Interaction of eigenmodes in a spherical dielectric resonator

heading:

Organization:

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: YuSvishchov@gmail.com

https://doi.org/10.15407/rej2019.04.011

Language: russian

Abstract:

Subject and purpose. It is known that with a change in the relative dielectric constant of a ball, for some of its eigenfrequencies and the corresponding eigenoscillations, anomalous behavior is characteristic (deviation from the norm in the behavior of eigenfrequencies, the transformation of eigenoscillations). The purpose of this work is to study the laws of anomalous behavior of the spectral characteristics of a dielectric ball.

Methods and methodology. To achieve this goal, the solution of the corresponding spectral problem is given. The method of solution is based on the representation of the electromagnetic field in the form of expansion in vector spherical wave functions.

Results. The dependences of the first eigenfrequencies of the spherical dielectric resonator on the relative dielectric constant of the sphere are calculated. A method for the classification of eigenoscillations is proposed. It is based on the structure of eigen oscillations. It is shown that the anomalous behavior of the spectral characteristics of a dielectric sphere corresponds to the well-known phenomenon of intertype coupling of oscillations. The relative dielectric constant of the spere is used as the control parameter of this phenomenon. It is established that internal and external modes interact. When the dielectric constant changes, multiple mode conversion is possible.

Conclusions. The results of the conducted studies allow us to explain the nature of the anomalous behavior of the spectral characteristics of a spherical dielectric resonator.

Keywords: eigenfrequency, interaction of eigenmodes, spherical dielectric resonator

Manuscript submitted 30.05.2019
PACS: 41.20.-q
Radiofiz. elektron. 2019, 24(4): 11-19
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References:

1. Mie, G., 1908. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Ann. Phys., 25(4), ss. 377-445. DOI: https://doi.org/10.1002/andp.19083300302
2. Debye, P., 1909. Der Lichtdruck auf Kugeln von beliebigem Material. Ann. Phys., 30(1), ss. 57-136. DOI: https://doi.org/10.1002/andp.19093351103
3. Gastine, M., Courtois, L., Dorman, J., 1967. Electromagnetic resonances of free dielectric spheres. IEEE Trans. Microwave Theory Tech., 15(12), pp. 694-700. DOI: https://doi.org/10.1109/TMTT.1967.1126568
4. Wolff, I., 2017. Electromagnetic fields in spherical microwave resonators - fundamental mathematics. Research Gate, June, 43 p.
5. Wolff, I., 2018. Electromagnetic Fields in Spherical Microwave Resonators H-Modes and E-Modes in Lossless Open Dielectric Spheres. Research Gate, May, 38 p.
6. Müller, C., 1969. Foundations of the Mathematical Theory of Electromagnetic Waves. Springer-Verlag Berlin Heidelberg. DOI: https://doi.org/10.1007/978-3-662-11773-6
7. Stratton, J., 1941. Electromagnetic Theory New York: McGraw-Hill Book Company.
8. Morse, F.M., Feshbach, G., 1960. Methods of Theoretical Physics. Translated from English and ed. by S.P. Alliluev. Moscow: Inostrannaya literatura Publ. Vol. 2 (in Russian).
9. Korn, G., Korn, T., 2000. Mathematical Handbook for Scientists and Engineers. Translated from English I.G. Aramanovich. Moscow: Nauka Publ.
10. Melezhik, P.N., Poedinchuk, A.E., Tuchkin, Yu.A., Shestopalov, V.P., 1988. On the Analytical Nature of the Phenomenon of Intertype Relationship of Natural Oscillations. Dok. Akad. Nauk SSSR, 300(6), pp. 1356-1359 (in Russian).
11. Svishchov, Yu., 2011. Resonant increase of electrical-type eigenmode quality of an open resonator with a spherical dielectric insert. Radiofizyka ta elektronika, 2(16)(4), pp. 20-26 (in Russian).

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Interaction of eigenmodes in a spherical dielectric resonator