Holographic phase-shifting surfaces (PSSs) have been proven to offer a cost-effective solution for enabling passive arrays to mechanically steer their beams toward desired directions. However, even though the principle of operation of PSSs is straightforward, designing a PSS is very challenging, because it involves an extremely high computational time, which in turn limits their usage and development. Notably, traditional design approaches of PSSs, with N number of layers that have M different variations of conductive patches, need [Formula: see text] full-wave simulations to be properly characterized. To address these challenges that are associated with the design of PSSs and reduce the needed computational effort, we present here a semi-numerical approach that enables the efficient design of holographic PSSs. Specifically, by representing an N-layer PSS unit-cell as N cascaded networks, where each network represents one layer of the PSS that has M different designs of sub-wavelength resonators, we only need to conduct [Formula: see text] full-wave simulations to collect all the required data needed to analyze the performance of the PSS. In turn, by utilizing the multiplication property of ABCD parameters we can evaluate very efficiently all the [Formula: see text] different combinations that characterize our PSS. To validate the accuracy of our design methodology, a 1-D beam steerable antenna system is designed that is comprised of a circularly polarized holographic metasurface antenna (HMA) and a hybrid PSS, both operating at 30 GHz. Comparisons between our semi-numerical results, full-wave simulations, and measurements demonstrate an angular error of less than [Formula: see text].
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