Perfect absorption and giant magnification with a thin metamaterial layer

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.