Vectorial approach of determining the wave propagation at metasurfaces

Vector approach often benefits optical engineers and physicists, and a vector formulation of the laws of reflection and refraction has been studied (Tkaczyk, 2012). However, the conventional reflection and refraction laws may be violated in the presence of a metasurface, and reflection and refraction at the metasurface obey generalized laws of reflection and refraction (Yu et al., 2011). In this letter, the vectorial laws of reflection and refraction at the metasurface were derived, and the matrix formulation of these vectorial laws are also obtained. These results enable highly efficient and unambiguous computations in ray-tracing problems that involve a metasurface.