Contents I. Introduction
Harmonically mode-locked lasers are attractive as sources of high-repetition-rate optical pulses that can be used in electrooptic sampling, optical analog-to-digital conversion, optical telecommunication systems, and ultrafast optical measurements [1]–[5]. Stability of the pulses in harmonically mode-locked lasers is important for most of these applications. A laser mode-locked at the th harmonic has optical pulses propagating inside the laser cavity. The requirements for pulse stability in fiber lasers were analyzed in [6] and [7]. It was shown that pulse stability results from the combination of Kerr nonlinearity and optical filtering. For soliton pulses, the pulse width is inversely proportional to the pulse energy. If the pulse energy increases, the pulse width decreases and the pulse experiences less loss from the active modulator. On the other hand, since the pulse bandwidth also increases with decrease in the pulse width, the pulse experiences more loss from the optical filter. The pulse energy fluctuations are damped if the increase in loss from the optical filter is more than the increase in gain from the active modulator. This condition was used to obtain a minimum value for the pulse energy for stable operation. The stability of soliton pulses in fiber lasers was also analyzed numerically in [8], and the stability requirements predicted in [6] and [7] were verified. It was also shown in [8] that, when the pulse power is smaller than the minimum value required for stable operation, instabilities can lead to pulse dropouts. In the case of harmonically mode-locked semiconductor lasers, the following questions arise: 1) what stabilizes the pulses and 2) what are the limits on the stable operating regime. In this paper, we present a theoretical model to answer these questions.
