Interactions between localized plasmons in proximal nanostructures is a well-studied phenomenon. Here we explore plasmon plasmon interactions in connected extended systems. Such systems can now be easily produced using graphene. Specifically we employ the finite element method to study such interactions in graphene nanoribbon arrays with a periodically modulated electrochemical potential or number of layers. We find a rich variation in the resulting plasmonic resonances depending on the dimensions and the electrochemical potentials (doping) of the nanoribbon segments and the involvement of transverse and longitudinal plasmon interactions. Unlike predictions based of the well-known orbital hybridization model, the energies of the resulting hybrid plasmonic resonances of the extended system can lie between the energies of the plasmons of the individual components. The results demonstrate the wide range tunability of the graphene plasmons and can help to design structures with desired spectra, which can be used to enhance optical fields in the infrared region of the electromagnetic spectrum.
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