Near-field analysis of strong coupling between localized surface plasmons and excitons

We simulate the near-field effects of strong coupling between molecular excitons and localized surface plasmons, supported by aluminum nanodisks. The simulations are done using a simple model of a two-level system, implemented in a commercial electromagnetic finite-difference time-domain solver. While the Rabi splitting is present in the near field, its spectral gap is seen to be smaller than the one obtained in the far field, although it follows a clear square root dependence on the molecular density as expected. Moreover, the energy exchange between the plasmonic mode and the excitonic material is evident in ``beats'' within the electromagnetic near field, which are out of phase with respect to the exciton population. Our results explicitly demonstrate the collective nature of strong coupling, which is expressed by the synchronized population oscillations at the collective Rabi frequency set by the number of molecules interacting with the plasmonic mode. This analysis sheds light on strong coupling effects in the near-field region using a versatile model, which provides a powerful tool to study strong coupling, near-field effects, and light-matter interactions in general.