Assessing the electromagnetic interaction of silver nanoparticles in the optical band

The object of the study is the resonant effects of electromagnetic wave scattering by two silver nanoparticles in the optical range. The study considered the problem of the influence of the electromagnetic interaction between nanoparticles on the characteristics of light scattering and absorption by a model of two silver nanoparticles and determining the limit when this interaction can be neglected. Methods for calculating the scattering characteristics by this model are proposed. The methods are based on solving the system of surface integral Muller equations for a set of nanoparticles. The values of the total scattering, attenuation and absorption cross sections for a model of two ellipsoidal nanoparticles of different sizes with variable distances between them on two orthogonal polarizations are obtained. The first model consists of two nanoparticles with semi-axes of 75 × 75 × 25 nm, the second – 100 × 100 × 20 nm. The calculations were performed taking into account the electromagnetic interaction between nanoparticles when determining the current densities on their surfaces and without taking into account the specified interaction. As a numerical measure of the degree of electromagnetic interaction, the relative error in the calculation of the scattering characteristics of the models when taking into account the interaction and when neglecting it was used. The estimation of the limiting distances at which the interaction between nanoparticles can be neglected with a given accuracy was carried out. For an error in the calculation of scattering cross sections of less than 5% at a wavelength of λ = 300 nm, the limiting distance is from 0.4λ to 3λ (from 120 nm to 900 nm) depending on the polarization. The use of the approximate method at these distances while maintaining accuracy allowed to reduce the dimensionality of the system of integral equations by a factor of 4, which significantly reduced the computational costs. The proposed method can be generalized to nanoparticles of different sizes and from other noble metals.