Calculation of Surface Plasmons of Two Closely Metallic Nanospheres Using the Hydrodynamic Model

In this study, The surface plasmon excitations in a dimer structure of closely spaced metallic nanospheres with different radii are investigated using the hydrodynamic model. Initially, an expression was derived to calculate this structure's multipolar surface plasmon excitations. Subsequently, the surface plasmon excitations in the dipole approximation were examined.The surface plasmon excitations in a dimer structure of closely spaced metallic nanospheres with different radii are examined using the hydrodynamic model in this study. It has been observed that the energy of in-phase modes is lower than that of out-of-phase modes in longitudinal or transverse excitations. Furthermore, at each separation distance between the nanospheres, the energy difference between in-phase and out-of-phase longitudinal modes is greater than that of transverse modes. The results show that with an increase in the separation distance between the nanospheres, the energies of in-phase modes increase, and the energies of out-of-phase modes decrease. At large separation distances, two plasmon modes are obtained, with the higher energy mode corresponding to the smaller nanosphere and the lower energy mode corresponding to the larger nanosphere. Finally, the local limit results are presented for comparison.