Mbsolve: An open-source solver tool for the Maxwell-Bloch equations

Abstract

The Maxwell-Bloch equations are a valuable tool to model light-matter interaction, where the application examples range from the description of pulse propagation in two-level media to the elaborate simulation of optoelectronic devices, such as the quantum cascade laser (QCL). In this work, we present mbsolve, an open-source solver tool for the Maxwell-Bloch equations. Here, we consider the one-dimensional Maxwell's equations, which are coupled to the Lindblad equation. The resulting generalized Maxwell-Bloch equations are treated without invoking the rotating wave approximation (RWA). Since this full-wave treatment is computationally intensive, we provide a flexible framework to implement different numerical methods and/or parallelization techniques. On this basis, we offer two solver implementations that use OpenMP for parallelization.

High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces

“…Yee's scheme was extended to the light-matter interactions with ultrashort pulse in anisotropic media for the unidimensional case in [36], and bidimensional case in [37], where a pesudo-spectral time-domain method was also discussed, along with similar splitting schemes for Bloch equations. In [38], a Maxwell-Bloch solver for two-level atomic systems was developed. A scrutiny of FDTD numerical methods based on Yee's scheme for nonlinear active materials revealed that they have limitations and restrictions to low-order accuracy, low dimensions, or only two-level atomic systems.…”