Damping-induced size effect in surface plasmon resonance in metallic nano-particles: Comparison of RPA microscopic model with numerical finite element simulation (COMSOL) and Mie approach

•Surface plasmon resonance in metallic nano-spheres is studied upon microscopic RPA model.•Size effect in resonance is explained by damping due to scattering and Lorentz friction.•Lorentz friction of plasmon oscillations exhibits strong irregular size effect.•RPA model is compared with finite element simulations, Mie theory and experimental data.•Modeled dielectric function for Mie/COMSOL is corrected by Lorentz friction damping.

We investigate metal nano-particle size influence on plasmon resonance within theoretical and numerical approaches and compare results with available experimental data in order to improve resolution of optical identification of metallic nano-particle size and shape. The developed microscopic approach is the quantum random phase approximation model of plasmons in metallic nano-particles including plasmon damping by electron scattering and by radiative losses (i.e., by the so-called Lorentz friction). The numerical approach is by the finite element method solution of Maxwell equations for incident planar wave in spherical (also nano-rod, spheroid) geometry upon the system COMSOL and Mie treatment, supplemented with phenomenologically modeled dielectric function of metallic nano-particle. Comparison with experimental data for light extinction in Au and Ag nano-particle colloidal solutions with different particle sizes is presented. The crucial role of the Lorentz friction in the size effect of plasmon resonance in large (e.g., 20-60 nm for Au in vacuum) metallic nanoparticles is evidenced.