Approximately Equal Cross-Polarized Reflection Coefficients for Metasurface

Traditionally, the reciprocity theorem is aimed at the waves with two reciprocal propagation directions. However, it is verified that two reflection coefficients of the sub-wavelength metasurface are approximately equal for the cross-polarized waves with the same propagation directions. Due to the sub-wavelength characteristics, the zero-order mode as free wave nearly dominates the metasurface, while the high-order modes as surface wave can be ignored. In this case, when the TM and TE plane waves impinge onto the metasurface at the same angle, the closed surface integrals of the reciprocity theorem are solved for the unit cell of periodic metasurface, yielding an approximate equation for two cross-polarized reflection coefficients. Finally, the simulation supports the proposed theory, regardless of the specific structure of the metasurface. The study not only reveals the inherent mechanism of the sub-wavelength metasurface, but also enriches the connotation of the existing reciprocity theorem.