# Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards

## TL;DR

The paper explores how ray-wave correspondence applies to anisotropic billiards, using examples like bilayer graphene and optical cavities to bridge dynamics and wave behavior.

## Contribution

The paper introduces anisotropic billiards as a new system class and applies ray-wave correspondence to both optical and electronic systems.

## Key findings

- Anisotropic dispersion in bilayer graphene and birefringent optical cavities can be analyzed using ray-tracing with non-spherical index ellipsoids.
- Transformation optics reveals that resonances in anisotropic systems match those of isotropic elliptical cavities.
- Differences in ray-wave correspondence exist between optical and electronic anisotropic systems.

## Abstract

Mesoscopic billiard systems for electrons and light, realized as quantum dots or optical microcavities, have enriched the fields of quantum chaos and nonlinear dynamics not only by enlarging the class of model systems, but also by providing access to their experimental realization. Here, we add yet another system class, two-dimensional billiards with anisotropies. One example is the anisotropic dispersion relation relevant in bilayer graphene known as trigonal warping, and another is the birefringent closed optical disk cavity. We demonstrate that the established concept of ray–wave correspondence also provides useful insight for anisotropic billiard systems. First, we approach the dynamics of the anisotropic disk from the ray-tracing side that takes the anisotropy in momentum space into account, based on the non-spherical index ellipsoid. Second, we use transformation optics to solve the wave problem and find the resonances to be those of the isotropic elliptical cavity. We illustrate ray–wave correspondence and mark differences in the description of optical and electronic anisotropic systems.