# Spectral theory of electromagnetic scattering by a coated sphere

## TL;DR

This paper develops a spectral theory for electromagnetic scattering by coated spheres, enabling tailored control of scattering properties through permittivity design, with applications in plasmonics and photonics.

## Contribution

It introduces a mode expansion framework independent of coating permittivity, simplifying the analysis and design of scattering characteristics.

## Key findings

- Designed coating permittivity to eliminate backscattering.
- Achieved control over specific multipolar scattering orders.
- Maximized electric field at targeted spatial points.

## Abstract

In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of modes that are independent of the permittivity of the coating, while the expansion coefficients are simple rational functions of the permittivity. The theory we develop represents both a framework for the analysis of plasmonic and photonic modes and a straightforward methodology to design the permittivity of the coating to pursue a prescribed tailoring of the scattered field. To illustrate the practical implications of this method, we design the permittivity of the coating to zero either the backscattering or a prescribed multipolar order of the scattered field, and to maximize an electric field component in a given point of space.