Relation between the localization length and level repulsion in 2D Anderson localization

We report on the relation between the localization length and level-spacing characteristics of two-dimensional (2D) optical localizing systems. Using the tight-binding model over a wide range of disorder, we compute spectro-spatial features of Anderson localized modes. The spectra allow us to estimate the level-spacing statistics while the localization length t is computed from the eigenvectors. We use a hybrid interpolating function to fit the level-spacing distribution, whose repulsion exponent beta varies continuously between 0 and 1, with the former representing Poissonian statistics and the latter approximating the Wigner-Dyson distribution. We find that the (xi, beta) scatter points occupy a well-defined nonlinear locus that is well fit by a sigmoidal function, implying that the localization length of a 2D disordered medium can be estimated by spectral means using the level-spacing statistics. This technique is also immune to dissipation since the repulsion exponent is insensitive to level widths, in the limit of weak dissipation. (C) 2020 Optical Society of America