Plane-Wave Propagation in Extreme Magnetoelectric (EME) Media

TL;DR

This paper investigates plane-wave propagation in extreme magnetoelectric media, revealing unique dispersion properties, wave restrictions, and boundary behaviors, with potential applications in metasurface engineering.

Contribution

It provides a detailed analysis of wave behavior in EME media, including dispersion relations, special cases, and boundary effects, expanding understanding of these complex materials.

Findings

Dispersion equation can be cubic and homogeneous, allowing arbitrary wave vector magnitude.

In many cases, no dispersion relation restricts the wave vector, leading to NDE media.

Uniaxial EME media exhibit boundary behaviors akin to DB boundaries.

Abstract

The extreme magnetoelectric medium (EME medium) is defined in terms of two medium dyadics, $\alpha$, producing electric polarization by the magnetic field and $\beta$, producing magnetic polarization by the electric field. Plane-wave propagation of time-harmonic fields of fixed finite frequency in the EME medium is studied. It is shown that (if $\omega\neq 0$) the dispersion equation has a cubic and homogeneous form, whence the wave vector $k$ is either zero or has arbitrary magnitude. In many cases there is no dispersion equation ("NDE medium") to restrict the wave vector in an EME medium. Attention is paid to the case where the two medium dyadics have the same set of eigenvectors. In such a case the $k$ vector is restricted to three eigenplanes defined by the medium dyadics. The emergence of such a result is demonstrated by considering a more regular medium, and taking the limit of zero permittivity and permeability. The special case of uniaxial EME medium is studied in detail. It is shown that an interface of a uniaxial EME medium appears as a DB boundary when the axis of the medium is normal to the interface. More in general, EME media display interesting wave effects that can potentially be realized through metasurface engineering.