  We study the laser regime of terahertz (THz) emission from a semiconductor
microcavity in the strong coupling regime, where optical transitions between
upper and lower exciton-polariton modes are allowed due to the mixing of the
upper mode with one of the dark exciton states. Using a system of
master-Boltzmann equations describing both polariton modes and the THz mode, we
calculate the first and second order coherences and the spectral shape of THz
emission. This analysis shows that THz lasing in microcavities is possible
provided that the system is embedded in a good THz cavity, that the optical
(polariton) lasing condition is fulfilled and if the depletion of the upper
polariton mode due to acoustic phonon assisted relaxation processes is reduced.
This latter condition is likely to be realised in pillar microcavities, which
seem to be the most suitable candidates for realisation of a THz laser.
