  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.
