volume | PIER Journals

Abstract

Guided and leaky modes for a circular dielectric rod are analyzed in detail in this paper. By considering the field distributions, these modes are well defined and classified. The relations for the mode solutions using different types of special functions and Riemann sheets are figured out. Further, completed forms of characteristic equations used to solve different modes are presented explicitly. Asymptotic expansion method and Lambert W function are employed to derive the initial guesses around cutoff frequency, low frequency limit and high frequency limit for both TM and TE cases. The behaviors of complex transverse attenuation constants for proper and two types of improper modes with different cases are presented with some modes not shown in literatures.

1. Elsasser, W. M., "Attenuation in a dielectric circular rod," J. Appl. Phys., Vol. 20, 1193-1196, 1949.
doi:10.1063/1.1698307 Google Scholar

2. Jablonski, D., "Attenuation characteristics of circular dielectric waveguide at millimeter wavelengths," IEEE Trans. Microw. Theory Techn., Vol. 26, No. 9, 667-671, 1978.
doi:10.1109/TMTT.1978.1129461 Google Scholar

3. Jablonski, D., "Power-handling capabilities of circular dielectric waveguide at millimeter wave wavelengths," IEEE Trans. Microw. Theory Techn., Vol. 33, No. 2, 85-89, 1985.
doi:10.1109/TMTT.1985.1132954 Google Scholar

4. Kao, K. C., "Dielectric-fiber surface waveguide for optical frequencies," Proc. IEE, Vol. 133, No. 7, 1151-1158 , 1966. Google Scholar

5. Snitzer, E., "Cylindrical dielectric waveguide modes," J. Opt. Soc. Am., Vol. 51, No. 5, 491-498, 1961.
doi:10.1364/JOSA.51.000491 Google Scholar

6. Safaai-Jazi, A. and G. L. Yip, "Classification of hybrid modes in cylindrical dielectric optical waveguides," Radio Sci., Vol. 12, No. 4, 604-609, 1977.
doi:10.1029/RS012i004p00603 Google Scholar

7. Chatterjee, R., Dielectric and Dielectric-Loaded Antennas, John Wiley & Sons, Inc., 1985.

8. Zucker, F. J., H. Jasik, and Eds., Antenna Engineering Handbook, McGraw-Hill, 1961.

9. Oliner, A. A., "Types and basic properties of leaky modes in microwave and millimeterwave integrated circuits," IEICE Trans. Electron., Vol. 83, No. 5, 675-686, 2000. Google Scholar

10. Kobayashi, S., R. Mittra, and R. Lampe, "Dielectric tapered rod antennas for millimeter-wave applications," IEEE Trans. Antennas Propag., Vol. 30, No. 1, 54-58, 1982.
doi:10.1109/TAP.1982.1142758 Google Scholar

11. Arnbak, J., "Leaky waves on a dielectric rod," Electron. Lett., Vol. 1.5, No. 3, 41-42, 1969.
doi:10.1049/el:19690027 Google Scholar

12. Sammut, R. and A. W. Snyder, "Leaky modes on circular optical waveguides," Appl. Opt., Vol. 15, No. 2, 477-482, 1976.
doi:10.1364/AO.15.000477 Google Scholar

13. Kim, K. Y., Guided and leaky modes of circular open electromagnetic waveguide, PhD thesis, Kyungpook National University, Daegu, Korea, 2004.

14. Kim, K. Y., H.-S. Tae, and J.-H. Lee, "Analysis of leaky modes in circular dielectric rod waveguides," Electron. Lett., Vol. 39, No. 1, 61-62, 2003.
doi:10.1049/el:20030053 Google Scholar

15. Lampariello, P., F. Frezza, H. Shigesawa, M. Tsuji, and A. A. Oliner, "A versatile leakywave antenna based on stub-loaded rectangular waveguide: Part I --- Theory," IEEE Trans. Microw. Theory Techn., Vol. 46, No. 7, 1032-1041, 1998. Google Scholar

16. Nallo, C. D., F. Frezza, A. Galli, P. Lampariello, and A. A. Oliner, "Properties of NRDguide and H-guide higher-order modes: Physical and Nonphysical ranges," IEEE Trans. Microw. Theory Techn., Vol. 42, No. 12, 2429-2434, 1994.
doi:10.1109/22.339777 Google Scholar

17. Zeng, X. Y., S. J. Xu, K. Wu, and K. M. Luk, "Properties of guided modes on open structures near the cuto® region using a new version of complex effective dielectric constant," IEEE Trans. Microw. Theory Techn., Vol. 50, No. 5, 1417-1424, 2002.
doi:10.1109/22.999157 Google Scholar

