On some behavioral peculiarities of magnetic type eigenmodes of a spherical particle with arbitrarily valued material parameters

Subject and Purpose. The spectral characteristics (eigenfrequencies, eigenmodes, Q-factors) of a spherical particle with arbitrarily valued permittivity and permeability are considered to take a further look into some important features of their behavior. The real and imaginary parts of the material parameters of the particle can be both positive and negative. The emphasis is on magnetic type modes.

Methods and Methodology. The spectral problem is solved using the electromagnetic field expansion in vector spherical wave functions.

Results. The first eigenfrequencies of a spherical particle have been calculated depending on its relative permittivity e ₁ and relative permeability m ₁ whose real and imaginary parts can take both positive and negative values. The eigenmodes split into two, internal and external, eigenmode families. The internal eigenmodes bear an independent, associated with eigenmode structure labeling in each quadrant of the plane (m ₁ , e ₁). The external eigenmodes, on the contrary, have a uniform labeling throughout the whole (m ₁ , e ₁) plane and bear a structural resemblance to surface plasmon oscillations distributed in the vicinity of the particle surface or outside it. In the first quadrant of the plane (m ₁ , e ₁), the external eigenmodes repeatedly interact with the internal eigenmodes, leading to either mode hybridization or mode type exchange. In the third quadrant of the plane (m ₁ , e ₁), the external eigenmodes can interact with one another. The anomalous behavior of the spectral characteristics of a spherical particle corresponds to the already known phenomenon of wave mode coupling described in the scientific literature well enough.

Conclusion. The performed study has revealed some new behavioral patterns as to the spectral characteristics of a spherical particle with arbitrarily valued permittivity and permeability