Space-Time Optical Hopfion Crystals

Hopfions-higher-dimensional topological quasiparticles with sophisticated 3D knotted spin textures discovered in condensed matter and photonic systems-show promise in high-density data storage and transfer. Here, we present crystalline structures of hopfions lying in space-time constructed by spatiotemporally structured light. Practical methodologies using bichromatic structured light beams or dipole arrays to assemble 1D and higher dimensional hopfion lattices are proposed, and a technique for tailoring topological orders is elucidated. Optical hopfion crystals constitute a new platform for high-dimensional topological information transfer.