Ideal cylindrical cloak and influence of tiny perturbation

The invisibility of cylindrical cloaks produced by arbitrary radially coordinate transformations is confirmed. The influence of a tiny geometrical perturbation at the inner boundary of the cloak is investigated. It is shown that a tiny perturbation would induce a noticeable field scattering, due to the slow convergence of the zero^th order scattering coefficients. However, by choosing appropriate coordinate transformation functions, the noticeable scattering can be reduced. More interestingly, the slow convergence can be overcome drastically by putting a PEC (PMC) layer at the interior boundary of the cloak shell for TM (TE) mode.