Voronoi-diagram-enabled arbitrary-path topological transport

Topological physics in electromagnetics has enabled topological edge-state waveguides, yet traditional propagation path designs of topological photonics are restricted by the geometry of the underlying periodic lattice. Here, we propose a topological waveguide scheme based on Voronoi diagrams, allowing for arbitrary propagation paths and offering greater flexibility beyond the constraints of conventional periodic structures. Focusing on gyromagnetic photonic topological insulators and valley topological insulators, we detail the construction and implementation process. Our method ensures smooth connections between unit cells and efficient wave transmission, which are validated through both simulations and experiments. The proposed scheme greatly expands the flexibility for topological transport and enables more applications for complex topological devices and systems.