Nanoparticles made of High Refractive Index (HRI) dielectric materials, such as Si, GaP, Ge or other semiconductor compounds have been proposed recently as an alternative to metals, driven by their low-losses and presence of magnetic response in spite of being non-magnetic materials. However, they are known to suffer relatively large losses and absence of magnetic response at optical frequencies. Here, we intend to show a brief overview of our recent research in light scattering by HRI dielectric nanostructures. In particular, we will show how the strong confinement of electromagnetic energy and the outstanding scattering efficiencies of these HRI dielectric structures make them promising candidates to act as basic units for the design of the next generation of nanoantennas that may be able to boost applications such as sensing, light directivity, optical switching, surface enhanced spectroscopies, all-dielectric metamaterials, or non linear phenomena, such as third harmonic generation
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