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

Input-output theory of cavities in the ultrastrong coupling regime: The case of time-independent cavity parameters