Pseudo-gap and Localization of Light in Correlated Disordered Media

Abstract

Among the remarkable scattering properties of correlated disordered materials, the origin of pseudo-gaps and the formation of localized states are some of the most puzzling features. Fundamental differences between scalar and vector waves in both these aspects make their comprehension even more problematic. Here we present an in-depth and comprehensive analysis of the order-to-disorder transition in 2D resonant systems. We show with exact ab initio numerical simulations in hyperuniform media that localization of 2D vector waves can occur in the presence of correlated disorder, in a regime of moderate density of scatterers. On the contrary, no signature of localization is found for white noise disorder. This is in striking contrast with scalar waves which localize at high density whatever the amount of correlation. For correlated materials, localization is associated with the formation of pseudo-gap in the density of states. We develop two complementary models to explain these observations. The first one uses an effective photonic crystal-type framework and the second relies on a diagrammatic treatment of the multiple scattering sequences. We provide explicit theoretical evaluations of the density of states and localization length in good agreement with numerical simulations. In this way, we identify the microscopic processes at the origin of pseudo-gap formation and clarify the role of the density of states for wave localization in resonant correlated systems.