Approximate cloaking for electromagnetic waves via transformation optics: Cloaking versus infinite energy

We study the approximate cloaking via transformation optics for electromagnetic waves in the time harmonic regime in which the cloaking device only consists of a layer constructed by the mapping technique. Due to the fact that no-lossy layer is required, resonance might appear and the analysis is delicate. We analyze both non-resonant and resonant cases. In particular, we show that the energy can blow up inside the cloaked region in the resonant case and/whereas cloaking is achieved in both cases. Moreover, the degree of visibility depends on the compatibility of the source inside the cloaked region and the system. These facts are new and distinct from known mathematical results in the literature.