Optical feedback induced irregular and chaotic dynamics in terahertz quantum cascade laser combs

Abstract: In this work, we systematically investigate the optical feedback dynamics of terahertz (THz) frequency combs generated from quantum cascade lasers (QCLs) using the effective semiconductor Maxwell-Bloch equations (ESMBEs). Starting from a free-running comb state at low bias (1.3Ith), we identify clear bifurcation routes as the external feedback is increased. In the weak feedback regime (C<1), the frequency comb operation remains stable; as feedback increases to the moderate feedback regime (1<C\<2.4), the system transitions through frequency splitting into period-one (P1) oscillations around each comb, followed by higher-order bifurcations (P2, P4, P8). Within the range 2.4<C\<13.86, only combs with P1 states are observed, with the split frequency increasing continuously with feedback strength. In the strong feedback regime (C\>13.86), complex feedback dynamics re-emerged but with significantly reduced complexity compared with the weak feedback regime. More interestingly, we show that optical feedback can induce chaotic THz emission at higher bias current conditions (>1.6Ith), when the free-running laser output (C=0) is originally a stable frequency comb. The resulting chaotic dynamics, characterized by broadband spectra and large positive Lyapunov exponents, are shown to depend strongly on the linewidth enhancement factor. Although THz QCLs widely considered as ultrastable under external perturbations, this work provides the first detailed report of chaotic dynamics and routes to chaos in THz QCLs under optical feedback. These findings not only deepen the understanding of nonlinear dynamics in THz QCLs but also open new possibilities for exploiting applications of chaotic light in THz sensing, imaging and secure communications.