We study the linear phenomenological Maxwell's equations in the presence of a
polarizable and magnetizable medium (magnetodielectric). For a dispersive,
non-absorptive, medium with equal electric and magnetic permeabilities, the
latter can assume the value -1 (+1 is their vacuum value) for a discrete set of
frequencies, i.e., for these frequencies the medium behaves as a negative index
material (NIM). We show that such systems have a well-defined time evolution.
In particular the fields remain square integrable (and the electromagnetic
energy finite) if this is the case at some initial time. Next we turn to the
Green's function (a tensor), associated with the electric Helmholtz operator,
for a set of parallel layers filled with a material. We express it in terms of
the well-known scalar s and p ones. For a half space filled with the material
and with a single dispersive Lorentz form for both electric and magnetic
permeabilities we obtain an explicit form for the Green's function. We find the
usual behavior for negative index materials, there is no refection outside the
evanescent regime and the transmission (refraction) shows the usual NIM
behavior. We find that the Green's function has poles, which lead to a
modulation of the radiative decay probability of an excited atom. The formalism
is free from ambiguities in the sign of the refractive index.Comment: 22 pages, accepted for publication in J. Math. Phys