Inverse Metasurface Design From 3-D Desired Power Patterns on Two Cuts

An electromagnetic inverse source algorithm, which was developed to infer the macroscopic properties of metasurfaces from desired power patterns for 2-D wave propagation, is extended to the 3-D configuration. This is pursued in conjunction with some simplifying assumptions that reduce the associated 3-D full-vectorial inverse metasurface design problem to a 3-D scalar one. This inversion algorithm takes the desired power patterns on two perpendicular far-field cuts, and outputs the required equivalent currents on the surface of the metasurface. The required metasurface macroscopic properties can be subsequently found. Finally, a discussion on the presence of surface waves in this formulation is presented which facilitates meeting the local power conservation constraint.