Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations

We investigate a general class of electromagnetic devices created with any continuous transformation functions by rigorously calculating the analytical expressions of the electromagnetic field in the whole space. Some interesting phenomena associated with these transformation devices, including the invisibility cloaks, concentrators, and field rotators, are discussed. By carefully choosing the transformation function, we can realize cloaks, which are insensitive to perturbations at both the inner and outer boundaries. Furthermore, we find that when the coating layer of the concentrator is realized with left-handed materials, energy will circulate between the coating and the core, and the energy transmitted through the core of the concentrator can be much bigger than that transmitted through the concentrator. Therefore, such concentrator is also a power flux enhancer. Finally, we propose a spherical field rotator, which functions as not only a wave vector rotator but also a polarization rotator, depending on the orientations of the spherical rotator with respect to the incident wave direction. The functionality of these transformation devices are all successfully confirmed by our analytical full-wave method, which also provides an alternate computational efficient validation method in contrast to numerical validation methods.