  We present an analytical model describing the transition to strong coupling
regime for an ensemble of emitters resonantly coupled to a localized surface
plasmon in a metal-dielectric structure. The response of a hybrid system to an
external field is determined by two distinct mechanisms involving collective
states of emitters interacting with the plasmon mode. First is the near-field
coupling between the bright collective state and the plasmon mode which
underpins energy exchange between the system components and gives rise to
exciton-induced transparency minimum in scattering spectra in the weak coupling
regime and to emergence of polaritonic bands as the system transitions to
strong coupling regime. The second mechanism is the Fano interference between
the plasmon dipole moment and plasmon-induced dipole moment of bright
collective state as the hybrid system interacts with the radiation field. The
latter mechanism is greatly facilitated by plasmon-induced coherence in a
system with characteristic size below the diffraction limit as the individual
emitters comprising the collective state are driven by same alternating plasmon
near field and therefore all oscillate in phase. This cooperative effect leads
to scaling of the Fano asymmetry parameter and of the Fano function amplitude
with the ensemble size and therefore it strongly affects the shape of
scattering spectra for large ensembles. Specifically, with increasing emitters
numbers, the Fano interference leads to a spectral weight shift towards the
lower energy polaritonic band.
