Optical response of surface-immobilized gold nanospheres on finite-thickness gold thin films

Surface-immobilized gold nanospheres (SIGNs) on a metal surface, also known as nanoparticle-on-a-film structures, constitute an efficient plasmonic platform that can be fabricated using bottom-up processes. These structures exhibit strong localized surface plasmon resonances. Although analytical solutions for the optical response of SIGNs on metals of semi-infinite thickness have been reported, no analytical method has been proposed for SIGNs on metal films of finite thickness. In this study, we address this issue by treating the metal film and substrate as an effective medium of semi-infinite thickness. Consistency is observed between the analytical results and numerical calculations based on the finite element method. The results are further supported by experimental observations. This analytical approach requires substantially fewer computational resources and less time, enabling comprehensive calculations for a wide range of models, materials, and computational conditions. Furthermore, the calculated spectra and optical fields can be readily used to evaluate optical phenomena, such as nonlinear optical effects and surface-enhanced Raman scattering.