Numerical Dispersion and Stability of an Extended FDTD Method Applied to Negative Refractive Index Media Modeling

The analogy between the FDTD Yee cell and a transmission-line network is invoked for the derivation of a scheme that lends itself to the implementation of a negative refractive index medium. Electric and magnetic currents, incorporated in the update equations, represent series capacitors and shunt inductors, which load the implicitly present transmission line network of an FDTD grid in a way that is fundamentally analogous to a recently proposed loaded negative refractive index transmission line medium. In addition, the numerical dispersion of this modified grid indicates its inherent ability to model a negative refractive index. The incorporation of the lumped elements contributes to a degradation of the stability limit of the scheme, which is also evaluated.