Invisibility in the plane

Invisibility cloaks are metrics of compact support which shield an object in the middle by moving light around it. Mathematically, it is an interesting questions, whether there are metrics of compact support in the plane (not conformal to the usual metric), which have the property that the geodesic flow has no conjugate points and flat wave fronts coming from infinity remain flat after passing through the object. Engineering applications require that waves pass around an object but don't need to have a perfect shielding. The pictures below are from a "Spiegel" article (in German). Source: I, II, III.
Added November 13, 2010: The idea is extended to Minkovski space. A recently published Dover book "Geometry and Light" by Ulf Leonhardt and Thomas Philbin explains some mathematics of light.