# Magnetoquasistatic Resonances of Small Dielectric Objects

## TL;DR

This paper explores magnetoquasistatic resonances in small high-permittivity dielectric objects, revealing their physical properties and providing a simplified analysis method for designing high-index resonators.

## Contribution

It introduces a new understanding of magnetoquasistatic resonances in arbitrary-shaped dielectrics using Maxwell's equations approximation.

## Key findings

- Resonances occur at specific permittivities and frequencies linked to eigenvalues of a magnetostatic operator.
- Resonances involve interplay between dielectric polarization energy and magnetic field energy.
- The approach simplifies the analysis and design of high-permittivity dielectric resonators.

## Abstract

A small dielectric object with positive permittivity may resonate when the free-space wavelength is large in comparison with the object dimensions if the permittivity is sufficiently high. We show that these resonances are described by the magnetoquasistatic approximation of the Maxwell's equations in which the normal component of the displacement current density field vanishes on the surface of the particle. They are associated to values of permittivities and frequencies for which source-free quasistatic magnetic fields exist, which are connected to the eigenvalues of a magnetostatic integral operator. We present the general physical properties of magnetoquasistatic resonances in dielectrics with arbitrary shape. They arise from the interplay between the polarization energy stored in the dielectric and the energy stored in the magnetic field. Our findings improve the understanding of resonances in high-permittivity dielectric objects and provide a powerful tool that greatly simplifies the analysis and design of high index resonators.