Causality-based conditions for a negative refractive index must be used with care

P. Kinsler, M. W. McCall

    Blackett Laboratory
    Imperial College London,
    Prince Consort Road,
    London SW7 2AZ
    United Kingdom.

    Phys. Rev. Lett. 101, 167401 (2008).

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.