Vol. 65

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2018-03-13

Analysis of a Non-Integer Dimensional Tunnel and Perfect Electric Conductor Waveguide

By Nayab Bhatti and Qaisar Naqvi
Progress In Electromagnetics Research M, Vol. 65, 165-174, 2018
doi:10.2528/PIERM18011604

Abstract

Solutions to the Maxwell equations for a planar non-integer dimensional perfect electric conductor (NID-PEC) waveguide are obtained. The space within the guide is NID in direction normal to walls of the waveguide. Field behaviour within the waveguide is noted for different values of the parameter, D, describing dimension of the NID space. For D = 2, classical results are recorded. The discussion is further extended by treating propagation in a tunnel within unbounded dielectric medium. The space within tunnel is also NID in direction perpendicular to walls of the tunnel. For different values of D field behaviors are also presented. It has been noted that for D = 2 and taking very high values of permittivity (ϵ → ∝) classical results for PEC waveguide are recorded. Whereas for ϵ → ∝, field behavior within tunnel matches with NID-PEC waveguide.

Citation


Nayab Bhatti and Qaisar Naqvi, "Analysis of a Non-Integer Dimensional Tunnel and Perfect Electric Conductor Waveguide," Progress In Electromagnetics Research M, Vol. 65, 165-174, 2018.
doi:10.2528/PIERM18011604
http://www.jpier.org/PIERM/pier.php?paper=18011604

References


    1. Mandelbrot, B. B. and J. W. V. Ness, "Fractional brownian motions, fractional noises and applications,", Vol. 10, No. 4, 422-437, 1968.
    doi:10.1007/3-540-26536-8_2

    2. Dimri, V. P. and R. P. Srivastava, Fractal Behaviour of the Earth System, 23-37, Springer Berlin Heidelberg, Hyderabad, 2005.
    doi:10.1016/j.physleta.2005.01.024

    3. Tarasov, V. E., "Continuous medium model for fractal media," Physics Letters A, Vol. 336, 167-174, 2005.
    doi:10.1063/1.523395

    4. Stillinger, F. H., "Axiomatic basis for spaces with non-integer dimensions," Journal of Mathematical Physics, Vol. 18, 1224-1234, 1977.
    doi:10.1088/0305-4470/37/27/009

    5. Palmer, C. and P. N. Stavrinou, "Equations of motion in a non-integer-dimensional space," Journal of Physics A, Vol. 37, 6987-7003, 2004.
    doi:10.1007/978-3-642-25358-4

    6. Zubair, M., M. J. Mughal, and Q. A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space, Springer-Verlag, New York, 2012.
    doi:10.1103/PhysRevA.11.42

    7. Herrick, D. R. and F. H. Stillinger, "Variable dimensionality in atoms and its effects on the ground state of the helium isoelastic sequence," Physical Review A, Vol. 11, 42-53, 1975.
    doi:10.1063/1.446210

    8. Pfeifer, P. and D. Avnir, "Chemistry in non-integer dimensions between two and three. I. Fractal theory of heterogeneous surfaces," Journal of Chemical Physics, Vol. 79, 3558-3565, 1983.

    9. Muslih, S. I., M. Saddallah, D. Baleanu, and E. Rabei, "Lagrangian formulation of Maxwell’s field in fractional D dimensional space-time," Romanian Journal of Physics, Vol. 55, 659-663, 2010.

    10. Muslih, S. I., M. Saddallah, D. Baleanu, and E. Rabei, "Lagrangian formulation of Maxwell’s field in fractional D dimensional space-time," Romanian Reports of Physics, Vol. 55, 659-663, 2010.
    doi:10.2528/PIERL10102103

    11. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "The wave equation and general plane wave solutions in fractional space," Progress In Electromagnetics Research Letters, Vol. 19, 137-146, 2010.
    doi:10.2528/PIER11021508

    12. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "An exact solution of the cylindrical wave equation for electromagnetic field in fractional dimensional space," Progress In Electromagnetics Research, Vol. 114, 443-455, 2011.

