  Achieving and controlling strong light-matter interactions in many-body
systems is of paramount importance both for fundamental understanding and
potential applications. In this paper we demonstrate both experimentally and
theoretically how to manipulate strong coupling between the Bragg-plasmon mode
supported by a organo-metallic array and molecular excitons in the form of
J-aggregates dispersed on the hybrid structure. We observe experimentally the
transition from a conventional strong coupling regime exhibiting the usual
upper and lower polaritonic branches to a more complex regime, where a third
nondispersive mode is seen, as the concentration of J-aggregates is increased.
The numerical simulations confirm the presence of the third resonance. We
attribute its physical nature to collective molecule-molecule interactions
leading to the collective electromagnetic response. A simple analytical model
is proposed to explain the physics of the third mode. The nonlinear dependence
on molecular parameters followed from the model are confirmed in a set of
rigorous numerical studies. It is shown that at the energy of the collective
mode molecules oscillate completely out of phase with the incident radiation
acting as an effective thin metal layer.
