Ray Chaos in a Photonic Crystal -- Supplementary Materials

These supplementary materials detail some calculations and some experimental results related to the propagation of light in the photonic billiard. We first justify why we focus only on the rays that are transmitted through the cylinders and justify the geometrical optics approximation. Then we explain the dynamical properties of ray propagation, demonstrate that asymptotically the Lyapunov exponent grows as $λ$ $\sim$ ln t$\star$ where t$\star$ = T /R is the photonic crystal period T divided by the cylinder radius R. Finally we close these supplementary materials by presenting some experimental results demonstrating the exponential sensitivity to the initial conditions.

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