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 theoretically 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.