On Transmission Coefficients of Periodic Metasurface Based on the Electromagnetic Reciprocity Theorem

In this brief, the reciprocity theorem is applied to the transmission coefficient between different Floquet' s modes of the periodic metasurface. The vector wave function theory is adopted to express the electromagnetic field of the periodic metasurface, so that the transmission coefficient can be defined between different Floquet's modes. The reciprocity theorem indicates that there is a special relationship between two transmission coefficients with reciprocal incident and transmitted modes. However, the above relationship depends on the basis vector of the Floquet's mode. For the transmission between different Floquet's modes, two transmission coefficients can be equal in terms of the reciprocal incident and transmitted modes only when the Poynting vector (whose field corresponds to the basis vector of Floquet's mode) are normalized along the normal direction of the metasurface, but the defined transmission coefficient does not represent the ratio of transmitted field to incident field. The study not only gives the reciprocity theorem of the transmission coefficients for the periodic metasurface, but also indicates the physical significance about the definition of the transmission coefficient between different modes.