Interacting plasmonic nanostructures beyond the quasi-static limit: A "circuit" model

The interaction between individual plasmonic nanoparticles plays a crucial role in tuning and shaping the surface plasmon resonances of a composite structure. Here, we demonstrate that the detailed character of the coupling between plasmonic structures can be captured by a modified "circuit" model. This approach is generally applicable and, as an example here, is applied to a dolmen-like nanostructure consisting of a vertically placed gold monomer slab and two horizontally placed dimer slabs. By utilizing the full-wave eigenmode expansion method (EEM), we extract the eigenmodes and eigenvalues for these constituting elements and reduce their electromagnetic interaction to the structures' mode interactions. Using the reaction concept, we further summarize the mode interactions within a "coupling" matrix. When the driving voltage source imposed by the incident light is identified, an equivalent circuit model can be constructed. Within this model, hybridization of the plasmonic modes in the constituting nanostructure elements is discussed. The proposed circuit model allows the reuse of powerful circuit analysis techniques in the context of plasmonic structures. As an example, we derive an equivalent of Thévenin's theorem in circuit theory for nanostructures. Applying the equivalent Thévenin's theorem, the well-known Fano resonance is easily explained.