Rule of Thumb for Cloaking Bandwidth Based on a Wave-Packet Argument

A simple rule is provided for the upper-bound bandwidth of 2-D invisibility cloaking in a free-space environment. The rule is based on a group-delay argument and avoids any dependence on material characteristics. It is found that the upper relative bandwidth is proportional to the ratio between wavelength and extra propagation length around the object to be cloaked. An analytical model is provided for fields on an equivalence plane just behind the cloak. In order to arrive at an upper-bound estimate for the bandwidth, the model is based on several key optimistic assumptions. The model provides an idea of the least-perturbed fields that may be expected for different quality factors.