Experimental determination of critical exponents in Anderson localisation of light

Abstract

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 ν = 1/2, consistent with the expectation for the exponent of an order parameter.