Photonic quasicrystal of spin angular momentum

Quasicrystals, characterized by long-range order without translational symmetry, have catalyzed transformative advances in various fields, including optics in terms of field quasicrystals. To our knowledge, we present the first demonstration of photonic quasicrystals formed by spin angular momentum, unveiling previously unidentified spin-orbit coupling effects absent in traditional field quasicrystals. A de Bruijn tiling like theoretical framework was built elucidating the formation mechanism of spin quasicrystals for diverse symmetries. Moreover, the configurations of these spin textures can be manipulated through the adjustments of the wavefronts, among which phason-like discontinuous dynamics is observed and quantitatively measured. Unlike optical quasicrystals shaped by electromagnetic fields, these spin-governed quasicrystals exhibit quasi-periodic properties of kinematic parameters, extending their potential applications to other physical systems. These findings hold promise for advancements in optical trapping, quasicrystal fabrication, and optical encryption systems.