Optical Phenomena in Spherical Metallic Nanoparticles. Nonlocal Theory

An influence of the nonlocal phenomena on the plasmonic properties of the metallic nanoparticles is investigated in the work. The mathematical model for determining the frequency dependences of such optical characteristics as dielectric function, polarizability, absorption and scattering cross-sections is proposed. The relation for the size dependence of the frequencies of the nonlocal multipole surface plasmonic resonances is obtained. It is shown that in the infrared frequency region the difference between the Drude theory and the nonlocal theory is very significant, while in the optical region of the spectrum the results of the calculations of the corresponding dielectric functions are practically identical. It is found that in both Drude and nonlocal theories, the change in the size of the nanoparticles affects only the width of the spectral line and not the magnitude of the frequency of nonlocal (or local) surface plasmonic resonances. The results of the calculations indicate the presence of the blue shift of the maxima of the imaginary part of the nonlocal polarizability with increasing order of multipolarity and the maximum of the imaginary part of the nonlocal dipole polarizability with respect to the maximum of the imaginary part of the local polarizability. It is shown that for the relatively small nanoparticles the maximum absorption and scattering cross-sections are of the same order, whereas with the increasing radius the scattering processes begin to dominate over the absorption processes. The complete analogy in the behavior of the frequency dependence curves of the imaginary part of the polarizability and absorption cross-section is demonstrated, which is explained by the linear coupling of these optical characteristics. The significant influence on the character of the frequency dependences of the absorption cross-section of both the material properties of the nanoparticles and the properties of the surrounding dielectric was established. It is shown that the behavior of the surface plasmonic resonance frequencies in Drude theory and nonlocal theory has both similarities and differences. In particular, with increasing multipolarity both theories predict the increase of this frequency. At the same time at the same multipolarity the resonance frequency according to the Drude theory does not depend on the particle radius, whereas according to the nonlocal theory the resonance frequency decreases with increasing of the particle radius.