  We present a quantization scheme for the electromagnetic field interacting
with atomic systems in the presence of dispersing and absorbing
magnetodielectric media, including left-handed material having negative real
part of the refractive index. The theory is applied to the spontaneous decay of
a two-level atom at the center of a spherical free-space cavity surrounded by
magnetodielectric matter of overlapping band-gap zones. Results for both big
and small cavities are presented, and the problem of local-field corrections
within the real-cavity model is addressed.
