Skip to main content
Log in

Coupled-Mode Theory of an Irregular Waveguide with Impedance Walls

  • Published:
Journal of Infrared, Millimeter, and Terahertz Waves Aims and scope Submit manuscript

Abstract

The eigenvalue problem is solved for a longitudinally inhomogeneous waveguide with impedance walls. The cross-section method is applied to reduce the problem to an infinite set of ordinary differential equations for amplitudes of basis modes. As a numerical example, a tapered metallic cavity of currently available THz gyrotron is considered. The combined effect of mode coupling (conversion) and ohmic wall losses on electromagnetic properties of the gyrotron cavity is considered and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. S. E. Miller, Coupled wave theory and waveguide applications, Bell System Technical Journal 33(3), 661–719 (1954).

    Article  Google Scholar 

  2. L. M. B. C. Campos, Some general properties of the exact acoustic field in horns and baffles, Journal of Sound and Vibration 95(2), 177–201 (1984).

    Article  Google Scholar 

  3. B. Z. Katsenelenbaum, L. Mercader del Rio, M. Pereyaslavets, M. S. Ayza, M. Thumm, Theory of non-uniform waveguides. The cross-section method (London: IEE, 1998).

    Book  MATH  Google Scholar 

  4. B. M. Mashkovtsev et al., Waveguide theory (Nauka, Moscow, 1966) (in Russian).

    Google Scholar 

  5. E. H. Khoo et al., Exact step-coupling theory for mode coupling behavior in geometrical variation photonic crystal waveguides, Phys. Rev. B 80(3), 035101 (2009).

    Article  Google Scholar 

  6. R. Quarfoth, D. Sievenpiper, Artificial tensor impedance surface waveguides, IEEE Trans. AP 61(7), 3597–3606 (2013).

    Article  Google Scholar 

  7. I.V. Lindell, A.H. Sihvola, Electromagnetic boundary and its realization with anisotropic metamaterial, Phys. Rev. E 79(2), 026604 (2009).

    Article  Google Scholar 

  8. I.V. Lindell, A.H. Sihvola, Circular waveguide with DB-boundary conditions, IEEE MTT 58(4), 903–909 (2010).

    Article  Google Scholar 

  9. Y. Ra’di, C.R. Simovski, S.A. Tretyakov, Thin perfect absorbers for electromagnetic waves: theory, design, and realizations, Phys. Rev. Appl. 3(3), 037001 (2015).

    Article  Google Scholar 

  10. C.K.W. Tam, Advances in numerical boundary conditions for computational aeroacoustics, Journal of Computational Acoustics 6(4), 377–402 (1998).

    Article  Google Scholar 

  11. F.D. Hastings, J.B. Schneider, S.L. Broschat, Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation, J. Acoust. Soc. Am. 100(5), 3061–3069 (1996).

    Article  Google Scholar 

  12. K.H. Yeap, S.S. Ong, H. Nisar, K.C. Lai, C.A. Ng, Attenuation in superconducting circular waveguides, Advanced electromagnetics 5(2), 34–38 (2016).

    Article  Google Scholar 

  13. V.I. Shcherbinin, V.I. Fesenko, V.R. Tuz, Low-loss forward and backward surface plasmons in a semiconductor nanowire coated by helical graphene strips, Journal of the Optical Society of America B 35(8), 2066–2074 (2018).

    Article  Google Scholar 

  14. V.I. Fesenko, V.I. Shcherbinin, V.R. Tuz, Multiple invisibility regions induced by symmetry breaking in a trimer of subwavelength graphene-coated nanowires, Journal of the Optical Society of America A 35(10), 1760–1768 (2018).

    Article  Google Scholar 

  15. A.S. Nifanov, A.I. Slepkov, The interaction of electron beams and electromagnetic fields in relativistic Cerenkov generators, Journal of Mathematical Sciences 172(6), 837–851 (2011).

    Article  MATH  Google Scholar 

  16. J.L. Doane, Design of circular corrugated waveguides to transmit millimeter waves at ITER, Fusion Sci. Tech. 53(1), 159–173 (2008).

