  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.
