# Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers

## TL;DR

This paper introduces a volume integral eigenvalue approach to compute material-independent electromagnetic modes of dielectric scatterers, enabling efficient analysis of scattering and resonances across various permittivities.

## Contribution

It presents a novel modal basis derived from an auxiliary eigenvalue problem, simplifying the calculation of scattered fields for different permittivities.

## Key findings

- Moderate number of modes suffices for accurate far-field scattering description.
- Method effectively analyzes plasmonic and photonic resonances.
- Computational efficiency improves over direct volume integral solutions for multiple permittivities.

## Abstract

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of its permittivity. This is accomplished by introducing an auxiliary eigenvalue problem, based on a volume integral operator. With this modal basis the expansion coefficients of the scattered field are simple rational functions of the permittivity of the scatterer. We show, by studying the electromagnetic scattering from a sphere and a cylinder of dimensions comparable to the incident wavelength, that only a moderate number of modes is needed to accurately describe the scattered far field. This method can be used to investigate resonant scattering phenomena, including plasmonic and photonic resonances, and to design the permittivity of the object to pursue a prescribed tailoring of the scattered field. Moreover, the presented modal expansion is computationally advantageous compared to direct solution of the volume integral equation when the scattered field has to be computed for many different values of the dielectric permittivity, given the size and shape of the dielectric body.