Do Cloaked Objects Really Scatter Less?

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.