volume | PIER Journals

Abstract

Fractional solutions of a parallel plate waveguide originally with impedance walls have been derived and fractional impedance of the guiding walls have been investigated. Two distinct ranges ofw all impedance have been found in which fractional impedance behaves in opposite ways. For 0 < α < 1, the fractional impedance is inductive in range 1 and is capacitive in range 2, where α is fractional parameter. For 1 < α < 2, the fractional impedance is capacitive in range 1 and is inductive in range 2. At the boundary ofthe two ranges, the fractional impedance is independent of α and is resistive. This behavior is periodic with period α = 2.

1. Oldham, K. B. and J. Spanier, The Fractional Calculus, Academic Press, 1974.

2. Engheta, N., "Fractional curl operator in electromagnetics," Microwave and Optical Technology Letters, Vol. 17, No. 2, 86-91, February 5, 1998.
doi:10.1002/(SICI)1098-2760(19980205)17:2<86::AID-MOP4>3.0.CO;2-E Google Scholar

3. Engheta, N., "On fractional paradigm and intermediate zones in Electromagnetism: I. Planar observation," Microwave and Optical Technology Letters, Vol. 22, No. 4, 236-241, August 20, 1999.
doi:10.1002/(SICI)1098-2760(19990820)22:4<236::AID-MOP6>3.0.CO;2-8 Google Scholar

4. Engheta, N., "On fractional paradigm and intermediate zones in Electromagnetism: II. Cylindrical and spherical observations," Microwave and Optical Technology Letters, Vol. 23, No. 2, 100-103, October 20, 1999.
doi:10.1002/(SICI)1098-2760(19991020)23:2<100::AID-MOP12>3.0.CO;2-W Google Scholar

5. Engheta, N., "Fractional paradigm in electromagnetic theory," a chapter in Frontiers in Electromagnetics, Chapter 12, 523-552, D. H. Werner and R. Mittra (eds.), IEEE Press, 1999. Google Scholar

6. Ozaktas, H. M., Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, 2001.

7. Machado, J. A. T., I. S. Jesus, A. Galhano, and J. B. Cunha, "Fractional order electromagnetics," Signal Processing, Vol. 86, No. 10, 2637-2644, October 2006. Google Scholar

8. Debnath, L., "Recent applications off ractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Vol. 2003, No. 54, 3413-3442, 2003.
doi:10.1155/S0161171203301486 Google Scholar

9. Naqvi, Q. A. and M. Abbas, "Complex and higher order fractional curl operator in Electromagnetics," Optics Communications, Vol. 241, 349-355, 2004.
doi:10.1016/j.optcom.2004.07.028 Google Scholar

10. Hussain, A. and Q. A. Naqvi, "Fractional curl operator in chiral medium and fractional nonsymmetric transmission line," Progress In Electromagnetics Research, Vol. 59, 199-213, 2006.
doi:10.2528/PIER05092801 Google Scholar

11. Hussain, A., S. Ishfaq, and Q. A. Naqvi, "Fractional curl operator and fractional waveguides," Progress In Electromagnetic Research, Vol. 63, 319-335, 2006.
doi:10.2528/PIER06060604 Google Scholar

12. Hussain, A., M. Faryad, and Q. A. Naqvi, "Fractional curl operator and fractional chiro-waveguide," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 8, 1119-1129, 2007. Google Scholar

13. Naqvi, Q. A. and M. Abbas, "Fractional duality and metamaterials with negative permittivity and permeability," Optics Communications, Vol. 227, 143-146, 2003.
doi:10.1016/j.optcom.2003.08.041 Google Scholar

14. Naqvi, Q. A. and A. A. Rizvi, "Fractional dual solutions and corresponding sources," Progress In Electromagnetic Research, Vol. 25, 223-238, 2000.
doi:10.2528/PIER99051801 Google Scholar

15. Naqvi, S. A., Q. A. Naqvi, and A. Hussain, "Modelling of transmission through a chiral slab using fractional curl operator," Optics Communications, Vol. 226, No. 2, 404-406, 2006.
doi:10.1016/j.optcom.2006.05.030 Google Scholar

16. Hussain, A., Q. A. Naqvi, and M. Abbas, "Fractional duality and perfect electromagnetic conductor (PEMC)," Progress In Electromagnetics Research, Vol. 71, 85-94, 2007.
doi:10.2528/PIER07020702 Google Scholar

17. Hussain, A. and Q. A. Naqvi, "Perfect electromagnetic conductor (PEMC) and fractional waveguide," Progress In Electromagnetics Research, Vol. 73, 61-69, 2007.
doi:10.2528/PIER07032401 Google Scholar

18. Mustafa, F., M. Faryad, and Q. A. Naqvi, "Fractional dual solutions using calculus ofdifferen tial forms," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2–3, 399-410, 2008.
doi:10.1163/156939308784160721 Google Scholar

19. Faryad, M. and Q. A. Naqvi, "Fractional rectangular waveguide," Progress in Electromagnetic Research, Vol. 75, 383-396, 2007.
doi:10.2528/PIER07052803 Google Scholar

20. Hussain, A., M. Faryad, and Q. A. Naqvi, "Fractional dual parabolic cylindrical reflector," 12th International Conference on Mathematical Methods in Electromagnetic Theory, Odesa, Ukraine, June 29-July 02, 2008. Google Scholar

21. Maab, H. and Q. A. Naqvi, "Fractional surface waveguide," Progress In Electromagnetics Research C, Vol. 1, 199-209, 2008.
doi:10.2528/PIERC08020801 Google Scholar

22. Naqvi, Q. A. and A. A. Rizvi, "Fractional solutions for the Helmholtz's equation in a multilayered geometry," Journal of Electromagnetic Waves and Applications, Vol. 13, No. 6, 815-816, 1999.
doi:10.1163/156939399X01384 Google Scholar

23. Ivakhnychenko, M. V., E. I. Veliev, and T. M. Ahmedov, "Fractional operators approach in electromagnetic wave reflection problems," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1787-1802, 2007. Google Scholar

24. Egheta, N., "Note on fractional calculus and the image method for dielectric spheres," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 9, 1179-1188, 1995. Google Scholar

25. Li, B., L. Li, and C. H. Liang, "The rectangular waveguide board wall slot array antenna with EBG structure," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 13, 1807-1815, 2005.
doi:10.1163/156939305775696847 Google Scholar

26. Hu, S. X. and W. B. Dou, "Analysis of waveguide junction circulators with partial-height ferrite of arbitrary shape," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 2, 203-220, 2005.
doi:10.1163/1569393054497267 Google Scholar

27. Hames, Y. and I. H. Tayyar, "Plane wave diffraction by dielectric loaded thick-walled parallel-plate impedance waveguide," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 2, 197-198, 2004.
doi:10.1163/156939304323062040 Google Scholar

28. Safwat, A. M. E., K. A. Zaki, W. Johnson, et al. "Mode-matching analysis of conductor backed coplanar waveguide with surface etching," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 5, 627-641, 2001.
doi:10.1163/156939301X00300 Google Scholar

29. Buyukaksoy, A. and F. Birbir, "Analysis ofan impedance loaded parallel-plate waveguide radiator," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 11, 1509-1525, 1998.
doi:10.1163/156939398X00449 Google Scholar

30. Ghosh, S., R. K. Jain, and B. N. Basu, "Fast-wave analysis ofan inhomogeneously-loaded helix enclosed in a cylindrical waveguide," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 2, 191-198, 1998.
doi:10.1163/156939398X00773 Google Scholar

Dr. Akhtar Hussain

Dr. Muhammad Faryad

Dr. Qaisar Abbas Naqvi