Diameter-bandwidth product limitation of isolated-object cloaking

We show that cloaking of isolated objects using transformation-based cloaks 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.