Birefringent left-handed metamaterials and perfect lenses for vectorial fields

We describe the properties of specific non-reflecting birefringent left-handed metamaterials and demonstrate a birefringent perfect lens for vectorial fields. We predict that, in a sharp contrast to the concept of a conventional perfect lens realized at epsilon =mu = - 1 ( where epsilon is the dielectric permittivity and mu is the magnetic permeability), the birefringent left-handed slab possesses the property of negative refraction either for TE- or TM-polarized waves or for both of them simultaneously. This allows selective focusing and a spatial separation of the images created at different polarizations. We discuss several applications of the birefringent left-handed lenses such as the beam splitting and near-field diagnostics at the sub-wavelength scale.