Minkowskian Isotropic Media and the Perfect Electromagnetic Conductor

• Published in: IEEE transactions on antennas and propagation 2012-07, Vol.60 (7), p.3231-3245
• Main Authors: Paiva, C. R., Matos, S. A.
• Format: Article
• Language: English
• Subjects: Algebra; Antennas; Applied classical electromagnetism; Bianisotropic media; Boundaries; Conductors; Conductors (devices); Electromagnetic fields; electromagnetic propagation; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); geometric algebra; Invariants; Isotropic media; Isotropy; Lorentz covariance; Lorentz invariance; Media; Observers; perfect electromagnetic conductor (PEMC); Physics; special relativity; Studies; Three dimensional; Three dimensional displays
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2012.2196929

The perfect electromagnetic conductor (PEMC) was introduced as an observer-independent "axion medium" that generalizes the concepts of perfect electric conductor (PEC) and perfect magnetic conductor (PMC). Following the original boundary definition, its 3-D medium definition corresponds to a 4-D representation that is, actually, observer-dependent (i.e., it is not isotropic for the whole class of inertial observers), leading to a nonunique characterization of the electromagnetic field inside. This characterization of the PEMC, then, violates the boundary conditions-unless some extraneous waves, called "metafields," are surgically extracted from the final solution. In this paper, using spacetime algebra, we define the PEMC as the unique limit of the most general class of isotropic media in Minkowskian spacetime, which we call Minkowskian isotropic media (MIM). An MIM is actually a "dilaton-axion medium." Its isotropy is a Lorentz invariant characterization: It is an observer-independent property, contrary to isotropy in 3-D Gibbsian characterization. Hence, a more natural definition of a PEMC is herein presented: It leads to a unique electromagnetic field in its interior; it corresponds, though, to the same original boundary definition. This new approach is applied to the analysis of an air-MIM interface that, as a particular case, reduces to an air-PEMC interface.