    Article  Google Scholar 

  17. S.C. Schaub, M.A. Shapiro, R.J. Temkin, G.R. Hanson, Mode conversion losses in expansion units for ITER ECH transmission lines, Journal of Infrared, Millimeter, and Terahertz Waves 37(1), 72–86 (2016).

    Article  Google Scholar 

  18. E.J. Kowalski et al., Linearly polarized modes of a corrugated metallic waveguide, IEEE MTT 58(11), 2772–2780 (2010).

    Article  Google Scholar 

  19. M. Yeddulla, S. Tantawi, J. Guo, V. Dolgashev, An analytical design and analysis method for a high-power circular to rectangular waveguide mode converter and its applications, IEEE Trans. MTT 57(6), 1516–1525 (2009).

    Article  Google Scholar 

  20. C.T. Iatrou, S. Kern, A.B. Pavelyev, Coaxial cavities with corrugated inner conductor for gyrotrons, IEEE Trans. MTT 44(1), 56–64 (1996).

    Article  Google Scholar 

  21. V.I. Shcherbinin, V.I. Tkachenko, Cylindrical cavity with distributed longitudinal corrugations for second-harmonic gyrotrons, Journal of Infrared, Millimeter, and Terahertz Waves 38(7), 838–852 (2017).

    Article  Google Scholar 

  22. T.I. Tkachova, V.I. Shcherbinin, and V.I. Tkachenko, Eigenvalues and eigenfields of a corrugated gyrotron cavity with conducting walls, Problems of Atomic Science and Technology. Ser. Plasma Physics 118(6), 67–70 (2018).

  23. V.I. Shcherbinin, G.I. Zaginaylov, V.I. Tkachenko, Analogy between circular core-cladding and impedance waveguides and their membrane functions, Progress in Electromagnetics Research M 53, 111–120 (2017).

    Article  Google Scholar 

  24. V.I. Shcherbinin, G.I. Zaginaylov, V.I. Tkachenko, Cavity with distributed dielectric coating for subterahertz second-harmonic gyrotron, Problems of Atomic Science and Technology. Ser. Plasma Physics 106, 255–258 (2016).

  25. V.I. Shcherbinin, B.A. Kochetov, A.V. Hlushchenko, V.I. Tkachenko, Cutoff frequencies of a dielectric-loaded rectangular waveguide with arbitrary anisotropic surface impedance, IEEE MTT 67(2), 577–583 (2019).

  26. J.H. Booske et al., Vacuum electronic high power terahertz sources, IEEE Trans., Terahertz Science and Technology 1(1), 54–75 (2011).

    Article  Google Scholar 

  27. A. Mohsen, On the impedance boundary condition, Appl. Math. Modeling 6(5), 405–407 (1982).

    Article  Google Scholar 

  28. A.R. Wenzel, Smoothed boundary conditions for randomly rough surfaces, J. Mat. Phys. 15(3), 317–323 (1974).

    Article  Google Scholar 

  29. I. Simonsen, A.A. Maradudin, T.A. Leskova, Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces, Phys. Rev. Lett. 104(22), 223904 (2010).

    Article  Google Scholar 

  30. J.A. Castiblanco, D. Seetharamdoo, M. Berbineau, M.M. Ney, F. Gallée, Surface impedance boundary conditions in time domain for guided structures of arbitrary cross section with lossy dielectric walls, IEEE Trans. AP 63(3), 1086–1097 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  31. V.I. Shcherbinin, A.V. Hlushchenko, A.V. Maksimenko, V.I. Tkachenko, Effect of cavity ohmic losses on efficiency of low-power terahertz gyrotron, IEEE Trans. on Electron Devices 64(9), 3898–3903 (2017).

    Article  Google Scholar 

  32. A.F. Stevenson, General theory of electromagnetic horns, J. Appl. Phys. 22(12), 1447–1460 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  33. G. Reiter, Generalized telegraphist’s equation for waveguides of varying cross-section, Proc. IEE – Part B: Elect. Comm. Eng. 106(13), 54–61 (1959).

    Google Scholar 

  34. L. Solymar, Spurious mode generation in nonuniform waveguide, IRE Trans. Microwave Theory Tech. 7(3), 379–383 (1959).

