Performance evaluation of numerical methods for the Maxwell–Liouville–von Neumann equations
- 89 Downloads
The Maxwell–Liouville–von Neumann (MLN) equations are a valuable tool in nonlinear optics in general and to model quantum cascade lasers in particular. Several numerical methods to solve these equations with different accuracy and computational complexity have been proposed in related literature. We present an open-source framework for solving the MLN equations and parallel implementations of three numerical methods using OpenMP. The performance measurements demonstrate the efficiency of the parallelization.
KeywordsQuantum cascade lasers Maxwell–Bloch equations Liouville–von Neumann equation Parallelization
This work was supported by the German Research Foundation (DFG) within the Heisenberg Program (JI 115/4-2) and under DFG Grant No. JI 115/9-1. Nikola Tchipev acknowledges the funding provided by Intel as part of the Intel Parallel Computing Center ExScaMIC-KNL. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (http://www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (http://www.lrz.de). Finally, the authors thank Mariem Kthiri for her help in the development of the mbsolve project.
- Cartar, W., Mørk, J., Hughes, S.: Self-consistent Maxwell–Bloch model of quantum-dot photonic-crystal-cavity lasers. Phys. Rev. A 96(023), 859 (2017)Google Scholar
- Deinega, A., Seideman, T.: Self-interaction-free approaches for self-consistent solution of the Maxwell–Liouville equations. Phys. Rev. A 89(022), 501 (2014)Google Scholar
- Guennebaud, G., Jacob, B. et al.: Eigen v3 (2010) http://eigen.tuxfamily.org
- Riesch, M., Jirauschek, C.: mbsolve: an open-source solver tool for the Maxwell–Bloch equations. https://github.com/mriesch-tum/mbsolve (2017)
- Slavcheva, G., Arnold, J.M., Wallace, I., Ziolkowski, R.W.: Coupled Maxwell-pseudospin equations for investigation of self-induced transparency effects in a degenerate three-level quantum system in two dimensions: finite-difference time-domain study. Phys. Rev. A 66(6), 63,418 (2002)CrossRefGoogle Scholar
- Sukharev, M., Nitzan, A.: Numerical studies of the interaction of an atomic sample with the electromagnetic field in two dimensions. Phys. Rev. A 84(043), 802 (2011)Google Scholar
- Taflove, A., Hagness, S. C.: Computational electrodynamics: the finite-difference time-domain method. Artech House (2005)Google Scholar
- Wang, C.Y., Diehl, L., Gordon, A., Jirauschek, C., Kärtner, F.X., Belyanin, A., Bour, D., Corzine, S., Höfler, G., Troccoli, M., Faist, J., Capasso, F.: Coherent instabilities in a semiconductor laser with fast gain recovery. Phys. Rev. A 75(031), 802 (2007)Google Scholar