Multi-mode Dynamics of Terahertz Quantum Cascade Lasers: spontaneous and actively induced generation of dense and harmonic coherent regimes

We present an extended study concerning the dynamics of dense and harmonic coherent regimes in quantum cascade lasers (QCLs) in a Fabry--Perot (FP) configuration emitting in the terahertz (THz) spectral region. Firstly, we study the device in free running operation, reproducing the main features of the self-generated of optical frequency combs (OFCs) and harmonic frequency combs (HFCs) in this spectral range, commenting on the points of difference from the mid-infrared region, and finding excellent agreement with the most recent experimental evidences. Then, we analyze the THz-QCL dynamics under radiofrequency (RF) injection, with a focus on the effect of the modulation of the current on the degree of locking of the system, and we perform a systematic investigation aimed to provide a procedure for the generation of train of pulses with short duration and high contrast. Furthermore, we extend our study to the generation of sequences of pulses with repetition frequency which is a multiple of the free-spectral range (FSR) of the laser cavity, reproducing harmonic mode-locking (HML) of the laser, a method which has been recently demontrated in experiments with THz-QCLs, and the results of which are particulary promising for a large stream of applications, ranging from optical communication to imaging.