Quantifying Fano properties in self-assembled metamaterials

Fano resonances in metamaterials can be explained by the coupling between different modes sustained by the meta-atom. While the associated spectral features are usually quite easy to identify for top-down metamaterials, thanks to the deterministic arrangement of the meta-atom relative to the illumination, the identification of spectral features due to Fano resonances is much more challenging for bottom-up metamaterials. There, the response is spurred by the random arrangement of the meta-atoms relative to the illumination. To improve the situation, we introduce a quantity that measures the nonorthogonality of the modes sustained by the meta-atom. The measure allows us to disclose whether specific details in the spectral response emerge from Fano features or whether they are only due to the incoherent superposition of different modes. We strengthen our argumentation while discussing the multipolar decomposition of the different modes that contribute to the Fano features for a representative meta-atom.