Multimode non-Hermitian framework for third harmonic generation in nonlinear photonic systems comprising two-dimensional materials

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.