  There is considerable interest in collective effects in hybrid systems formed
by molecular or atomic ensembles strongly coupled by an electromagnetic
resonance. For analyzing such collective effects, we develop an efficient and
general theoretical formalism based on the natural modes of the resonator. The
main strength of our approach is its generality and the high level of
analyticity enabled by modal analysis, which allows one to model complex hybrid
systems without any restriction on the resonator shapes or material properties,
and to perform statistical computations to predict general properties that are
robust to spatial and polarization disorders. Most notably, we establish that
superradiant modes remain even after ensemble averaging and act as an
invisibility cloak with a spectral bandwidth that scales with the number of
oscillators and the spatially-averaged Purcell factor.
