  We examine some of the optical properties of a metamaterial consisting of
thin layers of alternating metal and dielectric. We can model this material as
a homogeneous effective medium with anisotropic dielectric permittivity. When
the components of this permittivity have different signs, the behavior of the
system becomes very interesting: the normally evanescent parts of a P-polarized
incident field are now transmitted, and there is a preferred direction of
propagation.
  We show that a slab of this material can form an image with sub-wavelength
details, at a position which depends on the frequency of light used. The
quality of the image is affected by absorption and by the finite width of the
layers; we go beyond the effective medium approximation to predict how thin the
layers need to be in order to obtain subwavelength resolution.
