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This technical note describes the physical model, numerical implementation,and validation of multilevel atomic media for lasers and saturable absorbers inMeep: a free/open-source finite-difference time-domain (FDTD) software packagefor electromagnetics simulation. Simulating multilevel media in the time domaininvolves coupling rate equations for the populations of electronic energylevels with Maxwell's equations via a generalization of the Maxwell--Blochequations. We describe the underlying equations and their implementation usinga second-order discretization scheme, and also demonstrate their equivalence toa quantum density-matrix model. The Meep implementation is validated using aseparate FDTD density-matrix model as well as a frequency-domain solver basedon steady-state ab-initio laser theory (SALT).

Modeling lasers and saturable absorbers via multilevel atomic media in the Meep FDTD software: Theory and implementation