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



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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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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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).

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