Studying plasmonic resonance modes of hierarchical self-assembled meta-atoms based on their transfer matrix

Hierarchical self-assembled meta-atoms are made from a larger number of suitably arranged metallic nanoparticles. They constitute the basic building blocks for isotropic metamaterials. The properties of these metaatoms are usually studied upon illumination with a plane wave and by analyzing the multipolar composition of the scattered field. This, however, does not always provide full information. The coupling between multiple metaatoms is usually not considered, and a physical understanding for the cause of the response is often incomplete. Here we overcome these limitations by performing a spectral eigenvalue analysis of the transfer matrix of isolated and coupled self-assembled meta-atoms. Emphasis is put on using a transfer-matrix formulation in either a local or a global coordinate frame. We show that for the magnetic resonance, coupling to nearest neighbors is weak, suggesting the possibility to preserve the response of the isolated meta-atom upon tight packaging in a metamaterial.