A Uniaxial Time-Domain Wave Potential Analysis of the Electromagnetic Field in Nonuniform Media

The wave potential approach to the analysis of transient electromagnetic problems has been recently proposed and applied into a finite-difference algorithm. In its original form, when solving problems of nonuniform media, the time-domain wave potential (TDWP) method requires domain subdivision of the computational volume. In each domain, the field is described by a pair of collinear vector potentials of preferred direction called the domain distinguished axis. Here, we propose a different approach based on a new development in the theory of source equivalence. This approach allows the transient EM analysis in generally nonuniform media in terms of a vector potential pair of fixed orientation. Since a single fixed distinguished axis is assigned to the whole computational volume, the approach is referred to as the uniaxial TDWP technique. It has similar computational requirements as the original TDWP technique. However, it is simpler to implement and thus has improved versatility. We briefly review the relevant key concepts of the theory of source equivalence. We describe how we use them to model the field behavior at material nonhomogeneities so that a full-wave description is achieved in terms of two scalar potential functions. We demonstrate the approach through the analysis of waveguide filters and printed layered structures.