On the Equivalence of Several FDTD Formulations for Modeling Electromagnetic Wave Propagation in Double-Negative Metamaterials

Recently, several approaches have been proposed to incorporate double-negative media into finite-difference time-domain simulators. In this letter, a rigorous comparative study of the formulation introduced by Karkkainen and Maslovski and the bilinear frequency approximation technique applied by Feise (IEEE Trans. Antennas Propag., vol. 52, pp. 2955-2962, Nov. 2004) is presented. Although these two formulations are based on different approximation principles, we show that both lead to equivalent difference schemes. Moreover, these two methods are equivalent to a third one, previously published for dispersive dielectrics, which is based on a different approach. The stability of these formulations is also analyzed by means of the von Neumann method.