Coherent multi-mode dynamics in a Quantum Cascade Laser: Amplitude and Frequency-modulated Optical Frequency Combs

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.