We systematically demonstrate the influence of crystal orientation towards the phase matching condition in Lithium Niobate on insulator waveguide structure. The phase matching condition is one of the important elements that required prior to the development of ultracompact photonic integrated circuit. This is achieved as the effective refractive indices of fundamental mode, TE00 at pump wavelength overlapped with the second order mode, TE20 of second harmonic wavelength. With a proper selection of crystal orientation, the perfect phase matching condition is achievable over a broader telecommunication wavelength, hence, improve the efficiency of the device. In this work, we examine the phase matching interaction over the x-, y- and z- cut LNOI crystal structure. From the numerical analysis, the significant variation of phase matching width over crystal orientation is demonstrated with x-cut LNOI shows a strong ability to achieve the modal phase matching at narrower width, allowing the realization of ultracompact waveguide fabrication. Interestingly, z-cut LNOI, offers a broader range of phase matching wavelength tunability which beneficial for the development of optical modulator. Eventually, the y-cut LNOI suit for the fabrication of the wavelength-independent optical devices such as surface acoustic waveguide.
