The paper studies the mechanism of localised surface plasmon resonance in metal nanoparticles incorporated into organic matrices. The physical nature of plasmon excitations as coherent oscillations of the conduction band electron gas arising from interaction with electromagnetic radiation is analysed. Unlike surface plasmon polaritons, which propagate along an extended metal-dielectric interface, localised plasmons are confined to the volume of nanoparticles and exhibit radiative properties. Research into the dispersion characteristics of surface plasmon polaritons in silver-organic and gold-organic material systems shows significant deviations from the linear dependence characteristic of free electromagnetic radiation. It is shown that plasmon modes are characterised by an increased wave vector value compared to photons of similar energy, which causes the surface excitation effect and intense spatial localisation of the optical field. The dimensional correlations of the frequency and spectral width characteristics of localised surface plasmon resonance have been analysed. Two main physical mechanisms that control the dimensional correlations of plasmon characteristics have been identified. Increase in geometric dimensions results in a shift in long-wave resonance due to the retardation effect associated with the finite speed of electromagnetic excitation for large nanoparticles with a diameter greater than 20 nm. For ultrasmall nanoparticles with a diameter of less than 20 nm, quantum size effects dominate when the linear dimensions become comparable to the free path length of electrons. This leads to an increase in the intensity of surface scattering of charge carriers and a broadening of the spectral half-width. The results obtained demonstrate that the size correlations of the resonance frequencies of surface plasmons in metal nanoparticles are controlled by a variety of competing physical processes. The contribution of these processes varies depending on the size range and specifics of the material system. Obtained results allows to enhance fundamental understanding of the mechanisms by which plasmons and photons interact in nanocomposite systems, providing a theoretical basis for the targeted design of plasmonic nanostructures with specific functional properties.
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