Reciprocity Theorem Applied to Scattering Coefficients of 2-D Anisotropic Metasurface With Polarization Conversion

In this letter, the scattering coefficients of periodic metasurface are studied based on the reciprocity theorem. According to the vector wave function theory, the incident and scattered waves can be decomposed into a series of Floquet's modes. Thereby, the solution of closed surface integral from reciprocity theorem can be conducted in terms of scattering coefficients. It is verified that the scattering coefficients are equal for the reciprocal incident and scattered Floquet's modes, regardless of the metal structure and substrate layer. Note that the scattering coefficient is generally unequal to the ratio between electrical fields of incident and scattered Floquet's waves due to the normalized Poynting vector along the normal direction of the metasurface. Finally, an example is designed to support the proposed theory with great consistence. The theory extends the existing reciprocity theorem to periodic metasurface, enriching the physical connotation of the surface electromagnetics.