A spherical harmonic transform spectral analysis of a localized surface plasmon on a gold nano shell

We perform a study of the localized surface plasmon (LSP) modes of a gold nano shell having a silica core by means of discrete dipole approximation (DDA) and spherical harmonics transform for selected wavelengths. We demonstrate an efficient solution for the near and intermediate field terms by the dyadic Green function approach and determine the optical extinction efficiency by the far field term. Using this approach, we combine the advantages of a spectral analysis along with a DDA flexibility to solve an arbitrary shaped model and demonstrate the LSP dominant mode wavelength dependency. Our approach provides a metric which may be used to quantify the effects of minor changes in the model structure, or the external dielectric environment, in optical experiments.