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

Abstract

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 lightmatter 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 selfstarting 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.

Theoretical investigation of harmonic frequency comb formation dynamics in defect-engineered THz quantum cascade lasers

“…The final pattern has already emerged after 100 round trips, that is ≈ 6 ns, which is clearly faster than in free-running HFCs of defect-free cavities, which might take several ten or even hundred nanoseconds to converge to a final state. 9,12 This fast convergence of HFCs in defect-engineered cavities emphasizes the robustness of this system compared to self-assembled ones, which is of great value in practical applications. The state of the laser medium, depicted by the gain in Fig.…”

“…6,7 The underlying dynamics of the free-running transition to the HFC regime has been subject to several theoretical studies but appear to be highly complex, hardly robust, and may occur over long time-scales, making numerical simulations extremely challenging. [8][9][10][11][12] A controlled selection of the lasing modes obviously bears a large advantage for tailored applications and can be realized by defect-engineering of the cavity. 13,14 In this work, we aim to shed light on the coupled field-electron dynamics that lead to harmonic mode-locking in defect-engineered THz QCLs.…”