Optimizing imperfect cloaks to perfection

Transformation optics has been an essential tool for designing cloaking devices for electromagnetic and acoustic waves. All these designs have one requirement in common: material singularity. At the interface between the cloak and the cloaked region, some material properties have to approach infinity, while some others approach zero. This paper attempts to answer a central question in physically realizing such cloaks: is material singularity a requirement for perfect cloaking? This paper demonstrates that, through optimization, perfect cloaking can be achieved using a layered cloak construction without material singularity. Two examples are used for this demonstration. In one example, the initial design is based on the Cummer-Schurig prescription for acoustic cloaking that requires mass-anisotropic material. Another example uses the two isotropic layers to achieve the equivalent mass-anisotropy for each anisotropic layer. During the optimization processes, only material properties of cloaks' constituent layers are adjusted while the geometries remain unchanged. In both examples, the normalized total scattering cross section can be reduced to 0.002 (0.2%) or lower in numerical computations. The capabilities and other characteristics of the optimization in other tasks such as cloaking penetrable objects and isolating strong resonance in such objects are also explored.