Skip to main content
SpringerLink
Log in

Mathematical Problems of Radiation and Propagation in Electromagnetic Waveguides

  • ELECTRODYNAMICS AND WAVE PROPAGATION
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract—

The radiation problem in a regular waveguide with inhomogeneous filling and the scattering problem in a hollow irregular waveguide are considered. The completeness of the system of waveguide root vectors is proven. The radiation conditions are set and the solvability of the excitation problem is established. The dispersion curves of the waveguide with anisotropic filling are analyzed. The singular points of dispersion curves are considered. The excitation problem for a waveguide in a resonance regimen is investigated. The embedding theorems for the vector fields are proven. The solvability of the scattering problem in a waveguide is 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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. D. Houdras and P. Debye, Ann. Phys. (New York) 32, 465 (1910).

    Google Scholar 

  2. P. Frank and R. von Mises, Die Differential- und Integralgleichungen der Mechanik und Physik, (Vieweg, Brunswick, 1935; ONTI, Moscow, 1937).

  3. Louis de Broglie, Electromagnetic Waves in Waveguides and Hollow Resonators (OGIZ, Moscow, 1948) [in Russian].

  4. A. A. Samarskii and A. N. Tikhonov, Zh. Tekh. Fiz. 17, 1283 (1947).

    Google Scholar 

  5. A. A. Samarskii and A. N. Tikhonov, Zh. Tekh. Fiz. 17, 1431 (1947).

  6. A. A. Samarskii and A. N. Tikhonov, Zh. Tekh. Fiz. 18, 959 (1948).

    Google Scholar 

  7. A. S. Il’inskii, V. V. Kravtsov, and A. G. Sveshnikov, Mathematical Models in Electromagnetics (Vysshaya Shkola, Moscow, 1991) [in Russian].

    Google Scholar 

  8. A. G. Sveshnikov, Dokl. Akad. Nauk 73, 517 (1950).

    Google Scholar 

  9. A. G. Sveshnikov, Dokl. Akad. Nauk 80, 345 (1951).

    Google Scholar 

  10. A. G. Sveshnikov, Zh. Vychisl. Mat. Mat. Fiz. 1, 737 (1961).

    Google Scholar 

  11. A. G. Sveshnikov, Zh. Vychisl. Mat. Mat. Fiz. 3, 314 (1963).

    Google Scholar 

  12. A. G. Sveshnikov, Zh. Vychisl. Mat. Mat. Fiz. 3, 935 (1963).

    Google Scholar 

  13. A. G. Sveshnikov and A. S. Il’inskii, Zh. Vychisl. Mat. Mat. Fiz. 3, 478 (1963).

    Google Scholar 

  14. A. S. Il’inskii, Propagation of Electromagnetic Waves in Irregular Waveguides of Variable Cross Section (Mos. Gos. Uuiv., Moscow, 1970) [in Russian].

    Google Scholar 

  15. A. S. Il’inskii, Differ. Uravn. 17, 1868 (1981).

    Google Scholar 

  16. A. S. Il’inskii and G. Ya. Slepyan, Oscillations and Waves in Lossy Electrodynamic Systems (Mosk. Gos. Univ., Moscow, 1983) [in Russian].

    Google Scholar 

  17. P. E. Krasnushkin and E. I. Moiseev, Dokl. Akad. Nauk 264, 1123 (1982).

    Google Scholar 

  18. A. S. Il’inskii and A. G. Sveshnikov, Zh. Vychisl. Mat. Mat. Fiz. 8, 363 (1968).

    Google Scholar 

  19. A. N. Bogolyubov and A. G. Sveshnikov, Zh. Vychisl. Mat. Mat. Fiz. 14, 947 (1974).

    Google Scholar 

  20. A. G. Sveshnikov and A. N. Bogolyubov, Zh. Vychisl. Mat. Mat. Fiz. 19, 1496 (1979).

    MathSciNet  Google Scholar 

  21. G. I. Veselov and P. E. Krasnushkin, Dokl. Akad. Nauk 260, 576 (1981).

    Google Scholar 

  22. L. A. Vainshtein, Electromagnetic Waves, 2nd ed. (Radio i Svyaz’, Moscow, 1988) [in Russian].

    Google Scholar 

  23. B. Z. Katsenelenbaum, Theory of Irregular Waveguides with Slowly Varying Parameters (Akad. Nauk SSSR, Moscow, 1961) [in Russian].

