Figure 1

(a) The geometries of the 1-, 2-, and 4-cut single-ring SRRs are shown; the unit cell has the dimensions $a\times a$ in the SRR plane and $0.614a$ perpendicular to it. The SRR is made of aluminum, simulated using a Drude-model permittivity ($f_p={\omega }_p/2\pi =3570\mathrm{THz}$, $f_{\tau }=19.4\mathrm{THz}$), separated from the $0.343a$ thick substrate (glass, $\epsilon =2.14$) by a $0.014a$ thin indium tin oxide layer ($\epsilon =7$). The parameters of the SRR are side length $l=0.914a$, width and thickness $w=t=0.257a$, and cut width ($d$) $0.2a$, $0.1a$, and $0.05a$ for the 1-, 2-, and 4-cut SRRs, respectively. (b) The left panel shows the charge accumulation in a 4-cut SRR, as a result of the periodic boundary conditions in the $\overrightarrow{E}$ (and $\overrightarrow{H}$) direction. The right panel shows the equivalent $LC$ circuit describing this SRR. $C_g$ is the gap capacitance and $C_s$ the side capacitance resulting from the interaction with the neighboring SRR.Reuse & Permissions

Figure 2

The scaling of the simulated magnetic resonance frequency $f_m$ as a function of the linear size $a$ of the unit cell for the 1-, 2-, and 4-cut SRRs (solid lines with symbols). Up to the lower terahertz region, the scaling is linear, $f_m\propto 1/a$. The maximum attainable frequency is strongly enhanced with the number of cuts in the SRR ring. The hollow symbols as well as the vertical line at $1/a=17.9\mu {\mathrm{m}}^{-1}$ indicate that no $\mu <0$ is reached anymore. The nonsolid lines show the scaling of $f_m$ calculated through Eq. (1) ($LC$ circuit model).Reuse & Permissions

Figure 3

Simulation of the shape and amplitude of the magnetic resonance in $\mathrm{Re}\mu (\omega )$ of the 4-cut SRR for unit cell size $a=70$, 56, 49, and 35 nm (left to right).Reuse & Permissions