  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.
