Enhancement of magnetic dipole emission in the presence of a spherical particle

We discover regimes for promoting fluorescence of magnetic light by four orders of magnitude due to magnetic dipole (MD) transitions of trivalent rare-earth ions $\mathrm{Eu}^{3+}$ located inside or near dielectric homogeneous spheres. A number of configurations, including sphere parameters and the radial position of the rare-earth emitter, at which the transition coupling coefficient approaches the limit value $\approx 1$, which means that the transitions from a given level are completely dominated by the MD transition, have been determined. We present configurations for which the directivity of the resultant emission can be larger than 25.