Skip to main content
SpringerLink
Log in

Axisymmetric eigenmodes of magnetic type in an open resonator with spherical mirrors

  • Published:
Radiophysics and Quantum Electronics Aims and scope

Abstract

We develop a rigorous mathematical model describing axisymmetric eigenmodes of magnetic type of open resonators with spherical mirrors. On the assumption that the spectrum of complex eigenfrequencies of an open resonator exists, it is proved that this spectrum is discrete and has finite multiplicity with a single accumulation point at infinity. Theoretical analysis of the spectral characteristics of an open resonator is performed in the case where the wavelength is comparable with the resonator sizes. The limits of applicability of the well-known asymptotic models of open resonators are established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yu. A. Tuchkin and V. P. Shestopalov, Dif. Uravn., 18, No. 4, 663 (1982).

    MathSciNet  Google Scholar 

  2. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Non-Self-Adjoint Operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I. (1969).

    Google Scholar 

  3. V. P. Shestopalov, Spectral Theory and Excitation of Open Structures [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  4. L. A. Vainshtein, Electromagnetic Waves [in Russian], Sovetskoe Radio, Moscow (1957).

    Google Scholar 

  5. E. A. Ivanov, Diffraction of Electromagnetic Waves by Two Bodies [in Russian], Nauka i Tekhnika, Minsk (1968).

    Google Scholar 

  6. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, Dover, New York (1965).

    Google Scholar 

  7. Yu. V. Svishchev, Dif. Uravn., 28, No. 9, 1573 (1992).

    MathSciNet  Google Scholar 

  8. Yu. V. Svishchev and V. P. Shestopalov, Dokl. Akad. Nauk Ukrainy, No. 1, 42 (1994).

  9. Yu. V. Svishchev, “Semi-inversion method in the theory of diffraction of waves by nonclosed spherical screens,” Cand. Sci. (Phys.-Math.) Thesis, Kharkov (1989).

  10. G. M. Vainikko and O. O. Karma, Zh. Vych. Mat. Mat. Fiz., 14, No. 6, 1393 (1974).

    MathSciNet  Google Scholar 

  11. L. A. Weinstein, Open Resonators and Open Waveguides, Golem Press, Boulder, Co. (1969).

    Google Scholar 

  12. R. A. Valitov, S. F. Dyubko, V. V. Kamyshan, et al., Submillimeter Wave Techniques [in Russian], Sovetskoe Radio, Moscow (1976).

    Google Scholar 

  13. V. B. Shteinshleiger, Wave Interaction Phenomena in Electromagnetic Cavities [in Russian], Oboronizdat, Moscow (1955).

    Google Scholar 

  14. V. V. Migulin, V. I. Medvedev, E. P. Mustel’, et al., Fundamentals of the Theory of Oscillations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  15. P. N. Melezhik, A. E. Poyedinchuk, Yu. A. Tuchkin, and V. P. Shestopalov, Dokl. Akad. Nauk USSR, Ser. A, No. 8, 53 (1987).

  16. Yu. V. Svishchev, Yu. A. Tuchkin, and V. P. Shestopalov, Dokl. Akad. Nauk SSSR, 312, No. 5, 1111 (1990).

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A. Ya. Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkov, Ukraine

    Yu. V. Svishchev

Authors
  1. Yu. V. Svishchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 9, pp. 787–798, September 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Svishchev, Y.V. Axisymmetric eigenmodes of magnetic type in an open resonator with spherical mirrors. Radiophys Quantum Electron 49, 708–718 (2006). https://doi.org/10.1007/s11141-006-0105-2

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-006-0105-2

Keywords

Search

Navigation