Moiré Twisted Lieb Metasurface Enabled for All-Magic-Angle

Moiré metasurfaces generate novel optical characteristics, such as photonic polariton and topological Lifshitz transition by stacking multiple metasurfaces with periodic structures. This configuration demonstrates significant flexibility and tunability in the manipulation of optical, electrical, acoustic, and thermal properties. In this work, a bilayer twisted moiré elastic metasurface is presented, constructed using periodically arranged tilted and rhombic prism resonators in Lieb lattice configuration. By utilizing the twisting mechanism, the design enables systematic reconstruction of the moiré metasurface, which facilitates precise manipulation of elastic wave propagation, particularly achieving both the “all-magic-angle” and anisotropic transmission. The inherent band structure of the Lieb lattice plays a key role in reducing energy dissipation during wave transmission, thereby enhancing energy concentration. Furthermore, a novel phenomenon of unidirectional polariton-like polarized waveguide mode is observed, where propagation is biased along specific directions. This study establishes a comprehensive theoretical framework throughderivation of the governing wave equations and systematic construction of band structures with corresponding dispersion relations. These findings significantly enhance the potential applications of moiré metasurfaces in elastic wave manipulation, particularly in critical technologies such as non-destructive testing and energy harvesting.