Limitations of high-order transformation and incident angle on simplified invisibility cloaks.

We studied the scattering from the simplified cylindrical cloaks analytically at both normal and oblique incidences. We found that these simplified cylindrical cloaks may produce a larger scattering at nonnormal incidences than that from an object without any cloak, making this object more "visible". Even at normal incidence, the high-order transformation with impedance matched at the outer boundary can produce stronger scattering than the linear simplified one without matched impedance. This is due to the inefficiency of guided waves close to the inner boundary. Therefore, a square root transformation can improve scattering by guiding waves away from the inner boundary.