On the FDTD Formulations for Modeling Wideband Lorentzian Media

Several popular numerical approaches for modeling the dispersion characteristics of complex media are applied to simulate the wave propagation in the wideband Lorentzian (WBL) media under the second-order or fourth-order accurate finite-difference time-domain (FDTD) formulation. Their implementing algorithms and work performance for this type of dispersive materials are studied and compared to each other. The coefficients of a general second-order discrete numerical model pertaining to each of these approaches are derived respectively and a unified set of FDTD updating equations for implementing them is presented. In light of the analytical results calculated from the given numerical dispersion equations that determines the effective permittivity and permeability of a corresponding artificial WBL medium and the simulation results from the practical FDTD simulations for an exemplified WBL medium, the modeling accuracy and stability limits of these approaches are presented by evaluating the absolute errors of both the propagation and transmission functions of a plane electromagnetic pulse wave propagating in the WBL material and transmitting through an interface between the vacuum and the WBL medium under the second-order or fourth-order FDTD formulation combined with each of the discussed approaches.