Simple and effective finite difference time domain (FDTD) formulations are presented for modeling multi-pole linear dispersive electromagnetic applications. In the proposed formulations, the Maxwell's curl equations and the dispersive domain constitutive relations are cast into a set of first order differential matrix system and the fields update equations can be extracted directly from the matrix exponential approximation. The formulations have the advantage of simplicity as it allows modeling linear multi-pole electrically and/or magnetically dispersive materials in the same manner and also can be easily incorporated with the perfectly matched layer (PML) absorbing boundary conditions (ABCs) to model open region problems. Numerical examples are included to demonstrate the validity of the proposed formulations.
