Advertisement

The European Physical Journal Special Topics

, Volume 226, Issue 7, pp 1549–1561 | Cite as

Dynamic coherent backscattering of ultrasound in three-dimensional strongly-scattering media

  • L. A. Cobus
  • B. A. van Tiggelen
  • A. Derode
  • J. H. Page
Open Access
Regular Article
Part of the following topical collections:
  1. From Ill-condensed Matter to Mesoscopic Wave Propagation

Abstract

We present measurements of the diffusion coefficient of ultrasound in strongly scattering three-dimensional (3D) disordered media using the dynamic coherent backscattering (CBS) effect. Our experiments measure the CBS of ultrasonic waves using a transducer array placed in the far-field of a 3D slab sample of brazed aluminum beads surrounded by vacuum. We extend to 3D media the general microscopic theory of CBS that was developed initially for acoustic waves in 2D. This theory is valid in the strong scattering, but still diffuse, regime that is realized in our sample, and is evaluated in the diffuse far field limit encountered in our experiments. By comparing our theory with the experimental data, we obtain an accurate measurement of the Boltzmann diffusion coefficient of ultrasound in our sample. We find that the value of D B is quite small, 0.74 ± 0.03 mm2/μs, and comment on the implications of this slow transport for the energy velocity.

References

  1. 1.
    P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd edn. (Springer, Berlin, 2006)Google Scholar
  2. 2.
    M.P. van Albada, A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985)ADSCrossRefGoogle Scholar
  3. 3.
    P.E. Wolf, G. Maret, Phys. Rev. Lett. 55, 2696 (1985)ADSCrossRefGoogle Scholar
  4. 4.
    Y. Kuga, L. Tsang, A. Ishimaru, JOSA A Comm. 2, 3 (1985)CrossRefGoogle Scholar
  5. 5.
    E. Akkermans, P.E. Wolf, R. Maynard, G. Maret, J. Phys. France 49, 77 (1988)ADSCrossRefGoogle Scholar
  6. 6.
    G. Bayer, T. Niederdränk, Phys. Rev. Lett. 70, 3884 (1993)ADSCrossRefGoogle Scholar
  7. 7.
    A. Tourin, A. Derode, P. Roux, B.A. van Tiggelen, M. Fink, Phys. Rev. Lett. 79, 3637 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    T. Jonckheere, C. Müller, R. Kaiser, C. Miniatura, D. Delande, Phys. Rev. Lett. 85, 4269 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    P.E. Wolf, G. Maret, E. Akkermans, R. Maynard, J. Phys. France 49, 63 (1988)CrossRefGoogle Scholar
  10. 10.
    V. Mamou, Doctoral thesis, Université Paris VII, 2005Google Scholar
  11. 11.
    A. Aubry, A. Derode, Phys. Rev. E 75, 026602 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    A. Aubry, L.A. Cobus, S.E. Skipetrov, B.A. van Tiggelen, A. Derode, J.H. Page, Phys. Rev. Lett. 112, 043903 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    L.A. Cobus, A. Aubry, S.E. Skipetrov, B.A. van Tiggelen, A. Derode, J.H. Page, Phys. Rev. Lett. 116, 193901 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    L.A. Cobus, Doctoral thesis, University of Manitoba, 2016Google Scholar
  15. 15.
    D.S. Wiersma, M.P. van Albada, B.A. van Tiggelen, A. Lagendijk, Phys. Rev. Lett. 74, 4193 (1995)ADSCrossRefGoogle Scholar
  16. 16.
    B.A. van Tiggelen, D.A. Wiersma, A. Lagendijk, Europhys. Lett. 30, 1 (1995)ADSCrossRefGoogle Scholar
  17. 17.
    H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Nat. Phys. 4, 945 (2008)CrossRefGoogle Scholar
  18. 18.
    H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd edn. (Oxford University Press, 1995)Google Scholar
  19. 19.
    H.P. Schriemer, M.L. Cowan, J.H. Page, P. Sheng, Z. Liu, D.A. Weitz, Phys. Rev. Lett. 79, 3166 (1997)ADSCrossRefGoogle Scholar
  20. 20.
    A. Tourin, Doctoral thesis, Université Paris VII, 1999Google Scholar
  21. 21.
    The details of this simplification may be found in Appendix 4A of [14]Google Scholar
  22. 22.
    M.B. van der Mark, M.P. van Albada, A. Lagendijk, Phys. Rev. B 37, 3575 (1988)ADSCrossRefGoogle Scholar
  23. 23.
    J.H. Page, H.P. Schriemer, I.P. Jones, P. Sheng, D.A. Weitz, Phys. A. 241, 64 (1997)CrossRefGoogle Scholar
  24. 24.
    J. Zhu, D. Pine, D.A. Weitz, Phys. Rev. A 44, 3948 (1991)ADSCrossRefGoogle Scholar
  25. 25.
    J.H. Page, H.P. Schriemer, A.E. Bailey, D.A. Weitz, Phys. Rev. E 52, 3106 (1995)ADSCrossRefGoogle Scholar
  26. 26.
    L. Ryzhik, G. Papanicolaou, J.B. Keller, Wave Motion 24, 327 (1996)MathSciNetCrossRefGoogle Scholar
  27. 27.
    J.A. Turner, R.L. Weaver, J. Acoust. Soc. Am. 98, 2801 (1995)ADSCrossRefGoogle Scholar
  28. 28.
    M. van Albada, B.A. van Tiggelen, A. Lagendijk, A. Tip, Phys. Rev. Lett. 61, 3132 (1991)ADSCrossRefGoogle Scholar
  29. 29.
    G. Labeyrie, E. Vaujour, C.A. Müller, D. Delande, C. Miniatura, D. Wilkowski, R. Kaiser, Phys. Rev. Lett. 91, 223904 (2003)ADSCrossRefGoogle Scholar
  30. 30.
    For recent theoretical work on the energy velocity in the Anderson localization regime, see the article by B.A. van Tiggelen, S.E. Skipetrov and J.H. Page, “Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering” in this Special Issue of European Physical Journal honouring the scientific legacy of Roger MaynardGoogle Scholar

Copyright information

© The Author(s) 2017

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • L. A. Cobus
    • 1
  • B. A. van Tiggelen
    • 2
    • 3
  • A. Derode
    • 4
  • J. H. Page
    • 1
  1. 1.Department of Physics and AstronomyUniversity of Manitoba, WinnipegManitoba R3T 2N2Canada
  2. 2.Université Grenoble Alpes, LPMMCGrenobleFrance
  3. 3.CNRS, LPMMCGrenobleFrance
  4. 4.Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, Université Denis Diderot - Paris 7ParisFrance

Personalised recommendations