Ray engineering from chaos to order in two-dimensional optical cavities

TL;DR

This paper introduces a method to control and eliminate chaos in two-dimensional optical cavities by designing specific refractive index landscapes, enabling predictable and integrable ray trajectories with potential applications in optical microcavities.

Contribution

The authors develop a conformal mapping-based approach to transform chaotic optical billiards into predictable, integrable systems, including non-Euclidean geometries like spheres and black hole spacetimes.

Findings

Refractive index landscapes can fully predict chaotic billiard trajectories.

Chaotic billiards can be made integrable through conformal mapping.

The method enables real-time control of optical chaos.

Abstract

Chaos, namely exponential sensitivity to initial conditions, is generally considered a nuisance, inasmuch as it prevents long-term predictions in physical systems. Here, we present an easily accessible approach to undo deterministic chaos and tailor ray trajectories in arbitrary two-dimensional optical billiards, by introducing spatially varying refractive index therein. A new refractive index landscape is obtained by a conformal mapping, which makes the trajectories of the chaotic billiard fully predictable and the billiard fully integrable. Moreover, trajectory rectification can be pushed a step further by relating chaotic billiards with non-Euclidean geometries. Two examples are illustrated by projecting billiards built on a sphere as well as the deformed spacetime outside a Schwarzschild black hole, which respectively lead to all periodic orbits and spiraling trajectories in the resulting 2D billiards/cavities. An implementation of our method is proposed, which enables real-time control of chaos and could further contribute to a wealth of potential applications in the domain of optical microcavities.