  Efficient modeling of dispersive materials via time-domain simulations of the
Maxwell equations relies on the technique of auxiliary differential equations.
In this approach, a material's frequency-dependent permittivity is represented
via a sum of rational functions, e.g. Lorentz-poles, and the associated free
parameters are determined by fitting to experimental data. In the present work,
we present a modified approach for plasmonic materials that requires
considerably fewer fit parameters than traditional approaches. Specifically, we
consider the underlying microscopic theory and, in the frequency domain,
separate the hydrodynamic contributions of the quasi-free electrons in
partially filled bands from the interband transitions. As an illustration, we
apply our approach to gold and demonstrate how to treat the interband
transitions within the effective model via connecting to the underlying
electronic bandstructure, thereby assigning physical meaning to the remaining
fit parameters. Finally, we show how to utilize this approach within the
technique of auxiliary differential equations. Our approach can be extended to
other plasmonic materials and leads to efficient time-domain simulations of
plasmonic structures for frequency ranges where interband transitions have to
be considered.
