On the problem of normal modes of a waveguide

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Various approaches to calculating normal modes of a closed waveguide are considered. A review of the literature was given, a comparison of the two formulations of this problem was made. It is shown that using a self-adjoint formulation of the problem of normal waveguide modes eliminates the occurrence of artifacts associated with the appearance of a small imaginary additive to the eigenvalues. The implementation of this approach for a rectangular waveguide with rectangular inserts in the Sage computer algebra system is presented and tested on hybrid modes of layered waveguides. The tests showed that our program copes well with calculating the points of the dispersion curve corresponding to the hybrid modes of the waveguide.

作者简介

Oleg Kroytor

RUDN University

Email: kroytor_ok@pfur.ru
ORCID iD: 0000-0002-5691-7331
Scopus 作者 ID: 57212346588
Researcher ID: GLS-3788-2022

Candidate of Physical and Mathematical Sciences, Employee of the department of Mathematical Modeling and Artificial Intelligence

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Mikhail Malykh

RUDN University; Joint Institute for Nuclear Research

Email: malykh_md@pfur.ru
ORCID iD: 0000-0001-6541-6603
Scopus 作者 ID: 6602318510
Researcher ID: P-8123-2016

Doctor of Physical and Mathematical Sciences, Head of the department of Mathematical Modeling and Artificial Intelligence of RUDN University, research fellow of MLIT JINR

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 6 Joliot-Curie St, Dubna, 141980, Russian Federation

Leonid Sevastianov

RUDN University; Joint Institute for Nuclear Research

编辑信件的主要联系方式.
Email: sevastianov_la@pfur.ru
ORCID iD: 0000-0002-1856-4643
Scopus 作者 ID: 8783969400
Researcher ID: B-8497-2016

Doctor of Physical and Mathematical Sciences, Professor of the department of Mathematical Modeling and Artificial Intelligence of RUDN University, research fellow of LTPh JINR

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 6 Joliot-Curie St, Dubna, 141980, Russian Federation

参考

  1. Mogilevskii, I. E. & Sveshnikov, A. G. Mathematical problems of diffraction theory Russian. In Russian (MSU, Moscow, 2010).
  2. Karliner, M. M. Microwave electrodynamics: Course of lectures (NSU, Novosibirsk, 2006).
  3. Samarskii, A. A. & Tikhonov, A. N. Russian. To the theory of excitation of radiowaveguides in Selected works of A. A. Samarsky In Russian. Chap. 1 (Maks Press, Moscow, 2003).
  4. Chow, V. T. Handbook of Applied Hydrology, McGraw-Hill, New York, 1964. (1964).
  5. Tikhonov, A. N. & Samarskii, A. A. Equations of mathematical physics Russian (Dover Publications, New York, 1990).
  6. Bermfidez, A. & Pedreira, D. G. Mathematical analysis of a finite element method without spurious solutions for computation of dielectric waveguides. Numer. Math. 61, 39-57 (1992).
  7. Lezar, E. & Davidson, D. B. Electromagnetic waveguide analysis in Automated solution of differential equations by the finite element method 629-643 (The FEniCS Project, 2011).
  8. Novoselov, N. A., Raevsky, S. B. & Titarenko, A. A. Calculation of symmetrical wave propagation characteristics of a circular waveguide with radially inhomogeneous dielectric filling. Russian. Proceedings of the Nizhny Novgorod State Technical University named after R.E. Alekseev. In Russian, 30-38 (2010).
  9. Delitsyn, A. L. On the completeness of the system of eigenvectors of electromagnetic waveguides. Comput. Math. and Math. Phys. 51, 1771-1776 (2011).
  10. Delitsyn, A. L. & Kruglov, S. I. Mixed finite elements used to analyze the real and complex modes of cylindrical waveguides. Russian. Moscow University Physics Bulletin 66, 546 (2011).
  11. Delitsyn, A. L. & Kruglov, S. I. Application of mixed finite element method for calculation of modes of cylindrical waveguides with variable refractive index. Journal of Radio Electronics. In Russian, 1-28 (2012).
  12. Keldysh, M. V. Russian. On the completeness of the eigenfunctions of some classes of non-self-adjoint linear operators in Selected writings. Mathematics. In Russian. Chap. 31 (Nauka, Moscow, 1985).
  13. Gohberg, I. & Krein, M. Introduction to the Theory of Linear Nonselfadjoint Operators (American Mathematical Soc., Providence, Rhode Island, 1969).
  14. Markus, A. S. Introduction to the Spectral Theory of Polynomial Operator Pencils (American Mathematical Society, Providence, R.I., 1988).
  15. Kopachevsky, N. D. Spectral Theory of Operator Pencils: Special Course of Lectures (Forma, Simferopol’, 2009).
  16. Smirnov, Y. G. Completeness of the system of eigen- and associated waves of a partially filled waveguide with an irregular boundary. Dokl. Math. 32, 963-964 (1987).
  17. Smirnov, Y. G. The application of the operator pencil method in a problem concerning the natural waves of a partially filled wave guide. Dokl. Math. 35, 430-431 (1990).
  18. Smirnov, Y. G. The method of operator pencils in boundary value problems of conjugation for a system of elliptic equations. Differ. Equ. 27, 112-118 (1991).
  19. Shestopalov, Y. & Smirnov, Y. Eigenwaves in waveguides with dielectric inclusions: spectrum. Applicable Analysis 93, 408-427. doi: 10.1080/00036811.2013.778980 (2014).
  20. Bogolyubov, A. N., Delitsyn, A. L. & Sveshnikov, A. G. On the completeness of the set of eigenand associated functions of a waveguide. Comput. Math. Math. Phys. 38, 1815-1823 (1998).
  21. Bogolyubov, A. N., Delitsyn, A. L. & Sveshnikov, A. G. On the problem of excitation of a waveguide filled with an inhomogeneous medium. Comput. Math. Math. Phys. 39, 1794-1813 (1999).
  22. Delitsyn, A. L. An approach to the completeness of normal waves in a waveguide with magnetodielectric filling. Differ. Equ. 36, 695-700 (2000).
  23. Bogolyubov, A. N., Delitsyn, A. L., Malykh, M. D. & Sveshnikov, A. G. The basis property of root vectors for the radio waveguide. Moscow University Physics Bulletin 55, 22 (2000).
  24. Bogolyubov, A. N., Delitsyn, A. L. & Malykh, M. D. On the root vectors of a cylindrical waveguide. Comput. Math. Math. Phys. 41, 121-124 (2001).
  25. Kroytor, O. K. & Malykh, M. D. On a dispersion curve of a waveguide filled with inhomogeneous substance. Discrete and Continuous Models and Applied Computational Science 30, 330-341 (2022).

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