Among different approaches to designing metasurfaces, surface sheet impedance is proving to be a straightforward path for many applications. Recent publications have proposed several methods for optimizing this design approach, enabling rapid metasurface development. Upon finding the requirements using the sheet impedance approach, design continues with the selection of unit cell geometry. This choice is usually based on approximate expressions that have been published throughout the years. We review the approximate expressions for metasurface unit cell design, with consideration of their applicability to certain applications, namely polarization-dependent beam-shaping metasurfaces. We evaluate the accuracy of the approximate expressions against simulation results from a full-wave electromagnetic solver, and propose an optimization approach to correct the proposed design for the observed error. The applicability of different unit cell types is discussed, especially considering the limitations of technological processes typically used in metasurface production. A prototype was developed to verify the validity of this design approach.
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