By way of examples in vacuum and media, we show that the criterion used widely to determine
the occurrence of negative phase velocity propagation is not covariant. A new covariant
criterion is presented that reduces to the previous criterion in the rest frame of a medium. The
new criterion requires calculation of the plane wave electromagnetic modes of a generalized
medium in terms of the four-potential, Aν. Some of the subtleties of removing the gauge
freedom inherent in Aν are highlighted.
Martin W. McCall, Martin W. McCall,
"Negative refraction and covariance: the perils of P • k < 0", Proc. SPIE 7029, Metamaterials: Fundamentals and Applications, 70290Y (4 September 2008); doi: 10.1117/12.796495; https://doi.org/10.1117/12.796495