Fig. 1. Structural design. (a) Topological photonic crystal laser structure; (b) top view of the two-dimensional topological photonic crystal structure

Fig. 2. One-dimensional photonic crystal design. (a) Structure of one-dimensional photonic crystal; (b) band diagrams of PC1 and PC2 (inset: E_z intensity distribution in the z direction); (c) transmission spectrum of the resonant cavity; (d) distribution of light fields and refractive index inside one-dimensional topological photonic crystal

Fig. 3. Principle of photonic crystal surface emission and band inversion at the Γ point. (a) Diffraction at the Γ point of the photonic crystal structure; (b) band diagram of the photonic crystal before opening the Dirac point (inset: schematic of photonic crystal and reciprocal lattice); (c) band diagram of a trivial structure photonic crystal (inset: distribution of Hz modes of dipoles and quadrupoles at the Γ point); (d) band diagram of a topological structure photonic crystal (inset: distribution of Hz modes of quadrupoles and dipoles at the Γ point)

Fig. 4. Two-dimensional topological photonic crystals and common photonic crystals. (a) Electric field mode distribution of two-dimensional topological photonic crystal; (b) structure of a common photonic crystal and its electric field mode distribution; (c) intensity distribution of electric field mode |E|² in horizontal direction for a common photonic crystal (with and without defects)

Fig. 5. Robustness verification of topology photonic crystal (illustrations depict various methods of introducing defects, and red line indicating boundary between topological and trivial states). (a) Intensity distribution of electric field mode |E|² in horizontal direction (delete air holes); (b) intensity distribution of electric field mode |E|² in horizontal direction (enlarge air holes); (c) intensity distribution of electric field mode |E|² in horizontal direction (shift air holes)

Fig. 6. Pearson correlation coefficient of electric field distribution under different defect conditions