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

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.