  The electromagnetic characteristics of plane-transformed invisibility cloaks
are quantitatively studied in this paper. We take elliptical cylindrical cloak
as the example, and use an elliptical cylindrical wave expansion method to
obtain the scattered field. It is demonstrated that an ideal elliptical
cylindrical cloak is inherently visible. Noticeable field scattering and
penetration will be induced when the cloak is exposed directly to an
electromagnetic wave. However, as long as the cloak consists of a perfect
electric conducting lining at the interior surface, perfect invisibility can
still be achieved along the direction parallel to the major axis of the cloak
for transverse magnetic illumination. Another plane-transformed cloak with a
conical geometry is also proposed. The advantage of this cloak is that all the
permittivity and permeability elements are spatially invariant while none of
them is singular. Hence, it is easily realizable with artificially structured
metamaterials. Finally, we show that this kind of cloak can also be used to
cloak objects on a flat ground plane.
