Lorentz invariant materials and metamaterials

Abstract

We show that electromagnetic constitutive relations of materials, defined by a scalar permittivity, $\epsilon$, and permeability, $\hat{I}¼$, are the same for all inertial observers provided that $\epsilon \hat{I}¼=1$ 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.