  Dispersion properties of electromagnetic crystals formed by small uniaxial
resonant scatterers (magnetic or electric) are studied using the local field
approach. The goal of the study is to determine the conditions under which the
homogenization of such crystals can be made. Therefore the consideration is
limited by the frequency region where the wavelength in the host medium is
larger than the lattice periods. It is demonstrated that together with known
restriction for the homogenization related with the large values of the
material parameters there is an additional restriction related with their small
absolute values. From the other hand, the homogenization becomes allowed in
both cases of large and small material parameters for special directions of
propagation. Two unusual effects inherent to the crystals under consideration
are revealed: flat isofrequency contour which allows subwavelength imaging
using canalization regime and birefringence of extraordinary modes which can be
used for beam splitting.
