The recent development of the Lithium Niobate on Insulator (LNOI) fabrication process has opened a bright future for integrating ultra-compact photonic circuits. Due to its excellent nonlinear properties, as a waveguide material, Lithium Niobate supports nonlinear optical processes including efficient sum frequency generation and second harmonic generation. To enhance these effects, precise control of mode confinement and modal phase matching is required. In this work, we engineer an LNOI waveguide to match the effective refractive indices of the fundamental mode, TE00 at the fundamental wavelength and second-order mode, TE20 at the second harmonic wavelength. As waveguide geometry plays an essential role, optimization of waveguide parameters is crucial for the design of high-performance, feasible devices. Here, we numerically engineer and characterize the influence of rib waveguide geometry parameters including etching depth, D , width, W and sidewall angle, θ on the phase matching condition. We find that the waveguide phase matching condition is most susceptible to variations in the sidewall angle. For the optimized parameter values of {D,θ}={450nm,10o} , the phase-matching wavelength tunability is achieved through the waveguide width control.
