  Second-order nonlinear optical processes are used to convert light from one
wavelength to another and to generate quantum entanglement. Creating chip-scale
devices to more efficiently realize and control these interactions greatly
increases the reach of photonics. Optical crystals and guided wave devices made
from lithium niobate and potassium titanyl phosphate are typically used to
realize second-order processes but face significant drawbacks in scalability,
power, and tailorability when compared to emerging integrated photonic systems.
Silicon or silicon nitride integrated photonic circuits enhance and control the
third-order optical nonlinearity by confining light in dispersion-engineered
waveguides and resonators. An analogous platform for second-order nonlinear
optics remains an outstanding challenge in photonics. It would enable stronger
interactions at lower power and reduce the number of competing nonlinear
processes that emerge. Here we demonstrate efficient frequency doubling and
parametric oscillation in a thin-film lithium niobate photonic circuit. Our
device combines recent progress on periodically poled thin-film lithium niobate
waveguidesand low-loss microresonators. Here we realize efficient >10%
second-harmonic generation and parametric oscillation with microwatts of
optical power using a periodically-poled thin-film lithium niobate
microresonator. The operating regimes of this system are controlled using the
relative detuning of the intracavity resonances. During nondegenerate
oscillation, the emission wavelength is tuned over terahertz by varying the
pump frequency by 100's of megahertz. We observe highly-enhanced effective
third-order nonlinearities caused by cascaded second-order processes resulting
in parametric oscillation. These resonant second-order nonlinear circuits will
form a crucial part of the emerging nonlinear and quantum photonics platforms.
