  In this talk we present and discuss a new general approach to the synthesis
of metasurfaces for full control of transmitted and reflected fields. The
method is based on the use of an equivalent impedance matrix which connects the
tangential field components at the two sides on the metasurface. Finding the
impedance matrix components, we are able to synthesize metasurfaces which
perfectly realize the desired response. We will explain possible alternative
physical realizations and reveal the crucial role of bianisotropic coupling to
achieve full control of transmission through perfectly matched metasurfaces.
This abstract summarizes our results on metasurfaces for perfect refraction
into an arbitrary direction.
