We prove that, for arbitrary three-dimensional transformation-based invisibility cloaking of an object above a ground plane or of isolated objects, there are practical constraints that increase with the object size. In particular, we show that the cloak thickness must scale proportionally to the thickness of the object being cloaked, assuming bounded refractive indices, and that absorption discrepancies and other imperfections must scale inversely with the object thickness. For isolated objects, we also show that bounded refractive indices imply a lower bound on the effective cross section.

• Received 20 February 2011

DOI:https://doi.org/10.1103/PhysRevA.84.023815