Light chaotic dynamics in the transformation from curved to flat surfaces

Light propagation on a two-dimensional curved surface embedded in a threedimensional space has attracted increasing attention as an analog model of fourdimensional curved spacetime in the laboratory. Despite recent developments in modern cosmology on the dynamics and evolution of the universe, investigation of nonlinear dynamics of light on non-Euclidean geometry is still scarce, with fundamental questions, such as the effect of curvature on deterministic chaos, challenging to address. Here, we study classical and wave chaotic dynamics on a family of surfaces of revolution by considering its equivalent conformally transformed flat billiard, with nonuniform distribution of the refractive index. We prove rigorously that these two systems share the same dynamics. By exploring the Poincare ' surface of section, the Lyapunov exponent, and the statistics of eigenmodes and eigenfrequency spectrum in the transformed inhomogeneous table billiard, we find that the degree of chaos is fully controlled by a single, curvature-related geometric parameter of the curved surface. A simple interpretation of our findings in transformed billiards, the fictitious force, allows us to extend our prediction to other classes of curved surfaces. This powerful analogy between two a priori unrelated systems not only brings forward an approach to control the degree of chaos, but also provides potentialities for further studies and applications in various fields, such as billiards design, optical fibers, or laser microcavities.

Automated summary

This study investigates the nonlinear dynamics of light propagation on a two-dimensional curved surface in a three-dimensional space by considering its equivalent flat billiard with nonuniform distribution of refractive index. The researchers find that the degree of chaos is fully controlled by a single curvature-related geometric parameter of the curved surface, and this analogy between two unrelated systems not only provides a way to control chaos but also has potential applications in various fields.