Geometry-Driven Lattice of Photonic Spin-Meron Tubes in Free Space

We theoretically demonstrate the first photonic spin-meron tube lattice in free space using spin-angular momentum vectors. Square-block diffraction creates C_{4}-symmetric beams with π/2 phase steps. Nonparaxial spin-orbit coupling then forms finite-length meron tubes (N_{sk}≈±1/2), whose length is dependent on diffractive element dimensions. Extending the geometry driven formalism, we show that C_{3} geometry of triangular block yields spin-skyrmion tubes while effective moiré bilayer results in spin twistronics in free space without the need of strong near-field confinement. Stratton-Chu theory and full-vectorial finite-difference time-domain calculations both support this material-agnostic geometric driven approach as a platform to explore the symmetry-driven free-space topology.