Relation between the localization length and level repulsion in 2D Anderson localization
Abstract
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 ξ is computed from the eigenvectors. We use a hybrid interpolating function to fit the level-spacing distribution, whose repulsion exponent β varies continuously between 0 and 1, with the former representing Poissonian statistics and the latter approximating the Wigner–Dyson distribution. We find that the ( ξ , β ) 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.
- Publication:
-
Optics Letters
- Pub Date:
- February 2020
- DOI:
- 10.1364/OL.383748
- Bibcode:
- 2020OptL...45..997M