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.
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