We have studied the distribution of resonance widths P(Gamma) in one-, two-, and three-dimensional multiple light scattering systems. P(Gamma) should follow a universal power law P(Gamma) approximately Gamma(-1) in the localized regime as confirmed by extensive numerical calculations. This behavior can be interpreted as an unambiguous signature of exponential Anderson localization of light in open systems.

Abstract:In this comprehensive paper we have addressed structure-property relationships in a number of representative systems with periodic, random, quasi-periodic and deterministic aperiodic geometry using the interdisciplinary methods of spatial point pattern analysis and spectral graph theory as well as the rigorous Green's matrix method, which provides access to the electromagnetic scattering behavior and spectral fluctuations (distributions of complex eigenvalues as well as of their level spacing) of deterministic aperiodic optical media for the first time.

Light propagation through 1D disordered structures composed of alternating layers, with random thicknesses, of air and a dispersive metamaterial is theoretically investigated. Both normal and oblique incidences are considered. By means of numerical simulations and an analytical theory, we have established that Anderson localization of light may be suppressed: (i) in the long wavelength limit, for a finite angle of incidence which depends on the parameters of the dispersive metamaterial; (ii) for isolated frequencies and for specific angles of incidence, corresponding to Brewster anomalies in both positive-and negative-refraction regimes of the dispersive metamaterial. These results suggest that Anderson localization of light could be explored to control and tune light propagation in disordered metamaterials.