Modeling dispersive dielectric media in FDTD: a systematic approach

Two popular and distinct methods to model dispersive dielectric media in finite-difference time domain are the piecewise linear recursive convolution approach and the auxiliary differential equation approach. As they are used to model the same phenomenon and address the same equations, it is reasonable to think there is a close connection between the two. As a result of exploring this connection, we propose a new approach that can be seen as an extension of the two methods and thus, to some extent, serves to unify the two. In addition, the new approach has the advantages of being 1) more systematic-allowing the treatment of different types of dispersive dielectric media in the same manner-and 2) less ad hoc-the so-called recursive accumulators can be identified naturally and automatically.