Fig. 4.

Synthetic implementation of ENZ shells as a microwave cylindrical resonator. (A) Geometry of the resonator: cylindrical resonator of height $h=0.5{\lambda }_0$ (with arbitrarily chosen value ${\lambda }_0=0.03\hspace{0.17em}\text{m\hspace{0.17em}at}\hspace{0.5em}10\hspace{0.17em}\text{GHz}$) and radius $r_2$, containing a dielectric rod of relative permittivity ${\epsilon }_1=10$ and whose radius is set to satisfy the resonance condition $J_1\left({\beta }_1{r}_1\right)=0$ ($r_1\sim 0.2{\lambda }_0$). The resonator is bounded by copper walls ($\sigma =5.7\hspace{0.17em}{10}^7\hspace{0.17em}\text{S}/\text{m}$). Numerically simulated performance: (B) Eigenfrequency, ${\omega }_{\text{res}}$, and quality factor $Q$, as a function of the external radius $r_2$. (C) Spectral density, $g\left(\omega \right)$, normalized to the maximal computed value, for a QE located at $\mathit{r}=\left(\mathrm{0,0},h/2\right)$ with its dipole moment pointing along $\widehat{x}$ for three different external radii. (D) Electric and magnetic field magnitude distributions excited by such QE in the middle plane ($z=h/2$).