Although many successful single-molecule experiments or more) of molecules is coupled simultaneously to many modes of the cavity. These many coupled DOFs generate collective upper and lower polaritonic states as well as the dense manifold of "dark states" which contain minuscule amounts of photonic character and negligible transition dipole. The direct generalization of Eq. 13 for many molecules N mol and cavity modes N mode , including both parallel k x (quasi-continuous) and perpendicular k z (discrete) modes, can be written as,