Freespace twistronics for optical supertopologies

Twistronics, the study of moiré superlattices of twisted bilayer 2D materials creating nontrivial physical effects, has recently revolutionized diverse subjects from materials to optoelectronics, nanophotonics, and beyond. Here, breaking the reliance on materials, we present twistronics in higher-dimensional free space, where the twisted lattice is not a layer of 2D material but a 3D propagating light field with topological textures. Moiré structured light with a twist angle can generate a rich set of high-dimensional topologies, including skyrmionium bags, skyrmion bag superlattices, skyrmion clusters, and optical quasicrystals, with controllable symmetry. Many of these textures have not been reported before. Importantly, in contrast to prior moiré superlattices, our freespace optical moiré textures maintain their topologies over a long propagation distances, showing nondiffractive behavior and robustness against perturbations and obstacles. Our work unlocks higher dimensions to manipulate moiré photonics with high-capacity topologies to address modern challenges of robust information transfer and encryption.