Ray chaos in a photonic crystal

The ray dynamics in a photonic crystal was investigated. Chaos occurs for perfectly periodic crystals, the rays dynamics being very sensitive to the initial conditions. Depending on the filling factor, the ray dynamics can exhibit stable paths near (fully) chaotic motion. The degree of chaoticity is quantified through the computation of Lyapunov exponents. As a result, the more diluted is the geometry, the more chaotic is the dynamic. Therefore, despite the perfect periodicity of the geometry, light transport is a diffusive process which can be tuned from normal diffusion (Brownian motion) to anomalous diffusion because of the existence of Lévy flights.