Fig. 1. Resonant cavities based on topological photonic defects. (a) Topological edge state of 1D SSH model ^[12]; (b) Dirac-vortex topological cavity^[25]; (c) topological dislocation state of two-dimensional system^[30]; (d) topological defect state caused by disclination in two-dimensional system^[35]; (e) topological corner state in higher-order topological photonics ^[36]

Fig. 2. Topological optical cavities based on edge state modes. (a) Quantum Hall-based optical topological edge state resonator^[51]; (b)(c) valley Hall-based optical topological edge state resonator^[52-53]; (d)(e) quantum spin Hall-based optical topological edge state resonator^[54-55]

Fig. 3. Topological photonic cavities based on bulk modes. (a) High quality factor resonator formed by photonic band edge ^[59]; (b) optical cavity formed by Dirac linear dispersion localized in photonic band gap^[60]; (c) flat band mode formed by Landau level of photonic crystal ^[61]; (d) flat band mode formed by twisted Moiré photonic crystal ^[64]

Fig. 4. Topological edge-state laser based on 1D SSH model. (a) Zig-zag micro-pillar polarization lattice^[67]; (b) 1D SSH model^[8]; (c) photonic crystal cantilever^[68]; (d)(e) multi-layer quantum well resonant micro-ring arrays^[69-70]; (f) photonic crystal L3 defect cavity array ^[71]; (g) Frenkel exciton-polariton array in red fluorescent protein ^[72]; (h) zig-zag perovskite exciton-polariton array^[73]; (i) staked 1D photonic crystal^[74]

Fig. 5. Topological corner-state lasers based on 2D SSH model. (a) μPL enhancement achieved by combining two-dimensional topological corner states with quantum dots^[80]; (b)‒(e) 2D topological corner-state lasers follow similar device construction principle because in-plane electric field is required to excite gain material^[81,83-85]; (f) 2D perovskite exciton-polariton array^[86]

Fig. 6. Surface-emitting semiconductor lasers based on novel topological defects. (a) Dirac vortex cavity laser^[88]; (b) topological disclination state vortex laser^[91]

Fig. 7. Semiconductor topological laser based on 1D edge states in 2D topological photonic insulator. (a)(b) Topological edge state lasers based on quantum Hall effect^[92-93]; (c) topological edge state laser based on quantum spin Hall effect^[94-95]; (d) bias-magnet-free Haldane model based on long-range coupling link^[96]; (e)‒(g) topological edge state lasers based on pseudo-spin Hall effect^[97-99]; (h)‒(j) topological edge state lasers based on valley Hall effect^[100-102]

Fig. 8. Semiconductor surface emission laser based on 2D topological bulk optical mode. (a) Photonic bound state in continuum^[103]; (b) band-inverted topological photonic mode^[105]; (c) photonic Dirac cone^[104]; (d)(e) Moiré flat bands of twisted photonic crystals^[106-107]

Fig. 9. Electrically pumped semiconductor topological lasers. (a) Exciton-polariton laser with electro-optical hybrid pump^[110]; (b) electrically pumped topological valley Hall edge state laser^[111]; (c) electrically pumped quantum spin Hall topological edge state laser^[112]; (d) electrically pumped topological edge state laser based on 1D SSH model^[113]; (e) electrically pumped terahertz quantum cascade laser based on photonic Majorana zero mode^[89]