Europhys. Lett.
Volume 75, Number 4, August 2006
Page(s) 562 - 568
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 05 July 2006
Europhys. Lett., 75 (4), pp. 562-568 (2006)
DOI: 10.1209/epl/i2006-10144-3

Experimental determination of critical exponents in Anderson localisation of light

C. M. Aegerter, M. Störzer and G. Maret

Fachbereich Physik, University of Konstanz - Universitätstrasse 10 78457 Konstanz, Germany

received 17 May 2006; accepted in final form 21 June 2006
published online 5 July 2006

Anderson localisation predicts a phase transition in transport, where the diffuse spread of particles comes to a halt with the introduction of a critical amount of disorder. This is due to constructive interference on closed multiple scattering loops which leads to a renormalisation of the diffusion coefficient. This can be described by a slowing-down of diffusion, where the diffusion coefficient decreases with time according to a power law with an exponent a. In the case of strong localisation, where diffusion completely breaks down, the exponent is given by a = 1. This is due to the fact that such a dependence of the diffusion coefficient naturally leads to a limited spread of the diffusing particle even at infinite times. In the critical regime approaching the transition, a value of a = 1/3 has been predicted, which corresponds to a rescaling of the diffusion coefficient due to the presence of closed loops. Using time-resolved measurements of photon transport in very turbid media, we have determined these scaling exponents experimentally. We find good agreement with theory and determine the critical value of the disorder parameter kl* to be 4.2(2). Furthermore, we study the critical exponent of the divergence of the localisation length at the transition, where we find $\nu = 1/2$, consistent with the expectation for the exponent of an order parameter.

42.25.Dd - Wave propagation in random media.
05.60.-k - Transport processes.
42.25.Bs - Wave propagation, transmission and absorption.

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