| Topological photonics is an emerging field at the cross of photonics and topological physics,aiming at exploring novel topological phenomena and multifunctional photonic devices.Photonic crystals,as a typical photonic system,offer good design flexibility in regulating photonic bands,and provide a practical platform for realizing topological photonics.To overcome the material limitations in topological photonics,photonic topological states based on all-dielectric photonic crystals have attracted extensive attention,including photonic quantum-like spin Hall effects,photonic valley Hall effects,and photonic high-order topological effects.Since these effects mainly depend on the maintained/breaking of lattice symmetry,most of the existed work focuses on a single topological state in all-dielectric photonic crystals with specific symmetries.If the symmetry can be maintained/broken in the same photonic crystal,it is expected to obtain different photonic topological states and thus expand the flexibility of electromagnetic wave manipulation.To this end,we design a composite photonic crystal based on honeycomb lattice and kagome lattice---HoneycombKagome photonic crystal.Through theoretical analysis and simulation performances of Honeycomb-Kagome photonic crystals with different symmetries,we obtained the following results:1.With C6v symmetry,the pseudo-spin degree of freedom with specific angular momentum can be constructed in Honeycomb-Kagome photonic crystals.By changing the radius of the dielectric rods,the photonic band can be effectively regulated to achieve a complete photonic band gap featured with photonic quantum-like spin Hall phase.The topological properties can be judged from the symmetry eigenvalues of the unit cell.By constructing supercell consisting of different topological photonic crystals,pseudospinmomentum locked boundary states and corner states were also observed in their band gaps.In particular,as a special case of Honeycomb-Kagome photonic crystals,it is found that kagome photonic crystals are also a photonic topological insulator,which share the same band topological properties of the mentioned Honeycomb-Kagome photonic crystals.2.By changing the distance between adjacent dielectric rods in the Honeycomb-Kagome photonic crystals,the symmetry of the system reduced from C6v to C3,which results in opening the band gap of the first/second band at the Dirac point of K(K’),and thus introduces the valley freedom of freedom.According to the moving direction of adjacent dielectric rods,different valley Hall topological insulators can be obtained,and its topological invariants can be characterized by the Valley-Chern number and symmetry topological index,and the corresponding topological effect is observed in the existence of valley-momentum locked edge states and valley-selective higher-order topological corner states.3.Under the broken C6v(while maintaining C3)symmetry,as the distance between adjacent dielectric pillars increases,the feature of pseudo-spin-momentum locked gradually disappear,indicating the evident impact of symmetry breaking on the quantum-like spin Hall effect in Honeycomb-Kagome photonic crystals.However,the hybrid topological phases based with coexistence of photonic quantum-like Hall and valley Hall can be realized when the symmetry breaking is insignificant.Accordingly,we design a four-channel system,where the unidirectional routing of electromagnetic waves against sharp bends between two routes can be selectively controlled by the pseudospin and valley degrees of freedom. |
