Resonant Characteristics of Subwavelength Spherical Scatterers with Radial Inhomogeneities

Scattering by a homogeneous small sphere is a classical canonical problem, that can be found in the heart of many physical models [1]. The problem of a subwalength homogenous sphere can be rigorously analyzed through the corresponding electrostatic scattering point, for homogeneous or piecewise homogeneous spheres [1]. In this work the electrostatic scattering problem by a radially inhomogeneous sphere is considered. Specifically, it is shown that the analytical solution obtained for a graded index sphere with power law permittivity profile (rⁿ) [2] can be expanded for a whole new class of exponential profiles exp((ar)ⁿ). The scattering features are extracted and connected with the polarizability of a solid sphere. As a result, a generalization of the polarizability is introduced, encompassing the particular inhomogeneities to a simple model, and the impact of such inhomogeneities to the overall scattering spectrum is exposed.

[1] C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles. John Wiley & Sons, 2008.
[3] L. Dong, G. Gu, and K. Yu, “First-principles approach to dielectric response of graded spherical particles,” Phys. Rev. B, vol. 67, no. 22, p. 224205, Jun. 2003.