Fig. 2.

Decay dynamics of a quantum emitter (QE) within an ENZ shell. (A) Conceptual sketch of a QE embedded within a macroscopic EMNZ shell of arbitrary shape. (B) Spectral density $\overline{g}\left(\omega \right),$ normalized to its free-space counterpart, for a QE positioned at the center of a spherical shell with external radius $r_2=1{\lambda }_p$, and internal radius of $r_1=0.3{\lambda }_p$ (red) and $r_1=0.715{\lambda }_p$ (blue). The shell is characterized by relative permeability, ${\mu }_2\left(\omega \right)=1$, and relative permittivity, ${\epsilon }_2\left(\omega \right)=1-{\omega }_p^2/\left(\omega \left(\omega +i{\omega }_c\right)\right)$, with ${\omega }_p={\omega }_0$, and ${\omega }_c={10}^{-4}\hspace{0.17em}{\omega }_p.$ (Inset) Sketch of the geometry. (C) Time evolution of the probability of occupation of the excited state, $P_e\left(t\right)$, for nonresonant case of $r_1=0.3{\lambda }_p$ and resonant case of $r_1=0.715{\lambda }_p$ internal radii. For comparison, the black line shows the decay in free space. The magnitude of the transition dipole moment is fixed such that $\mathrm{\Omega }=2\pi \hspace{0.17em}10\hspace{0.17em}\gamma$.