  We cast a theoretical model based on Effective Semiconductor Maxwell-Bloch
Equations and study the dynamics of a multi-mode mid-Infrared Quantum Cascade
Laser in Fabry Perot with the aim to investigate the spontaneous generation of
optical frequency combs. This model encompasses the key features of a
semiconductor active medium such as asymmetric,frequency-dependent gain and
refractive index as well as the phase-amplitude coupling of the field dynamics
provided by the linewidth enhancement factor. Our numerical simulations are in
excellent agreement with recent experimental results, showing broad ranges of
comb formationin locked regimes, separated by chaotic dynamics when the field
modes unlock. In the former case, we identify self-confined structures
travelling along the cavity, while the instantaneous frequency is characterized
by a linear chirp behaviour. In such regimes we show that OFC are characterized
by concomitant and relevant amplitude and frequency modulation.