    Google Scholar 

  24. B. Z. Katsenelenbaum, High-Frequency Electrodynamics (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  25. Yu. G. Smirnov, Differ. Uravn. 27, 140 (1991).

    Google Scholar 

  26. Yu. G. Smirnov, Dokl. Akad. Nauk SSSR 297, 829 (1987).

    Google Scholar 

  27. Yu. G. Smirnov, Dokl. Akad. Nauk SSSR 297, 829 (1987).

    Google Scholar 

  28. A. L. Delitsyn, Differ. Uravn. 36, 629 (2000).

    Google Scholar 

  29. A. L. Delitsyn, Izv. Ross. Akad. Nauk, Ser. Mat. 71, 61 (2007).

    Google Scholar 

  30. A. L. Delitsyn, Zh. Vychisl. Mat. Mat. Fiz. 51, 1883 (2011).

    MathSciNet  Google Scholar 

  31. A. L. Delitsyn, Differ. Uravn. 41, 375 (2005).

    MathSciNet  Google Scholar 

  32. V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms (Springer-Verlag, Berlin, 1986).

    Book  MATH  Google Scholar 

  33. I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Non-Self-Adjoint Operators (Nauka, Moscow, 1965).

    Google Scholar 

  34. M. V. Keldysh, Usp. Mat. Nauk. 26 (4), 15 (1971).

    Google Scholar 

  35. G. I. Veselov and S. B. Raevskii, Layered Metal–Dielectric Waveguides (Radio i Svyaz’, Moscow, 1988) [in Russian].

    Google Scholar 

  36. G. I. Veselov and P. E. Krasnushkin, Dokl. Akad. Nauk 260, 576 (1981).

    Google Scholar 

  37. A. L. Delitsyn, Zh. Vychisl. Mat. Mat. Fiz. 58, 1189 (2018).

    MathSciNet  Google Scholar 

  38. A. Ramm and P. Werner, J. Reine Angew. Mat. 360, 19 (1985).

    Google Scholar 

  39. A. L. Delitsyn, Zh. Vychisl. Mat. Mat. Fiz. 56, 2086 (2016).

    MathSciNet  Google Scholar 

  40. P. A. Raviart and J. M. Thomas, Mathematical Aspects of Finite Element Methods in Lecture Notes in Mathematics, Ed. A. Dold, B. Eckman (Springer, Berlin, 1976), Vol. 66, p. 292.

    Google Scholar 

  41. J. C. Nedelec, Numer. Math. 35, 315 (1980).

    Article  MathSciNet  Google Scholar 

  42. J. C. Nedelec, Numer. Math. 50, 57 (1986).

    Article  MathSciNet  Google Scholar 

  43. A. Bermudes and D. G. Pedreira, Numer. Math. 61, 39 (1992).

    Article  MathSciNet  Google Scholar 

  44. A. L. Delitsyn, Zh. Vychisl. Mat. Mat. Fiz. 39, 315 (1999).

    MathSciNet  Google Scholar 

  45. J. Descloux, N. Nassif, and J. Rappaz, Num. Anal., No. 2, 97 (1978).

  46. O. A. Ladyzhenskaya, Boundary Problems of Mathematical Physics (Nauka, Moscow, 1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, 127051 , Moscow, Russia

    A. L. Delitsyn

  2. National Research University Higher School of Economics, 125319, Moscow, Russia

    A. L. Delitsyn

Authors
  1. A. L. Delitsyn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. L. Delitsyn.

Additional information

Translated by E. Oborin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Delitsyn, A.L. Mathematical Problems of Radiation and Propagation in Electromagnetic Waveguides. J. Commun. Technol. Electron. 64, 1323–1338 (2019). https://doi.org/10.1134/S1064226919110068

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226919110068

Search

Navigation