Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells

This work aims to provide simple and accurate closed-form approximations to predict the scattering and absorption spectra of metallic nanospheres and nanoshells supporting localised surface plasmon resonances. Particular attention is given to the validity and accuracy of these expressions in the range of nanoparticle sizes relevant to plasmonics, typically limited to around 100 nm in diameter. Using recent results on the rigorous radiative correction of electrostatic solutions, we propose a new set of long-wavelength polarizability approximations for both nanospheres and nanoshells. The improvement offered by these expressions is demonstrated with direct comparisons to other approximations previously obtained in the literature, and their absolute accuracy is tested against the exact Mie theory.