Design and theoretical analysis of polarization manipulation metasurface based on Generalized Fresnel’s Law

The electromagnetic (EM) metasurface, or dielectric interfaces with conductive surface structures, can adjust the parameters including amplitude, phase, and wavefront of the incident EM waves by reflection or transmission, and have been widely used in antennas, absorbers, polarization converters and many other applications. However, the theoretical model of the EM metasurface is still mostly based on the generalized Snell’s law, which only studies the phase abrupt discontinuity on the metasurface and lacks theoretical guidance for the changes of reflection and transmission amplitudes. In this paper, "equivalent surface conductivity σ" is defined to describe the effect of artificially designed conductive structures at the dielectric interface, and analytical formulas for reflection and transmission coefficients are established based on the Maxwell’s equations. The formulas are natural expansion of the traditional Fresnel’s law, so named as the generalized Fresnel’s law, with both co-polarization and cross-polarization components included. In this paper, the practicality of the Generalized Fresnel’s law in the case of normal incident was discussed. It can also be applied to more general situations such as anisotropic dielectric interfaces. Simulation and experiment results confirm that the proposed theoretical model can be used to analyze and design various EM metasurfaces, and can be further used to analyze EM devices with the sandwich structures. The fabricated reflective polarization converter achieved over 80% PCR in (14.86-21.09) GHz.