Fig. 1. Cross-sectional schematic of uniform grating

Fig. 2. Grating couplers in different design schemes. (a) Partial schematic of linearly chirped grating with linearly changed fill-factor and fixed period; (b) partial schematic of proposed linearly apodized grating; (c) cross-sectional schematic of proposed linearly apodized grating

Fig. 3. Variation trends of effective index n_e and coupling efficiency. (a) Effective index n_e as a function of etching depth e in TE₀ mode at 1550 nm; (b) 2D contour map of coupling efficiency at 1550 nm as a function of e and R

Fig. 4. Effect comparison of uniform grating, apodized grating in Ref. [18], and apodized grating in this work. (a) Normalized field distributions at 1550 nm along x direction; (b) upward transmission; (c) coupling efficiency

Fig. 5. Grating couplers with etching inclination angle. (a) Cross-sectional schematic of waveguide with etching inclination angle; (b) cross-sectional schematic of apodized grating with etching inclination angle

Fig. 6. Diffraction electric field distribution and coupling efficiency. (a) Diffraction electric field distribution of apodized grating for TE polarization; (b) diffraction electric field distribution of apodized grating with etching inclination angle for TE polarization; (c) coupling efficiency of apodized grating with etching inclination angle as a function of F_fb,1

Table 1. Optimal periods and fill-factorsobtained from optimization of apodized grating in 500 nm Z-cut LNOI platform, when e=340 nm and R=0.035 μm^-1

Table 2. Coupling efficiency comparison of demonstrated LNOI grating couplers in recent years