  Optical nonlinear processes are indispensable in a wide range of applications
including ultrafast laser sources, microscopy, metrology, and quantum
information technologies. Combinations of the diverse nonlinear processes
should further lead to the development of unique functionalities, but
simultaneous use of second- and third-order nonlinear processes is generally
difficult. Second-order effects usually overwhelm the higher-order ones, except
in centrosymmetric systems where the second-order susceptibility vanishes to
allow the use of the third-order nonlinearity. Here we demonstrate a hybrid
photonic platform whereby the balance between second- and third-order
susceptibilities can be tuned flexibly. Ultrahigh-Q silica microcavities
capable of generating third-order effects are functionalized by atomically thin
tungsten diselenide, and we observe cavity-enhanced second-harmonic generation
and sum-frequency generation with continuous-wave excitation at a power level
of only a few hundred microwatts. Pump power dependence exhibits drastic
increase and saturation of the second-harmonic light, originating from the
dynamic phase-matching process. We show that the coexistence of second- and
third-order nonlinearities in a single device can be achieved by carefully
choosing the size and the location of the two-dimensional material. Our
approach can be generalized to other types of cavities, unlocking the potential
of hybrid systems with controlled nonlinear susceptibilities for novel
applications.
