A Discontinuous Galerkin Time-Domain Scheme to Model Lasing Dynamics in Four-Level Two-Electron Atomic Systems

A discontinuous Galerkin time-domain scheme is formulated and implemented to analyze three-dimensional transient lasing dynamics. The proposed scheme solves a coupled system of the Maxwell and the rate equations. The atomic transitions through different energy levels are quantum-mechanically described by a four-level two-electron model, while the electro-magnetic interactions are treated using the Maxwell equations. The resulting solver accounts for the Pauli Exclusion Principle and permits robust simulation of lasing dynamics under optical pumping. Numerical results are presented to demonstrate the applicability and the accuracy of the proposed scheme.