Continual–quantum plasmonics with kinematical functions: dipolar resonance and nonlocal polarizability of simple metal made nanoparticles

In this work we formulate the theory of a mesoscopic oscillator equivalent to sp-electron excitations in simple metal made nanoparticles illuminated by incident light. The principles of continuum mechanics have been applied to maintain this goal: the primary hypotheses about the dependences of electron density function upon kinematical generalized coordinates, the stationary action principle, and the perturbation method. On their grounds, dynamic equations describing the motion of electron gas subject to alternating potentials together with the ground state equations have been derived. A methodological advantage of the latter is in the correct (qualitative and quantitative) prediction of Friedel oscillations and electron spill-out through an ion lattice with no demands to use high power computer resources as opposed to the orbital density functional theory. The dynamic equations allow studying of the nanoparticle resonant properties in an analytical form without need of numerically solving them. It has been shown with their use that the resonant frequency of the main dipolar resonance becomes the density functional of the ground state. On the basis of the dynamic equations, the theory of nonlocal polarizability has been deduced that does not impose the homogeneity (or weak inhomogeneity) constraints on the electron gas density. In this context the two following results are of importance. We manage to: (1) to demonstrate the effect of giant nonlocality of the dipole moment—its formation by the events separated by distances significantly larger than nanoparticle dimensions and temporal intervals much larger than the mean free time; (2) to derive the expression of the volumetric mode of compression-tension that is resonant on frequency of the main dipolar resonance.