Geometry of Refractions and Reflections Through a Biperiodic Medium

The behaviour of light rays obeying Snell’s Law in a medium made up of two materials with different refractive indices and which are arranged in a periodic chessboard pattern is described. The analysis is in some ways analogous to the study of rational billiards and uses a return map on one surface to prove, amongst other things, that the number of angles with which any individual ray intersects the lattice is bounded and that if the ratio of refractive indices is large enough then the dynamics can be described by interval exchange maps.