is now evident, that we can simply apply the scalar recipe to each eigenpolarizability separately. An alternative notation for this method is: $$\boldsymbol{\alpha}^{-1}=\boldsymbol{\alpha}_0^{-1}-\frac{2}{3}k^3i\mathbb{I}
\label{Eq:TensorRadiationDamping}$$ We note that this expression, which is identical to Eq. (\[Eq:scalarRadiationDamping\]) upon replacement of $1/(\cdot)$ by matrix inversion, provides a unique relation to translate a magneto-/electrostatic polarizability tensor $\boldsymbol{\alpha}_0$ derived from RLC circuit theory, to the corresponding electrodynamic polarizability that satisfies the optical theorem. We can hence consistently assess how intuitive ideas based on a microscopic RLC circuit model for electrostatic dipoles lead to quantitative predictions for extinction, scattering, as well as resonance hybridization, diffraction and super/sub radiant damping in coupled systems, such as periodic systems, or arbitrary finite clusters.

Polarizability of split ring resonators\[section:singleSRR\]
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![image](SersicetalFig1.eps){width="\textwidth"}

Symmetry
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As an example of our general theory we consider the specific example of split ring resonators. The electrostatic polarizability of split ring resonators was discussed for instance by Garcìa-Garcìa et al [@Garcia-Garcia05]. We consider the LC resonance of an infinitely thin split ring in the $xy$ plane, with split oriented along the $x$ axis, as shown in Fig. \[Fig1:radpats\](a). Incident electric field polarized along the $x$ direction gives rise to an electric dipole $\bm{p}=(\alpha_{EE}^{xx}E_x,0,0)$ oriented along the 