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The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional FDTD method that enables the incorporation of linear one-port LNs in a single FDTD cell. This paper studies the stability and the numerical dispersion of this technique. To this end, an isotropic medium that is uniformly loaded with LNs in the x-direction is considered as a working model. The stability analysis, based on the von Neumann method, is performed for general Mth-order LNs and closed-form stability conditions are derived for some particular cases. The numerical dispersion relation is obtained for plane-wave propagation in the proposed LN-loaded medium. It is shown that LNs can be interpreted in terms of an effective frequency-dependent permittivity and, as a consequence, the LN-loaded medium can be viewed as a uniaxial medium. The numerical admittance of the LNs is also obtained showing that, as a side-effect of the time discretization, the LN parameters become frequency-dependent, e.g. for the resistor case, the resistance becomes a function of the frequency. [ABSTRACT FROM AUTHOR]

This paper introduces an extension of the original finite-difference time-domain (FDTD) method for modeling double-negative media characterized by high-order frequency-dependent permittivity and permeability. The approach basically consists of adding electric and magnetic current densities to Maxwell's curl equations and considering Ohm's law as a constitutive relationship. Current densities are discretized by using a weighted average in time and Ohm's law by applying the Mobius transformation technique. The extended FDTD formulation is validated and its numerical features are carefully examined. More specifically, analytical stability conditions are derived for several types of double-negative media and the numerical dissipation issue is discussed. In addition, the numerical dispersion equation for general high-order double-negative media is given and the order of accuracy of the scheme is studied. Finally, the definition of numerical refractive index is addressed and it is shown that, when the discretization parameters of the problem are not properly chosen, a negative refractive index may become a positive one in the discrete world, thus changing the physics of the problem. [ABSTRACT FROM AUTHOR]