Vol. 4

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2008-10-03

Fractional Waveguide with Impedance Walls

By Akhtar Hussain, Muhammad Faryad, and Qaisar Naqvi
Progress In Electromagnetics Research C, Vol. 4, 191-204, 2008

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.

Citation


Akhtar Hussain, Muhammad Faryad, and Qaisar Naqvi, "Fractional Waveguide with Impedance Walls," Progress In Electromagnetics Research C, Vol. 4, 191-204, 2008.
http://jpier.org/PIERC/pier.php?paper=08080101

References


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

    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

    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

    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.

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

    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

    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

    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

    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

    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.

    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

    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

    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

    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

    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

    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

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

    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.

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

    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

    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.

    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.

    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

    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

    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

    28. Safwat, A. M. E., 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

    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

    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