18. Lampariello, P., F. Frezza, and A. A. Oliner, "The transition region between bound-wave and leaky-wave ranges for a partially dielectric-loaded open guiding structure," IEEE Trans. Microw. Theory Techn., Vol. 38, No. 12, 1831-1836, 1990.
doi:10.1109/22.64563 Google Scholar

19. Zhu, J. and Y. Lu, "Leaky modes of slab waveguides-asymptotic solutions," J. Lightwave Techno., Vol. 24, No. 3, 1619-1623, 2006.
doi:10.1109/JLT.2005.863275 Google Scholar

20. Rogier, H. and D. Vande Ginst, "A fast procedure to accurately determine leaky modes in multilayered planar dielectric substrates," IEEE Trans. Microw. Theory Techn., Vol. 56, No. 6, 1413-1422, 2008.
doi:10.1109/TMTT.2008.923896 Google Scholar

21. Rogier, H. and D. De Zutter, "Berenger and leaky modes in optical fibers terminated with a perfectly matched layer," J. Lightwave Techo., Vol. 20, No. 7, 1141-1148, 2002.
doi:10.1109/JLT.2002.800378 Google Scholar

22. Vande Ginste, D., H. Rogier, and D. De Zutter, "Efficient computation of TM- and TE-polarized leaky modes in multilayered circular waveguides," J. Lightwave Techo., Vol. 28, No. 11, 1661-1669, 2010.
doi:10.1109/JLT.2010.2047244 Google Scholar

23. Zhu, J., Z. Shen, and Z. Chen, "Dispersion relations of the modes for open nonhomogeneous waveguides terminated by perfectly matched layers," J. Opt. Soc. Am. B, Vol. 29, No. 9, 2524-2530, 2012.
doi:10.1364/JOSAB.29.002524 Google Scholar

24. NIST Handbook of Mathematical Function, Cambridge University Press, 2010.

25. Corless, R., G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math., Vol. 5, 329-359, 1996.
doi:10.1007/BF02124750 Google Scholar

26. Zvorykin, V. D., A. O. Levchenko, A. V. Shutov, E. V. Solomina, N. N. Ustinovskii, and I. V. Smetanin, "Long-distance directed transfer of microwaves in tubular sliding-mode plasma waveguides produced by KrF laser in atmospheric air," Phys. Plasmas, Vol. 19, 033509, 2012.
doi:10.1063/1.3692090 Google Scholar

27. Jin, J. M., Theory and Computation of Electromagnetic Fields, John Wiley & Sons, Inc., 2010.
doi:10.1002/9780470874257

28. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, Inc., 1989.

29. Tsang, L. and B. P. Wu, "Electromagnetic fields of hertzian dipoles in layered media of moderate thickness including the effects of All modes," IEEE Antennas Wireless Propag. Lett., Vol. 6, 316-319, 2007.
doi:10.1109/LAWP.2007.899917 Google Scholar

30. Shu, W. and J. M. Song, "Wave propagation in grounded dielectric slabs with double negative metamaterials," Progress In Electromagnetics Research Symposium, Vol. 2, No. 3, 246-250, 2006. Google Scholar

31. Kim, K. Y., "Comparative analysis of guided modal properties of double-positive and double-negative metamaterial slab waveguides," Radioengineering, Vol. 18, No. 2, 117-123, 2009. Google Scholar

32. Wang, Z. J. and J. F. Dong, "Analysis of guided modes in asymmetric left-handed slab waveguides," Progress In Electromagnetics Research, Vol. 62, 203-215, 2006.
doi:10.2528/PIER06021802 Google Scholar

33. Li, C., Q. Sui, and F. Li, "Complex guided wave solutions of grounded dielectric slab made of metamaterials," Progress In Electromagnetics Research, Vol. 51, 187-195, 2005.
doi:10.2528/PIER04011203 Google Scholar

34. Mahmoud, S. F. and A. J. Viitanen, "Surface wave character on a slab of metamaterial with negative permittivity and permeability," Progress In Electromagnetics Research, Vol. 51, 127-137, 2005.
doi:10.2528/PIER03102102 Google Scholar

35. Yang, S. M. and J. M. Song, "Guided and leaky modes of circular dielectric waveguide solved with multiple special functions," IEEE Antennas and propagation Int. Symp., Paper 108.6, 125-126, 2014. Google Scholar

36. Yang, S. M. and J. M. Song, "Efficient initial guesses for solving guided and leaky modes in dielectric rod," Annual Review of Progress in Applied Computational Electromagnetics, 148-149, 2015. Google Scholar

37. Sommerfeld, A., Electrodynamics, translated by Ramberg, E. G., Academic Press, 1952.

38. Ishimaru, A., Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice Hall, Inc., 1991.

39. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.

Dr. Siming Yang

Professor Jiming Song