### INTERACTION OF EIGENMODES IN A SPHERICAL PARTICLE WITH NEGATIVE VALUES OF ITS MATERIAL PARAMETERS

#### Abstract

PACS number: 41.20.-q

**Purpose:** The behavior of spectral characteristics (eigenfrequencies, natural oscillations, Q-factors) of a spherical particle whose permittivity and permeability simultaneously take on negative values (a “left-handed” sphere) is considered. It is known that in the vicinity of some values of the material parameters a transformation of natural oscillations in such a particle is observed. The purpose of this work is to study the patterns of the behavior of spectral characteristics of a particle under the conditions of transformation of natural oscillations.

**Design/Methodology/Approach:** To achieve this goal, the solution of the corresponding spectral problem is given. The solution method is based on the electromagnetic field representation in the form of expansion in vector spherical wave functions.

**Findings:** The dependences of the eigenfrequencies of a spherical particle on the permittivity and permeability, which can simultaneously take on negative values, are calculated. A method for classification of natural oscillations is proposed. It is based on the structure of natural oscillations. It is shown that the anomalous behavior of the spectral characteristics of a spherical particle corresponds to the previously known and well-described phenomenon of inter-type coupling of oscillations in the scientific literature. For the control parameter of this phenomenon, both the relative permittivity and the relative permeability of the particle can be used. It is established that the natural oscillations of a spherical particle being distributed in the vicinity of the particle surface or outside it interact. As a result, when changing the material parameters of a particle, either hybridization or exchange of oscillation types is observed.

**Conclusions:** The results of the research allowed us to establish new laws of the anomalous behavior of the spectral characteristics of a spherical particle with simultaneously negative values of its permittivity and permeability.

**Key words:** metamaterial, spherical particle, eigenfrequency, interaction

of eigenmodes

Manuscript submitted 30.05.2019**Radio phys. radio astron. 2019, 24(3): 206-217** **REFERENCES**

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