  We present a full quantum theory for the dissipative dynamics of an optical
cavity in the ultra-strong light-matter coupling regime, in which the vacuum
Rabi frequency is comparable to the electronic transition frequency and the
anti-resonant terms of the light-matter coupling play an important role. In
particular, our model can be applied to the case of intersubband transitions in
doped semiconductor quantum wells embedded in a microcavity. The coupling of
the intracavity photonic mode and of the electronic polarization to the
external, frequency-dependent, dissipation baths is taken into account by means
of quantum Langevin equations in the input-output formalism. Observable spectra
(reflection, absorption, transmission and electroluminescence) are calculated
analytically in the case of a time-independent vacuum Rabi frequency.
