Harmonic active mode locking in terahertz quantum cascade lasers

We present a numerical study of the active harmonic mode locking (HML) of quantum cascade lasers (QCLs) in the terahertz (THz) spectral range. This is a recently experimentally demonstrated technique based on the modulation of the bias current of the laser by radio-frequency (rf) injection, allowing for the generation of multiple short pulses per round-trip in the QCL cavity. We first study the Fabry-P\'erot (FP) configuration, unraveling the impact of both laser intrinsic parameters and rf injection on the characteristics of the generated harmonic pulses. Our study demonstrates that the key parameter for the achievement of ultrashort pulses is the QCL gain bandwidth: by pushing this quantity beyond 1 THz, we reproduce second-order ultrashort harmonic pulses with a duration of 2.5 ps. This suggests that the combination of the HML technique with the design of optimized cavities providing a larger gain, such as multistack active regions, can allow for the generation of narrow pulses approaching the picosecond limit in THz QCLs. Then a direct comparison with the experiment is presented, which reveals that the introduction of an unmodulated section in the laser cavity is crucial to considerably reduce the duration of the generated pulses. Finally, motivated by recent observations of high-contrast localized structures such as optical solitons in free-running ring QCLs, we investigate the formation of harmonic pulses in these unidirectional cavities. We make a comparative analysis aimed at understanding if this configuration can guarantee an improvement in the performance of the HML with respect to the FP case. We find that the intrinsic properties of ring QCLs, such as unidirectionality and the absence of spatial hole burning, lead to a 1.5-ps pulse duration, promoting these devices as strong candidates for the generation of ultrashort pulses in the THz range.