On some constraints that limit the design of an invisibility cloak

Using the idea of transformation medium, a cloak can be designed to make a domain invisible for one target frequency. In this article, we examine the possibility to extend the bandwidth of such a cloak. We obtained a constraint of the band width, which is summarized as a simple inequality that states that limits the bandwidth of operation. The constraint originates from causality requirements. We suggest a simple strategy that can get around the constraint.