Sign of refractive index and group velocity in left-handed media
  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. 
A. L. Pokrovsky and A. L. Efros