# Resonant Scattering Characteristics of Homogeneous Dielectric Sphere

## TL;DR

This paper revisits electromagnetic scattering by a dielectric sphere, introducing Padé approximants to analyze resonances, damping, and absorption, providing compact formulas and insights into the scattering mechanisms.

## Contribution

It introduces Padé approximants as an alternative to Mie coefficients for analyzing dielectric sphere resonances, enabling accurate predictions and physical insights.

## Key findings

- Padé approximants effectively model scattering resonances.
- Resonant linewidth is fundamentally linked to radiative damping.
- The system approach offers a circuit-inspired understanding of absorption.

## Abstract

In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for all electric and magnetic resonances of a dielectric sphere. Specifically, the Pad\'e approximants are introduced and utilized as an alternative system expansion of the Mie coefficients. Low order Pad\'e approximants can give compact and physically insightful expressions for the scattering system and the enabled dynamic mechanisms. Higher order approximants are used for predicting accurately the resonant pole spectrum. These results are summarized into general pole formulae, covering up to fifth order magnetic and forth order electric resonances of a small dielectric sphere. Additionally, the connection between the radiative damping process and the resonant linewidth is investigated. The results obtained reveal the fundamental connection of the radiative damping mechanism with the maximum width occurring for each resonance. Finally, the suggested system ansatz is used for studying the resonant absorption maximum through a circuit-inspired perspective.