applied sciences Article Impact of Graphene on the Polarizability of a Neighbour Nanoparticle: A Dyadic Green’s Function Study B. Amorim 1,† ID , P. A. D. Gonçalves 2,3 ID , M. I. Vasilevskiy 4 ID and N. M. R. Peres 4,*,† ID 1 Department of Physics and CeFEMA, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais, PT-1049-001 Lisboa, Portugal;
[email protected] 2 Department of Photonics Engineering and Center for Nanostructured Graphene, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark;
[email protected] 3 Center for Nano Optics, University of Southern Denmark, DK-5230 Odense, Denmark 4 Department and Centre of Physics, and QuantaLab, University of Minho, Campus of Gualtar, PT-4710-374 Braga, Portugal; mikhail@fisica.uminho.pt * Correspondence: peres@fisica.uminho.pt; Tel.: +351-253-604-334 † These authors contributed equally to this work. Received: 15 October 2017; Accepted: 9 November 2017; Published: 11 November 2017 Abstract: We discuss the renormalization of the polarizability of a nanoparticle in the presence of either: (1) a continuous graphene sheet; or (2) a plasmonic graphene grating, taking into account retardation effects. Our analysis demonstrates that the excitation of surface plasmon polaritons in graphene produces a large enhancement of the real and imaginary parts of the renormalized polarizability. We show that the imaginary part can be changed by a factor of up to 100 relative to its value in the absence of graphene. We also show that the resonance in the case of the grating is narrower than in the continuous sheet. In the case of the grating it is shown that the resonance can be tuned by changing the grating geometric parameters.