Laser feedback interferometry in multi-mode terahertz quantum cascade lasers.

The typical modal characteristics arising during laser feedback interferometry (LFI) in multi-mode terahertz (THz) quantum cascade lasers (QCLs) are investigated in this work. To this end, a set of multi-mode reduced rate equations with gain saturation for a general Fabry-Pérot multi-mode THz QCL under optical feedback is developed. Depending on gain bandwidth of the laser and optical feedback level, three different operating regimes are identified, namely a single-mode regime, a multi-mode regime, and a tuneable-mode regime. When the laser operates in the single-mode and multi-mode regimes, the self-mixing signal amplitude (peak to peak value of the self-mixing fringes) is proportional to the feedback coupling rate at each mode frequency. However, this rule no longer holds when the laser enters into the tuneable-mode regime, in which the feedback level becomes sufficiently strong (the boundary value of the feedback level depends on the gain bandwidth). The mapping of the identified feedback regimes of the multi-mode THz QCL in the space of the gain bandwidth and feedback level is investigated. In addition, the dependence of the aforementioned mapping of these three regimes on the linewidth enhancement factor of the laser is also explored, which provides a systematic picture of the potential of LFI in multi-mode THz QCLs for spectroscopic sensing applications.