  This work presents a theory of the frequency-resolved light emission of
active two-dimensional dielectric microresonators, which are characterized by a
highly non-paraxial mode structure and frequently feature a position-dependent
dielectric constant and non-uniform gain. The Lorentzian intensity profile is
characterized by an appropriately generalized Petermann factor, a renormalized
peak position, and the cold-cavity resonance lifetime Gamma. The theory also
delivers a relation of Gamma to the laser threshold that improves earlier
phenomenological expressions even for the case of a homogeneous medium.
