  Using the principle of causality as expressed in the Kramers-Kronig
relations, we derive a generalized criterion for a negative refractive index
that admits imperfect transparency at an observation frequency $\omega$. It
also allows us to relate the global properties of the loss (i.e. its frequency
response) to its local behaviour at $\omega$. However, causality-based criteria
rely the on the group velocity, not the Poynting vector. Since the two are not
equivalent, we provide some simple examples to compare the two criteria.
