A method of effective potentials for calculating the frequency spectrum of eccentrically layered spherical cavity resonators

ABSTRACT

A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The spectrum is determined through the introduction of effective “dynamic” potentials which encode the infill inhomogeneity. For angularly symmetric cavity, regardless of its radial non-uniformity, the set of modes is shown to be a superposition of TE and TM oscillations which can be described in terms of a single scalar function independently of each other. The violation of polar symmetry in the infill dielectric properties, the azimuthal symmetry being preserved, suppresses all azimuthally non-uniform modes of TM oscillations. In the absence of angular symmetry of both electric and magnetic properties of the infill, only azimuthally uniform distribution of both TM and TE fields is expected to occur in the resonator. The method is quite efficient for computational complex algorithms for solving different spectral problems, including those for studying the chaotic properties of systems' spectra.

KEYWORDS:

• Spherical cavity
• layered resonator
• Debye potentials
• mode decoupling
• intermode scattering
• spectral chaos

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Z. E. Eremenko  http://orcid.org/0000-0002-9635-2611

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Notes on contributors

Z. E. Eremenko

Z. E. Eremenko (IEEE Senior Member’05) received the M.Sc. degree in radio technology from Kharkov Aviation Institute with honor, Kharkov, Ukraine, 1984. She received the Ph.D. and the Dr. Sc. Degrees in Physics and Mathematics at The A. Ya. Usykov Institute for Radiophysics and Electronics, The National Academy of Sciences of Ukraine, Kharkov, in 1996 and 2011, respectively. She is the head of the department of acoustic and electromagnetic spectroscopy at The A. Ya. Usykov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine. Her current research interests include wave propagation in the resonator layered structures with high loss liquids and microwave resonator modelling of chaos phenomena. She has authored more than 170 research articles.

Yu. V. Tarasov

Yu. V. Tarasov has received M.Sc. degree in theoretical physics from V. N. Karazin Kharkiv National University, Kharkiv, Ukraine, in 1972. In 1978 he received Ph.D. degree in theoretical physics from B. Verkin Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine, and in 2007 the Dr. Sc. degree in theoretical physics from the Institute for Single Crystals NAS of Ukraine, Kharkiv. Current research interests of Yu. V. Tarasov include wave and quantum particle propagation in systems with random and/or regular inhomogeneity of different kinds, in particular, resonator an waveguiding systems; chaotic phenomena in both open and closed wave/quantum billiards; propagation and scattering of surface plasmon-polariton waves.

I. N. Volovichev

I. N. Volovichev has received M.Sc. degree in physics of metals from Kharkov Polytechnical Institute, Kharkov, Ukraine, in 1992. In 1996 he received Ph.D. degree in semiconductor and dielectric physics from the Institute for Single Crystals, and in 2018 the Dr. Sc. degree in physical electronics from A. Ya. Usykov Institute for Radiophysics and Electronics, Kharkov, Ukraine. Since 2020 he is a Senior Research Fellow in A. Ya. Usykov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine. Current research interests of I. N. Volovichev include transport phenomena in semiconductors; solid state electronics; thermoelectrics and photoelectrics; computer simulations of non-linear systems; high performance computing technologies.