Reflection and refraction of light from metasurfaces with phase discontinuities

A three-dimensional extension of the recently demonstrated generalization of the laws of refraction and reflection was investigated for both flat and curved metasurfaces. We found that out-of-plane refraction occurs for a metasurface that imparts a wavevector out of the plane of incidence onto the incident light beam. Metasurfaces provide arbitrary control over the direction of refraction, and yield new critical angles for both reflection and refraction. A spherical metasurface with phase discontinuities leads to unconventional light bending compared to standard refractive lenses.