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 especially, 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 emphasize the unusual properties of the magnetic scatters, which could be important in some applications.

An exact expression is derived for the time-averaged electromagnetic energy within a magnetodielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave. Both the spherical shell and core are considered to be dispersive and lossy, with a realistic dispersion relation of an isotropic split-ring resonator metamaterial. We obtain analytical expressions for the stored electromagnetic energies inside the core and the shell separately and calculate their contribution to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: the dielectric shell and dispersive metamaterial core, and vice-versa. An explicit relation between the stored energy and the optical absorption efficiency is also obtained. We show that the stored electromagnetic energy is an observable sensitive to field interferences responsible for the Fano effect. This result, together with the fact that the Fano effect is more likely to occur in metamaterials with negative refraction, suggest that our findings may be explored in applications.

We investigate light scattering by coated spheres composed of a dispersive plasmonic core and a dielectric shell. By writing the absorption cross-section in terms of the internal electromagnetic fields, we demonstrate it is an observable sensitive to interferences that ultimately lead to the Fano effect. Specially, we show that unconventional Fano resonances, recently discovered for homogeneous spheres with large dielectric permittivities, can also occur for metallic spheres coated with single dielectric layers. These resonances arise from the interference between two electromagnetic modes with the same multipole moment inside the shell and not from interactions between various plasmon modes of different layers of the particle. In contrast to the case of homogeneous spheres, unconventional Fano resonances in coated spheres exist even in the Rayleigh limit. These resonances can induce an off-resonance field enhancement, which is approximately one order of magnitude larger than the one achieved with conventional Fano resonances. We find that unconventional and conventional Fano resonances can occur at the same input frequency provided the dispersive core has a negative refraction index. This leads to an optimal field enhancement inside the particle, a result that could be useful for potential applications in plasmonics.

We analytically study the spontaneous emission of a single optical dipole emitter in the vicinity of a plasmonic nanoshell, based on the Lorenz-Mie theory. We show that the fluorescence enhancement due to the coupling between optical emitter and sphere can be tuned by the thickness ratio of the core-shell nanosphere and by the distance between the quantum emitter and its surface. In particular, we demonstrate that both the enhancement and quenching of the fluorescence intensity are associated with plasmonic Fano resonances induced by near-and far-field interactions. These Fano resonances have asymmetry parameters whose signs depend on the orientation of the dipole with respect to the spherical nanoshell. We also show that if the atomic dipole is oriented tangentially to the nanoshell, the interaction exhibits saddle points in the near-field energy flow. This results in a Lorentzian fluorescence enhancement response in the near field and a Fano lineshape in the far field. The signatures of this interaction may have interesting applications for sensing the presence and the orientation of optical emitters in close proximity to plasmonic nanoshells.

We analytically calculate the time-averaged electromagnetic energy stored inside a nondispersive magnetic isotropic cylinder that is obliquely irradiated by an electromagnetic plane wave. An expression for the opticalabsorption efficiency in terms of the magnetic internal coefficients is also obtained. In the low absorption limit, we derive a relation between the normalized internal energy and the optical-absorption efficiency that is not affected by the magnetism and the incidence angle. This relation, indeed, seems to be independent of the shape of the scatterer. This universal aspect of the internal energy is connected to the transport velocity and consequently to the diffusion coefficient in the multiple scattering regime. Magnetism favors high internal energy for low size parameter cylinders, which leads to a low diffusion coefficient for electromagnetic propagation in 2D random media.