  We first present a quasinormal mode (QNM) theory for coupled loss-gain
resonators working near an exceptional point. Assuming linear media, which can
be fully quantified using the complex pole properties of the QNMs, we show how
the QNMs yield a quantitatively good model to a full dipole spontaneous
emission response in Maxwell's equations at various spatial positions and
frequencies (linear response). We also develop a highly accurate and intuitive
QNM coupled-mode theory, which can be used to rigorously model such systems
using only the QNMs of the bare resonators, where the hybrid QNMs of the
complete system are automatically obtained. Near a lossy exceptional point, we
analytically show how the QNMs yield a Lorentzian-like and a
Lorentzian-squared-like response for the spontaneous emission lineshape,
consistent with other works. However, using rigorous analytical and numerical
solutions for microdisk resonators, we demonstrate that the general lineshapes
are far richer than what has been previously predicted. Indeed, the classical
picture of spontaneous emission can take on a wide range of positive and
negative Purcell factors from the hybrid modes of the coupled loss-gain system.
These negative Purcell factors are unphysical and signal a clear breakdown of
the classical dipole picture of spontaneous emission in such media, though the
negative local density of states is correct. We also show the rich spectral
features of the Green function propagators, which can be used to model various
physical observables. Second, we present a QNM approach to model index
modulated ring resonators working near an exceptional point and show unusual
chiral power flow from linearly polarized emitters, in agreement with recent
experiments, which is quantitatively explained without invoking the
interpretation of a missing dimension (the Jordan vector) and a decoupling from
the cavity eigenmodes.
