A diameter--bandwidth product limitation of isolated-object cloaking
  We show that cloaking of isolated objects is subject to a diameter-bandwidth product limitation: as the size of the object increases, the bandwidth of good (small cross-section) cloaking decreases inversely with the diameter, as a consequence of causality constraints even for perfect fabrication and materials with negligible absorption. This generalizes a previous result that perfect cloaking of isolated objects over a nonzero bandwidth violates causality. Furthermore, we demonstrate broader causality-based scaling limitations on any bandwidth-averaged cloaking cross-section, using complex analysis and the optical theorem to transform the frequency-averaged problem into a single scattering problem with transformed materials. 
Hila Hashemi, Cheng Wei Qiu, Alexander P. McCauley, J. D.   Joannopoulos, Steven G. Johnson
physics.optics physics.pop-ph