Topological decomposition of hierarchical skyrmion lattices

The decomposition of topological lattices is crucial for understanding their evolution and behavior in complex systems. Typically, decomposed substructures retain the primary lattice's topology. However, achieving domains with different topologies remains challenging due to interaction complexity. Here, we theoretically propose and experimentally demonstrate the topological synthesis and decomposition of hierarchical skyrmion lattices in light field. Constrained by optical symmetry, distinct sublattice configurations and skyrmionic topologies emerge. The hierarchical structure enables the primary and decomposed lattices to exhibit different topologies, distinct from other systems, revealing interactions between skyrmion lattices and topological state transitions. We demonstrate the formation of triangle meron, square skyrmion, and hexagonal skyrmionium lattices, which require specific conditions in condensed matter systems, using the interference of skyrmionic beams with different rotational symmetry. This approach enables the exploration of interactions between topological phases and may uncover previously unexplored physical phenomena, with potential applications in optical communications and spintronics.