Multimode dynamics and mode locking phenomena in QCLs

The dynamics of Quantum Cascade Lasers is investigated using modified MaxwellBloch Equations. It is shown that spatial hole burning and the Risken-Nummedal-Graham-Haken (RNGH) instability are the main causes for multimode operation in these semiconductor lasers. In 2000, R. Paiella et al. reported strong evidence of self-pulsations at the cavity roundtrip frequency in electrically pumped quantum cascade lasers (QCLs) [1]. The emission of a 3-5 picosecond train of pulses at ~10 GHz repetition rate was supported by this data. At that time, no detailed pulse characterization was available, because of the lack of suitable mid-infrared autocorrelation techniques for this low energy pulse train and many questions regarding the extent of the mode locking mechanism remained open. Given that the gain recovery time of QCLs is extremely short compared to the cavity round-trip time, conventional mode locking models predict incomplete mode locking [2,3]. To explain the mechanisms responsible for triggering the multimode regime in QCLs, we suggest two scenarios. The first is by the onset of a coherent instability related to the so-called Risken-Nummedal-Graham-Haken (RNGH) instability [4,5]. The second is spatial hole burning. We show that due to the very fast gain recovery of QCLs and very large Rabi frequency of the intracavity laser field, these mechanisms are enhanced, whereas mode locking is suppressed. Different multimode regimes in QCLs triggered by these two mechanisms will be discussed. Theoretical modeling based on modified Maxwell-Bloch equations for a linear cavity will be presented. We show that this simple model, where the QCL is described as a two-level system, reproduces the measured nontrivial multimode spectra and autocorrelation traces fairly well. Furthermore, we discuss two routes to generate stable periodic pulse trains from a QCL. First, the possibility of stable mode-locking of QCLs through engineering of the gain medium to achieve slower gain recovery times: the gain recovery timescale should be comparable with the cavity roundtrip time. Second, by allowing multiple pulses per roundtrip with repetition rates on the order of the gain recovery rate, i.e. multiple 100GHz repetition rates.