Evaluation of the dipole interaction of a pair of metal particles in the region of the plasmon resonance

We consider the electric field of an induced dipole moment of a single small particle characterized by the absence of frequency dispersion of the permittivity and the field of a metal particle, which has frequency dispersion and is described in the free electron approximation taking into account the size effects of restriction of the electron free path. The influence of the induced field on the optical properties of a system of small particles is analyzed. It is shown that, for an ensemble of particles without frequency dispersion, the effective medium theory can be used up to concentrations corresponding to filling factors ƒ ≤ 0.52. In the case of metal particles, with frequency dispersion of dielectric functions and, especially, for the frequency range of the plasmon resonance, this theory can be used only for concentrations not exceeding the threshold ƒ ≈ 0.01.