Anderson Transition for Light in a Three-Dimensional Random Medium

Abstract

We study Anderson transition for light in three dimensions by performing large-scale simulations of electromagnetic wave transport in disordered ensembles of perfect-electric-conducting spatially overlapping spheres. A mobility edge that separates diffusive transport and Anderson localization is identified, revealing a sharp transition from diffusion to localization for light. Critical behavior in the vicinity of the mobility edge is well described by a single-parameter scaling law. The critical exponent is found to be consistent with the value known for the Anderson transition of the orthogonal universality class. Statistical distribution of total transmission at the mobility edge is described without any fit parameter by the diagrammatic perturbation theory originally developed for scalar wave diffusion, but notable deviation from the theory is found when Anderson localization sets in.