Directional localization of light rays in a periodic array of retro-reflector lenses

TL;DR

This paper investigates the behavior of light rays in a periodic array of retro-reflector lenses, revealing that most vertical rays are confined within specific strips, using advanced mathematical tools like Teichmüller flow.

Contribution

It introduces a novel analysis of light ray dynamics in Eaton lens arrays through the application of Teichmüller theory and foliation analysis on moduli spaces.

Findings

Vertical light rays are confined within bounded strips in almost all Eaton lens arrays.

The behavior of light rays is modeled using non-orientable foliations and their flow on the orientation cover.

Mathematical analysis links the flow to Teichmüller dynamics and the Kontsevich-Zorich cocycle.

Abstract

We show that vertical light rays in almost every periodic array of Eaton lenses do not leave certain strips of bounded width. The light rays are traced by leaves of a non-orientable foliation on a singular plane. We study the flow defined by the induced foliation on the orientation cover of the singular plane. The behavior of that flow and ultimately our claim for the light rays is based on an analysis of the Teichm\"uller flow and the Kontsevich-Zorich cocycle on the moduli space of two branched, two sheeted torus covers in genus two.