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.

Localization of light in a disordered medium

Abstract

Among the unusual transport properties predicted for disordered materials is the Anderson localization1 phenomenon. This is a disorder-induced phase transition in the electron-transport behaviour from the classical diffusion regime, in which the well-known Ohm's law holds, to a localized state in which the material behaves as an insulator. The effect finds its origin in the interference of electrons that have undergone multiple scattering by defects in the solid2,3,4,5,6,7,8,9,10. A similar phenomenon is anticipated for multiple scattering of electromagnetic waves, but with one important simplification: unlike electrons, photons do not interact with one another. This makes transport of photons in disordered materials an ideal model system in which to study Anderson localization10,11,12,13,14,15,16,17. Here we report direct experimental evidence for Anderson localization of light in optical experiments performed on very strongly scattering semiconductor powders.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Anderson localization of waves in disordered systems originates from interference in multiple elastic scattering.
Figure 2: Comparison of the temperature dependence of the transmission of pure GaAs crystals and powders.
Figure 3: Coherent backscattering cones from coarse-grained (a) and fine-grained (b) GaAs powder.
Figure 4: Comparison of the transmission coefficients for two GaAs powders with different average particle diameters.
Figure 5: The transmission coefficient of very fine GaAs powder as a function of thickness.

References

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

    Google Scholar 

  2. Bergmann, G. Quantitative analysis of weak localization in thin Mg films by electroresistance measurements. Phys. Rev. B 25, 2937–2939 (1982).

    Google Scholar 

  3. Altshuler, B. L., Aronov, A. G., Khmel'nitskii, D. E. & Larkin, A. I. in Quantum Theory of Solids (ed. Lifshits, I. M.) 130–237 (MIR, Moskow, (1983)).

    Google Scholar 

  4. Khmel'nitskii, D. E. Localization and coherent scattering of electrons. Physica B 126, 235–241 (1984).

    Google Scholar 

  5. Lee, P. A. & Ramakrishnann, T. V. Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985).

    Google Scholar 

  6. Condat, C. A., Kirkpatrick, T. R. & Cohen, S. M. Acoustic localization in one dimension in the presence of a flow field. Phys. Rev. B 35, 4653–4661 (1987).

    Google Scholar 

  7. Souillard, B. in Chance and Matter (eds Souletie, J., Vannimenus, J. & Stora, R.) Ch. 5 (North-Holland, Amsterdam, (1987).

    MATH  Google Scholar 

  8. Ando, T. & Fukuyama, H. (eds) Anderson Localization, Springer Proceedings in Physics Vol. 28 (Springer, Berlin, (1988).

    Book  Google Scholar 

  9. Vollhardt, D. & Wölfle, P. in Electronic Phase Transitions (eds Hanke, W. & Kopaev, Yu. V.) 1–78 (Elsevier, Amsterdam, (1992)).

    Book  Google Scholar 

  10. Sheng, P. Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, (1995).

    Google Scholar 

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

    Google Scholar 

  12. Anderson, P. W. The question of classical localization: a theory of white paint? Phil. Mag. B 52, 505–509 (1985).

    Google Scholar 

  13. Sheng, P. & Zhang, Z.-Q. Scalar-wave localization in a two-component composite. Phys. Rev. Lett. 57, 1879–1882 (1986).

    Google Scholar 

  14. 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).

    Google Scholar 

  15. Lagendijk, A., van Albada, M. P. & van der Markk, M. B. Localization of light: the quest for the white hole. Physica A 140, 183–190 (1986).

    Google Scholar 

  16. Kaveh, M. Localization of photons in disordered systems. Phil. Mag. B 56, 693–703 (1987).

    Google Scholar 

  17. Soukoulis, C. M., Economou, E. N., Grest, G. S. & Cohen, M. H. Existence of Anderson localization of classical waves in a random two-component medium. Phys. Rev. Lett. 62, 575–578 (1989).

    Google Scholar 

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

    Google Scholar 

  19. Mott, N. F. Metal-Insulator Transitions (Taylor & Francis, London, (1974).

    Google Scholar 

  20. Dalichaouch, R., Armstrong, J. P., Schultz, S., Platzman, P. M. & McCall, S. L. Microwave localization by two-dimensional random scattering. Nature 354, 53–55 (1991).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  22. Genack, A. Z. & Garcia, N. Observation of photon localization in a three-dimensional disordered system. Phys. Rev. Lett. 66, 2064–2067 (1991).

    Google Scholar 

  23. Kuga, Y. & Ishimaru, J. Retroflection of a dense distribution of spherical particles. J. Opt. Soc. Am. A 1, 831–835 (1984).

    Google Scholar 

  24. Albada, M. P. & Lagendijk, A. Observation of weak localization of light in a random medium. Phys. Rev. Lett. 55, 2692–2695 (1985).

    Google Scholar 

  25. Wolf, P. E. & Maret, G. Weak localization and coherent backscattering of photons in disordered media. Phys. Rev. Lett. 55, 2696–2699 (1985).

    Google Scholar 

  26. Mark, M. B., Albada, M. P. & Lagendijk, A. Light scattering in strongly scattering media: multiple scattering and weak localization. Phys. Rev. B 37, 3575–3592 (1988).

    Google Scholar 

  27. Akkermans, E., Wolf, P. E., Maynard, R. & Maret, G. Theoretical study of the coherent backscattering of light by disordered media. J. Phys. (Paris) 49, 77–98 (1988).

    Google Scholar 

  28. Edrei, I. & Stephen, M. J. Optical coherent backscattering and transmission in a disordered media near the mobility edge. Phys. Rev. B 42, 110–117 (1990).

    Google Scholar 

  29. Zhu, J. X., Pine, D. J. & Weitz, D. A. Internal reflection of diffusive light in random media. Phys. Rev. A 44, 3948–3957 (1991).

    Google Scholar 

  30. Wiersma, D. S., Albada, M. P., van Tiggelen, B. A. & Lagendijk, A. Experimental evidence for recurrent multiple scattering events of light in disordered media. Phys. Rev. Lett. 74, 4193–4196 (1995).

    Google Scholar 

Download references

Acknowledgements

We thank F. Bogani, M. Colocci, R. Torre and M. Gurioli for discussions, and M. Colocci also for supplying GaAs crystals. D.S.W. thanks M. van Albada for advice and continuous support during the experiments, and M. Brugmans for reading of the manuscript. A.L. was supported by the ‘Stichting voor Fundamenteel Onderzoek der Materie’ (FOM). This work was supported by the Commission of the European Community.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Diederik S. Wiersma.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wiersma, D., Bartolini, P., Lagendijk, A. et al. Localization of light in a disordered medium. Nature 390, 671–673 (1997). https://doi.org/10.1038/37757

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/37757

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

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