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 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.

© 2020 Optical Society of America

Refractive index and group velocity of electromagnetic modes in a relativistic Fermi gas at finite temperatures

J. D. Mazo-Vasquez, L. M. Hincapie-Zuluaga, and E. Reyes-Gómez
J. Opt. Soc. Am. B 37(2) 211-217 (2020)

Negative refraction through an impedance-matched left-handed metamaterial slab

Koray Aydin and Ekmel Ozbay
J. Opt. Soc. Am. B 23(3) 415-418 (2006)

Sign of the refractive index in a gain medium with negative permittivity and permeability

Yi-Fan Chen, Peer Fischer, and Frank W. Wise
J. Opt. Soc. Am. B 23(1) 45-50 (2006)

Negative refraction in indefinite media

David R. Smith, Pavel Kolinko, and David Schurig
J. Opt. Soc. Am. B 21(5) 1032-1043 (2004)

Is there an experimental verification of a negative index of refraction yet?

N. Garcia and M. Nieto-Vesperinas
Opt. Lett. 27(11) 885-887 (2002)