Stefan Gutschling

Time-domain simulation of dispersive media with the finite integration technique

Since simulations of broadband applications have gained in importance in the last few years, the dispersive characteristics of various materials must not be neglected anymore. As a result many frequency-dependent FDTD methods have been set up which in most cases model special dispersions of low order. Furthermore, only few authors present proposals for the examination of stability behaviour of their algorithms. Our approach refers to the general FIT method and is based on state-space formulation. On foundation of discrete system analysis we present an algorithm applicable to arbitrary material dispersions and a detailed description of a practicable stability derivation. The applicability of the presented method is demonstrated with an example using a parallel plate transmission line filled with dielectric layers. Copyright

MAFIA version 4

MAFIA Version 4.0 is an almost completely new version of the general purpose electromagnetic simulator known since 13 years. The major improvements concern the new graphical user interface based on state of the art technology as well as a series of new solvers for new physics problems. MAFIA now covers heat distribution, electro-quasistatics, S-parameters in frequency domain, particle beam tracking in linear accelerators, acoustics and even elastodynamics. The solvers that were available in earlier versions have also been improved and/or extended, as for example the complex eigenmode solver, the 2D–3D coupled PIC solvers. Time domain solvers have new waveguide boundary conditions with an extremely low reflection even near cutoff frequency, concentrated elements are available as well as a variety of signal processing options. Probably the most valuable addition are recursive sub-grid capabilities that enable modeling of very small details in large structures.

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