  It was proposed that perfect invisibility cloaks can be constructed for
hiding objects from electromagnetic illumination (Pendry et al., Science 312,
p. 1780). The cylindrical cloaks experimentally demonstrated (Schurig et al.,
Science 314, p. 997) and proposed (Cai et al., Nat. Photon. 1, p. 224) have
however simplified material parameters in order to facilitate easier
realization as well as to avoid infinities in optical constants. Here we show
that the cylindrical cloaks with simplified material parameters inherently
allow the zeroth-order cylindrical wave to pass through the cloak as if the
cloak is made of a homogeneous isotropic medium, and thus visible. To all
high-order cylindrical waves, our numerical simulation suggests that the
simplified cloak inherits some properties of the ideal cloak, but finite
scatterings exist.
