RADIO PHYSICS AND RADIO ASTRONOMY

Purpose: The behavior of spectral characteristics (eigenfrequencies, eigenmodes, Q-factors) of a spherical particle with the arbitrary values of permittivity and permeability is considered. The aim of this work is to study some important laws of behavior of the spectral characteristics of a particle with both positive and negative values of the real and imaginary parts of material parameters. The emphasis is made on the electric type eigenmodes.

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

Findings: The dependences of the first eigenfrequencies of a spherical particle on the relative permittivity ε₁ and relative permeability µ₁, which real and imaginary parts can take both positive and negative values, are calculated. The eigenmodes are divided into two families: internal and external eigenmodes. The internal eigenmodes in each of the quadrants of plane (µ₁, ε₁) have an independent classification based on the structure of eigenmodes. Unlike internal eigenmodes, external eigenmodes have a single classification in plane (µ₁, ε₁). By their structure, external eigenmodes have the form of surface plasmon eigenmodes, which are distributed in the vicinity of a particle surface or outside it. In the first quadrant of plane (µ₁, ε₁), they repeatedly interact with internal eigenmodes that leads either to a hybridization of eigenmodes or to an exchange of types of eigenmodes. In the third quadrant of plane (µ₁, ε₁), the external eigenmodes can interact with each other. The anomalous behavior of the spectral characteristics of a spherical particle corresponds to the phenomenon of inter-type coupling of eigenmodes, being previously known and well described in the scientific literature.

Conclusions: The results of the studies made it possible to establish new patterns of behavior of the spectral characteristics of a spherical particle with arbitrary values of its permittivity and permeability.

Key words: spherical particle, dielectric ball, metamaterial, eigenfrequencies, eigenmodes

Manuscript submitted  23.03.2020

Radio phys. radio astron. 2020, 25(2): 147-157

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