  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.
