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

Abstract

A metasurface is a surface, tipically 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, they are Monge-Ampère partial differential equations, and we prove existence of solutions.

arXiv comment20 pages, 4 figures

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• General Metasurface Synthesis Based on Susceptibility Tensors
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• Tunable Graphene Metasurface Reflectarray for Cloaking, Illusion and Focusing