Theory of mode-locked semiconductor lasers

We present a theoretical study of semiconductor mode-locked lasers at a phenomenological level. We use the slow absorber model of New and Haus, but extend the analysis by taking into account the shift in the gain maximum due to the changing number of carriers. In our analysis of the resulting equation, we show that due to stability requirements the shortest attainable pulse duration is limited. The use of self-phase modulation due to a slow medium can at most lead to a shortening of the pulse by a factor of 2. We show that the shifting of the gain maximum due to the changing number of carriers in the laser is a crucial aspect in the operation of mode-locked semiconductor lasers. We further find that the end mirrors must be reflecting more than about half of the light intensity to prevent a self-pulsation type instability similar to the relaxation oscillation.