  Resonant structures in modern nanophotonics are non-Hermitian (leaky and
lossy), and support quasinormal modes. Moreover, contemporary cavities
frequently include 2D materials to exploit and resonantly enhance their
nonlinear properties or provide tunability. Such materials add further modeling
complexity due to their infinitesimally thin nature and strong dispersion.
Here, a formalism for efficiently analyzing third harmonic generation (THG) in
nanoparticles and metasurfaces incorporating 2D materials is proposed. It is
based on numerically calculating the quasinormal modes in the nanostructure, it
is general, and does not make any prior assumptions regarding the number of
resonances involved in the conversion process, in contrast to conventional
coupled-mode theory approaches in the literature. The capabilities of the
framework are showcased via two selected examples: a single scatterer and a
periodic metasurface incorporating graphene for its high third-order
nonlinearity. In both cases, excellent agreement with full-wave nonlinear
simulations is obtained. The proposed framework may constitute an invaluable
tool for gaining physical insight into the frequency generation process in
nano-optic structures and providing guidelines for achieving drastically
enhanced THG efficiency.
