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Orthogonal System of Eigenwaves of an Open Cylindrical Gyrotropic Waveguide Located in Free Space

By Vasiliy A. Es'kin, Alexander V. Kudrin, and Nadezhda V. Yurasova
Progress In Electromagnetics Research B, Vol. 92, 91-107, 2021


A new method for obtaining an orthogonal system of eigenwaves of an open cylindrical waveguide filled with a gyrotropic medium and located in free space is presented. The advantage of the method is that it enables one to explicitly represent the fields of eigenwaves, which correspond to the discrete and continuous parts of the eigenvalue spectrum of such a guiding structure. Orthogonality relations for the eigenwaves and the procedure of expanding an electromagnetic field in terms of these modal solutions are discussed. The limiting transition from the case of a closed cylindrical waveguide with a perfectly conducting wall and a coaxial cylindrical gyrotropic core to the case of an open waveguide is considered. To illustrate the completeness of the obtained system of eigenwaves, a given field is expanded in terms of the found discrete- and continuous-spectrum waves and then resynthesized by evaluating the corresponding expansion numerically. Perfect coincidence between the initially specified field and the result yielded by this evaluation is demonstrated.


Vasiliy A. Es'kin, Alexander V. Kudrin, and Nadezhda V. Yurasova, "Orthogonal System of Eigenwaves of an Open Cylindrical Gyrotropic Waveguide Located in Free Space," Progress In Electromagnetics Research B, Vol. 92, 91-107, 2021.


    1. Lord Rayleigh, J. W., The Theory of Sound, Macmillan, London, 1894.

    2. Sommerfeld, A., "Ueber die fortpflanzung elektrodynamischer wellen langs eines drahtes," Ann. Phys. Chem., Vol. 303, No. 2, 233-290, 1899.

    3. Hondros, D. and P. Debye, "Elektromagnetische wellen an dielektrischen drahten," Ann. Phys., Vol. 337, No. 8, 465-476, 1910.

    4. Marcuvitz, N., "On field representations in terms of leaky modes or eigenmodes," IRE Trans. Antennas Propag., Vol. 4, No. 3, 192-194, 1956.

    5. Angulo, C. and W. Chang, "A variational expression for the terminal admittance of a semi-infinite dielectric rod," IRE Trans. Antennas Propag., Vol. 7, No. 3, 207-212, 1959.

    6. Shevchenko, V. V., Continuous Transitions in Open Waveguides, Golem Press, Boulder, 1971.

    7. Manenkov, A. B., "The excitation of open homogeneous waveguides," Radiophys. Quantum Electron., Vol. 13, No. 5, 578-586, 1970.

    8. Polat, B., "High-frequency scattering from a semi-infinite cylindrical dielectric rod," ZAMM — J. Appl. Math. Mech., Vol. 80, No. 6, 389-398, 2000.

    9. Collin, R. E., Field Theory of Guided Waves, IEEE Press, New York, 1990.

    10. Manenkov, A. B., "Propagation of waves in open waveguides with anisotropic dielectrics," Radiophys. Quantum Electron., Vol. 24, No. 1, 60-69, 1981.

    11. Manenkov, A. B., "Irregular magneto-optical waveguides," IEEE Trans. Microw. Theory Tech., Vol. 29, No. 9, 906-910, 1981.

    12. Uzunoglu, N. K., P. G. Cottis, and J. G. Fikioris, "Excitation of electromagnetic waves in a gyroelectric cylinder," IEEE Trans. Antennas Propagat., Vol. 33, No. 1, 90-95, 1985.

    13. Kudrin, A. V., V. A. Es’kin, C. Krafft, and T. M. Zaboronkova, "Whistler wave excitation by a loop antenna in a bounded collisional magnetoplasma," Phys. Scr., Vol. 77, No. 5, 055501, 2008.

    14. Marcuse, D., "Radiation losses of the dominant mode in round dielectric waveguides," Bell Syst. Tech. J., Vol. 49, No. 8, 1665-1693, 1970.

    15. Snyder, A. W., "Continuous mode spectrum of a circular dielectric rod," IEEE Trans. Microw. Theory Tech., Vol. 19, No. 8, 720-727, 1971.

    16. Tigelis, I., C. N. Capsalis, and N. K. Uzunoglu, "Computation of the dielectric rod waveguide radiation modes," Int. J. Infrared Millim. Waves, Vol. 8, No. 9, 1053-1068, 1987.

    17. Manenkov, A. B., "Orthogonality relations for the eigenmodes of lossy anisotropic waveguides (fibres)," IEE Proc. J, Vol. 140, No. 3, 206-212, 1993.

    18. Kondrat’ev, I. G., A. V. Kudrin, and T. M. Zaboronkova, Electrodynamics of Density Ducts in Magnetized Plasmas, Gordon and Breach, Amsterdam, 1999.

    19. Kostrov, A. V., A. V. Kudrin, L. E. Kurina, G. A. Luchinin, A. A. Shaykin, and T. M. Zaboronkova, "Whistlers in thermally generated ducts with enhanced plasma density: Excitation and propagation," Phys. Scr., Vol. 62, No. 1, 51-65, 2000.

    20. Zaboronkova, T. M., A. V. Kudrin, and M. Yu. Lyakh, "Excitation of nonsymmetric waves by given sources in a magnetoplasma in the presence of a cylindrical plasma channel," Radiophys. Quantum Electron., Vol. 46, No. 5–6, 407-424, 2003.

    21. Boswell, R. W. and F. F. Chen, "Helicons — The early years," IEEE Trans. Plasma Sci., Vol. 25, No. 6, 1229-1244, 1997.

    22. Chen, F. F. and R. W. Boswell, "Helicons — The past decade," IEEE Trans. Plasma Sci., Vol. 25, No. 6, 1245-1257, 1997.

    23. Arnush, D., "The role of Trivelpiece-Gould waves in antenna coupling to helicon waves," Phys. Plasmas, Vol. 7, No. 7, 3042-3050, 2000.

    24. Gurevich, A. G. and G. A. Melkov, Magnetization Oscillations and Waves, CRC Press, Boca Raton, 1996.

    25. Kudrin, A. V., E. Yu. Petrov, G. A. Kyriacou, and T. M. Zaboronkova, "Electromagnetic radiation from sources embedded in a cylindrically stratified unbounded gyrotropic medium," Progress In Electromagnetics Research B, Vol. 12, 297-331, 2009.

    26. Es’kin, V. A. and A. V. Kudrin, "Diffraction of an electromagnetic vortex Bessel beam by the end of a semi-infinite magnetized plasma cylinder," 2017 Progress In Electromagnetics Research Symposium — Spring (PIERS), 1372-1379, St. Petersburg, Russia, May 22–25, 2017.

    27. Es’kin, V. A. and A. V. Kudrin, "Diffraction of an electromagnetic Laguerre-Gaussian beam by the end of a semi-infinite gyrotropic cylinder," 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 133-138, Granada, Spain, September 9–13, 2019.

    28. Ginzburg, V. L., The Propagation of Electromagnetic Waves in Plasmas, Pergamon Press, Oxford, 1970.

    29. Capolino, F., Theory and Phenomena of Metamaterials, CRC Press, Boca Raton, 2017.

    30. Abramowitz, M., I. A. Stegun, and eds., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Dover, Mineola, 1974.

    31. Shevchenko, V. V., "On the completeness of spectral expansion of the electromagnetic field in the set of dielectric circular rod waveguide eigenwaves," Radio Sci., Vol. 17, No. 1, 229-231, 1982.