Electromagnetic energy within magnetic spheres

TL;DR

This paper provides an exact analytical expression for electromagnetic energy within magnetic spheres using Mie theory, revealing significantly larger internal energies at resonances compared to nonmagnetic particles, even at low size parameters.

Contribution

It introduces new analytical formulas for electromagnetic energy and absorption in magnetic spheres, highlighting their unique properties and potential applications.

Findings

Internal energy at resonance is much larger for magnetic spheres.

Derived exact expressions for internal energy contributions of field components.

Provided analytical formulas for absorption cross section in weak absorption regime.

Abstract

Consider that an incident plane wave is scattered by a homogeneous and isotropic magnetic sphere of finite radius. We determine, by means of the rigorous Mie theory, an exact expression for the time-averaged electromagnetic energy within this particle. For magnetic scatterers, we find that the value of the average internal energy in the resonance picks is much larger than the one associated with a scatterer with the same nonmagnetic medium properties. This result is valid even, and specially, for low size parameter values. Expressions for the contributions of the radial and angular field components to the internal energy are determined. For the analytical study of the weak absorption regime, we derive an exact expression for the absorption cross section in terms of the magnetic Mie internal coefficients. We stress that although the electromagnetic scattering by particles is a well-documented topic, almost no attention has been devoted to magnetic scatterers. Our aim is to provide some new analytical results, which can be used for magnetic particles, and empha- size the unusual properties of the magnetic scatters, which could be important in some applications.