An Alternating-Direction Implicit FDTD Modeling of Dispersive Media Without Constitutive Relation Splitting

In recent years, the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method has been extended to dispersive media. To this end, a constitutive relation is appended to Maxwell's curl equations. A common feature of all of the existing formulations is that the integration over a full time step, of Maxwell's equations and the constitutive relation, is split into two sub-steps.