We reveal the existence of optical super-resonance modes supported by dielectric microspheres. These modes,with field-intensity enhancement factors on the order of 10^4-10^5, can be directly obtained from analytical calculations. In contrast to usual optical resonances, which are related to the poles of the electric and magnetic scattering amplitudes, super-resonance modes are related to the poles of the internal field coefficients, obtained for specific values of the size parameter. We also reveal the connection of these super-resonances in the generation of magnetic nanojets and of giant magnetic fields in particles with high refractive index.
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