Manifestations of quantum chaos in spectra of 2D photonic crystals

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