Analytical Modeling of Coated Plasmonic Particles

Biomedical applications of plasmonic nanoparticle (NP) conjugates need control over their optical properties modulated by surface coating with stabilizing or targeting molecules often attached to or embedded in the secondary functionalization shell, such as silica. Although current numerical techniques can simulate the plasmonic response of such structures, it is desirable in practice to have analytical models based on simple physical ideas that can be implemented without considerable computer resources. Here, we present two efficient analytical methods based on improved electrostatic approximation (IEA) and modal expansion method (MEM) combined with the dipole equivalence method. The last approach avoids additional electromagnetic simulations and provides a direct bridge between analytical IEA and MEM models for bare particles and those with multilayer shells. As simple as the original IEA and MEM, the developed analytical extensions provide accurate extinction and scattering spectra for coated particles compared to exact calculations by separation of variable method and COMSOL. The possibility and accuracy of analytical models are illustrated by extensive simulations for prolate and oblate gold and silver NPs with a maximal size of up to 200 nm, aspect ratio from 2 to 6, and 3–30 nm dielectric coating.