Liouvillian Superoperator and Maxwell–Bloch Dynamics Under Optical Feedback via the Self-Mixing Effect in Terahertz Quantum Cascade Lasers

We present a Maxwell–Bloch dynamics model for Terahertz Quantum Cascade Lasers (THz QCLs) that integrates a density matrix transport model, independent of the number of states per QCL period, with the Maxwell wave equation under the slow-varying envelope approximation. This model is extended to include external homodyne feedback, generalizing the Lang–Kobayashi model typically used for diode lasers. Unlike previous approaches, our model allows for the simulation of the self-mixing (SM) effect in THz QCLs without the need for effective parameters, commonly used in diode laser models. We demonstrate the model’s ability to capture laser dynamics and analyze the SM effect through numerical simulations. The model enables us to evaluate the quality of THz QCL designs for SM applications, which is not possible with effective two-level treatment via the Lang–Kobayashi approach.