Journal of electromagnetic engineering and science

The Korean Institute of Electromagnetic Engineering and Science (한국전자파학회)
권호 표지

Leaky Dispersion Characteristics in Circular Dielectric Rod Using Davidenko's Method

  • Kim Ki Young (School of Electrical Engineering and Computer Science, Kyungpook National University) ;
  • Tae Heung-Sik (School of Electrical Engineering and Computer Science, Kyungpook National University) ;
  • Lee Jeong-Hae (Department of Radio Science and Communication Engineering, Hongik University)
  • Published : 2005.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

The leaky dispersion characteristics of a circular dielectric rod were investigated using Davidenko's method for several lower-order transverse magnetic(TM) modes. The normalized complex propagation constants were precisely determined and their tolerances below $10^{-10}$ compared with zero for both real and imaginary parts. It was also checked whether the normalized complex propagation constants obtained represented forward leaky waves. The leaky modes existing below the cutoff frequency of the guided mode were classified as a nonphysical mode, reactive mode, antenna mode, and spectral gap based on a precise determination of the complex propagation constants. Finally, the effects of the dielectric constant and radius of the dielectric rod on the leaky dispersion characteristics were also considered.

Keywords

References

  1. E. Snitzer, 'Cylindrical dielectric waveguide modes', J. Opt. Soc. Am., vol. 51, no. 5, pp. 491-498, May 1961 https://doi.org/10.1364/JOSA.51.000491
  2. F. Mesa, D. R. Jackson, 'Investigation of integration paths in the spectral-domain analysis of leaky modes on printed circuit lines', IEEE Trans. on Microwave Theory & Tech., vol. 50, no. 10, pp. 2267-2275, Oct. 2002 https://doi.org/10.1109/TMTT.2002.803433
  3. J. Ambak, 'Leaky waves on a dielectric rod', Electronics Letters, vol. 5, no. 3, pp. 41-42, Feb. 1969 https://doi.org/10.1049/el:19690027
  4. H. A. N. Hejase, 'On the use of Davidenko's method in complex root search', IEEE Trans. on Microwave Theory & Tech., vol. 41, no. 1, pp. 141-143, Jan. 1993 https://doi.org/10.1109/22.210241
  5. K. Naishadham, L. B. Felsen, 'Dispersion of waves guided along a cylindrical substrate-superstrate layered medium', IEEE Trans. on Antennas & Prop., vol. 41, no. 3, pp. 304-313, Mar. 1993 https://doi.org/10.1109/8.233133
  6. K. Naishadham, H. W. Yao, 'An efficient computation of transient scattering by a perfectly conducting cylinder', IEEE Trans. on Antennas and Prop., vol. 41, no. 11, pp. 1509-1515, Nov. 1993 https://doi.org/10.1109/8.267350
  7. S. H. Talisa, 'Application of Davidenko's method to the solution of dispersion relations in lossy wave-guiding systems', IEEE Trans. on Microwave Theory & Tech., vol. 33, no. 10, pp. 967-971, Oct. 1985 https://doi.org/10.1109/TMTT.1985.1133157
  8. M. Shabat, 'Numerical algorithms for modeling hybrid surface plasmon polaritons guided by metal films', Microwave & Opt. Tech. Lett., vol. 16, no. 2, pp. 122-124, Oct. 1997 https://doi.org/10.1002/(SICI)1098-2760(19971005)16:2<122::AID-MOP16>3.0.CO;2-A
  9. M. M. Shabat, M. A. Abdel-Naby, Y. S. Madi, and D. Jager, 'Complex zeros of moving optical wave-guides', Microwave & Opt. Tech. Lett., vol. 21, no. 6, pp. 465-470, Jun. 1999 https://doi.org/10.1002/(SICI)1098-2760(19990620)21:6<465::AID-MOP18>3.0.CO;2-6
  10. M. M. Shabat, D. Jager, M. A. Abdel-Naby, and N. M. Barakat, 'Numerical and analytical solutions of dispersion equation in lossy nonlinear wave-guideing system', Microwave & Opt. Tech. Lett., vol. 22, no. 4, pp. 273-278, Aug. 1999 https://doi.org/10.1002/(SICI)1098-2760(19990820)22:4<273::AID-MOP18>3.0.CO;2-2
  11. S. D. Conte, C. Boor, Elementary Numerical Analysis: An Algorithmic Approach, Third Edition, McGraw-Hill Kogakusha, Ltd., 1980
  12. J. A. Stratton, Electromagnetic Theory, McGrawHill Book Company, Inc., 1941
  13. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice Hall, Inc., 1991
  14. D. G. Zill, M. R. Cullen, Advanced Engineering Mathematics, PWS Publishing Company, 1992
  15. S. Wolfram, The MATHEMATICA$^{\circleR}$ Book, 4th Ed., Cambridge University Press, 1999
  16. P. Lampariello, F. Frezza, H. Shigesawa, M. Tsuji, and A. A. Ohner, 'A versatile leaky-wave antenna based on stub-loaded rectangular waveguide: Part I - Theory', IEEE Trans. on Antennas & Prop., vol. 46, no. 7, pp. 1032-1041, Jul. 1998 https://doi.org/10.1109/8.704806
  17. X. Y. Zeng, S. J. Xu, K. Wu, and K. M. Luk, 'Properties of guided modes on open structures near the cutoff region using a new version of complex effective dielectric constant', IEEE Trans. on Microwave Theory & Tech., vol. 50, no. 5, pp. 1417-1424, May 2002 https://doi.org/10.1109/22.999157
  18. P. Lampariello, F. Frezza, and A. A. Ohner, 'The transition region between bound-wave and leaky-wave ranges for a partially dielectric-loaded open guiding structure', IEEE Trans. Microwave Theory & Tech., vol. 38, no. 12, pp. 1831-1836, Dec. 1990 https://doi.org/10.1109/22.64563