On the noise-amplifier model of the laser

When the relaxation of the pumping process in a laser is slow, the gain saturation does not follow the fluctuation of the field amplitude instantaneously. Then the noise-amplifier model of the laser can be valid even at and above threshold. Assuming a Lorentzian line shape, we derive the linewidth formula for such a laser and show that a necessary condition for the validity of the model is to have a small saturation parameter.