Limitations on bandwidth-integrated passive cloaking

We present a general framework for the computation of structure-Agnostic bounds on the performance of passive cloaks over a nonzero bandwidth. We apply this framework in two dimensions to the canonical scenario of cloaking a circular object. We find that perfect cloaking using a finite-sized isotropic cloak is impossible over any bandwidth, with the bounds scaling linearly with the bandwidth before saturating due to the finite size of the cloak and the presence of material loss. The bounds also exhibit linear scaling with material loss in the cloak and linear scaling with the inverse of the radial thickness of the design region before saturation due to finite-size effects or the presence of material loss. The formulation could readily find applications in the development of cloaking devices, setting expectations, and benchmarks for optimal performance.