  Nonmagnetic cloak offers a feasible way to achieve invisibility at optical
frequencies using materials with only electric responses. In this letter, we
suggest an approximation of the ideal nonmagnetic cloak and quantitatively
study its electromagnetic characteristics using a full-wave scattering theory.
It is demonstrated that the forward scattering of the impedance matched cloak
increases dramatically as the thickness of the cloak decreases. Nevertheless,
it is still possible to effectively reduce the total scattering cross section
with a very thin cloak whose impedance is not matched to the surrounding
material at the outer boundary. Our analysis also provides the flexibility of
reducing the scattering in an arbitrary direction.
