We reveal that the resonant Mie scattering by high-index dielectric nanoparticles can be presented through cascades of Fano resonances. We employ the exact solution of Maxwell's equations and demonstrate that the Lorenz-Mie coefficients of the Mie problem can be expressed generically as infinite series of Fano functions as they describe interference between the background radiation originated from an incident wave and narrow-spectrum Mie scattering modes that lead to Fano resonances.

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We have developed an approach to building superluminal medium for transformation opticsbased 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.

We propose to implement a nonmetallic low-loss cloak for the infrared range from identical chalcogenide glass resonators. Based on transformation optics for cylindrical objects, our approach does not require metamaterial response to be homogeneous and accounts for the discrete nature of elementary responses governed by resonator shape, illumination angle, and inter-resonator coupling. Air fractions are employed to obtain the desired distribution of the cloak effective parameters. The effect of cloaking is verified by full-wave simulations of the true multiresonator structure. The feasibility of cloak fabrication is demonstrated by prototyping glass grating structures with the dimensions characteristic for the cloak resonators.