  We investigate the rich physics of photonic molecule lasers using a
non-Hermitian dimer model. We show that several interesting features, predicted
recently using a rigorous steady state ab-initio laser theory (SALT), can be
captured by this toy model. In particular, we demonstrate the central role
played by exceptional points in both pump-selective lasing and laser
self-terminations phenomena. Due to its transparent mathematical structure, our
model provides a lucid understanding for how different physical parameters
(optical loss, modal coupling between microcavities and pump profiles) affect
the lasing action. Interestingly, our analysis also confirms that, for
frequency mismatched cavities, operation in the proximity of exceptional points
(without actually crossing the square root singularities) can still lead to
laser self-termination. We confirm this latter prediction for two coupled slab
cavities using scattering matrix analysis and SALT technique. In addition, we
employ our model to investigate the pump-controlled lasing action and we show
that emission patterns are governed by the locations of exceptional points in
the gain parameter space. Finally we extend these results to multi-cavity
photonic molecules, where we found the existence of higher-order EPs and
pump-induced localization.
