General Refraction Problems with Phase Discontinuity

Abstract

This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase discontinuities. The approach contains both the near and far field cases. A starting point is the formulation of a vector Snell law in presence of abrupt discontinuities on the interfaces.