Unified matrix-exponential FDTD formulations for modeling electrically and magnetically dispersive materials

Unified matrix-exponential finite difference time domain (ME-FDTD) formulations are presented for modeling linear multi-term electrically and magnetically dispersive materials. In the proposed formulations, Maxwellʼs curl equations and the related dispersive constitutive relations are cast into a set of first-order differential matrix system and the fieldʼs update equations can be extracted directly from the matrix-exponential approximation. The formulations have the advantage of simplicity as it allows modeling different linear dispersive materials in a systematic manner and also can be easily incorporated with the perfectly matched layer (PML) absorbing boundary conditions (ABCs) to model open region problems. Apart from its simplicity, it has been shown that the proposed formulations necessitate less storage requirements as compared with the well-know auxiliary differential equation FDTD (ADE-FDTD) scheme while maintaining the same accuracy performance.