Walk dimension for light in complex disordered media

Transport in complex systems is characterized by a fractal dimension -- the walk dimension -- that indicates the diffusive or anomalous nature of the underlying random walk process. Here we report on the experimental retrieval of this key quantity, using light waves propagating in disordered media. The approach is based on measurements of the time-resolved transmission, in particular on how the lifetime scales with sample size. We show that this allows one to retrieve the walk dimension and apply the concept to samples with varying degree of fractal heterogeneity. In addition, the method provides the first experimental demonstration of anomalous light dynamics in a random medium.