Modified Long Wavelength Approximation for the Optical Response of a Graded-Index Plasmonic Nanoparticle

The optical response of graded-index spherical metallic nanoparticles is studied in the modified long wavelength approximation with electrodynamic effects accounted for to the lowest order of the inverse of the wavelength. An effective-medium approach is adopted which leads to the conclusion that the first-order dynamical effects will enter mainly via the polarizability and not the effective dielectric function of the system. Numerical studies using various graded Drude functions show that these effects are not only significant for particles of large sizes but can also be appreciable for smaller particles with varying index profile.