  We show that anisotropic negative effective dispersion relation can be
achieved in pure dielectric rod-type metamaterials by turning from the symmetry
of a square lattice to that of a rectangular one, i.e. by breaking the rotation
symmetry of effective homogeneous medium. Theoretical predictions and
conclusions are verified by both numerical calculations and computer based
simulations. The proposed anisotropic metamaterial, is used to construct a
refocusing slab-lens and a subdiffraction hyperlens. The all-dielectric origin
makes it more straightforward to address loss and scaling, two major issues of
metallic structures, thus facilitating future applications in both the
terahertz and optical range.
