  We describe a fourth-order accurate finite-difference time-domain scheme for
solving dispersive Maxwell's equations with nonlinear multi-level carrier
kinetics models. The scheme is based on an efficient single-step three
time-level modified equation approach for Maxwell's equations in second-order
form for the electric field coupled to ODEs for the polarization vectors and
population densities of the atomic levels. The resulting scheme has a large
CFL-one time-step. Curved interfaces between different materials are accurately
treated with curvilinear grids and compatibility conditions. A novel
hierarchical modified equation approach leads to an explicit scheme that does
not require any nonlinear iterations. The hierarchical approach at interfaces
leads to local updates at the interface with no coupling in the tangential
directions. Complex geometry is treated with overset grids. Numerical stability
is maintained using high-order upwind dissipation designed for Maxwell's
equations in second-order form. The scheme is carefully verified for a number
of two and three-dimensional problems. The resulting numerical model with
generalized dispersion and arbitrary nonlinear multi-level system can be used
for many plasmonic applications such as for ab initio time domain modeling of
nonlinear engineered materials for nanolasing applications, where
nano-patterned plasmonic dispersive arrays are used to enhance otherwise weak
nonlinearity in the active media.
