Title: 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.