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

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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. 29552962, 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. </para>