Ray tracing in metasurfaces

Abstract

Ray tracing in a metasurface is the process to obtain the three-dimensional (3D) light path under reflection and transmission, which may be helpful in the optical design of metalenses and other metaoptical devices. In this work, first we deduce the 3D vector form of Snell's law for metasurfaces by using a geometric approach. And then, we deduce the general equations to calculate the direction of the reflected and refracted beams in any metasurface, and for any incident beam. In other words, we derive vector form equations for the 3D direction of transmitted and reflected beams at a metasurface with arbitrary 2D phase profile, and for any 3D direction of incident light.