Effect of retardation on localized surface plasmon resonances in a metallic nanorod

The localized surface plasmon resonances in a metallic nanorod are determined using the "electrostatic approximation" and by a finite-difference time-domain numerical solution of Maxwell's equations. The difference between the two methods is related to the effects of re-radiation, or retardation, which is not included in the electrostatic formulation. It is shown that high-order modes in a metallic nanorod can be modeled by both methods, even beyond the point where the electrostatic method is supposed to fail. This suggests that the simple analytical expressions derived from the electrostatic approximation are valid for describing the large range of resonant modes associated with metallic nanoparticles, including dark modes.