Fig. 1. Structural diagrams of edge coupler. (a) Overall structure diagram of cross-type waveguide coupler; (b) cross section of cross-type heterogeneous multi-core waveguide; (c) mode field distribution of cross-type heterogeneous multi-core waveguide

Fig. 2. Overlap between cross-type waveguide and fiber. (a) TM mode overlap between HNAF and cross-type waveguide; (b) TE mode overlap between HNAF and cross-type waveguide

Fig. 3. Overlap between cross-type waveguide and fiber (within the dashed line,both TE mode overlap and TM mode overlap are beyond 0.97 or 0.98). (a)(b) Overlap of TE and TM modes when the thickness of the bottom Si waveguide of the cross-type waveguide is 70 nm; (c)(d) overlap of TE and TM modes when the thickness of the bottom Si waveguide of the cross-type waveguide is 150 nm

Fig. 4. Optimization of taper parameters. (a)(b) Relative difference of effective refractive index of double waveguides and single waveguide for TE mode and TM mode varying with waveguide width; (c)(d) effective refractive indexes of TE mode and TM mode varying with waveguide width; (e)(f) mode field distributions of TE mode and TM mode

Fig. 5. Design of taper length. (a) Mode conversion efficiency varying with length of adiabatic taper; (b) mode conversion efficiency varying with length of Si₃N₄-cross waveguide taper; (c) top view of adiabatic taper and Si₃N₄-cross waveguide taper

Fig. 6. Propagation of optical field in mode-spot converter. (a) Mode field distribution corresponding to each cross-section; (b) side view of optical field distribution

Fig. 7. Bandwidth simulation analysis. (a) Overlap varying with wavelength; (b) coupling efficiency of end coupler varying with wavelength

Fig. 8. Overlap between designed coupler and HNAF varying with horizontal and vertical displacements. (a) TE mode; (b) TM mode