  It is shown that perfect absorption and giant amplification can be realized
when a wave impinges on a special metamaterial layer with zero real parts of
the permittivity and permeability. The imaginary parts of the permittivity and
permeability remain nonzero, corresponding to finite loss or gain. Perfect
absorption and giant magnification can still be achieved even if the thickness
of the metamaterial layer is arbitrarily thin and the absolute imaginary parts
of the permittivity and permeability are very small. The metamaterial layer
needs a total-reflection substrate for perfect absorption, while this is not
required for giant magnification.
