Reflection and refraction problems for metasurfaces related to Monge-Ampère equations.

A metasurface is a surface, typically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisfy, i.e., Monge-Ampère partial differential equations, and we prove the existence of solutions.