  The phenomenon of anomalous localized resonance (ALR) is observed at the
interface between materials with positive and negative material parameters and
is characterized by the fact that, when a given source is placed near the
interface, the electric and magnetic fields start to have very fast and large
oscillations around the interface as the absorption in the materials becomes
very small while they remain smooth and regular away from the interface.
  In this paper, we discuss the phenomenon of anomalous localized resonance
(ALR) in the context of an infinite slab of homogeneous, nonmagnetic material
($\mu=1$) with permittivity $\epsilon_s=-1-\mathrm{i}\delta$ for some small
loss $\delta \ll 1$ surrounded by positive, nonmagnetic, homogeneous media. We
explicitly characterize the limit value of the product between frequency and
the width of slab beyond which the ALR phenomenon does not occur and analyze
the situation when the phenomenon is observed. In addition, we also construct
sources for which the ALR phenomenon never appears.
