Ray Chaos in a Photonic Crystal -- Supplementary Materials

TL;DR

This paper investigates ray chaos in a photonic crystal, combining theoretical calculations and experimental results to analyze light propagation, dynamical properties, and exponential sensitivity to initial conditions.

Contribution

It provides a detailed analysis of ray chaos in photonic crystals, including justification of geometrical optics and demonstration of exponential sensitivity through experiments.

Findings

Lyapunov exponent grows as ln t*

Exponential sensitivity to initial conditions demonstrated

Ray propagation exhibits chaotic behavior

Abstract

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 $\lambda$ $\sim$ 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.