Influence of direct dipole-dipole interactions on the optical response of two-dimensional materials in strongly inhomogeneous infrared cavity fields

A two-dimensional (2D) material, formed, for example, by a self-assembled molecular monolayer or by a single layer of a van der Walls material, can couple efficiently with photonic nanocavities, potentially reaching the strong-coupling regime. The coupling can be modeled using classical harmonic-oscillator models or cavity quantum electrodynamics Hamiltonians that often neglect the direct dipole-dipole interactions within the monolayer. Here we diagonalize the full Hamiltonian of the system, including these direct dipole-dipole interactions. The main effect on the optical properties of a typical 2D system is simply to renormalize the effective energy of the bright collective excitation of the monolayer that couples with the nanophotonic mode. On the other hand, we show that for situations of extreme field confinement, large transition dipole moments, and low losses, fully including the direct dipole-dipole interactions is critical to correctly capture the optical response, with many collective states participating in it. To quantify this result, we propose a simple equation that indicates the condition for which the direct interactions strongly modify the optical response.