Lorentz invariant materials and metamaterials

TL;DR

This paper demonstrates that certain electromagnetic materials and metamaterials exhibit Lorentz invariance in their constitutive relations when specific conditions are met, with implications for optical phenomena in moving media.

Contribution

It establishes a Lorentz invariance condition for electromagnetic materials and extends this property to anisotropic media and metamaterials, highlighting its practical significance.

Findings

Electromagnetic constitutive relations are Lorentz invariant if εμ=1.

The invariance applies to uniaxial anisotropic media.

The property extends to negative refractive index metamaterials.

Abstract

We show that electromagnetic constitutive relations of materials, defined by a scalar permittivity, $\varepsilon$, and permeability, $\mu$, are the same for all inertial observers provided that $\varepsilon\mu = 1$ is satisfied. To highlight the practical power of our general result, we discuss schemes in which this property plays a significant role, such as Fresnel-Fizeau optical drag or modified Snell's law for moving dielectrics. We also proof that such a particular behavior can be extended to systems like uniaxial anisotropic media or negative refractive index metamaterials.