Optical Thouless conductance and level-spacing statistics in two-dimensional Anderson localizing systems

TL;DR

This study experimentally and theoretically investigates spectral statistics and optical conductance in two-dimensional Anderson localized systems, revealing a log-normal distribution of conductance and near Wigner-Dyson level spacing despite localization.

Contribution

It provides the first experimental measurement of optical Thouless conductance and level-spacing statistics in 2D Anderson localization, supported by a modified tight-binding model.

Findings

Thouless conductance $g_{Th}$ is below unity.

Distribution of $g_{Th}$ is log-normal.

Level spacings follow a near Wigner-Dyson distribution.

Abstract

We experimentally investigate spectral statistics in Anderson localization in two-dimensional amorphous disordered media. Intensity distributions captured over an ultrabroad wavelength range of $\sim 600$~nm and averaged over numerous configurations provided the Ioffe-Regel parameter to be $\sim2.5$ over the investigated wavelength range. The spectra of the disordered structures provided access to several quasimodes, whose widths and separations allowed to directly estimate the optical Thouless conductance $g_{Th}$, consistently observed to be below unity. The probability distribution of $g_{Th}$ was measured to be a log-normal. Despite being in the Anderson localization regime, the spacings of energy levels of the system was seen to follow a near Wigner-Dyson function. Theoretical calculations based on the tight-binding model, modified to include coupling to a bath, yielded results that were in excellent agreement with experiments. From the model, the level-spacing behavior was attributed to the degree of localization obtained in the optical disordered system.