Influence of the confinement potential on the size-dependent optical response of metallic nanometric particles

In this paper, different confinement potential approaches are considered in the simulation of size effects on the optical response of silver spheres with radii at the few nanometer scale. By numerically obtaining dielectric functions from different sets of eigenenergies and eigenstates, we simulate the absorption spectrum and the field enhancement factor for nanoparticles of various sizes, within a quantum framework for both infinite and finite potentials. The simulations show significant dependence on the sphere radius of the dipolar surface plasmon resonance, as a direct consequence of energy discretization associated to the strong confinement experienced by conduction electrons in small nanospheres. Considerable reliance of the calculated optical features on the chosen wave functions and transition energies is evidenced, so that discrepancies in the plasmon resonance frequencies obtained with the three studied models reach up to above 30%. Our results are in agreement with reported measurements and shade light on the puzzling shift of the plasmon resonance in metallic nanospheres.