[@jacksonbook]. The two eigenmodes can be selectively excited by impinging with a plane wave incident along the $z$-axis with $x$-polarized $E$-field (electric eigenmode), or with a plane wave incident along the $x$-axis with $y$-polarization ($z$-polarized $H$-field, magnetic eigenmode). The extinction cross section of a single split ring at these two incidence conditions is set by $\sigma_{\mathrm{ext}}=4 \pi k \mathrm{Im}(\alpha_{EE})$ and $\sigma_{\mathrm{ext}}=4 \pi k \mathrm{Im}(\alpha_{HH})$.

Next, we consider extinction and eigenmodes for arbitrary values of the cross coupling. It is easy to see that the extinction cross section at the two special illumination conditions (incident along $z$, $x$-polarized, respectively, incident along $x$, with $y$-polarization) remain equal to $\sigma_{ext}=4 \pi k
\mathrm{Im}(\alpha_{EE})$ and $\sigma_{ext}=4 \pi k
\mathrm{Im}(\alpha_{HH})$. However, for nonzero $\eta_C$, these incidence conditions and polarizabilities do not correspond anymore to the eigenvalues and eigenvectors of the polarizability tensor, which now have mixed magneto-electric character. In the extreme case of strongest magneto-electric coupling ($\eta_C=\sqrt{\eta_E\eta_H}$), the eigenvectors reduce to $(p_x,m_z)=(1,i\sqrt{\eta_E/\eta_H})$ and $(p_x,m_z)=(1,-i\sqrt{\eta_H/\eta_E})$. The associated far-field radiation patterns of these eigenvectors correspond to coherent superpositions of the radiation pattern of an $x$-oriented electric dipole, and a $z$-oriented magnetic dipole, with a quarter wave phase difference. Figures  \[Fig1:radpats\](d,e) show the on-resonance radiation pattern, assuming $\eta_E=0.7$, 