The study of resonant dielectric nanostructures with high refractive index is a new research direction in nanoscale optics and metamaterial-inspired nanophotonics. Because of the unique optically-induced electric and magnetic Mie resonances, high-index nanoscale structures are expected to complement or even replace different plasmonic components in a range of potential applications. Here we study strong coupling between modes of a single subwavelength high-index dielectric resonator and analyse the mode transformation and Fano resonances when resonators aspect ratio varies. We demonstrate that strong mode coupling results in resonances with high quality factors, which are related to the physics of bound states in the continuum when the radiative losses are almost suppressed due to the Friedrich-Wintgen scenario of destructive interference. We explain the physics of these states in terms of multipole decomposition and show that their appearance is accompanied by drastic change of the far-field radiation pattern. We reveal a fundamental link between the formation of the high-quality resonances and peculiarities of the Fano parameter in the scattering cross-section spectra. Our theoretical findings are confirmed by microwave experiments for the scattering of a high-index cylindrical resonators with a tunable aspect ratio. The proposed mechanism of the strong mode coupling in single subwavelength high-index resonators accompanied by resonances with high quality factor helps to extend substantially functionalities of all-dielectric nanophotonics that opens new horizons for active and passive nanoscale metadevices.
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