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

Abstract

We show that the 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 behaviour of that flow and ultimately our claim for the light rays are based on an analysis of the Teichmüller flow and the Kontsevich–Zorich cocycle on the moduli space of two-branched, two-sheeted torus covers in genus 2.