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In this work the polarizability of a subwavelength core-shell sphere isconsidered, where the shell exhibits a radially inhomogeneous permittivityprofile. A mathematical treatment of the elec- trostatic polarizability isformulated in terms of the scattering potentials and the correspondingscattering amplitudes. As a result, a generalized expression of thepolarizability is presented as a function of the radial inhomogeneity function.The extracted general model is applied for two particular cases, i.e., thewell-known power-law profile and a new class of permittivity profiles thatexhibit exponential radial dependence. The proposed analysis quantifies in asimple manner the inhomogeneity effects, allowing the direct implementation ofnaturally or artificially occurring permittivity inhomogeneities for a widerange of applications within and beyond the metamaterial paradigm. Furthermore,the described analysis open avenues towards the phenomenological andfirst-principles modeling of the electrodynamic scattering effects forgraded-index plasmonic par- ticles at the nanoscale. Finally, such descriptioncan be readily used either for the benchmarking of novel computational methodsincorporating inhomogeneous materials or for inverse scattering purposes.

Polarizability of Radially Inhomogeneous Subwavelength Spheres