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Hyperbolic metamaterials (HMMs) gained a lot of interest amongst researchers in recent years due to their novel properties stemming from hyperbolic dispersion, such as anomalous scattering, subwavelength confinement of light or enhancing far-field radiation. In our work, we investigate optical properties of nanostructured HMMs in a form of spherical nanoresonators composed of stacked alternating metal-dielectric layers, which is one way to realize hyperbolic dispersion. Using T-matrix analysis, combined with a quasistatic approach, we explore their unique spectral response to unravel fundamental electromagnetic properties of hyperbolic nanoresonators. The modal structure of hyperbolic nanospheres (HNSs) is richer than those of conventional nanoantennas and can be tuned either with material properties or incident light conditions. We show that, depending on the direction and polarization of incident light, such nanoresonators can exhibit a plasmonic-like response or one with an atypical modal order, with electric and magnetic modes of higher orders appearing at energies below those of lower order modes. We underline how constructive or destructive cross coupling between various electric and magnetic multipoles, determined by the hyperbolic dispersion, influences the overall optical response and enables phenomena absent in the isotropic medium. Such an example is a negative contribution of a given mode to the extinction cross-section, stemming from destructive cross coupling and is an indicator of energy transfer between modes. We show how mode cross coupling (and thus HNS optical properties) change with material properties – varying the metal fill-factor allows for significant tunability from a uniaxial dielectric through a type I or II hyperbolic material to a uniaxial metal. By applying the quasistatic approach we also analyse the origin of the dipolar modes and obtain material-dependent resonance conditions for both electric and magnetic mode. Furthermore, we conclude that magnetic dipolar resonance presence is determined by the hyperbolic disperison, i.e. opposite signs of the ordinary and extraordinary permittivities.
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