Polarizability of Radially Inhomogeneous Subwavelength Spheres

In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. A mathematical treatment of the elec- trostatic polarizability is formulated in terms of the scattering potentials and the corresponding scattering amplitudes. As a result, a generalized expression of the polarizability is presented as a function of the radial inhomogeneity function. The extracted general model is applied for two particular cases, i.e., the well-known power-law profile and a new class of permittivity profiles that exhibit exponential radial dependence. The proposed analysis quantifies in a simple manner the inhomogeneity effects, allowing the direct implementation of naturally or artificially occurring permittivity inhomogeneities for a wide range of applications within and beyond the metamaterial paradigm. Furthermore, the described analysis open avenues towards the phenomenological and first-principles modeling of the electrodynamic scattering effects for graded-index plasmonic par- ticles at the nanoscale. Finally, such description can be readily used either for the benchmarking of novel computational methods incorporating inhomogeneous materials or for inverse scattering purposes.