Fig. 1. One-dimensional SSH model and its band structure relationship. (a) Single cell arrangement scheme in SSH model^[20]; (b) different band relations as the transition intensities α and β changed^[31]

Fig. 2. Honeycomb lattice of two-dimensional Haldane model and its band structure relationship. (a) Honeycomb lattice structure under the quantum Hall effect of light^[39]; (b) (c) band structure before and after opening Dirac point^[40]

Fig. 3. Band structure of the one-way transmission channel formed by the quantum spin Hall effect^[42]

Fig. 4. Lattice unit and its band structure under the two-dimensional valley Hall effect. (a) Periodic lattice cell; (b) band structure under the valley Hall effect^[51]; (c) band structure for the formation of the edge states at different valley points

Fig. 5. Topological microlaser array. (a) Basic structure; (b) light field output effect under the optical pump; (c) single-supermode lasing from the topological microlaser

Fig. 6. Topological insulator laser^[56]. (a) Geometric structure, the inner illustration shows the robustness of the array against defect states; (b) (c) output intensity effects

Fig. 7. Terahertz quantum cascade laser with topologically protected valley edge states^[60]. (a) Laser structure; (b) (c) energy-band structure; (d) (e) topological interface formed by cell lattice; (f) output of an electrically pumped laser at different currents

Fig. 8. Silicon-on-insulator valley photonic crystal planar structure^[65]. (a) Schematic structure; (b) unit lattice arrangement of VPC1 and VPC2; (c) topological edge states do not scatter at the corners; (d) unidirectional coupling of the planar waveguide in the valley dependent edge states

Fig. 9. Honeycomb CROW array^[70]. (a) Schematic of structure, the enlarged part is a single repeating unit; (b) transmission spectrum and output effect

Fig. 10. Photonic crystal heterostructure^[72]. (a) Optical path transmission; (b) transmission spectra of UDT topological interface states; (c) electric field diagram shows that light can only travel in one direction in this structure

Fig. 11. Diagram of TPMZI and VPC structures^[19]. (a) TPMZI structure; (b) VPC structure; (c) broadband high transmission of TPMZI; (d) TPMZI exhibits the periodicity of coherent phase length and coherent cancellation