  We solve the low-energy part of the spectrum of a model that describes a
cavity mode strongly coupled to an exciton, and both modes coupled to continua
of bosonic excitations which give rise to homogeneous broadenig. The spectral
density of the cavity modes in the low-energy manifold agrees with measured
photoluminiscense spectra. We suggest fitting these spectra with a sum of two
asymmetric Lorentzians.
