Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Statistical signatures of photon localization

Nature volume 404, pages 850–853 (2000)Cite this article

Abstract

The realization that electron localization in disordered systems1 (Anderson localization) is ultimately a wave phenomenon2,3 has led to the suggestion that photons could be similarly localized by disorder3. This conjecture attracted wide interest because the differences between photons and electrons—in their interactions, spin statistics, and methods of injection and detection—may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of three-dimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave4,5,6,7,8 as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption9,10,11, and because absorption itself may suppress localization3. Here we show that the extent of photon localization can be determined by a different approach—measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminium spheres.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Influence of absorption and localization, separately and together, on var(sa) in random polystyrene samples.
Figure 2: Statistics of intensity in quasi-one-dimensional alumina samples.
Figure 3: Scaling of var(sa) in alumina samples.
Figure 4: Var(sa) versus frequency in a wire-mesh photonic crystal containing metal scatterers.

References

  1. Anderson,P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    Article  ADS  CAS  Google Scholar 

  2. Ioffe,A. F. & Regel,A. R. Non-crystalline, amorphous and liquid electronic semiconductors. Prog. Semicond. 4, 237–291 (1960).

    Google Scholar 

  3. John,S. Electromagnetic absorption in a disordered medium near a photon mobility edge. Phys. Rev. Lett. 53, 2169–2172 (1984).

    Article  ADS  Google Scholar 

  4. Garcia,N. & Genack,A. Z. Anomalous photon diffusion at the threshold of the Anderson localization transition. Phys. Rev. Lett. 66, 1850–1853 ( 1991).

    Article  ADS  CAS  Google Scholar 

  5. Genack,A. Z. & Garcia,N. Observations of the Anderson transition for electromagnetic radiation. Phys. Rev. Lett. 66, 2064–2067 (1991).

    Article  ADS  CAS  Google Scholar 

  6. Wiersma,D. S., Bartolini,P., Lagendijk,A. & Righini,R. Localization of light in a disordered medium. Nature 390, 671–673 (1997).

    Article  ADS  CAS  Google Scholar 

  7. Wiersma,D. S., Rivas,J. G., Bartolini,P., Lagendijk,A. & Righini,R. Localization or classical diffusion of light? (Reply) Nature 398, 207 (1999).

    Article  ADS  CAS  Google Scholar 

  8. Vlasov,Ya. A., Kaliteevski,M. A. & Nikolaev, V. V. Different regimes of light localization in a disordered photonic crystal. Phys. Rev. B 60, 1555– 1562 (1999).

    Article  ADS  CAS  Google Scholar 

  9. Scheffold,F., Lenke,R., Tweer,R. & Maret,G. Localization or classical diffusion of light? Nature 398, 206– 207 (1999).

    Article  ADS  CAS  Google Scholar 

  10. Weaver,R. L. Anomalous diffusivity and localization of classical waves in disordered media: The effect of dissipation. Phys. Rev. B 47, 1077–1080 (1993).

    Article  ADS  CAS  Google Scholar 

  11. Yosefin,M. Localization in absorbing media. Europhys. Lett. 25 , 675–680 (1994).

    Article  ADS  Google Scholar 

  12. Abrahams,E., Anderson P. W., Licciardello,D. C. & Ramakrishnan,T. V. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979).

    Article  ADS  Google Scholar 

  13. Landauer,R. Electrical resistance of disordered one-dimensional lattices. Philos. Mag. 21, 863–867 (1970).

    Article  ADS  CAS  Google Scholar 

  14. van Rossum,M. C. W. & Nieuwenhuizen,Th. M. Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion. Rev. Mod. Phys. 71, 313–372 (1999).

    Article  ADS  CAS  Google Scholar 

  15. Kogan,E. & Kaveh,M. Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium. Phys. Rev. B 52, R3813–R3815 (1995).

    Article  ADS  CAS  Google Scholar 

  16. van Langen,S. A., Brouwer,P. W. & Beenakker, C. W. J. Nonperturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide. Phys. Rev. E 53, R1344–R1347 (1996).

