Fig. 1. Line defect in Kagome lattice, black dot frame is the supercell schematic and inset in the upper left is the Brillouin region

Fig. 2. Simulation results of the line defect in Kagome lattice. (a) TM energy band structure; (b) transmission spectrum

Fig. 3. Steady-state field distribution of beams of different wavelengths and variation of light intensity value with time. (a) λ=3.124 μm; (b) λ=3.75 μm; (c) λ=4.597 μm

Fig. 4. Waveguide based on Kagome lattice. (a) Waveguide structure parameters; (b) relationship between the first band gap width and r_c

Fig. 5. Relationship between transverse wave vector frequencies of waveguide mode and r_d

Fig. 6. Newly designed Kagome lattice waveguide.(a) New defect structure; (b) relationship between its defect mode frequency and r_d

Fig. 7. TM energy band structure of each node in Fig. 6(b). (a) r_d=0.06a; (b) r_d=0.09a; (c) r_d=0.14a; (d) r_d=0.18a

Fig. 8. When r_d=0.1a, relationship between defect mode frequency and l

Fig. 9. TM band structures of the line defect. (a) Before the movement; (b) after the movement (l=0.5a)

Fig. 10. Relationship between defect mode frequency and r₁

Fig. 11. Optimized Kagome lattice. (a) Optimized Kagome line defect structure; (b) transmission spectrum