Mode-expansion theory for inhomogeneous meta-surfaces.

Modeling meta-surfaces as thin metamaterial layers with continuously varying bulk parameters, we employed a rigorous mode-expansion theory to study the scattering properties of such systems. We found that a meta-surface with a linear reflection-phase profile could redirect an impinging light to a non-specular channel with nearly 100% efficiency, and a meta-surface with a parabolic reflection-phase profile could focus incident plane wave to a point image. Under certain approximations, our theory reduces to the local response model (LRM) established for such problems previously, but our full theory has overcome the energy non-conservation problems suffered by the LRM. Microwave experiments were performed on realistic samples to verify the key theoretical predictions, which match well with full-wave simulations.