Fig. 1. (a) Three-dimensional structure schematic diagram of the coupler; (b) cross-sectional view and (c) top view of coupler.

Fig. 2. (a) The simulated overlap between the lensed fiber mode and the ${\mathrm{SiO}}_2$ waveguide mode at 1550 and 775 nm under different waveguide widths. Coupling loss from the ${\mathrm{SiO}}_2$ waveguide to the LN bottom layer at (b) 775 nm and (c) 1550 nm with different bottom dimensions (inset: dimensional parameters of the bottom cone). The simulated curves of coupling lengths (d) $L_1$, (e) $L_2$, and (f) $L_3$ at 1550 and 775 nm. The red stars represent the designed parameter values of the coupler.

Fig. 3. (a) The simulated distribution of ${\mathrm{TE}}_{00}$ mode of 1550 and 775 nm at different cross sections I, II, III, IV, and V; simulated mode propagation in the designed coupler at wavelengths (b) 1550 nm and (c) 775 nm.

Fig. 4. The simulated coupling efficiency of double-layer structure and tri-layer structure at (a) 1550- and (b) 775-nm band.

Fig. 5. SEM pictures of (a) bottom tip, (b) middle tip, and (c) top tip. (d) SEM picture and (e) larger view of suspended ${\mathrm{SiO}}_2$ waveguide.

Fig. 6. The coupling losses of the fabricated edge couplers at (a) 1535 to 1565 nm and (b) 765 to 780 nm. Shadowed areas show the standard deviation measured over six devices.

Fig. 7. (a) Period domain observed by SHG-confocal microscope imaging; red frame is the domain-inverted region. (b) Experimental setup for SHG. FPC, fiber polarization controller; OSA, optical spectrum analyzer. (c) Measured normalized SHG conversion efficiency versus pump wavelengths. (d) Quadratic power dependence of the SH wave on the pump wave.

Table 1. Parameters of the designed coupler.

Table 2. A comparison with other SHG works based on periodically poled TFLN waveguides.