CALCULATION METHODS AT THE PLASMONIC. 1. THE MI THEORY AND QUASI-STATIC APPROXIMATION

Abstract

Plasmonics is a new direction of electronics. It operates with nanoscale objects and an optical frequency range. Therefore, direct research in the field of plasmonics is associated with complex expensive experiments. It is more advantageous to conduct a computational experiment first.

The article presents a part of the review of computational calculation methods, which are actively used in the tasks of plasmonics. The dimensional effect affects the dielectric permittivity of metals in excessive particle sizes. In order to take into account this influence of dimensional effect in the calculations, the authors use the Drude model.

The paper proposes to use the Mi theory for metallic particles close to the spherical form and the interaction between which can be neglected. To demonstrate the possibilities of such calculations, a method for determining the size distribution of metal particles in ashes over optical spectra of nanoparticles is presented. The method involves counting the spectra of a set of particles of different sizes. Each spectrum from the set has its influence on the overall spectrum. To determine the effect of particles of each size on the overall spectrum, Monte-Carlo methods were used. This method is patented by the authors. The efficiency of the method is confirmed by microscopic research.

For metal particles whose dimensions are smaller than the wavelength of light, optical spectra can be calculated using quasi-static approximation. This approximation is not limited to a spherical form, but the most applicable are the formulas presented in the article for elliptical particles. Depending on the shape of the particles, the optical spectra change. There are two maximums of plasmonic absorption for one particle. Energy splitting of spectra allows us to estimate the parameters of the form of metal particles. Such a conclusion is obtained from the comparison of the results of calculations with the data obtained by atomic force microscopy.

Key words: plasmonic, modeling, quasi-static approximation, the Mi theory, the Drude model.