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High complexity, dense integrated nanophotonic circuits possessing strong nonlinearities are desirable for a breadth of applications in classical and quantum optics. In this work, we study natural phase matching via modal engineering in lithium niobate (LN) waveguides and microring resonators on chip for second harmonic generation (SHG). By carefully engineering the geometry dispersion, we observe a $26\%~W^{-1}cm^{-2}$ normalized efficiency for SHG in a waveguide with submicron transverse mode confinement. With similar cross-sectional dimensions, we demonstrate phase matched SHG in a microring resonator with 10 times enhancement on the out-coupled second-harmonic power. Our platform is capable of harnessing the strongest optical nonlinear and electro-optic effects in LN on chip with unrestricted planar circuit layouts. It offers opportunities for dense and scalable integration of efficient photonic devices with low loss and high nonlinearity.

Modal phase matched lithium niobate nanocircuits for integrated nonlinear photonics