Negative refraction in the relativistic electron gas

TL;DR

This paper demonstrates that a relativistic electron gas acts as a left-handed material with negative refraction index at low frequencies, showing potential for novel electromagnetic properties and applications.

Contribution

It provides a theoretical analysis showing the relativistic electron gas has negative permittivity and permeability, leading to negative refraction index, a novel insight into plasma electromagnetic behavior.

Findings

The gas exhibits negative permittivity and permeability below the same frequency.

Electromagnetic waves propagate without dissipation in the gas, with speed of light in vacuum.

The gas has an effective refractive index of -1, affecting Snell's law and reflection/transmission.

Abstract

We show that a gas of relativistic electrons is a left-handed material at low frequencies by computing the effective electric permittivity and effective magnetic permeability that appear in Maxwell's equations in terms of the responses appearing in the constitutive relations, and showing that the former are both negative below the {\it same} frequency, which coincides with the zero-momentum frequency of longitudinal plasmons. We also show, by explicit computation, that the photonic mode of the electromagnetic radiation does not dissipate energy, confirming that it propagates in the gas with the speed of light in vacuum, and that the medium is transparent to it. We then combine those results to show that the gas has a negative effective index of refraction $n_{\rm eff}=-1$. We illustrate the consequences of this fact for Snell's law, and for the reflection and transmission coefficients of the gas.