# Polarizability Expressions for Predicting Resonances in Plasmonic and Mie Scatterers

## TL;DR

This paper introduces a new modeling approach using factorization of special functions to accurately predict resonances in dielectric and metallic particles, improving upon traditional Taylor series methods.

## Contribution

It proposes a novel factorization-based model for Mie scattering coefficients that accurately predicts resonances in dielectric and plasmonic particles.

## Key findings

- Accurately predicts electric and magnetic Mie resonances in dielectric particles.
- Reproduces plasmonic resonances in metallic particles.
- Provides simple, robust tools for resonance prediction.

## Abstract

Polarizability expressions are commonly used in optics and photonics to model the light scattering by small particles. Models based on Taylor series of the scattering coefficients of the particles fail to predict the morphologic resonances hosted by dielectric particles. Here, we propose to use the factorization of the special functions appearing in the expression of the Mie scattering coefficients to derive point-like models. These models can be applied to reproduce both Mie resonances of dielectric particles and plasmonic resonances of metallic particles. They provide simple but robust tools to predict accurately the electric and magnetic Mie resonances in dielectric particles.