An Analysis of the Quantum Effect of Nonlocality in Plasmonics Using the Discrete Sources Method

We consider the mathematical problem of electromagnetic wave scattering by a plasmonic dimer composed of noble metal nanoparticles with sizes less than tens of nanometers. To develop mathematical models, the efficient discrete sources method is used, which makes it possible to take all peculiar features of such systems into account, including the shapes of particles and the effects of spatial dispersion, which are also known as nonlocal effects. It is shown that in the case of external fields that are independent of the azimuthal harmonics, it is possible to approximate the problem solution using the system of vertical dipoles on the axis of symmetry of the particle. Based on the hybrid scheme of the discrete sources method, the problem of excitation of a dimer by the field of a point charge in uniform straight motion in a homogeneous space is first solved.