Photon Localization and Exponential Scaling of Intensity Variance

  • Andrey A. Chabanov
  • Azriel Z. Genack
Conference paper


We show that the extent of photon localization can be characterized by the relative size of fluctuations of intensity or of total transmission, even in absorbing samples. We find that above a value of approximately unity, the variance of normalized total transmission scales exponentially. Using this approach, we identify the spectral range for localization of microwave radiation in an ensemble of random configurations of alumina spheres contained in a copper tube at a volume fraction of 0.068.


Copper Tube Total Transmission Localization Threshold Classical Wave Random Laser 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. W. Anderson: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)ADSCrossRefGoogle Scholar
  2. 2.
    A. F. Ioffe, A. R. Regel: Non-crystalline, amorphous and liquid electronic semiconductors. Prog. Semicond. 4, 237–291 (1960)Google Scholar
  3. 3.
    S. John: Electromagnetic absorption in a disordered medium near a photon mobility edge. Phys. Rev. Lett. 53, 2169–2172 (1984)ADSCrossRefGoogle Scholar
  4. 4.
    B. L. Altshuler, P. A. Lee, R. A. Webb (Eds.): Mesoscopic Phenomena in Solids ( Elsevier, Amsterdam 1991 )Google Scholar
  5. 5.
    R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz: Observations of hl Aharonov-Bohm oscillations in normal-metal rings. Phys. Rev. Lett. 54, 2696–2700 (1985)ADSCrossRefGoogle Scholar
  6. 6.
    N. Garcia, A. Z. Genack: Anomalous photon diffusion at the threshold of the Anderson localization transition. Phys. Rev. Lett. 66, 1850–1853 (1991)ADSCrossRefGoogle Scholar
  7. 7.
    A. Z. Genack, N. Garcia: Observations of the Anderson transition for electromagnetic radiation. Phys. Rev. Lett. 66, 2064–2067 (1991)ADSCrossRefGoogle Scholar
  8. 8.
    D. S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini: Localization of light in a disordered medium. Nature, 390, 671–673 (1997)ADSCrossRefGoogle Scholar
  9. 9.
    D. S. Wiersma, J. G. Rivas, P. Bartolini, A. Lagendijk, R. Righini: Nature, 398, 207 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    Ya. A. Vlasov, M. A. Kaliteevski, V. V. Nikolaev: Different regimes of light localization in a disordered photonic crystal. Phys. Rev. B 60, 1555–1562 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    F. Scheffold, R. Lenke, R. Twèer, G. Maret: Nature, 398, 206 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    R. L. Weaver: Anomalous diffusivity and localization of classical waves in disordered media: The effect of dissipation. Phys. Rev. B 47, 1077–1080 (1993)ADSCrossRefGoogle Scholar
  13. 13.
    M. Yosefin: Localization in absorbing media. Europhys. Lett. 25, 675–680 (1994)ADSCrossRefGoogle Scholar
  14. 14.
    E. Abrahams, P. W. Anderson, D. C. Licciardello, T. V. Ramakrishnan: Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979)ADSCrossRefGoogle Scholar
  15. 15.
    R. Landauer: Electrical resistance of disordered one-dimensional lattices. Phil. Mag. 21, 863–867 (1970)ADSCrossRefGoogle Scholar
  16. 16.
    M. C. W. van Rossum, Th. M. Nieuwenhuizen: Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion. Rev. Mod. Phys. 71, 313–372 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    E. Kogan, M. Kaveh: Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium. Phys. Rev. B 52, R3813–3815 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    S. A. van Langen, P. W. Brouwer, C. W. J. Beenakker: Nonperturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide. Phys. Rev. E 53, R1344–1347 (1996)ADSCrossRefGoogle Scholar
  19. 19.
    D. J. Thouless: Maximum metallic resistance in thin wires. Phys. Rev. Lett. 39, 1167–1169 (1977)ADSCrossRefGoogle Scholar
  20. 20.
    M. Stoytchev, A. Z. Genack: Measurement of the probability distribution of total transmission in random waveguides. Phys. Rev. Lett. 79, 309–312 (1997)ADSCrossRefGoogle Scholar
  21. 21.
    M. Stoytchev, A. Z. Genack: Observations of non-Rayliegh statistics in the approach to photon localization. Opt. Lett. 24, 262–264 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    B. L. Altshuler, V. E. Kravtsov, I. V. Lerner: Distribution of mesoscopic fluctuations and relaxation processes in disordered conductors. In: Mesoscopic Phenomena in Solids B. L. Altshuler, P. A. Lee, R. A. Webb (Eds.) ( Elsevier, Amsterdam 1991 ) pp. 449–521CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andrey A. Chabanov
    • 1
  • Azriel Z. Genack
    • 1
  1. 1.Queens College of the City University of New YorkFlushingUSA

Personalised recommendations