Fig. 1. Schematic diagram of the optical path of a mid infrared integrated external cavity tunable narrow linewidth quantum cascade laser based on silicon-based germanium waveguide

Fig. 2. Schematic diagram of micro-ring resonator structure

Fig. 3. Schematic diagram of Sagnac ring reflector structure

Fig. 4. (a) The relationship between effective refractive index of waveguide mode and waveguide thickness; (b) Schematic diagram of single-mode waveguide electric field

Fig. 5. The FDTD solver in Lumerical was used to simulate the micro-ring transmission spectra of micro rings with different radii

Fig. 6. The FDTD solver in Lumerical was used to simulate the micro-ring transmission spectra corresponding to different micro ring coupling lengths:(a) coupling length of 2 μm; (b) coupling length of 4 μm; (c) coupling length of 6 μm; (d) coupling length of 8 μm

Fig. 7. The variation curve of k values corresponding to different gap values at 4.5-4.7 μm

Fig. 8. The variation curve of k values corresponding to different coupling lengths values at 4.5-4.7 μm

Fig. 9. Transmission spectra corresponding to different micro-ring coupling gap

Fig. 10. (a) The variation curve of the reflectivity corresponding to different coupling intervals of the Sagnac loop mirror at 4.5-4.7 μm; (b) Coupling coefficient variation curves corresponding to different gap of mirrors between 4.5-4.7 μm

Fig. 11. Link simulation diagram

Fig. 12. The link emulation output port outputs a spectral pattern

Fig. 13. Schematic diagram of the spectral changes at the output end after changing the effective refractive index of the material （The black line represents the corresponding output spectrum of the original waveguide, and the red line represents the corresponding output spectrum after changing the effective refractive index）