▎ 摘　　要

Passive mode-locking in quantum cascade lasers (QCLs) remains one of the huge challenges because of the fast relaxation time of the excited carriers which is typically in the range of sub-picoseconds. The use of conventional techniques such as the semiconductor saturable absorber mirror is inefficient because the spatial hole burning effect dominates the carrier dynamics. To overcome this effect, longitudinal transition structures with relaxation time around 50 ps were proposed. However, mode-locking is assured with an external modulation at a cavity roundtrip frequency. In this paper, we demonstrate that a single-layer graphene used as a saturable absorber permits to generate stable pulses in such structures. The graphene is integrated with a highly reflective mirror to increase the internal electric field and achieve the saturation intensity. The dynamic of the QCL is modeled with Maxwell-Bloch equations while Maxwell-Ampere equation is used for the graphene layer by considering a nonlinear conductivity. This system of equations is solved using the one-dimensional Finite-Difference Time-Domain (FDTD) method. To model the single-layer graphene of a 0.33 nm thickness, a specific subcell is implemented based on Maloney method. Simulation results of a 6.2 mu m QCL with a diagonal radiative transition show a generation of isolated pulses with a peak electric field of 80 MV.m(-1) and a duration of 51 fs. The mode-locking remains stable for QCLs with a vertical transition having a relaxation time below 5 ps.