  In this paper, we establish the full-wave electromagnetic scattering theory
to study the electromagnetic scattering from infinitely long cylinders with
radially anisotropic coatings. We show that the total effective scattering
width can be dramatically reduced by the suitable adjustment of the dielectric
anisotropy of the shell, while it is not the case for tuning the dielectric
anisotropy of the core. Furthermore, we could make the cylindrical objects
invisible when both dielectric and magnetic anisotropies are adjusted. In the
long wavelength limit, we develop effective medium theory to derive the
effective isotropic permittivity and permeability for the anisotropic coated
cylinders, and the invisibility radius ratio derived from the full-wave theory
for small coated cylinders can be well described within the effective medium
theory.
