Universal Analytical Modeling of the Optical Properties for Coated Plasmonic Nanoparticles

We describe a new analytical method for coated plasmonic nanoparticles, combining the modal expansion method (MEM) with the dipole equivalence method (DEM). The universality and accuracy of our approach are demonstrated through comparisons of extinction and scattering spectra for variously shaped two-layer gold and silver nanoparticles (rods, disks, triangle prisms, bicones, and bipyramids) with dielectric coatings from 0 to 100 nm, benchmarked against numerical calculations using COMSOL. Due to its universality, the MEM + DEM approach accurately reproduces the dependence of extinction and scattering spectra on particle size, shape, shell thickness, and orientation relative to the incident light polarization. We also investigate the effects of size-corrected dielectric functions for gold and silver, along with related damping mechanisms, on the spectra. As expected, size-dependent damping broadens and reduces plasmonic peaks, especially for small silver nanoparticles. Although MEM inherently does not depend on particle shape, the MEM + DEM method fails for coated bicones with sharp tips but performs satisfactorily for rounded bicones. This limitation is due to strong localization of plasmonic fields near the tips, which violates the assumption of homogeneous internal fields and the applicability of DEM. To avoid this difficulty, we introduce a factorized version of MEM that ensures accurate analytical calculations for coated sharp bicones. In summary, the MEM + DEM approach provides a simple yet accurate analytical tool for simulating various plasmonic properties of coated metal nanoparticles and for developing machine learning models.