  In an electromagnetic cloak based on a transformation approach, reduced sets
of material properties are generally favored due to their easier implementation
in reality, although a seemingly inevitable drawback of undesired reflection
exists in such cloaks. Here we suggest using high-order transformations to
create smooth moduli at the outer boundary of the cloak, therefore completely
eliminating the detrimental scattering within the limit of geometric optics. We
apply this scheme to a non-magnetic cylindrical cloak and demonstrate that the
scattered field is reduced substantially in a cloak with optimal quadratic
transformation as compared to its linear counterpart.
