  The gain spectrum of a terahertz quantum cascade laser is analysed by a non
equilibrium Green's functions approach. Higher harmonics of the response
function were retrievable, providing a way to approach nonlinear phenomena in
quantum cascade lasers theoretically. Gain is simulated under operation
conditions and results are presented both for linear response and strong laser
fields. An iterative way of reconstructing the field strength inside the laser
cavity at lasing conditions is described using a measured value of the level of
the losses of the studied system. Comparison with recent experimental data from
time-domain-spectroscopy indicates that the experimental situation is beyond
linear response.
