along sˆb and sˆb. The diagrams on the left depend on Δsˆb but not on Δsˆa and the opposite for the diagrams on the right.

Fig. 9
Fig. 9

Classification of the contributions to the correlation-function Cabab in terms of the number of crossings of two diffusons. At each crossing, the corresponding contribution is multiplied by 1/g1. The three contributions represented in (a), (b), (c) are denoted, respectively, C(1), C(2), C(3).

Fig. 10
Fig. 10

Two crossings terms. Such diagrams do not give rise to an angular structure.

Fig. 11
Fig. 11

Trajectories contributing to the time-correlation functions.

Equations (63)

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

γ12(r, T)=E(r, T)E*(r, 0)|E(r, 0)|2 .
A(k, k)=r1,r2f(r1, r2)exp[i(k·r1-k·r2)],
|A(k, k)|2=r1,r2r3,r4f(r1, r2)f*(r3, r4)×exp[i(k·r1-k·r2)]×exp[-i(k·r3-k·r4)]
f(r1, r2)f*(r3, r4)=j,jaj*(r1, r2)aj(r3, r4)=j,j|aj||aj|exp[2iπ(δj-δj)].
|A(k, k)|2¯=r1,r2|f(r1, r2)|2¯×{1+exp[i(k+k)·(r1-r2)]}.
P(r, r, ω)=4πc fω0(r, r)fω0-ω*(r, r)¯,
(-iω-DΔr)P(r, r, ω)=δ(r-r),
αd=c4πle2S dr1dr2 exp-z1leexp-z2μleP(r1, r2),
αd=c4πle2 0dz1dz2 exp-z1le×exp-z2μleSd2ρP(ρ, z1, z2).
P(ρ, z1, z2)=14πD 1ρ2+(z1-z2)2-1ρ2+(z1+z2+2z0)2,
αd=34πμz0le+μμ+1.
αc=c4πle2 dr1dr2 exp-μ+12µ z1+z2leP(r1, r2)×exp[ik(sˆi+sˆe)·(r2-r1)].
αc(θ=0)=αd.
αc=c4πle2 0dz1dz2×exp-μ+12µ z1+z2le×Sd2ρP(ρ, z1, z2)exp(ik·ρ).
P(k, z1, z2)=12Dk{exp(-k|z1-z2|)-exp[-k(z1+z2+2z0)]}.
αc(θ)=38π 1(1+kle)2 1+1-exp(-2kz0)kle.
αc(θ)αc(0)-34π (le+z0)2lek+O(k2).
αc(θ)αc(0)-βkle,
β=34π 1+z0le2=2512π.
P(k, z, z, t)=exp(-Dk2t)(4πDt)1/2{exp[-(z-z)2/4Dt]-exp[-(z+z+2z0)2/4Dt]}.
αc(θ)259cle20dt exp(-Dk2t)(4πDt)3/2.
Cabab=δTabδTab¯T¯abT¯ab,
δTab2¯=Tab¯2.
T¯ab=c4πle2 dz1dz2d2ρ exp(-z1/μale)×exp(-|L-z2|/μble)P(ρ, z1, z2),
T¯ab=c4πμaμbSd2ρP(ρ, μale, L-μble)=c4πμaμbP(k=0, μale, L-μble),
P(k, z, z)=1D sinh kzm sinh k(L-zM)k sinh kL,
P(0, z, z)=zmD 1-zML.
T¯ab=34π leL.
δTabδTab¯=c4πle2 d2ρdz1dz2×exp[ik(Δsˆa·ρ1-Δsˆb·ρ2)]exp(-z1/le)×exp(-|L-z2|/le)P(ρ, z1, z2)2.
Cabab(1)=δΔsˆa,ΔsˆbF1(qaL)=δΔsˆa,ΔsˆbqaLsinh qaL2
F1(x)=xsinh x2
δRabΔRab¯=c4πle2 d2ρdz1dz2×exp[ik(Δsˆa·r1-Δsˆb·r2)]exp(-z1/le)×exp(-z2/le)P(ρ, z1, z2)2,
δRabδRab¯=δΔsˆa,Δsˆbc4πle2 0dz1dz2×exp(-z1/le)exp(-z2/le)P(qa, z1, z2)2,
δRabδRab¯=R¯abR¯abδΔsˆa,Δsˆbαc(qa)αc(0)2.
g=k2leS3πL,
(aa)(aa)(bb)(bb)
(aa)(aa)(bb)(bb).
δTabδTab¯(2)=cSle22i=14dri{exp[ikΔsˆb·(r2-r4)]+exp[ikΔsˆa·Δ(r1-r3)]}E(zi)×i=14dRiH(Ri)P(r1, R1)P(r3, R3)×P(R2, r2)P(R4, r4),
H(r1, r2, r3, r4)=le524πk2 dri=14δ(r-ri)2·4,
E(zi)=exp[-(z1+z3)/le]×exp(-|L-z2|/le)exp(-|L-z4|/le).
δTabδTab¯(2)=lec424πk2S 0Ldz[zP(0, le, z)]2×P(qb, z, L-le)2,
zP(0, le, z)=-leDL,P(qb, z, L-le)=leD sinh qbzsinh qbL,
δTabδTab¯(2)=8148π lek2LSF2(qbL),
F2(x)=1sinh2 x sinh 2x2x-1.
Cabab(2)=δTabδTa,b¯Tab¯2=1g[F2(qaL)+F2(qbL)].
Cabab(2)=1g 23+F2(kLΔsˆb)bb 23g
C(3):(aa)(aa)(bb)(bb).
δTabδTab¯(3)|K1=(2h4)2 le4(4π)4S2 4πcle24×0LaLdzdz[zP(0, le, z)]2×P(0, z, z)2[zP(0, z, L-le)]2,
Cabab(3)|K1=4g2 D2L4 0L0LdzdzP(z, z)2.
Cabab(3)=δTabδTab¯(3)T¯ab2=215 1g2.
E(r, T)=n=1Cn|A[Cn(T)]|exp[iϕn(T)],
γ12(r, T)n,nCn,Cn|A[Cn(T)]||A[Cn(0)]|×exp{i[ϕn(T)-ϕn(0)]},
γ12(r, T)nP(r0, r, n)exp{i[ϕn(T)-ϕn(0)]},
exp[iΔϕn(T)]exp-12Δϕn2(T)=exp[-nτe/τϕ(T)]=exp[-t/τϕ(T)],
g2(T)=I(T)I(0)I(0)2-1,
γ12(r, T)=0dtP(r, t)exp(-tT/2τbτe),
Dk21τϕ=T2τeτb.
g2(T)=|γ12(T)|2.
g2(1)(T)=F1(L/Lϕ)=L/Lϕsinh L/Lϕ2,
g2(2)(T)=2gF2(L/Lϕ),
g2(3)(T)=0L0LdzdzP2(1/Lϕ, z, z)=L48D2F3(L/Lϕ),
g2(3)(T)=1g2F3(L/Lϕ),
F3(x)=32 2+2x2-2 cosh 2x+x sinh 2xx4 sinh2 x.

Metrics