Fig. 1. Schematic of sample structure and variation of coupling coefficient. (a) Cross-sectional schematic of a single waveguide; (b) cross-sectional schematic of two waveguides, the left side represents waveguide 1, and the right side represents waveguide 2; (c) variation in coupling coefficient κ with the gap g between two waveguides; (d) schematic of quaternary waveguide array in a unit cell

Fig. 2. Energy band and Weyl point in parameter space. (a) Band dispersion of a quaternary waveguide array under two different (p, q) parameters; (b) Weyl point and Fermi arc like edge state (dashed line); (c) right edge state; (d) left edge state

Fig. 3. Schematic of Weyl point parameter space and Berry phase variation diagram. (a) Three-dimensional parameter space, and θn represents the angle between the loop ln and k axis; (b) Berry phases corresponding to different angles θn

Fig. 4. Energy spectra and interface states. (a) Energy spectrum of gapless topological interface state (dotted line) in path φ2=-φ1+0.1π; (b) energy spectrum of trivial state in path φ2=φ1+0.1π; (c) one eigenstate of topological interface state; (d) another eigenstate of topological interface state

Fig. 5. Twisted Weyl lattice structure. (a) Interface of three Weyl points, introducing three rotation paths of the same size encircling the Weyl points in the parameter space; (b) actual one-dimensional waveguide array lattice structure

Fig. 6. Multi twisted Weyl point. (a) Energy spectrum of multi twisted Weyl point (dotted lines represent the topological interface states); (b) coupling topological interface state 1; (c) coupling topological interface state 2

Fig. 7. Diagram of coupling topological interface state transmission. (a) Diagram of simulated transmission path evolution; (b) cross-sectional diagram at 1 mm transmission; (c) cross-sectional diagram at 1.5 mm transmission; (d) cross-sectional diagram at 2 mm transmission

Fig. 8. Experimental demonstration of coupling waveguide array. (a) Schematic of experimental steup; (b) actual experimental setup; (c) optical microscope image of waveguide array sample; (d) SEM image of waveguide array sample

Fig. 9. Comparison of theoretical calculation and experimental measurement results. (a)‒(c) Theoretical calculation results of output light intensity at 1.0, 1.5, and 2.0 mm; (d)‒(f) experimental measurement results of output light intensity at 1.0, 1.5, and 2.0 mm