The effect of transformation order on the invisibility performance of a practical cylindrical cloak

A class of polynomial coordinate transformation functions with an arbitrary order number is used to design cylindrical invisibility cloaks. Since an ideal cylindrical cloak is inevitably unphysical at its inner boundary, our investigation involves the replacement of a thin layer of material at the cloak's inner surface by a homogeneous material layer. This approach effectively avoids the infinities in the material parameters, and at the same time produces practical near-ideal invisibility cloaks. The cloaks obtained are perfectly matched in impedance at the outer boundary. We quantitatively show the effect of the transformation order on the proposed cloak's scattering coefficients.