Nonsingular cylindrical cloaks with internal–external invisible regions

Two-dimensional nonsingular cloaks with internal and external invisible regions are presented. Objects can be hidden either in the internal cavity or the external concealment regions without being detected. Also in the latter case, the cloaked objects can receive incoming signals. In order to avoid the singularity (an infinitely large value of the constitutive parameters) which may appear at the inner boundary, the method of adjusting the principal stretches out of the cloaking plane is adopted. Detailed examples and their electromagnetic simulations are presented to validate the design. In addition, the effect of the material loss on the invisible property of the cloaks is also discussed