Manifestations of quantum chaos in spectra of 2D photonic crystals

Abstract

An electromagnetic wave propagating in a 2D photonic crystal is considered as an example of a chaotic dynamical system. For a fixed Bloch vector k → , the photon frequencies form a discrete sequence ω n( k → ) , where n=1,2,3,… is the band index. We study the level spacing distribution at the center of the Brillouin zone ( k → =0) . A square unit cell contains two “atoms”, that are circular cylinders with dielectric constant ε a, arranged asymmetrically in order to break all the discrete symmetries. The level spacing distribution reveals a smooth transition from the Poisson to the Wigner distribution when ε a increases. We show that the onset of chaos in the spectrum occurs at rather low values of the dielectric constant, 2< ε a<5, but it reveals strong features of regularity when ε a exceeds 10. The latter tendency is due to the modes, which propagate mostly inside the cylinders and do not undergo chaotic scattering.