  An inverse way to define the parameters of ideal cylindrical cloaks is
developed, in which the interconnection between the parameters is revealed for
the first time without knowing a specific coordinate transformation. The
required parameters are derived in terms of the integral form of cloaking
generators, which is very general and allows us to examine the significance of
the parametric profiles. The validity of such inverse way and the invisibility
characteristics are presented in full-wave numerical simulation of plane wave
scattering by cloaked cylinders.
