Abstract
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.
Highlights
Since terahertz (THz) quantum cascade lasers (QCLs) were first successfully demonstrated in 2002 [1], the development of THz QCL technology has witnessed remarkable growth over the past 17 years
It should be noted that we used three modifications as follows to speed up the dynamical process as in order to reach the temporal steady state with reduced computational effort: 1) we solved the rate equation for the mode frequency with optical feedback νm instead of the mode phase φm(t) to avoid its accumulation with the time, considering that dφm(t)/dt = 2π(νm − νr,m); 2) the optical feedback terms in the rate equations of photon population and the frequency at each mode were replaced by their steady state versions as (2κ/τin)Sm(t) cos (2πνmτext) and −(κ/τin) sin (2πνmτext), respectively [20]; 3) the photon and carrier populations were normalized by 106 so that they are on the same order of magnitude as the mode frequency
We explored the general characteristics of a FP multi-mode THz QCL under optical feedback through developing an original theoretical model that involves multi-mode reduced rate equations (RREs) and gain saturation
Summary
Since terahertz (THz) quantum cascade lasers (QCLs) were first successfully demonstrated in 2002 [1], the development of THz QCL technology has witnessed remarkable growth over the past 17 years. The laser behavior in a multi-longitudinal-mode (indicated as multi-mode ) THz QCL under optical feedback are very different from that of the single-mode case, due to mode competition of the optical gain in the active region of the laser created by stimulated emission through transitions of the injected carriers. The dependence of the absorption coefficient and complex refractive index within a range of THz frequencies can be extracted directly from the multi-mode SM amplitude by extending the external cavity length when the laser operates in the multi-mode regime. Unlike the single-mode and multi-mode cases, the amplitude of the SM signal is no longer proportional to the feedback coupling coefficient when the feedback is sufficiently strong that the laser enters into tuneable-mode regime This suggests that a multi-mode laser operating in the tuneable-mode regime cannot be used for spectroscopic sensing directly via the external cavity extension method.
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