Skip to main content

Correlation of Speckle in Random Media

  • Chapter
Book cover Waves and Imaging through Complex Media

Abstract

The diagram technique for waves propagating in disordered media is reviewed and the short, long and infinite range correlations — known as C 1 , C 2 and C 3 , respectively — are calculated using the Langevin scheme. This enables one to consider several experimentally relevant effects: absorption, frequency shifts, internal reflections and the effect of geometry. Fluctuations in optical transmission through disordered slabs are described in detail. Spatial correlations and deviations from Rayleigh statistics in quasi-one-dimensional systems are discussed as well.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Google Scholar 

  2. J. Goodman, in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1984), p. 9–75.

    Google Scholar 

  3. For recent reviews see e.g. M. C. W. van Rossum and Th. Nieuwenhuizen, Rev. Mod. Phys 71, 313 (1999); R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1

    Article  ADS  Google Scholar 

  4. B. L. Altshuler, P. A. Lee and R. A. Webb (Eds.), Mesoscopic Phenomena in Solids, (North-Holland, Amsterdam, 1991).

    Google Scholar 

  5. For a comprehensive discussion of enhanced backscattering, with references to earlier work, see E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. France 49, 77 (1988); M. B. van der Mark, M. P. van Albada, A. D. Lagendijk, Phys. Rev. B 37, 3575 (19

    Article  ADS  Google Scholar 

  6. S. Feng in Scattering and Localization in Classical Waves, edited by P. Sheng (Word Scientific, 1990); M. J. Stephen, in Ref. [4] p. 81–107; S. Feng and P. A. Lee, Science 251, 633 (1991).

    Google Scholar 

  7. A vector electromagnetic field was considered by M. J. Stephen and G. Cwilich, Phys. Rev. B 34, 7564 (1986); K. Arya, Z. B. Su and J. L. Birman, Phys. Rev. Lett. 57, 2725 (19

    Article  ADS  Google Scholar 

  8. A more realistic assumption would be to allow for a finite correlation length in (μ(r)μ(r1)) or use discrete short-range scatterers. However, if one is not interested in the corrections to the speed of propagation, one can as well use the white-noise model.

    Google Scholar 

  9. A. A. Abrikosov, L. P. Gorkov and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Pergamon, 1965), Sec 39; U. Frisch, in Probabilistic Methods in Applied Mathematics, edited by A. T. Baracha Reid (Academic, 1968), Vol. 1, p. 76–198; B. Shapiro, in Recent Progress in Many-Body Theories, edited by Y. Avishai (Plenum Press, 1990), Vol. 2, p. 95-104.

    Google Scholar 

  10. B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).

    Article  ADS  Google Scholar 

  11. M. J. Stephen and G. Cwilich, Phys. Rev. Lett. 59, 285 (1987).

    Article  ADS  Google Scholar 

  12. S. Hikami, Phys. Rev. B 24, 2671 (1981); K. B. Efetov, A. I. Larkin and D. E. Khmel’nitskii, Sov. Phys. — JETP 52, 568 (1980).

    Article  ADS  Google Scholar 

  13. S. Feng, C. Kane, P. A. Lee and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).

    Article  ADS  Google Scholar 

  14. P.A. Mello, E. Akkermans and B. Shapiro, Phys.Rev.Lett. 61, 459(1988).

    Article  ADS  Google Scholar 

  15. P. A. Lee and A. D. Stone, Phys. Rev. Lett. 55, 1622 (1985); B. L. Altshuler, JETP Lett. 41, 648 (1985); P. A. Lee, A. D. Stone and H. Fukuyama, Phys. Rev. B 35, 1039 (1986).

    Article  ADS  Google Scholar 

  16. B. Shapiro, Phys. Rev. Lett. 83, 4733 (1999).

    Article  ADS  Google Scholar 

  17. S. Skipetrov and R. Maynard, unpublished.

    Google Scholar 

  18. M. C. W. van Rossum, Th. M. Nieuwenhuizen and R. Vlaming, Phys. Rev. E 51, 6158 (1995).

    Article  ADS  Google Scholar 

  19. C. L. Kane, R. A. Serota and P.A. Lee, Phys. Rev. B 37, 6701 (1988).

    Article  ADS  Google Scholar 

  20. A. Yu. Zyuzin and B. Z. Spivak, Sov. Phys. — JETP 66, 560 (1987); B. Z. Spivak and A. Yu. Zyuzin, Solid-State Comm. 65, 311 (1988).

    Google Scholar 

  21. This is, admittedly, a somewhat arbitrary choice and other types of boundary conditions for the diffusion equation occur in the literature [1]. For a discussion of the improved diffusion approximation and the effects of skin layers see A. Lagendijk, R. Vreeker and P. de Vries, Phys. Lett. A 136, 81 (1989); Th. M. Nieuwenhuizen and J. M. Luck, Phys. Rev. E 48, 569 (1993); and Ref. [30].

