The dual role of phase-conjugate feedback in distributed-feedback quantum cascade lasers

Phase-conjugate feedback (PCF) provides an unexplored route to control the nonlinear dynamics of quantum cascade lasers (QCLs). This manuscript presents a numerical study of distributed-feedback (DFB) QCLs subject to PCF, using a self-consistent framework based on the Effective Semiconductor Maxwell-Bloch Equations (ESMBEs). A direct comparison between PCF and conventional optical feedback (COF) under identical operating conditions reveals different dynamical behaviors. While COF promotes phase-sensitive instabilities and broadband chaos driven by the competition between external-cavity modes and internal longitudinal modes, PCF suppresses external-cavity resonances and reshapes the dynamics toward phase-robust oscillatory regimes governed by internal cavity interactions. A key outcome of PCF is the emergence of radio-frequency (RF) oscillations at even multiples of the internal cavity free spectral range (FSR), enabling millimeter-wave generation without external electronic modulation. The robustness of this mechanism is demonstrated over a wide range of feedback strengths and for both long and short external-cavity regimes. In the short-cavity configuration, compatible with future on-chip or hybrid integration, the millimeter-wave emission exhibits enhanced spectral stability and enables the excitation of higher-order harmonics extending into the upper millimeter-wave and sub-terahertz range. In the long-cavity regime, increasing the linewidth enhancement factor (LEF) allows the emergence of structured chaotic dynamics while preserving clear spectral signatures. Although the present results are numerical, they provide motivation for experimental investigations of PCF in mid- and long-wave infrared QCLs, opening perspectives for millimeter-wave photonic sources and hybrid photonic-RF systems.