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Two exact approaches to synthesize metasurfaces for time-harmonic waves are discussed. The first approach is a spectral approach based on wave momentum conservation. Here, the spectral approach is applied to scalar and paraxial wave transformations. This approach effectively allows the arbitrary translation of the transformation plane parallel to the metasurface. The second approach is a direct-space approach based on the extraction of the susceptibility tensors of the metasurface elements. This approach is applied to vectorial field transformation and can be used for single or multiple transformations. An example of wave transformation by a metasurface is illustrated for each of the two approaches.

METASURFACE SYNTHESIS FOR TIME-HARMONIC WAVES: EXACT SPECTRAL AND SPATIAL METHODS (Invited Paper)