    Google Scholar 

  22. R. Pnini and B. Shapiro, Phys. Rev. B 39, 6986 (1989).

    Article  ADS  Google Scholar 

  23. R. Pnini and B. Shapiro, Phys. Lett. A 157, 265 (1991).

    Article  ADS  Google Scholar 

  24. B. Z. Spivak and A. Yu. Zyuzin, in Ref. [4] p. 37–80.

    Google Scholar 

  25. A. A. Burkov and A. Yu. Zyuzin, Phys. Rev. B 55, 5736 (1997).

    Article  ADS  Google Scholar 

  26. N. Garcia and A. Z. Genack, Phys. Rev. Lett. 63, 1678 (1989); A. Z. Genack, N. Garcia, W. Polkosnik, Phys. Rev. Lett. 65, 2129 (1990).

    Article  ADS  Google Scholar 

  27. M. P. van Albada, J. F. de Boer and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990); J. F de Boer, M. P. van Albada and A. Lagendijk, Phys. Rev. B 45, 658 (1992).

    Google Scholar 

  28. N. Garcia, A. Z. Genack and A.A. Lisyansky, Phys. Rev. B 46, 14475 (1992); N. Garcia, A. Z. Genack, R. Pnini and B. Shapiro, Phys. Lett. A 176, 458 (1993).

    Article  ADS  Google Scholar 

  29. F. Scheffold, W. Häti, G. Maret and E. Matijevic, Phys. Rev. B 56, 10942 (1997); F. Scheffold and G. Maret, Phys. Rev. Lett. 81, 5800 (1998).

    Article  ADS  Google Scholar 

  30. A modified diffuson for the treatment of internal reflections was considered by M. C. W. van Rossum and Th. M. Nieuwenhuizen, Phys. Lett. A 177, 452 (1993). This diffuson contains the injection depth, Z 0, as additional parameter. In Eq. (31) it is assumed that Z 0 ≪ L.

    Google Scholar 

  31. E. Kogan and M. Kaveh, Phys. Rev. B 45, 1049 (1992).

    Article  ADS  Google Scholar 

  32. R. L. Weaver, Phys. Rev. B 47, 1077 (1993).

    Article  ADS  Google Scholar 

  33. P. W. Brouwer, Phys. Rev. B 57, 10526 (1998).

    Article  ADS  Google Scholar 

  34. P. Sebbah, R. Pnini and A. Z. Genack, to appear in Phys. Rev. E (2000).

    Google Scholar 

  35. N. Garcia and A. Z. Genack, Opt. Lett. 16, 1132 (1991); A. Z. Genack and N. Garcia, Europhys. Lett. 21, 753 (1993).

    Article  ADS  Google Scholar 

  36. J. F. de Boer, M. C. W van Rossum, M. P. van Albada, Th. M. Nieuwenhuizen and A. Lagendijk, Phys. Rev. lett. 73, 2567, (1994).

    Article  ADS  Google Scholar 

  37. M. Stoytchev and A.Z. Genack, Phys. Rev. Lett. 79, 309 (1997); Opt. Lett. 24, 262 (1999).

    Article  ADS  Google Scholar 

  38. E. Jackman and P. Pusey, Phys. Rev. Lett. 40, 546 (1978).

    Article  ADS  Google Scholar 

  39. R. Dashen Opt. Lett. 10, 110 (1984).

    Article  ADS  Google Scholar 

  40. E. Kogan, M. Kaveh, R. Baumgartner and R. Berkovits, Phys. Rev. B 48, 9404(1993); Physica A 200, 469 (1993).

    Article  ADS  Google Scholar 

  41. Th. M. Nieuwenhuizen, M. C. W. van Rossum, Phys. Rev. Lett. 74, 2674 (1995); E. Kogan, M. Kaveh, Phys. Rev. B 52, R3813 (1995).

    Article  ADS  Google Scholar 

  42. S. A. van Langen, P. W. Brouwer and C. W. J. Beenakker, Phys. Rev. E 53, R1344 (1996).

    Article  ADS  Google Scholar 

  43. A. D. Mirlin, R. Pnini, B. Shapiro, Phys. Rev.E 57, R6285 (1998).

    Google Scholar 

  44. N. Shnerb and M. Kaveh, Phys. Rev. B 43, 1279 (1991).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Pnini, R. (2001). Correlation of Speckle in Random Media. In: Sebbah, P. (eds) Waves and Imaging through Complex Media. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0975-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0975-1_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0372-1

  • Online ISBN: 978-94-010-0975-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics