Approximate cloaking for electromagnetic waves via transformation\n optics: cloaking vs infinite energy

We study the approximate cloaking via transformation optics for\nelectromagnetic waves in the time harmonic regime in which the cloaking device\n{\\it only} consists of a layer constructed by the mapping technique. Due to the\nfact that no-lossy layer is required, resonance might appear and the analysis\nis delicate. We analyse both non-resonant and resonant cases. In particular, we\nshow that the energy can blow up inside the cloaked region in the resonant case\nand/whereas cloaking is {\\it achieved} in {\\it both} cases. Moreover, the\ndegree of visibility {\\it depends} on the compatibility of the source inside\nthe cloaked region and the system. These facts are new and distinct from known\nmathematical results in the literature.\n