Extending the bandwidth of electromagnetic cloaks

Using the idea of a transformation medium, a cloak can be designed to make a domain invisible to one target frequency. We examine the possibility of extending the bandwidth of such a cloak. We find that causality requirements impose severe constraints on the system parameters of the transformation medium, and we show that a specific form of "reduction" can help us to create a cloak that offers a reduced cross section in a finite frequency range. We also give a simple inequality that limits the bandwidth of operation.