Comparison of two synthesis methods for birefringent metasurfaces

Birefringent metasurfaces are two-dimensional structures capable of independently controlling the amplitude, phase, and polarization of orthogonally polarized incident waves. In this work, we propose an in-depth discussion on the mathematical synthesis of such metasurfaces. We compare the two methods, one that is rigorous and based on the exact electromagnetic fields involved in the transformation and one that is based on approximate reflection and transmission coefficients. We next validate the synthesis technique in metasurfaces performing the operations of a half- and quarter-wave plates, polarization beam splitting, and orbital angular momentum multiplexing and present the corresponding microwave experimental demonstrations.