Scaling Behavior of Individual Nanoparticle Plasmon Resonances

By using experiments and an intuitive model, this study reports on the dependence of different dipole resonances in gold nanoparticles (NPs) with rectangular, elliptical, and diamond-like footprints on the length of the three principal axes and on particle geometry. The length of the two in-plane principal axes of the NPs studied is between 50 and 300 nm, while the particle height is between 10 and 50 nm. The scattering experiments reveal characteristic dependencies of the in-plane dipolar resonances on axis lengths and particle geometry. These experimental findings are discussed according to an intuitive resonance condition based on the electrostatic eigenmode method extended to include terms for retardation (dynamic depolarization) and particle curvature. Focus is laid on the dependence of the retardation term on the relevant depolarization factor, the contributions of static and dynamic depolarization to the resonance wavelength, and to a generalization of the depolarization factors that describe the static depolarization in order to account for the differences in the dipolar surface modes of NPs with different geometries. The result of these studies is a detailed description and improved understanding of the scaling behavior of individual dipolar NP plasmon resonances.