$\eta_H=0.3$ and $\eta_C=$0.4`.` Note that these parameters are close to the limit of strongest possible magneto-electric coupling. Figures  \[Fig1:radpats\](d,e) reveal that the radiation pattern of each eigenmode is non-dipolar. Rather than a $\sin^2\theta$ donut-shaped pattern, an elongated radiation pattern occurs, with maximum extent in the $y$-direction. The polarization in the far field is linear for directions along the cartesian axis, but is generally elliptical.

Extinction cross sections to measure polarizability
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![image](SersicetalFig2.eps){width="\figwidth"}

Figure \[Fig2:extinction\] shows the extinction cross section predicted by our point scattering model of a single split ring for different incidence conditions. In Fig. \[Fig2:extinction\](a), the incident wave vector is swept from the $z$-direction to the $y$-direction, while maintaining $x-$ polarized light. For this set of incidence conditions the resulting extinction cross sections only depend on $\alpha_{EE}$ and $\alpha_{HH}$, and are entirely independent of the off-diagonal coupling strength $\alpha_{EH}$. The cross section increases from $\sigma_{\mathrm{ext}}= 4 \pi k\mathrm{Im}\alpha_{EE}$ as the split ring is only driven by the incident $E_x$ field when light is incident along $z$, to $\sigma_{\mathrm{ext}}= 4 \pi
k(\mathrm{Im}\alpha_{EE}+ \mathrm{Im}\alpha_{HH})$, as the split ring is driven by the incident $E_x$ field plus the incident $H_z$ field. When the wavevector is rotated to the the $x$-axis, the 