Perfect invisibility cloaking by isotropic media

In this paper the authors report that perfect invisibility cloaking could be achieved in a medium designed by a non-Euclidean conformal transformation. Wave behaviors could be controlled as well as the cloaking device configured by the general Euclidean approach dealing with the full Maxwell's equations. The cloaking medium proposed here is totally isotropic and can work in waves without the geometry and polarization limits; thus it is very promising for applications to build a device to hide large objects.