Metasurface synthesis using reduced susceptibility tensors

We propose a general method to synthesize metasurfaces based on a polarizability-susceptibility scattering approach. We show that a minimal set of four non-zero effective electric and magnetic susceptibility tensor components is sufficient to theoretically transform an incident electromagnetic wave into a great diversity of transmitted and/or reflected waves, where the metasurface can provide positive and negative refraction, focusing, polarization rotation, power absorption and orbital angular momentum manipulation.