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Improper resonance oscillations of dielectric sphere

Keywords:

I. P. Kovalyov – Ph.D. (Eng.), Associate Professor of Department of Theory of Circuits and Telecommunications, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. E-mail: kovalyov@nntu.nnov.ru N. I. Kuzikova – Ph.D. (Eng.), Associate Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. E-mail: physics@nntu.nnov.ru


Modes of the second type of dielectric sphere – natural oscillations with the properties that poorly depend on the dielectric permeability of sphere material are discussed in the article. Moreover the dielectric permeability can be either smaller or larger than the permeability of external environment. The equations for calculation of complex natural frequencies and mode fields are presented. The method of solution of the equations for natural frequencies is indicated. The analysis of limiting cases (ε → ∞ and ε → 0) gives the simple asymptotic solutions that allow discovering physical meaning of field sources of modes of second type. In addition the asymptotic solutions of equations for frequencies are used as initial approximations for step-by-step building of relations between natural frequencies of modes of second type and permeability ε. The fields of some modes are calculated and the figures are presented.
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