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Journal Antennas №2 for 2021 г.
Article in number:
Features of search for complex solutions of non-self-adjoint boundary value problems of electrodynamics
Type of article: scientific article
DOI: https://doi.org/10.18127/j03209601-202102-02
UDC: 621.396
Authors:

T. V. Kozhevnikova¹, V. A. Malakhov², A. S. Nechaev³, A. A. Nikitin4, A. S. Raevskij5, S. B. Raevskij6, A. Yu. Sedakov7, A. A. Titarenko8, A. S. Kuzyaev8

1–3, 5–8 Nizhny Novgorod State Technical University n.a. R.E. Alekseev (Nizhny Novgorod, Russia)

3, 4, 7–9 Branch of the Russian Federal Nuclear Center – All-Russian Research Institute of Experimental Physics «Measuring Systems Research Institute n.a. Yu.E. Sedakov» (Nizhny Novgorod, Russia)

Abstract:

The features of finding of complex solutions of the dispersion equations of guiding electrodynamic structures waves described by non-self-adjoint operators have been considered. These solutions are found using the combined numerical method for complex roots finding combining the Muller method and the phase variation method. A brief explanation of the combined search method essence has been given, and its advantages have been described.

As examples, structures with simple geometry are selected in order to avoid difficult mathematical expressions and focus on the process of complex solutions finding.

The guiding electrodynamic structures both without losses and with absorbing metal films have been considered in the approximation of the surface current method and based on its real thickness.

A new approach to evaluate the physical correctness and accuracy of the results of solving dispersion problems set in an open form for guiding structures described by non-self-adjoint operators has been shown – by the tendency to zero of the power flow of proper complex waves on average over a period through the cross section of a non-dissipative guide structure.

The formulation and the solution features of the adjoint boundary value problem for a round open dielectric waveguide have been considered. The existence possibility of the adjoint waves in this waveguide has been shown.

Pages: 7-19
For citation

Kozhevnikova T.V., Malakhov V.A., Nechaev A.S., Nikitin A.A., Raevskij A.S., Raevskij S.B., Sedakov A.Yu., Titarenko A.A., Kuzyaev A.S. Features of search for complex solutions of non-self-adjoint boundary value problems of electrodynamics. Antennas. 2021. № 2. P. 7–19. DOI: https://doi.org/10.18127/j03209601-202102-02 (in Russian)

References
  1. Veselov G.I., Raevskij S.B. Sloistye metallo-dielektricheskie volnovody. M.: Radio i svyaz'. 1988. (in Russian)
  2. Raevskij A.S., Raevskij S.B. Kompleksnye volny. M.: Radiotekhnika. 2010. (in Russian)
  3. Malakhov V.A., Raevskij A.S. Kompleksnye volny v volnovodno-shchelevoj linii i novyj podkhod k otsenke korrektnosti reshenij elektrodinamicheskikh zadach, postavlennykh v nezamknutoj forme. Radiotekhnika i elektronika. 2001. T. 46. № 5. S. 517–521. (in Russian)
  4. Muller D.E. A method for solving algebraic equations using an automatic computer. Mathematical Tables and Other Aids to Computation. 1956. № 10. P. 208–215.
  5. Britov I.E., Raevskij A.S., Raevskij S.B. Tselenapravlennyj poisk kompleksnykh voln v napravlyayushchikh elektrodinami-cheskikh strukturakh. Antenny. 2003. № 5 (72). S. 64–71. (in Russian)
  6. Privalov I.I. Vvedenie v teoriyu funktsii kompleksnogo peremennogo. M.: Nauka. 1967. (in Russian)
  7. Malakhov V.A., Raevskij A.S., Raevskij S.B. O reshenii dispersionnykh uravnenij voln napravlyayushchikh elektrodinamicheskikh struktur na kompleksnykh ploskostyakh volnovykh chisel. Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki. 2015. T. 55. № 6. S. 1028–1038. (in Russian)
  8. Veselov G.I., Egorov E.N., Alekhin Yu.N. i dr. Mikroelektronnye ustrojstva SVCh: Ucheb. posobie dlya radiotekhnicheskikh spetsial'nostej vuzov. Pod red. G.I. Veselova. M.: Vysshaya shkola. 1988. (in Russian)
  9. Malakhov V.A., Raevskij A.S. Kompleksnye volny v ekranirovannoj mikropoloskovoj linii. Radiotekhnika i elektronika. 1999. T. 44. № 1. S. 58–61. (in Russian)
  10. Shevchenko V.V. Naglyadnaya klassifikatsiya voln, napravlyaemykh regulyarnymi otkrytymi volnovodami. Radiotekhnika i elektronika. 1969. T. 14. № 10. S. 1768–1772. (in Russian)
  11. Unger Kh.G. Planarnye i volokonnye opticheskie volnovody. M.: Mir. 1988. (in Russian)
  12. Britov I.E., Raevskij A.S. O kharakteristikakh nesimmetrichnykh voln otkrytogo dielektricheskogo volnovoda vblizi kriticheskikh chastot. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 1999. T. 2. № 2. S. 33–36. (in Russian)
  13. Bakharev S.I., Vol'man V.I., Lib Yu.N. i dr. Spravochnik po raschetu i konstruirovaniyu SVCh poloskovykh ustrojstv. Pod red. V.I. Vol'mana. M.: Radio i svyaz'. 1982. (in Russian)
  14. Klimov V.V. Nanoplazmonika. M.: Fizmatlit. 2010. (in Russian)
  15. Fedyanin D.Yu., Arsenin A.V., Lejman V.G., Gladun A.D. Poverkhnostnye plazmon-polyaritony s otritsatel'noj i nulevoj gruppovymi skorostyami, rasprostranyayushchiesya po tonkim metallicheskim plenkam // Kvantovaya elektronika. 2009. T. 39. № 8. S. 745–750. (in Russian)
  16. Malakhov V.A., Popkov K.V., Raevskij A.S. Kompleksnye volny i kompleksnyj rezonans v strukturakh s metallicheskimi nanoplenkami na opticheskikh chastotakh. Trudy NGTU. 2012. № 1. S. 120–127. (in Russian)
  17. Il'inskij A.S., Slepyan G.Ya. Kolebaniya i volny v elektrodinamicheskikh sistemakh s poteryami. M.: Izd-vo MGU. 1983. (in Russian)
  18. Malakhov V.A., Nechaev A.S., Raevskij A.S., Raevskij S.B. Prisoedinennaya volna kruglogo otkrytogo dielektricheskogo volnovoda. Pis'ma v zhurnal tekhnicheskoj fiziki. 2019. T. 45. № 17. S. 35–38. (in Russian)
  19. Malakhov V.A., Raevskij A.S., Raevskij S.B. Prisoedinennye volny v kruglom dvukhslojnom ekranirovannom volnovode. Pis'ma v zhurnal tekhnicheskoj fiziki. 2011. T. 37. № 2. S. 71–79. (in Russian)
Date of receipt: 03.02.2021
Approved after review: 15.02.2021
Accepted for publication: 02.03.2021