Equivalent Circuit (EC) FDTD Method for Dispersive Materials: Derivation, Stability Criteria and Application Examples

Although many computational methods are currently available to analyze electro-magnetic problems of high complexity, further progress is necessary to unify thedifferent approaches and to improve the robustness of some algorithms. This chap-ter aims at reaching these two goals. It presents an equivalent circuit (EC) finitedifference time domain (FDTD) method which both represents a complete circuitalformulation of conventional FDTD [1] based on the electric and magnetic fields Yeescheme and provides guaranteed stability criteria for dispersive media.A circuital formulation of FDTD offers several benefits. Since its update valuesare voltages and currents (as opposed to electric and magnetic fields), it facilitatesthe integration of electronic components, such as for instance diodes and transistors,into the simulation. In addition, it provides increased computational speed thanks toa reduced number of multiplications in the update equations [2, 3]. Finally, it maybe easily generalized to arbitrary dispersive media via simple manipulations of themesh immittances.While no convenient explicit guaranteed stability criterion for dispersive mediais available in the framework of the conventional FDTD technique, the EC FDTDprovides such a criterion. This is a distinct advantage for both emerging metamate-rials [4], which are inherently dispersive, and for various natural materials [5], suchas metals at the optical frequencies, ferrimagnetic and ferromagnetic materials andbiological tissues, which exhibit various types of more or less complex dispersionresponses.