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

Abstract

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 2l-TM (2l-TE) and 2l+1-TE (2l+1-TM) modes for " 0 ( 0) material, and the 2l-TM and 2l-TE for both " 0 and 0. Such extraordinary resonance nesting and degeneracy provide additional principles to manipulate cavity behaviors.

Inhibition and enhancement of the spontaneous emission in spherical cavities surrounded by zero-index-materials

“…For the 2-TE mode, it can exist in different radii of dielectric cavities embedded in ENZ, so-called resonance nesting. 20 In the cavities of R = 315.4, 631.1, 947 nm, only 2-TE mode is allowed at a working wavelength of 630 nm. Fig.…”

“…30 At the resonance wavelength of 630 nm, the dielectric cavities with radii of 450.5 nm, 776.5 nm, and 1094 nm embedded in the ENZ environment all support the degenerate 2-TM and 4-TE modes due to the nesting effect. 20 In Fig. 5, we give the Purcell factors of cavities with different radii when a z-polarized emitter is placed along the x-axis to excite the degenerate modes in these cavities.…”

“…Using Mie theory, electromagnetic boundary conditions, and the special electromagnetic parameters of ZIMs, we obtained the cavity radius corresponding to the resonance of different modes at a fixed wavelength, such as R = 450.5 nm, 776.5 nm, 1093 nm… for the 2-TM mode in ENZ, and observed the phenomenon of resonance degeneracy and nesting. 20…”

“…for the 2-TM mode in ENZ, and observed the phenomenon of resonance degeneracy and nesting. 20 A linearly polarized emitter moves radially in the cavity to excite modes and is used to characterize the SE rate. The inhibition or enhancement of SE is given by the Purcell factor…”

“…And the resonance nesting means that there is a series of cavities with different radii supporting the same resonances. 20 However, the inhibition and enhancement of SE with the effect of resonance degeneracy and nesting of spherical dielectric cavities within ZIM have not been studied.…”