  We discuss the global scattering response of invisibility cloaks over the
entire frequency spectrum, from static to very high frequencies. Based on
linearity, causality and energy conservation we show that the total extinction
and scattering, integrated over all wavelengths, of any linear, passive, causal
and non-diamagnetic cloak necessarily increases compared to the uncloaked case.
In light of this general principle, we provide a quantitative measure to
compare the global performance of different cloaking techniques and we discuss
solutions to minimize the global scattering signature of an object using thin,
superconducting shells. Our results provide important physical insights on how
invisibility cloaks operate and affect the global scattering of an object,
suggesting ways to defeat countermeasures aimed at detecting cloaked objects
using short impinging pulses.
