This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the von Neumann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expressions. This technique is applied to the problem of determining the stability conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispersive media are considered. It is shown that, for the former case, the stability limit of the conventional FDTD method is preserved. However, for the latter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of the conventional FDTD method to be maintained.

This paper introduces a technique for finite-difference time-domain modeling of wave propagation in general th-order dispersive media. Ohm's law in the Laplace domain with an th-order rational model for the complex conductivity is considered as a constitutive relation. In order to discretize this model, the complex conductivity is mapped onto the-transform domain by means of the Mobius transformation. This leads finally to a set of difference equations that is consistent with Yee's scheme. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The numerical stability problem is discussed and the numerical dispersion equation for th-order media is given.

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Two different extensions of the finite-difference timedomain (FDTD) method for the treatment of lossy dielectrics are considered: the time-average (TA) and the time-forward (TF) difference schemes. An analytical study of the stability properties and numerical dispersion of these schemes is presented. The stability analysis is based on the Von Neumann (Fourier series) method, while the numerical dispersion properties are established in terms of the numerical permittivity of discrete lossy dielectrics. The analytical stability limits are compared with those obtained numerically in previous works. The accuracy of the two schemes is compared by computing the reflection coefficient of a lossy dielectric slab.

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