    Article  ADS  CAS  Google Scholar 

  17. Thouless,D. J. Maximum metallic resistance in thin wires. Phys. Rev. Lett. 39, 1167–1169 (1977).

    Article  ADS  CAS  Google Scholar 

  18. Shapiro,B. Scaling properties of probability distributions in disordered systems. Philos. Mag. B 56, 1031–1044 (1989).

    Article  ADS  Google Scholar 

  19. Stoytchev,M. & Genack,A. Z. Measurement of the probability distribution of total transmission in random waveguides. Phys. Rev. Lett. 79, 309–312 ( 1997).

    Article  ADS  CAS  Google Scholar 

  20. Stoytchev,M. & Genack,A. Z. Observations of non-Rayleigh statistics in the approach to photon localization. Opt. Lett. 24, 262–264 (1999).

    Article  ADS  CAS  Google Scholar 

  21. Garcia,N., Genack,A. Z. & Lisyansky, A. A. Measurement of the transport mean free path of diffusing photons. Phys. Rev. B 46, 14475– 14479 (1992).

    Article  ADS  CAS  Google Scholar 

  22. Lagendijk,A., Vreeker,R. & de Vries, P. Influence of internal reflection on diffusive transport in strongly scattering media. Phys. Lett. A 136, 81–88 (1989).

    Article  ADS  CAS  Google Scholar 

  23. Garcia,N. & Genack,A. Z. Crossover to strong intensity correlation for microwave radiation in random media. Phys. Rev. Lett. 63, 1678–1681 (1989).

    Article  ADS  CAS  Google Scholar 

  24. Garcia,N., Genack,A. Z., Pnini,R. & Shapiro,B. Intensity correlation in waveguides. Phys. Lett. A 176, 458– 461 (1993).

    Article  ADS  Google Scholar 

  25. Brouwer,P. W. Transmission through a many-channel random waveguide with absorption. Phys. Rev. B 57, 10526–10531 (1998).

    Article  ADS  CAS  Google Scholar 

  26. John,S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    Article  ADS  CAS  Google Scholar 

  27. Sigalas,M. M., Chan,C. T., Ho,K. M. & Soukoulis,C. M. Metallic photonic band-gap materials. Phys. Rev. B 52, 11744 –11751 (1995).

    Article  ADS  CAS  Google Scholar 

  28. Stoytchev,M. & Genack,A. Z. Microwave transmission through a periodic three-dimensional metal-wire network containing random scatterers. Phys. Rev. B 55, R8617– 8621 (1997).

    Article  ADS  CAS  Google Scholar 

  29. Arya,K., Su,Z. B. & Birman,J. L. Anderson localization of electromagnetic waves in a dielectric medium of randomly distributed metal particles. Phys. Rev. Lett. 57, 2725–2728 ( 1986).

    Article  ADS  CAS  Google Scholar 

  30. Condat,C. A. & Kirkpatrik,T. R. Observability of acoustical and optical localization. Phys. Rev. Lett. 58, 226–229 (1987).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank P. W. Brouwer and E. Kogan for discussions. This work was supported by the NSF.

Author information

Author notes

  1. M. Stoytchev

    Present address: Bell Labs, Lucent Technologies, Murray Hill, New Jersey, 07974-0636, USA

Authors and Affiliations

  1. Physics Department, Queens College The City University of New York, Flushing, 11367, New York, USA

    A. A. Chabanov, M. Stoytchev & A. Z. Genack

Authors
  1. A. A. Chabanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Stoytchev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Z. Genack
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Chabanov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chabanov, A., Stoytchev, M. & Genack, A. Statistical signatures of photon localization. Nature 404, 850–853 (2000). https://doi.org/10.1038/35009055

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/35009055

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing