Two-dimensional optical binding based on graphene surface plasmon excitation

In this work, we present a detailed analysis of the optical binding force resulting from the near field scattering between dielectric nanoparticles and a graphene substrate. We pay special attention to the two-dimensional array formation for which the stability is raised owing to the multiple surface plasmon (SP) scattering. Because of the small values of the SP wavelength on graphene in comparison with those of the photon, the size of these particle arrangements falls below the diffraction limit. By using a rigorous formalism based on the electromagnetic Green theory, we calculate the binding energy potential whose depth quantifies the stability of such configurations. We find multiple configurations for a given number of nanoparticles, from which only a subset of them remains stable under thermal fluctuations. Our contribution can be valuable for understanding the formation of new optically reconfigurable polaritonic materials.