We review a new, rapidly developing field of all-dielectric nanophotonics which allows to control both magnetic and electric response of structured matter by engineering the Mie resonances in high-index dielectric nanoparti-cles. We discuss optical properties of such dielectric nanoparticles, methods of their fabrication, and also recent advances in all-dielectric metadevices including couple-resonator dielectric waveguides, nanoantennas, and meta-surfaces.
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