Modeling of quantum cascade laser frequency combs in the mid-infrared and terahertz spectral region
Final Report Abstract
In this research project, we focused on the modeling of quantum cascade laser (QCL) frequency combs. The QCL is an extremely versatile light source, employing artificially engineered optical transitions in the conduction band of a semiconductor nanostructure rather than electron-hole recombination. In this way, large portions of the mid-infrared (MIR) and terahertz (THz) spectral range can be covered, which are otherwise inaccessible to compact semiconductor lasers. In addition, giant optical nonlinearities can be integrated into the QCL nanostructure which give rise to fourwave mixing, promoting multimode lasing with a fixed phase relationship between the longitudinal modes. The resulting comb-like spectrum consists of discrete equidistant lines. Such so-called frequency combs are widely used as a ruler in the frequency domain for spectroscopic and sensing applications. Within recent years, QCL frequency comb sources have been experimentally demonstrated by various groups, offering a compact approach for the MIR and THz range. However, apart from a perturbative approach, simulation models were not available, as required for further design optimization. The main goal of this project was to develop a fully time dependent simulation model of QCL comb operation, taking into account all relevant effects. Such an approach not only provides an accurate description of the resulting comb spectrum, but also enables the identification of the allowed parameter regime for the formation of stable combs and the investigation of imperfect combs, extending only over a fraction of the laser modes. Since extended simulations of the laser dynamics over many thousand cavity roundtrips were required to eliminate transient effects, the model had to feature high computational efficiency. Multilevel Maxwell-Bloch equations were found to provide an adequate description of the coherent nonlinear light-matter coupling as well as dephasing. The model was extended to take into account further relevant effects such as electron tunneling in the nanostructured active region, chromatic waveguide dispersion, and spatial hole burning, i.e., the formation of an inversion grating in the laser resonator due to the standing wave modes. The simulation approach was then applied to an experimental THz QCL comb source, yielding good agreement with experimental data in both time and frequency domain. Furthermore, the simulations allowed us to identify the beneficial and detrimental effects, as required for a further optimization of QCL-based frequency comb sources. Since the rotating-wave approximation (RWA), which is commonly invoked to reduce the numerical complexity of the Maxwell-Bloch equations, fails for very broadband spectra such as octave-spanning combs, our project also addressed the development of numerical methods and parallelization techniques for non-RWA simulations. In this context, we set up the open source project mbsolve on the GitHub software development platform and implemented parallelized versions of a predictor–corrector, Runge-Kutta and operator splitting scheme for the Bloch equations, combined with the finite difference time-domain algorithm for Maxwell’s equations. It was found that the parallelization could be significantly improved by trading synchronization calls versus redundant calculations. It turned out that the operator splitting approach is especially attractive for long-term simulations since it preserves the positive semidefinite character of the density matrix by direct evaluation of the time evolution in terms of matrix exponentials. We have considerably improved the performance of this method by optimizing the evaluation of the matrix exponential. Our open source project mbsolve will serve as a basis for the further development of numerical methods related to Maxwell-Bloch-type simulations beyond the RWA.
Publications
- “Analysis of operating regimes of terahertz quantum cascade laser frequency combs,” IEEE Trans. Terahertz Sci. Technol. 7, 351–359 (2017)
P. Tzenov, D. Burghoff, Q. Hu, and C. Jirauschek
(See online at https://doi.org/10.1109/TTHZ.2017.2693822) - “Density matrix Monte Carlo modeling of quantum cascade lasers,” J. Appl. Phys. 122, 133105 (2017)
C. Jirauschek
(See online at https://doi.org/10.1063/1.5005618) - “Performance evaluation of numerical methods for the Maxwell–Liouville–von Neumann equations,” Opt. Quant. Electron. 50, 112 (2018)
M. Riesch, N. Tchipev, S. Senninger, H.-J. Bungartz, and C. Jirauschek
(See online at https://doi.org/10.1007/s11082-018-1377-4)
