Geodesic
On solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1028-1038 
V. A. Malakhov; A. S. Raevskii; S. B. Raevskii. On solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1028-1038. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a10/
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     title = {On solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers is considered. A method combining the positive features of the Muller method and the phase variation method based on the argument principle is proposed. The implementation of the method is described. For estimating the correctness of the solutions obtained, a new approach employing the convergence to zero of the period-averaged power flux of complex waves is suggested.

[1] Veselov G. I., Raevskii S. B., Sloistye metallo-dielektricheskie volnovody, Radio i svyaz, M., 1988

[2] Raevskii S. B., “O suschestvovanii kompleksnykh voln v nekotorykh dvukhsloinykh izotropnykh strukturakh”, Radiofizika, 15:12 (1972), 1926–1931

[3] Raevskii S. B., “Kompleksnye volny v dvukhsloinom kruglom ekranirovannom volnovode”, Radiofizika, 15:1 (1972), 112–116

[4] Raevskii A. S., Raevskii S. B., Kompleksnye volny, Radiotekhnika, M., 2010

[5] Malakhov V. A., Raevskii A. S., “Kompleksnye volny v volnovodno-schelevoi linii i novyi podkhod k otsenke korrektnosti reshenii elektrodinamicheskikh zadach, postavlennykh v nezamknutoi forme”, Radiotekhnika i elektronika, 46:5 (2001), 517–521 | MR

[6] Malakhov V. A., Raevskii A. S., “Vozmozhnye podkhody k otsenke skhodimosti reshenii zadachi o raschete dispersionnykh kharakteristik ekranirovannoi mikropoloskovoi linii”, Fizika volnovykh protsessov i radiotekhnicheskie sistemy, 1:4 (1998), 13–17

[7] Malakhov V. A., Raevskii A. S., “Kompleksnye volny v ekranirovannoi mikropoloskovoi linii”, Radiotekhnika i elektronika, 44:1 (1999), 58–61 | Zbl

[8] Mikroelektronnye ustroistva SVCh, Vyssh. shk., M., 1988

[9] Avtomatizirovannoe proektirovannoe proektirovanie ustroistv SVCh, Radio i svyaz, M., 1982

[10] Queffelec P., Gelin Ph., “Influence of higher order modes on the measurements of complex permittivity and permeability of Materials using a microstrip discontinuity”, IEEE Transaction on microwave theory and techniques, 44:6 (1996), 816–824 | MR

[11] Ridders C. J. F., “A new algorithm for computing a single root of a real continuous function”, IEEE Transactions on Circuits and Systems, 26 (1979), 979 | Zbl

[12] Muller D. E., “A method for solving algebraic equations using an automatic computer”, Math. Tables and Other Aids to Computation, 10 (1956), 208–215 | MR | Zbl

[13] Pirumov U. G., Chislennye metody, Uchebnoe posobie, Izd. MAI, M., 1998

[14] Britov I. E., Raevskii A. S., Raevskii S. B., “Tselenapravlennyi poisk kompleksnykh voln v napravlyayuschikh elektrodinamicheskikh strukturakh”, Antenny, 2003, no. 5(72), 64–71

[15] Privalov I. I., Vvedenie v teoriyu funktsii kompleksnogo peremennogo, Nauka, M., 1967 | MR

[16] Babkin A. A., Malakhov V. A., Popkov K. V., Raevskii A. S., “Primenenie kombinirovannogo metoda poiska kompleksnykh kornei k resheniyu dispersionnogo uravneniya voln kruglogo dielektricheskogo volnovoda, pokrytogo pogloschayuschei plenkoi”, Tezisy dokladov IX Mezhdunarodnoi Nauchno-tekhnicheskoi konferentsii “Fizika i tekhnicheskie prilozheniya volnovykh protsessov” (Chelyabinsk, 2010), 23

[17] Malakhov V. A., Raevskii A. S., Programma nakhozhdeniya kompleksnykh reshenii dispersionnykh uravnenii, Gosudarstvennyi reestr programm dlya EVM. Svidetelstvo No 2010615410 ot 23.08.2010 g.