    Article  Google Scholar 

  35. I.A. Chernyavskiy et al., Current status of the large-signal code TESLA: recent development and new applications, In Proc. of IVEC, 533–534 (2012).

  36. A.N. Vlasov, T.M. Antonsen, Numerical solution of fields in lossy structures using MAGY, IEEE Trans. Electron Devices 48(1), 45–55 (2001).

    Article  Google Scholar 

  37. J. Shafii, R.J. Vernon, Investigation of mode coupling due to ohmic losses in overmoded uniform and varying radius circular waveguides by the method of cross sections, IEEE Trans. MTT 50(5), 1361–1369 (2002).

    Article  Google Scholar 

  38. Sh.E. Tsimring, V.G. Pavelyev, The theory of nonhomogeneous electromagnetic waveguides containing critical cross-sections, Radio Eng. Electron. Phys. 27(6), 41–44 (1982).

    Google Scholar 

  39. D. Wagner, M. Thumm, G. Gantenbein, W. Kasparek, T. Idehara, Analysis of a complete gyrotron oscillator using the scattering matrix description, Int. J. Infrared and Millimeter Waves 19(2), 185–194 (1998).

    Article  Google Scholar 

  40. T. Idehara, N. Nishida, K. Yoshida, I. Ogawa, T. Tatsukawa, D. Wagner, G. Gantenbein, W. Kasparek, M. Thumm, High frequency and high mode purity operations of gyrotron FU IVA, Int. J. Infrared and Millimeter Waves 19(7), 919–930 (1998).

    Article  Google Scholar 

  41. I. Ederra, M.S. Ayza, M. Thumm, B.Z. Katsenelenbaum, Comparative analysis of mode reflection and transmission in presence of a cutoff cross section of nonuniform waveguide by using cross section and the mode-matching and generalized scattering-matrix methods, IEEE trans. MTT 49(4), 637–645 (2001).

    Article  Google Scholar 

  42. W.A. Huting, K.J. Webb, Comparison of mode-matching and differential equation techniques in the analysis of waveguide transitions, IEEE Trans. MTT 39(2), 280–286 (1991).

    Article  Google Scholar 

  43. A. S. Il’inskii, A.G. Sveshnikov, Methods for investigating irregular waveguides, USSR Comput. Math. Math. Phys. 8(2), 167–180 (1968).

    Article  Google Scholar 

  44. A.A. Kuraev, T.L. Popkova, A.K. Sinitsyn, Electrodynamics and propagation of radio waves (Minsk, Bestprint, 2004) (in Russian).

  45. V.A. Malakhov, A.V. Nazarov, A.S. Raevskii, S.B. Raevskii, Multiplicity of eigenvalues in certain boundary value problems for the helmholtz equation, Computational Mathematics and Mathematical Physics, 53(5), 616–624 (2013).

    Article  MathSciNet  Google Scholar 

  46. G.I. Zaginaylov, V.I. Shcherbinin, M Yu Glyavin, New approach to the theory of irregular lossy waveguides and its application to design of terahertz gyrotrons, in Proc. of 43rd EuMW, 971–974 (2013).

  47. G.I. Zaginaylov, V.I. Shcherbinin, K. Schuenemann, M.Yu. Glyavin, Novel approach to the theory of longitudinally inhomogeneous lossy waveguides, Proc. of MSMW’13, 523–525 (2013).

    Google Scholar 

  48. G.I. Zaginaylov, A.V. Maksimenko, V.I. Shcherbinin, K. Schuenemann, Theory of irregular impedance waveguides: generalized method of separation of variables, in Proc. of Math. Meth. Electrom. Theory, 31–35 (2014).

  49. A.V. Maksimenko, G.I. Zaginaylov, V.I. Shcherbinin, On the theory of longitudinally inhomogeneous waveguide with impedance walls, Physics of Particles and Nuclei Letters 12(2), 362–370 (2015).

    Article  Google Scholar 

  50. G.I. Zaginaylov, A.V. Maksimenko, K. Schunemann, Coupled mode theory for longitudinally inhomogeneous impedance waveguides, in Proc. of MSMW’16, 1–4 (2016).

  51. H. Li, M. Thumm, Mode coupling in corrugated waveguides with varying wall impedance and diameter change, Int. J. Electronics 71(5), 827–844 (1991).