    13. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "An exact solution of the spherical wave equation in D-dimensional fractional space," Journal of Electromagnetics Waves and Applications, Vol. 25, No. 10, 1481-1491, 2011.
    doi:10.1016/j.ijleo.2015.12.019

    14. Naqvi, Q. A. and M. Zubair, "On cylindrical model of electrostatic potential in fractional dimensional space," Optik-International Journal for Light and Electron Optics, Vol. 127, 3243-3247, 2016.
    doi:10.1080/09205071.2015.1032436

    15. Noor, A., A. A. Syed, and Q. A. Naqvi, "Quasi-static analysis of scattering from a layered plasmonic sphere in fractional space," Journal of Electromagnetic Wave and Applications, Vol. 29, No. 8, 1047-1059, 2015.
    doi:10.1016/j.ijleo.2017.04.081

    16. Munawar, Y., M. A. Ashraf, Q. A. Naqvi, and M. A. Fiaz, "Two dimensional green’s function for planar grounded dielectric layer in non-integer dimensional space," Optik-International Journal for Light and Electron Optics, Vol. 140, 610-618, 2017.
    doi:10.1080/09205071.2016.1276859

    17. Abbas, M., A. A. Rizvi, M. A. Fiaz, and Q. A. Naqvi, "Scattering of electromagnetic plane wave from a low contrast circular cylinder buried in non-integer dimensional half space," Journal of Electromagnetic Waves and Applications, Vol. 31, No. 3, 263-283, 2017.
    doi:10.1016/j.ijleo.2017.05.043

    18. Naqvi, Q. A., "Scattering from a cylindrical obstacle buried in non-integer dimensional dielectric half space using kobayashi potential method," Optik-International Journal for Light and Electron Optics, Vol. 141, 39-49, 2017.
    doi:10.1007/s10582-006-0093-7

    19. Sadallah, M., S. I. Muslih, and D. Baleanu, "Equations of motion for Einstein’s field in non-integer dimensional space," Czechoslovak Journal of Physics, Vol. 56, 323-328, 2006.
    doi:10.1080/09205071.2013.840543

    20. Khan, S. and M. J. Mughal, "General solution for TEM, TE, and TM waves in fractional dimensional space and its application in rectangular waveguide filled with fractional space," Journal of Electromagnetic Waves and Applications, Vol. 27, No. 18, 2298-2307, 2013.
    doi:10.1016/j.physleta.2015.06.032

    21. Tarasov, V. E., "Fractal electromagnetics via non-integer dimensional space approach," Physics Letters A, Vol. 379, 2055-2061, 2015.
    doi:10.1016/j.cnsns.2014.05.025

    22. Tarasov, V. E., "Vector calculus in non-integer dimensional space and its applications to fractal media," Journal of Communications in Nonlinear Science and Numerical Simulation, Vol. 21, No. 2, 360-374, 2015.
    doi:10.1063/1.4892155

    23. Tarasov, V. E., "Anisotropic fields media by vector calculus in non-integer dimensional space," Journal of Mathematical Physics, Vol. 55, 083510, 2014.
    doi:10.1080/09205071.2017.1358108

    24. Naqvi, Q. A. and M. A. Fiaz, "Electromagnetic behavior of a planar interface of non-integer dimensional spaces," Journal of Electormagnetic Waves and Applications, Vol. 31, No. 16, 1625-1637, 2017.

    25. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, U.S. Department of Commerce, 1972.
    doi:10.1016/j.physleta.2013.01.030

    26. Balankin, A. S., B. Mena, J. Patino, and D. Morales, "Electromagnetic fields in fractional continua," Physics Letter A, Vol. 377, 783-788, 2013.
    doi:10.2528/PIERM12121903

    27. Omar, M. and M. J. Mughal, "Behavior of electromagnetic waves at dielectric fractal-fractal interface in fractional spaces," Progress in Electromagnetic Research M, Vol. 28, 229-244, 2013.