We report a new finite-difference time-domain (FDTD) computational model of the lasing dynamics of a four-level two-electron atomic system. Transitions between the energy levels are governed by coupled rate equations and the Pauli Exclusion Principle. This approach is an advance relative to earlier FDTD models that did not include the pumping dynamics, or the Pauli Exclusion Principle. Further, the method proposed in this paper is more versatile than the conventional modal expansion of the electromagnetic field for complex inhomogeneous laser geometries constructed in photonic crystals or light-localizing random media. For such complex geometries, the lasing modes are either difficult or impossible to calculate. The present work aims at the self-consistent treatment of the dynamics of the 4-level atomic system and the instantaneous ambient optical electromagnetic field. This permits in principle a much more robust treatment of the overall lasing dynamics of four-level gain systems integrated into virtually arbitrary electromagnetic field confinement geometries.
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