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This paper presents Mie scattering theory as compared to rigorous electromagnetic theory of free oscillations in magnetic and electric plasmon spheres. It is shown that the maxima of Mie scattering and absorption spectra well correspond to resonance frequencies of plasmon modes occurring in dielectric and magnetic spheres, similarly as it takes place for ordinary dielectric resonator modes. Mie theory is well applicable to determine resonance frequencies and scattering parameters of spherical plasmons. However, this theory cannot be applied to determine intrinsic properties of modes induced in the object by the incident plane wave, like quality factors. On the contrary, rigorous electromagnetic theory of free oscillations allows one to determine the complex resonance frequency of each mode that can occur in a given object, and the corresponding quality factor accounting for various kind of losses, including medium and radiation losses. The advantage of the free oscillations theory, as shown in this paper, is in the determination of the quality factors of modes occurring in magnetic plasmon spheres made of a strongly dispersive magnetic medium. Graphical Abstract

Mode spectra of magnetic and dielectric plasmon spheres obtained from Mie scattering and free oscillation theories