Coherent Pulse Progression of Mid-Infrared Quantum-Cascade Lasers under Group-Velocity Dispersion and Self-Phase Modulation

The effect of group-velocity dispersion (GVD) and self-phase modulation (SPM) on the coherent pulse progression in mid-infrared quantum-cascade lasers (QCLs) is investigated. The background saturable absorber (SA) effect is included in this paper. In this case, the lasing pulses can be built up from the instable continuous wave operation condition related to both SA effect and GVD under the influence of a small initial disturbance. The theoretical model is built based on the Maxwell-Bloch formulism accounting for the couplings among the electric field, the polarization, and the population inversion. The pulse evolution in time-spatial domains is simulated by the finite difference method with prior nondimensionalization, which is necessary for convergent solution. It is found that the anomalous GVD, which receives less attention in the study of QCL dynamics, can significantly narrow the spectrum splitting between side modes. The SPM can broaden the linewidth of the spectral modes. Their combined effects can lead the possibility of forming solitons.