Superluminal media formed by photonic crystals for transformation optics-based invisibility cloaks

We have developed an approach to building superluminal medium for transformation optics-based devices, including invisibility cloaks, from photonic crystals. Analysis of dispersion diagrams of 2D arrays composed from dielectric rods has shown that at frequencies corresponding to the second bands formed due to bandgap opening at increase of rod permittivity, the medium formed by arrays exhibits refractive indices providing for superluminal phase velocities of propagating waves. It is further demonstrated that rod arrays with various lattice constants could be used for realizing a range of superluminal index values prescribed by transformation optics for cylindrical cloaks at arbitrary chosen operating frequency. The performed studies allowed for solving a row of problems with employment rod arrays in the cloak medium: in particular, formulating transformation optics-based prescriptions for refractive index dispersion in the cloaking shell, defining the dimensions of array fragments capable of responding similar to infinite arrays, finding optimal distribution of linear arrays sets at their coiling to form concentric material layers in the cloaking shell, and employing interaction between neighboring array sets with various lattice constants to assist the realization of prescribed index dispersion. The performance of the superluminal medium formed by rod array sets was demonstrated on an example of a cloaking shell developed for microwave frequency range. In contrast to metamaterial-based cloak media, the developed media requires neither material homogenization, nor obtaining the effective parameters with peculiar values and Lorentz's type resonances in rods. Combination of these advantages and low losses makes photonic crystals perspective materials for invisibility cloaks operating in THz and optical ranges.