Anderson localization of light in two dimensions

Abstract

Anderson localization is a physical phenomenon that occurs when waves propagate in disordered media. However, there is no conclusive observation of the existence of electromagnetic wave localization in three dimensions, most likely due to its vectorial nature. Interestingly, two-dimensional media possess both scalar and vector scattering channels for light, with localization in the former, and absence of localization in the latter where polarization effects must be taken into account. One characteristic of Anderson localization is the decay of the dimensionless conductance (also called Thouless number) with the system size ,according to the so-called scaling theory. For example, in a 2D dense system the vector channel has a conductance nearly constant with respect to the size of the system, whereas the scalar channel present an exponential decay. This work is devoted to studying the influence of the near-field and polarization coupling terms in the transport of 2D systems, in the limit of low density and large size. Indeed, the polarization-coupling term which prevent light localization in the vector channel is expected to be very weak, so localization may occur in this limit. We consider a two-dimensional circular cloud of point-like scatterers in a two-dimensional vacuum. Numerical simulations are realized to study the conductance as the system size increases, tuning the scatterers density.We present preliminary results on the scaling of the dimensionless conductance in the limit of decreasing densities, giving hints on the behaviour of localization in low-density 2D systems.