Generalization of Perfect Electromagnetic Conductor (PEMC) Boundary

TL;DR

This paper introduces a new class of electromagnetic boundaries called GPEMC, generalizing PEMC boundaries by analyzing wave dispersion equations and their conditions for boundary matching, with implications for wave reflection analysis.

Contribution

It extends PEMC boundaries to GPEMC boundaries by studying dispersion equations, including cases with first-order or no dispersion equations, and derives reflection properties.

Findings

GPEMC boundaries generalize PEMC boundaries.

Conditions for first-order and no dispersion equations are established.

Analytic reflection dyadic expression derived and visualized.

Abstract

Certain classes of electromagnetic boundaries satisfying linear and local boundary conditions can be defined in terms of the dispersion equation of waves matched to the boundary. A single plane wave is matched to the boundary when it satisfies the boundary conditions identically. The wave vector of a matched wave is a solution of a dispersion equation characteristic to the boundary. The equation is of the second order, in general. Conditions for the boundary are studied under which the dispersion equation is reduced to one of the first order or to an identity, whence it is satisfied for any wave vector of the plane wave. It is shown that, boundaries associated to a dispersion equation of the first order, form a natural generalization of the class of perfect electromagnetic conductor (PEMC) boundaries. As a consequence, the novel class is labeled as that of generalized perfect electromagnetic conductor (GPEMC) boundaries. As another case, boundaries for which there is no dispersion equation (NDE) for the matched wave (because it is an identity) are labeled as NDE boundaries. They are shown to be special cases of GPEMC boundaries. Reflection of the general plane wave from the GPEMC boundary is considered and an analytic expression for the reflection dyadic is found. Some numerical examples on its application are presented for visualization.