We measured the optical linewidths of a passively mode-locked quantum dot laser and show that, in agreement with theoretical predictions, the modal linewidth exhibits a parabolic dependence with the mode optical frequency. The minimum linewidth follows a Schawlow-Townes behavior with a rebroadening at high power. In addition, the slope of the parabola is proportional to the RF linewidth of the laser and can therefore provide a direct measurement of the timing jitter. Such a measurement could be easily applied to mode-locked semiconductor lasers with a fast repetition rate where the RF linewidth cannot be directly measured
