摘要： The challenge of nonlinear optics stems from the negligible interaction among electromagnetic waves in free space, motivating substantial efforts to identify materials with sufficient anharmonic response as to enable optical nonlinearities at low light powers. On the nanoscale, near-field intensity enhancement through optical resonators has been widely explored to design active photonic devices operating on subwavelength scales. Further interest in nanoscale nonlinear optics has arisen with the isolation of graphene and other atomically-thin materials that combine a large electro-optic response with strong intrinsic nonlinearities. Despite their large nonlinear optical susceptibilities, the response of 2D materials is limited by their inherently small volumes. Optical resonances provide a promising way for circumventing this limitation, as they can enhance the driving electric field, thus boosting the effective nonlinear response. In the present work we introduce a figure-of-merit (FoM) that quantifies the enhancement of the nonlinear optical response that can be achieved in 2D materials by means of resonant cavities. As concrete examples, we apply our FoM to explore the extrinsic near-field enhancement provided by (1) localized nanoparticle plasmons acting on a 2D material; (2) the extrinsic enhancement in a 2D material produced by Mie-like resonances in dielectric nanoparticles; (3) the intrinsic enhancement of optical nonlinearity in a dielectric nanoparticle by its supported Mie resonances; (4) the effect of lattice resonances on the nonlinear response for a periodic 2D array of dielectric nanodisks. We focus in particular on the enhancement in second- and third-harmonic generation, as well as the Kerr nonlinearity, quantifying the yield of these nonlinear processes in each of the systems. Our FoM provides an efficient tool to explore the dependence of the nonlinear response enhancement by optical resonances on the size-to-wavelength ratio, composition, and geometry, thus facilitating the design of structures with optimal nonlinear yields.