Thin-shell approximation of Mie theory for a thin anisotropic layer spaced away from a spherical core: Application to dye-coated nanostructures

Abstract

We here develop a thin-shell approximation of the Mie scattering problem for a spherical multilayer structure consisting of central core, a spacer layer, and a thin layer with radially anisotropic dielectric function. This thin layer can, for example, represent a uniform layer of adsorbed dyes at a fixed distance from a spherical nanoparticle, with an effective anisotropic dielectric tensor to account for dye-orientation effects. This geometry with the spacer layer was recently shown to be necessary to precisely account for all electromagnetic effects in such systems [C. Tang, B. Augui\'e, and E. C. Le Ru, Phys. Rev. B 103, 085436 (2021)]. The Mie theory solution involves Bessel functions of complex order, which are not commonly available in many numerical calculations. We show that this hurdle is overcome in the thin-shell approximation, where the solution is of similar complexity to that of isotropic Mie theory with only spherical Bessel functions of integer order. We also apply this approximation to the calculation of the optical absorption in each individual layer. Using the dye-on-metal-nanoparticle system as illustration, we show that the thin-shell predictions agree extremely well with the full solution for experimentally relevant parameters, and can therefore be used instead. This speeds up the numerical implementation and will simplify further analytical developments.