Generation of giant magnetic fields in a hollow mesoscale sphere

The superresonance effect for a hollow dielectric sphere is numerically simulated with the Mie theory. It is shown for the first time that weakly dissipative mesoscale spheres with an air-filled cavity exhibit a high-order Fano resonance related to internal Mie modes. Superresonance in a hollow sphere is achieved by the accurate choice of the cavity radius, while for a monolithic dielectric sphere, it is ensured by the accurate choice of the outer diameter of the particle under study. In this case, the relative intensities of the resonance peaks in the optical range for both magnetic and electric fields near the sphere poles can have enormous values of 10$^6$–10$^7$, if the magnetic field magnitude exceeds that of the electric field by a factor larger than 15 for the hollow sphere with a Mie size parameter about 40.