  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.
