In this talk, I will present the meeting of different dynamical systems: tiling billiards, the wind-tree model and Eaton lenses. The three of them are motivated by physics. The wind-tree model was introduced by Paul and Tatyana Ehrenfest to study a gaz: a particle is moving in a plane where obstacles are periodically placed, on which the particle bounces. The Eaton lenses are a periodic array of lenses in the plane, in which we consider a light ray that is reflected each time it crosses a lens. In the beginning of the 2000's, physicists have conceived metamaterials with negative index of refraction. Tilling billiards' trajectories consist of light rays moving in a arrangement of metamaterials with opposite indew of refraction. After having introduced these dynamical systems, I will consider a mix of them: an arrangement of rectangles in the plane, like in the wind-tree model, but made of metamaterials, like for tiling billiards. I study the trajectories of light in this plane. They are refracted each time they cross a rectangle. I show that these trajectories are traped in a strip, for almost every parameter. This behavior is similar to the one of Eaton lenses.
