Holger Spachmann

Dispersion and asymmetry effects of ADI-FDTD

In this paper, a generalized derivation of the alternating direction implicit finite-difference time-domain algorithm based on operator splitting is proposed. The formulation follows the notation of the finite integration technique. A straightforward proof of stability is given and the numerical dispersion formula is presented and verified by numerical experiments. As an additional parasitic effect, the asymmetric behavior of the algorithm even for exactly symmetric setups is revealed. Both the dispersion error and the asymmetry error are discussed in terms of the applicability of ADI for low-frequency problems.

FIT-formulation for non-linear dispersive media†

A new approach using FIT-formulation (Finite Integration Technique) (T. Weiland, Electron. Commun., 31, 116–120 (1977); Int. J. Numer. Model., 9, 295–319 (1996)) for simulating waveguide propagation of optical pulses is presented. FIT-methods are widespread in use for broadband linear simulations. In recent years, several attempts have been made to describe different dispersive material-characteristics such as Drude, Debye or Lorentz dispersion. Today advanced FDTD-formulations (Finite Difference Time Domain) also consider non-linear effects (P. M. Goorjian and A. Taflove, IEEE Opt. Lett., 17(3), 180–182 (1992); D. M. Sullivan, IEEE Trans. Microwave Theory Techniques, 43(3), 676–682 (1995)). In the following presented method third-order non-linear effects were described, which can be observed in isotropic media in frequency ranges of optical pulses, by updating material polarization terms using classical descriptions of Lorentz dispersion, Raman scattering and the Kerr effect. The basic idea is transforming these description formulas into sets of linear differential equations and solving them with the help of the general exponential solution. Copyright

Time domain modeling of gyromagnetic materials using the finite integration technique

Since simulations of broadband applications have gained importance in recent years, stable and efficient time domain methods are needed which in particular consider realistic modeling of complex material properties. Thus for many microwave applications like circulators or one-way transmission devices, the dispersive and anisotropic character of gyrotropic media is of great significance. On the basis of general system theory, the extension of the finite integration technique to gyromagnetic material behavior is presented, in combination with a modified stability analysis. The applicability of the presented method is demonstrated by a broadband simulation of an H-plane waveguide circulator.

Explicit temporal integrators for low-pass filtering of FDTD signals

The numerical dispersion properties of some higher order explicit marching-on-in-time methods for transient electromagnetic field simulations are investigated. In contrast to the most commonly used leapfrog time integration scheme, these alternative methods exhibit a numerical dissipation for high-frequency components. This property can be interpreted as a low-pass digital filter and exploited to suppress parasitic high-frequency noise (HF noise) in the field signals. The prospective application is the enhancement of the coupled simulation of electromagnetic fields and moving charges.