Invisibility cloak
Invisibility. Transformation of space and applications

In the case of the invisibility cloak, the space transformation concerned a cylindrical space of radius b, which was transformed into an annular space between radii a and b (figure 4). Points in the initial space are marked with the coordinates r, q and z. Those in the transformed space are marked by r′, q′ and z′ in cylindrical coordinates. Both spaces are assumed to be infinite in the z and z′ directions, which are merged.

The transformation is therefore defined by a set of relatively simple equations (12):