  We calculate the static dielectric tensor of a periodic system of aligned
anisotropic dielectric cylinders. Exact analytical formulas for the effective
dielectric constants for the E- and H- eigenmodes are obtained for arbitrary 2D
Bravais lattice and arbitrary cross-section of anisotropic cylinders. It is
shown that depending on the symmetry of the unit cell photonic crystal of
anisotropic cylinders behaves in the low-frequency limit like uniaxial or
biaxial natural crystal. The developed theory of homogenization of anisotropic
cylinders is applied for calculations of the dielectric properties of photonic
crystals of carbon nanotubes.
