Fig. 1. Glass waveguides prepared by ultrafast laser direct writing (ULDW). (a) Schematic illustration of ultrafast laser direct writing setup^[37]; (b) 1D Raman scanning and microscopic images of waveguides written in glass with different applied ultrafast pulse energies and scan speed^[44]

Fig. 2. SSH model^[59]. (a) Schematic of one-dimensional periodic dimerization lattice; (b) two-level energy band diagram; (c) edge state wave function distribution; (d) wave function distribution of bulk mode

Fig. 3. 1D SSH systems prepared by ULDW. (a) Edge state injection in SSH structure^[60]; (b) bulk excitation in SSH structure^[61]; (c) dimerized lattice arranged in zigzag geometry^[62]; (d) quasi-1D waveguide array of diamond lattice with defect in each plaquette^[63]; (e) multiorbital diamond lattice 1D array^[64]

Fig. 4. Thouless pumped photonic systems prepared by ULDW. (a) Illustration and (b) spectrum of AAH model^[67]; (c) topological pumping of Fibonacci-like quasicrystal^[68]; (d) schematic of LRM model and experimental results of quantized topological transport^[7]

Fig. 5. Photonic graphene prepared by ULDW. (a) Diagram and (b) edge band structure for bearded and zig-zag edges of photonic graphene^[72]; (c) unconventional edge band structure and (d) fraction of power confined to edge for zigzag and bearded edges of photonic graphene^[73]; (e) uncompressed and strongly compressed honeycomb structures; (f) ratio of optical power on bearded edge to that diffracted into bulk for different kx and compression factor^[74]

Fig. 6. Higher-order topological insulators and topological disclinations prepared by ULDW. (a) Diagram and (b) cross-section view under microscope of square SSH HOTI^[78]; Kagome lattice in (c) triangular and (d) rhombic geometry^[9]; (e) diagrams and (f) microscope images of C6 symmetric photonic waveguide lattices^[82]; (g) honeycomb array with Kekulé distortion; (h) disclination array with pentagonal core^[16]

Fig. 7. Floquet topological insulators prepared by ULDW. (a) Hybrid structure composed of 1D straw input structure and 2D spiral waveguide honeycomb structure^[11]; (b) 2D topological pump structure^[89]; (c) four different bond cyclic driving protocol in anomalous photonic Floquet topological insulator^[90]; (d) Sierpinski triangle fractal Floquet topological insulator^[13]; (e) Sierpinski carpet fractal anomalous Floquet topological insulator^[93]; (f) edge state corresponding to structure in Fig. 7(e)^[93]; (g) time-varying super honeycomb structure^[94]; (h) 2D time-varying SSH array^[95]; (i) 2D synthetic-space lattice^[96]

Fig. 8. Non-Hermitian topological insulators prepared by ULDW. (a) Non-Hermitian SSH model^[99]; (b) topological interface in PT-symmetric waveguide array^[100]; (c) schematic of non-Hermitian interface of SSH model^[101]; (d) 2D PT-symmetric graphene lattice^[102]; (e) parallel and diagonal non-Hermitian 2D SSH arrays^[103]; (f) bipartite helical waveguide non-Hermitian array^[104]

Fig. 9. Nonlinear photonic topological insulators prepared by ULDW. (a) Nonlinearity-induced anomalous Floquet photonic topological insulator^[107]; (b) nonlinear corner excitations in dimerized Kagome lattices^[106]; (c) linear and nonlinear topological Thouless pump^[108]; (d) relationship between nonlinearity intensity and nonlinearity pump distance in AAH^[21]

Fig. 10. Topologically protected quantum entanglement and quantum interference in photonic topological insulators. (a) Measured cross-correlation of entangled double photons in nondiagonal AAH lattice^[113]; (b) schematic of dynamics of entangled double photons in non-mediocre and mediocre SSH lattices^[27]; (c) topological beam splitter based on AAH waveguide array^[114]

Fig. 11. Non-Abelian braiding structures prepared by ULDW. (a) Schematic of two-mode non-Abelian braiding structure based on four-waveguide time-varying coupling^[116]; (b) non-Abelian braiding structure with Lieb lattice based on four-waveguide time-varying coupling^[28]