Correct Definition of the Poynting Vector in Electrically and Magnetically Polarizable Medium Reveals that Negative Refraction is Impossible

TL;DR

This paper derives the local heating rate in magnetically and electrically polarizable media, showing that thermodynamic principles prevent negative refraction, challenging previous claims about its possibility.

Contribution

It provides a first-principles calculation of the heating rate and demonstrates that negative refraction is thermodynamically impossible in such media.

Findings

Heating rate has volume and surface contributions.

Thermodynamics requires the volume contribution to be positive.

Negative refraction is ruled out by thermodynamic constraints.

Abstract

I compute from first principles the local heating rate $q$ (the amount of electromagnetic energy converted to heat per unit time per unit volume) for electromagnetic waves propagating in magnetically and electrically polarizable media. I find that, in magnetic media, this rate has two separate contributions, $q^{(V)}$ and $q^{(S)}$, the first coming from the volume of the medium and the second from its surface. I argue that the second law of thermodynamics requires that the volume contribution be positive and that this requirement, in turn, prohibits negative refraction. This result holds for active or passive media and in the presence of anisotropy and spatial dispersion.