Lagrangian descriptors for the Bunimovich stadium billiard

TL;DR

This paper demonstrates how Lagrangian descriptors can effectively analyze phase space structures in the Bunimovich stadium billiard, including open systems relevant to microlaser experiments, revealing insights into their emission profiles.

Contribution

It introduces the application of Lagrangian descriptors to the Bunimovich stadium billiard and its open variant, linking phase space structures to experimental optical phenomena.

Findings

Lagrangian descriptors reveal phase space structures in the stadium billiard.

Open stadium analysis relates emission profiles to phase space features.

Method applies to optical systems like microlasers.

Abstract

We apply the concept of Lagrangian descriptors to the dynamics on the Bunimovich stadium billiard, a 2D ergodic system with singular families of trajectories, namely, the bouncing ball and the whispering gallery orbits. They play a central role in structuring the phase space, which is unveiled here by means of the Lagrangian descriptors applied to the associated map on the boundary. More interestingly, we also consider the open stadium, which in the optical case (Fresnel's laws) can be directly related to recent microlaser experiments. We find that the structure of the emission profile of these systems can be easily described thanks to the open version of the Lagrangian descriptors.