Modeling Molecular Orientation Effects in Dye-Coated Nanostructures Using a Thin-Shell Approximation of Mie Theory for Radially Anisotropic Media

We here develop a thin-shell approximation of the Mie scattering problem for a spherical core–shell structure with radial anisotropy in the shell. The solution of the full anisotropic Mie theory requires the computation of Bessel functions of complex orders, which has severely limited its application to relevant problems. The proposed thin-shell approximation removes this hurdle and is of a similar complexity to the isotropic Mie theory. We show that the predictions agree with those of the full anisotropic theory for nanoparticles with a shell thickness of the order of 1 nm or less. The approximation is therefore of great relevance to calculations of the optical properties of adsorbed molecular monolayers, for example, the optical response of dye-coated nanoparticles. In this context, we also propose a simple effective medium shell model to account for the radial anisotropy of a dye layer arising from a preferred adsorption geometry, for example, in-plane or out-of-plane. We show that the model agrees with the predictions of a simple microscopic model, but provides additional insights on how the molecular orientation in the dye layer affects its interaction with the nanoparticle, for example, with plasmon resonance of metallic particles. These simple thin-shell approximation and effective medium anisotropic shell models pave the way for further theoretical understanding of orientation and anisotropic effects in the context of dye-plasmon resonance coupling.