Multi-branch wave transmission in topological disclination-induced valley photonic crystals

Topological photonics serves as an ideal platform for steering robust light propagation. Traditional topological photonic waveguides are confined to the interface between two materials with distinct topological properties, which limits their application scenarios to specific cases such as free-form transmission paths or specialized optical devices. In this Letter, we propose a disclination-induced crystalline structure in a valley photonic system to realize multi-branch and multi-form optical routing. Different types of disclination cores generate directional valley domains, and sub-branches are connected by additional disclination cores to expand transmission paths. By deforming the basic building blocks of these cores and branches, arbitrary shapes of photonic waveguides can be achieved. Protected by the interplay between lattice symmetry rotational invariants and the valley-Hall effect, these models exhibit localized wave transmission. Our work establishes a promising topological waveguide framework that enables complex and tailored light modulations.