▎ 摘　　要

The active mode-locking technique of quantum cascade lasers is highly affected by the bias current level and the magnitude of the modulated signal because of the spatial hole burning effect. The laser generates a stable pulse train near the threshold current and for a high modulation magnitude. We show in this paper an improvement of these conditions with an integration of a single-layer graphene which works as a saturable absorber. The light-matter interaction in the laser active region is described by the two-level Maxwell-Bloch equations and in graphene layer by the Maxwell-Ampere equation and Maxwell-Bloch equations. These system equations are solved using the Finite-Difference Time-Domain (FDTD) method which has the main advantage of not involving any approximation. The weakly coupled splitting scheme is adopted for the time discretization of Maxwell and Bloch equations. The graphene saturable absorption is modelled by a saturable conductivity in Maxwell-Ampere equation and with the dipole moment and carrier density in Maxwell-Bloch equations. For a QCL structure with a gain recovery time of 50 ps, simulation results show better stability of the mode-locking over a broad range of injection current and for smaller magnitude of the modulated signal. QCL structure with gain recovery time close to 1 ps reveals the generation of two pulses per roundtrip linked to spatial hole burning. The carrier grating strength can be reduced by changing the boundary conditions of the cavity such as with a high reflectivity mirror in front of graphene layer.