Molecular polaritonics in dense mesoscopic disordered ensembles.

We study the dependence of the vacuum Rabi splitting (VRS) on frequency disorder, vibrations, near-field effects and density in molecular polaritonics. In the mesoscopic limit, static frequency disorder introduces a loss mechanism from polaritonic states into a dark state reservoir, which we quantitatively describe, providing an analytical scaling of the VRS on the level of disorder. The combination of disorder, vibronic coupling, dipole-dipole interactions and vibrational relaxation induces an incoherent FRET (F\"{o}rster resonance energy transfer) migration of excitations from donor-type to acceptor-type molecules within the collective molecular state. This is equivalent to a dissipative disorder and has the effect of saturating and even reducing the VRS in the mesoscopic, high-density limit.