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In recent years, there has been increasing interest in the study of the optical properties of metallic nanostructures. This interest is primarily related to the practical application of such nanostructures in quantum optical computers, micro-and nanosensors. These applications are based on the fundamental optical effect of excitation of surface plasmons. Surface plasmons are electromagnetic excitations of electron plasma of metals at the metal-dielectric interface, which are accompanied by fluctuations in the surface charge density. The consequence of this phenomenon is surface plasmon resonance (SPR)an increase in the energy absorption cross-section of a metal nanoparticle as the incident light frequency (laser irradiation) approaches to the frequency of the nanoparticle SPR. The SPR frequency for metallic nanoparticles in a dielectric matrix  m is found. Light-excited plasmon vibrations of conduction electrons in metallic nanoparticles located in a dielectric matrix will eventually attenuate due to various relaxation processes, in particular due to interaction of the conduction electrons with the crystal lattice (electron-phonon interaction) or due to electron-electron interaction at the surface of the nanoparticles, when the average free electron path in the nanoparticles exceeds its size. It defines the natural width of SPR line. It has been shown that oscillations of the SPR line width can be observed in metallic nanoparticles with a change in the dielectric constant of the medium in which they are. The oscillations are well expressed in nanoparticles with smaller radii and disappear for nanoparticles of larger radii. The magnitude of these oscillations increases with decreasing the nanoparticle radius and increases markedly with increasing the dielectric constant of the environment.

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