Sign of refractive index and group velocity in left-handed media

TL;DR

This paper challenges the common belief that left-handed media have a negative refractive index, showing that the index n is not fundamental and proposing thermodynamic inequalities to distinguish left-handed from regular media.

Contribution

It clarifies that the negative refractive index is not an intrinsic property of left-handed media and introduces thermodynamic inequalities to differentiate them from regular media.

Findings

Group velocity is negative in LHM and positive in RM.

The product of real and imaginary parts of n is negative in LHM.

Refractive index n is not a fundamental parameter for media classification.

Abstract

We argue that the widely spread opinion that the left-handed media (LHM) are characterized by a negative refractive index $n_-$ is misleading. Since n does not enter into Maxwell's equations and boundary conditions, any medium may be described by both positive n and negative $n_-=-n$. Two thermodynamic inequalities are presented, that make a difference between the LHM and the regular media (RM). The first one reads that the group velocity is positive in the RM and negative in the LHM. The second one is that the product ${\rm Re}(n) {\rm Im}(n)$ is positive in the RM and negative in the LHM. Both inequalities are invariant with respect to the change $n \to n_-$. However, to use $n_-$ one should change some traditional electrodynamics definitions.