Description: A cylindrical wave expansion method is developed to obtain the scattering field for an ideal
two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up
to solve the boundary problem at the inner boundary of the cloak shell. We confirm that a cloak
with the ideal material parameters is a perfect invisibility cloak by systematically studying the
change of the scattering coefficients from the near-ideal case to the ideal one. However, due to the
slow convergence of the zeroth order scattering coefficients, a tiny perturbation on the cloak would
induce a noticeable field scattering and penetration.
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