Solving the Maxwell-Bloch equations efficiently on parallel architectures

Summary form only given. The Maxwell-Bloch equations (MBE) describe the interaction between a two-level quantum mechanical system and an electromagnetic wave. They are widely used in nonlinear optics in general and to model quantum cascade lasers (QCLs) in particular [1]. Due to their nonlinearity, numerical methods are usually required to solve the equations. In order to cope with the computational complexity that arises, the rotating wave approximation (RWA) is frequently applied. However, Ziolkowski et al. showed that the RWA result omits substantial features of the solution [2].We present a flexible, open-source framework containing a variety of MBE solvers. The solvers are implementations of the finite difference time domain (FDTD) numerical scheme from Ziolkowski et al. [2] and use different parallelization techniques (OpenMP, CUDA, etc.). With the help of our framework we evaluate and compare the different parallelization techniques with respect to performance and programming effort. Finally, we discuss the advantages and drawbacks of each technique and thus provide guidance for simulation code developers.