Metasurface synthesis using momentum transformation

A systematic method to synthesize metasurfaces for light manipulation is introduced. For a specified wave field impinging on one side of the metasurface and specified desired fields reflected and transmitted from the metasurface, a momentum boundary condition based on conservation of wave momentum is established. The momentum conservation relation determines the amplitude, phase and polarization transformation to be induced by the metasurface. This method, named the momentum transformation method, formally allows for complete control over the reflected and transmitted fields and provides physical guidelines for metasurface synthesis. The method is applied to scalar and vector wave fields, and a relevant illustrative example is shown.