Optical response of supported particles

TL;DR

This paper introduces a versatile multipole expansion method to calculate the optical polarizability of supported particles, accounting for their position and substrate interactions, improving upon previous models.

Contribution

A novel multipole expansion technique allowing multipoles to move along the sphere's axis, enhancing accuracy in modeling supported particle optical responses.

Findings

Method accurately predicts polarizability across parameter space.

Interaction with substrate effectively incorporated via image multipoles.

Improves upon previous centered multipole models.

Abstract

The present work reports a general method for the calculation of t he polarizability of a truncated sphere on a substrate. A multipole ex pansion is used, where the multipoles are not necessarily localized in the center of the sphere but can freely move on the revolution axis. From the weak formulation of the boundary conditions, an infinite set of linear equations for the multipole coefficients is derived. To obta in this set, the interaction between the island and the substrate is t aken into account by the technique of image multipoles. For numerical implementation, this set is truncated at an arbitrary mu ltipole order. The accuracy of the method is jugded through the stabil ity of the truncated sphere polarizability and the the fulfilment of t he boundary conditions which are demonstrated to be satisfied in large regions of the parameter space. This method brings an improvement wit h respect to the Bedeaux's case \cite{Wind87a,Wind87b} where the multi poles are located in the center of the sphere.