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Direct determination of the transition to localization of light in three dimensions

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Abstract

Diffusive wave transport in three-dimensional media should show a phase transition, with increasing disorder, to a state without transport. This transition was first discussed by Anderson1 in the context of the metal–insulator transition, but is generic for all waves, as was realized later2,3. However, the quest for the experimental demonstration of ‘Anderson’ localization in three dimensions has been a challenging task. For electrons4 and cold atoms5,6, the challenge lies in the possibility of bound states in a disordered potential. Therefore, electromagnetic and acoustic waves have been the prime candidates for the observation of Anderson localization7,8,9,10,11,12,13,14,15,16,17. The main challenge in using light lies in the distinction between the effects of absorption and localization11,12. Here, we present measurements of the time dependence of the transverse width of the transmitted-light intensity distribution, which provides a direct measure of the localization length, independent of absorption. This provides direct evidence for a localization transition in three dimensions.

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Figure 1: A section of the raw data (fit displayed via contours) for a R104 sample, featuring a plateau.
Figure 2: Time dependence of the mean-square width scaled with sample size σ2/L2 for different samples.
Figure 3: Spectral measurement of σ2 for a R700 sample, ranging from 550 nm to 650 nm, corresponding to kl* values between 2.1 and 3.6.
Figure 4: Inverse of the mean-square width of the plateau versus kl* for different samples.
Figure 5: Value of exponent a, describing the temporal increase of the mean-square width (see main text).

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References

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

    Article  ADS  Google Scholar 

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

    Article  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. Altshuler, B. L. et al. Mesoscopic Phenomena in Solids (North-Holland, 1991).

    Google Scholar 

  5. Kondov, S. S. et al. Three-dimensional Anderson localization of ultracold matter. Science 334, 66–68 (2011).

    Article  ADS  Google Scholar 

  6. Jendrzejewski, F. et al. Three-dimensional localization of ultracold atoms in an optical disordered potential. Nature Phys. 8, 398–403 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Drake, J. M. & Genack, A. Z. Observation of nonclassical optical diffusion. Phys. Rev. Lett. 63, 259–262 (1989).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Scheffold, F., Lenke, R., Tweer, R. & Maret, G. Localization or classical diffusion of light? Nature 398, 206–270 (1999).

    Article  ADS  Google Scholar 

  13. Fiebig, S. et al. Conservation of energy in coherent backscattering at large angles. Europhys. Lett. 81, 64004 (2008).

    Article  ADS  Google Scholar 

  14. Störzer, M., Gross, P., Aegerter, C. M. & Maret, G. Observation of the critical regime in the approach to Anderson localization of light. Phys. Rev. Lett. 96, 063904 (2006).

    Article  ADS  Google Scholar 

  15. Aegerter, C. M., Störzer, M. & Maret, G. Experimental determination of critical exponents in Anderson localization of light. Europhys. Lett. 75, 562–568 (2006).

    Article  ADS  Google Scholar 

  16. Bayer, G. & Niederdränk, T. Weak localization of acoustic waves in strongly scattering media. Phys. Rev. Lett. 70, 3884–3887 (1993).

    Article  ADS  Google Scholar 

  17. Hu, H., Strybulevych, A., Page, J. H., Skipetrov, S. E. & van Tiggelen, B. A. Localization of ultrasound in a three-dimensional elastic network. Nature Phys. 4, 945–948 (2008).

    Article  ADS  Google Scholar 

  18. Lenke, R. & Maret, G. Multiple Scattering of Light: Coherent Backscattering and Transmission (Gordon & Breach, 2000).

    Google Scholar 

  19. 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 

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

    Google Scholar 

  21. Berkovits, R. & Kaveh, M. Propagation of waves through a slab near the Anderson transition: a local scaling approach. J. Phys. C 2, 307–321 (1990).

    Google Scholar 

  22. Skipetrov, S. E. & van Tiggelen, B. A. Dynamics of Anderson localization in open 3D media. Phys. Rev. Lett. 96, 043902 (2006).

    Article  ADS  Google Scholar 

  23. Cherroret, N., Skipetrov, S. E. & van Tiggelen, B. A. Transverse confinement of waves in random media. Phys. Rev. E 82, 056603 (2010).

    Article  ADS  Google Scholar 

  24. Gross, P. et al. A precise method to determine the angular distribution of backscattered light to high angles. Rev. Sci. Instrum. 78, 033105 (2007).

    Article  ADS  Google Scholar 

  25. Gentilini, S., Fratalocchi, A. & Conti, C. Signatures of Anderson localization excited by an optical frequency comb. Phys. Rev. B. 81, 014209 (2010).

    Article  ADS  Google Scholar 

  26. MacKinnon, A. & Kramer, B. One-parameter scaling of localization length and conductance in disordered systems. Phys. Rev. Lett. 47, 1546–1549 (1981).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was funded by Deutsche Forschungsgemeinschaft, Swiss National Science Foundation and the Land Baden-Württemberg via the Center for Applied Photonics. The authors thank N. Cherroret for support and fruitful discussions.

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Contributions

T.S., W.B., C.M.A. and G.M. conceived and designed the experiments. T.S. and W.B. carried out the experiments. T.S., W.B., C.M.A. and G.M. analysed and interpreted the data. T.S., W.B., C.M.A. and G.M. wrote the manuscript.

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Correspondence to C. M. Aegerter.

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The authors declare no competing financial interests.

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Sperling, T., Bührer, W., Aegerter, C. et al. Direct determination of the transition to localization of light in three dimensions. Nature Photon 7, 48–52 (2013). https://doi.org/10.1038/nphoton.2012.313

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