On the Uniqueness of Inverse Electromagnetic Problems for Invisibility Cloaks

Devices like invisibility cloaks are designed based on the method of transformation optics, which have anisotropic inhomogeneous structures. In this paper, we examine uniqueness of the inverse problem for such structures. We prove all these materials have the same surface field distribution on a surface enclosing the area of interest, while solutions to Maxwell's equations inside them are different. The uniqueness theory suggests that within the surface, the same medium should exactly be present. However, for anisotropic inhomogeneous media of our interest, this paper illustrates that this might not be true, despite the result of a previous study that shows uniqueness could be true for some anisotropic inhomogeneous structures. For the analysis, the transverse electric (TE) Z-polarization is used. The simulation results are obtained by a commercial Finite-Element based simulator.