Kinetic theory of surface plasmon resonance in metal nanoparticles

In recent years, interest in studying the optical properties of metallic nanostructures has grown. This interest is primarily related to the possibility of practical application of such nanostructures in quantum optical computers, micro- and nanosensors. These applications are based on the fundamental optical effect of surface plasmon excitation. The consequence of this phenomenon is surface plasmon resonance (SPR) - an increase in the cross section of energy absorption by a metal nanoparticle as the frequency of incident light (laser radiation) approaches the SPR frequency of the nanoparticle. Plasmon structures are used to improve the efficiency of thin-film SC. In such structures, metal nanoparticles can primarily act as additional scattering elements for the long-wavelength component of sunlight illuminating SC. As a collective phenomenon, SPR can be described using kinetic approaches, ie using the Boltzmann kinetic equation for the conduction electrons of metal nanoparticles. In this work, the theory of SPR based on the kinetic equation for the conduction electrons of nanoparticles is constructed. to the well-known results derived from the Drude-Sommerfeld theory. Second, the kinetic method makes it possible to study metal nanoparticles with sizes larger or ptical conductivity tensor for spheroidal metal nanoparticles. It is shown that the effect of nanoparticle asymmetry on the ratio of the components of the optical conductivity tensor differs not only smaller than the average electron free path length. The developed theory is used to calculate the oquantitatively but also qualitatively in high-frequency and low-frequency surface scattering. It was found that in metal nanoparticles in a dielectric matrix, under SPR conditions, the full width of the SPR line in a spherical metal nanoparticle depends on both the radius of the particle and the frequency of the electromagnetic (laser) radiation exciting this SPR. It is shown that oscillations of the SPR line width with a change in the dielectric constant of the medium in which they are located can be observed in metal nanoparticles. The magnitude of these oscillations is greater the smaller the size of the nanoparticle and increases significantly with increase. As the radius of the spherical nanoparticle increases, the width of the SPR line decreases significantly and prevails around a certain constant value in media with a higher value of dielectric constant.