fields of $\bm{p}$ and $\bm{m}$. Hence the relative phase between the induced $\bm{p}$ and $\bm{m}$ is important for the differential scattering cross section. To obtain the total scattered power, one should integrate Eq. (\[Eq:radiationpattern\]) over all solid angle. The interference term integrates to 0, as is easily seen from the fact it is an odd function of $\hat{\bm{r}}$. Therefore, Larmor’s formula immediately generalizes, and the scattering cross section equals: $$P=\frac{4\pi}{3Z}k^4\left\|
\begin{array} {c} \bm{p}\\
\bm{m}\end{array}\right\|^2.\label{Eq:tensorLarmor}$$ Equating extinction to scattering results in a condition that must be satisfied for any incident field $(\bm{E}_\mathrm{in},\bm{H}_\mathrm{in})$ $$\begin{aligned}
\mathrm{Im}\left[\left(
\begin{array} {c c}
\bm{E}_\mathrm{in} & \bm{H}_\mathrm{in}
\end{array} \right)^{*}\boldsymbol{\alpha}\left(
\begin{array} {c}
\bm{E}_\mathrm{in}\\
\bm{H}_\mathrm{in}
\end{array} \right)\right]
  = \qquad\qquad \qquad\qquad& \nonumber \\
 \qquad\qquad\qquad\qquad
\frac{2}{3}k^3\left[\left(
\begin{array} {c c}
\bm{E}_\mathrm{in} & \bm{H}_\mathrm{in}
\end{array}\right)^{*}\boldsymbol{\alpha}^{*T}\boldsymbol{\alpha}\left(
\begin{array}
{c} \bm{E}_\mathrm{in}\\
\bm{H}_\mathrm{in}
\end{array} \right)\right], &
\nonumber \\  \label{Eq:trickyOpticalTheorem}\end{aligned}$$ Due to the tensorial character of $\boldsymbol{\alpha}$ it is not immediately evident how to extract a useful optical theorem that constrains just the polarizability tensor $\boldsymbol{\alpha}$ without reference to any incident field $(\bm{E}_\mathrm{in},\bm{H}_\mathrm{in})$. In order to eliminate $(\bm{E}_\mathrm{in},\bm{H}_\mathrm{in})$ we make the assumption (verified below for split rings) that $\boldsymbol{\alpha}$ can be diagonalized. We call the eigenvectors $\bm{v}_i$, and denote the eigenvalues, which we will refer to as ‘eigenpolarizabilities’, with 