The influence of a geometrical perturbation δ at the inner boundaries of both cylindrical and spherical invisibility cloaks on invisibility performance is presented. The analytic solutions for such influence in the case of the general coordinate transformation are given. We show that the cylindrical cloak is more sensitive than a spherical cloak to such a perturbation. The difference results from the different asymptotic properties of eigenfunctions for the cylindrical and spherical wave equations. In particular, the zeroth-order scattering coefficient for a cylindrical cloak determined by converges to zero very slowly. The noticeable scattering induced by the slow convergence speed can be decreased by choosing appropriate coordinate transformation functions. More interestingly, the slow convergence can be overcome dramatically by putting a PEC (PMC) layer at the interior boundary of the cloak shell for TM (TE) wave.
© 2008 Optical Society of America
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