Theory of non-cw operation of a laser with a distributed feedback. Model of the effective Q factor

An approximate (relating to the case of a small excess above the threshold) model of the interaction of waves in active media with a distributed feedback (DFB) is proposed and justified. The amplitude of the generated field, averaged over the length of the active medium, is given by a general equation which is derived for the description of non-cw (pulsed) excitation and saturation of lasing in the three main DFB laser configurations. The output intensity of cw lasing and the parameters of relaxational oscillations (spike intensity and duration, period, and decay time) are calculated analytically. A comparison of the approximate solutions obtained in this way with numerical solutions of the exact equations shows that the proposed model gives accurate results right up to the a priori limit of its validity.