Understanding the functionality of an array of invisibility cloaks
This paper describes the operation and the interaction of cloaking devices when they are periodically arranged. The main focus is on analyzing the dispersion relation of structures, which should mimic that of the vacuum in the ideal scenario. We distinguish between two cloaking mechanisms: cloaks designed within the framework of transformation optics and cloaks designed on the basis of the scattering cancellation technique. The difference between the two approaches is that the first operates independently of the frequency by assuming nondispersive materials, whereas the latter is designed to operate for a single frequency. Our numerical simulations demonstrate that arrays made of such invisible dielectric obstacles act like a homogeneous medium with permittivity and permeability equal to those of the surrounding medium, except for a countable set of eigenfrequencies associated with Mie resonances for the former type of (transformation-based) cloak. For the latter type of (plasmonic) cloak, the marginal scattering response indicates the effectiveness of cloaking arrays of individual particles. Our spectral (Floquet-Bloch) approach to cloaking might be useful to implement realistic applications such as biomedical sensing, noninvasive probing, sensing networks, or multiobjective camouflaging.