    Article  Google Scholar 

  52. A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and series, 2 (New York: Gordon and Breach, 1986).

    MATH  Google Scholar 

  53. T. Idehara et al., A THz gyrotron FU CW III with a 20 T superconducting magnet, Plasma Fusion Res. 8, 1508–1511 (2009).

    Google Scholar 

  54. L. Agusu et al., Design of a CW 1 THz gyrotron (gyrotron Fu CW III) using a 20 T superconducting magnet, J. Infrar. Millim. Waves 28(5), 315–328 (2007).

    Article  Google Scholar 

  55. S.H. Kao, C.C. Chiu, K.R. Chu, A study of sub-terahertz and terahertz gyrotron oscillators, Physics of Plasmas 19(2), 023112 (2012).

    Article  Google Scholar 

  56. A.V. Maksimenko, G.I. Zaginaylov, V.I. Shcherbinin, K. Schünemann, Influence of mode conversion and ohmic losses on electromagnetic properties of THz gyrotron cavities, Intern. Young Sci. Forum on Appl. Phys., YSF-2015, MTE 6 (2015).

  57. O Maksimenko, S. Khizhnyak, G. Zaginaylov, Efficient method for analysis of mode conversion and ohmic losses in terahertz gyrotrons, Bull. of T. Shevchenko Nat. Univ. of Kiev, Ser.: Radiophys. and Electr. 23(1), 49–54 (2015).

    Google Scholar 

  58. T. Idehara, I. Ogawa, D. Wagner, M. Thumm, K. Kosuga, S. P. Sabchevski, High purity mode CW gyrotron covering the subterahertz to terahertz range using a 20 T superconducting magnet, IEEE Trans. Electron Devices, 65(8), 3486–3481 (2018).

    Article  Google Scholar 

  59. K. Kosuga et al., Development of THz gyrotron using 20 T superconductor magnet, Proc. of 3rd Int. Workshop on Far-Infrared Technologies 2010 (IW-FIRT 2010), 214–217 (2010).

  60. G.S. Nusinovich, T.B. Pankratova, in Gyrotrons, Theory of submillimetre wave gyrotron, Institute of Applied Physics, Academy of Sciences of the USSR, Gorky, Collection of scientific papers, edited by A.V. Gaponov-Grekhov (1981), pp. 178.

  61. I. Ogawa, K. Kosuga, T. Idehara, R. Ikeda, J. C. Mudiganti, (2011, October), Development of THz Gyrotron FU CW III using a 20 T superconducting magnet, Proc. of IRMMW-THz, 1–2 (2011).

  62. T. Idehara, H. Tsuchiya, O. Watanabe, La Agusu, S. Mitsudo, The first experiment of a THz gyrotron with a pulse magnet, Int. J. Infrared Millim. Waves 27(3), 319–331(2006).

    Article  Google Scholar 

  63. A.V. Maksimenko, V.I. Shcherbinin, A.V. Hlushchenko, V.I. Tkachenko, K.A. Avramidis, J. Jelonnek, Starting currents for eigenmodes of a gyrotron cavity with mode conversion, IEEE Trans. on Electron Devices, 66(3), 1552–1558 (2019).

    Article  Google Scholar 

  64. O.V. Sinitsyn, G.S. Nusinovich, Analysis of aftercavity interaction in gyrotrons, Physics of Plasmas 16(2), 023101 (2009).

    Article  Google Scholar 

  65. S. Sabchevski, I. Zhelyazkov, E. Benova, V. Atanassov, P. Dankov, M. Thumm, A. Arnold, J. Jin, T. Rzesnicki, Quasi-optical converters for high-power gyrotrons: a brief review of physical models, numerical methods and computer codes, Journal of Physics: Conference Series, 44, 102–109, (2006).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aleksandr V. Maksimenko.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maksimenko, A.V., Shcherbinin, V.I. & Tkachenko, V.I. Coupled-Mode Theory of an Irregular Waveguide with Impedance Walls. J Infrared Milli Terahz Waves 40, 620–636 (2019). https://doi.org/10.1007/s10762-019-00589-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10762-019-00589-x

Keywords

Navigation