Fig. 1. (a) Coupling structure from a pulley bus waveguide to a ring resonator; (b) cross section of the coupling system composed of the pulley bus waveguide and the microring resonator; θ corresponds to the angle of the interaction part between the two curved waveguides. R represents the radius of the microring. W_ring and W_bus represent the width of the ring and the bus waveguide, respectively. H represents the thickness of the structure. H_etch represents the etching depth. G represents the distance between the microring and the waveguide. α represents the inclination of the waveguide.

Fig. 2. (a) The periodic coupling length and mismatched phase vary with the radius of the ring and the width of the waveguide of vertical polarization at 775 nm. (b) The periodic coupling length and mismatched phase vary with the radius of the ring and the width of the waveguide of horizontal polarization at 1550 nm. Inset in (a) (upper), mode field distribution when W_bus is 1.2 µm and R is 700 µm at 775 nm; inset in (a) (lower), mode field distribution when W_bus is 1.2 µm and R is 400 µm at 775 nm; inset in (b) (upper), mode field distribution when W_bus is 1.2 µm and R is 200 µm at 1550 nm; inset in (b) (lower), mode field distribution when W_bus is 1.2 µm and R is 800 µm at 1550 nm. W_ring is 1.7 µm, G is 0.4 µm, α is 70°, H is 0.7 µm, and H_etch is 0.34 µm.

Fig. 3. (a) Energy transmission coefficient coupling from the pulley bus waveguide to the ring resonator with different coupling angles considering only the curved waveguide section with CMT; (b) energy transmission coefficient coupling from the input port to the ring resonator with different coupling angles θ at dual wavelengths through 3D FDTD simulation; (c) demonstration diagram of the mode field when light propagates in a curved bus waveguide.

Fig. 4. (a) Transmission of coupling energy from the input port to the ring resonator with different coupling angles θ at dual wavelengths; (b) considering only the curved waveguide section, the transmission of coupling energy from the pulley bus waveguide to the ring resonator with different coupling angles θ calculated by the CMT.

Fig. 5. (a) Coupling structure from the pulley bus waveguide to the ring resonator after adding an offset in the interface of the pulley bus waveguide; (b) relationship between the energy coupled into the ring and angle-θ at dual wavelengths in the offset waveguide with 3D FDTD; (c) relationship between the energy coupled into the ring and angle-θ at dual wavelengths in the offset waveguide.