Nesting and degeneracy of Mie resonances of dielectric cavities within zero-index materials

Resonances in optical cavities are used to manipulate light propagation, enhance light-matter interaction, modulate quantum states, and so on. However, the index contrast between the traditional cavities and the host is generally not high, which to some extent limited their performances. By putting dielectric cavities into a host of zero-index materials, index contrast in principle can approach infinity. Here, we analytically deduced Mie resonance conditions at this extreme circumstance. Interestingly, we discovered a so-called resonance nesting effect, in which a set of cavities with different radii can possess the same type of resonance at the same wavelength. We also revealed previously unknown degeneracy between the 2(l)-TM (2(l)-TE) and 2(l+1)-TE (2(l + 1) -TM) modes for epsilon approximate to 0 (mu approximate to 0) material, and the 2(l)-TM and 2(l)-TE for both epsilon approximate to 0 and mu approximate to 0. Such extraordinary resonance nesting and degeneracy provide additional principles to manipulate cavity behaviors.