Floquet-Domain Synthesis of Multilayer Metasurfaces for Broadband and Nearly Perfect Beam Tilting

This work evaluates the performance of three-layer beam-tilting metasurfaces (MTSs) for anomalous refraction designed via a Floquet-mode optimization (FM-OPT) approach under realistic implementation conditions. A comparative investigation is conducted against an analytical design approach based on bianisotropic MTSs, focusing on the symmetric (impedance-equalized Huygens’, IEH) case. Prior works have identified limitations of analytical models arising from higher-order Floquet mode excitation due to inherent macroperiodicity, wave impedance mismatch, and breakdown of assumptions for nonnegligible substrate thickness. Practical implementations further introduce discrepancies associated with unit-cell discretization due to the local periodicity assumption, and spatial dispersion effects (incidence-angle dependence). To address these challenges, a low spatial dispersion subwavelength unit cell is proposed, enabling consistent realization of beam-tilting MTSs with purely reactive, sign-changing impedance profiles. The unit-cell response transitions smoothly from inductive to capacitive behavior via a geometry evolving from a Jerusalem-cross slot to a convoluted square patch. Full-wave simulations at 29 GHz using Rogers RO3003 substrates demonstrate that, for a 0°–to-50° refraction, the IEH design achieves ≈ 70% peak efficiency with limited bandwidth, whereas FM-OPT reaches 86.1% efficiency and more than doubles the bandwidth under lossy conditions. Extending FM-OPT to a 0°–to-73° refractor yields 88.4% efficiency. These results surpass state-of-the-art implementations without macroperiodic-level optimization, establishing Floquet-domain optimization as a key enabler of broadband, high-efficiency multilayer MTSs.