Multi-Domain Modeling of Free-Running Harmonic Frequency Comb Formation in Terahertz Quantum Cascade Lasers

Optical frequency comb (OFC) emission in quantum cascade lasers (QCLs) is highly attractive for applications in metrology and sensing. Recently, coherent OFC mode-locking with large intermodal spacing was demonstrated in QCLs. These self-starting harmonic frequency combs (HFCs) show highly phase-stable operation and promise interesting perspectives towards optical or even quantum communication. Here, we present a detailed multi-domain modeling approach for the numerical study of QCLs. Our theoretical characterization is divided into stationary carrier transport simulations, based on the ensemble Monte Carlo method, and dynamical simulations of the light-matter interaction, based on multi-level Maxwell-density matrix equations. We investigate the influence of the chosen eigenstate basis on the gain spectrum and present self-consistent simulation results of stable HFC operation in a double metal terahertz QCL. In our simulations, the studied QCL gain medium shows self-starting harmonic mode-locking for different bias and waveguide configurations, resulting in a mode spacing of up to twelve times the cavity round trip frequency. Furthermore, we characterize the spectral time evolution of the coherent HFC formation process, yielding the spontaneous build-up of a dense multimode state which is gradually transferred into a broad and clear harmonic OFC state.