# Level spacing statistics for light in two-dimensional disordered photonic crystals

## TL;DR

This paper investigates the statistical distribution of eigenfrequency spacings in 2D disordered photonic crystals, revealing Poisson statistics for localized modes within the band gap and Wigner-Dyson statistics for extended modes outside the gap.

## Contribution

It provides the first detailed analysis of level spacing statistics for light in disordered 2D photonic crystals, distinguishing between localized and extended modes.

## Key findings

- Localized TM modes in the band gap follow Poisson distribution.
- Extended TM and TE modes follow Wigner-Dyson distribution.
- Disorder induces localization and affects spectral statistics.

## Abstract

We study the distribution of eigenfrequency spacings (the so-called level spacing statistics) for light in a two-dimensional (2D) disordered photonic crystal composed of circular dielectric (silicon) rods in air. Disorder introduces localized transverse-magnetic (TM) modes into the band gap of the ideal crystal. The level spacing statistics is found to approach the Poisson distribution for these modes. In contrast, for TM modes outside the band gap and for transverse-electric (TE) modes at all frequencies, the level spacing statistics follows the Wigner-Dyson distribution.