Fig. 1. Highly efficient SHG in modal phase-matched z-cut Si-LNOI hybrid waveguide. (a) Schematic and working principle of the Si-LN hybrid waveguide. (b) Cross-section schematic of the waveguide structure.

Fig. 2. Design of the LN etchless hybrid waveguide. Effective indices of the hybrid modes at both pump and SH wavelengths varying with (a) Si height and (c) Si width. (b), (d) Detailed phase matching conditions between TM₀₁ at 775 nm and TM₀₀ at 1550 nm of (a), (c). (e) Optical field (E_z components) of the phase-matched modes at both wavelengths in the all space and nonlinear region. (f) E_z as a function of the vertical position z at the center of the waveguide.

Fig. 3. Theoretical calculations and full-wave simulations. (a) Calculated normalized conversion efficiency as a function of the propagation length. (b) Simulation result in comparison with theory result. (c) Simulated SHG process in a 10-µm-long hybrid z-cut waveguide for demonstration. (d) Schematic of a fully integrated Si/LN hybrid system.