Search search
Publication Date
to
Vol. 65
Latest Volume
All Volumes
PIERM 139 PIERM 138 PIERM 137 PIERM 136 PIERM 135 PIERM 134 PIERM 133 PIERM 132 PIERM 131 PIERM 130 PIERM 129 PIERM 128 PIERM 127 PIERM 126 PIERM 125 PIERM 124 PIERM 123 PIERM 122 PIERM 121 PIERM 120 PIERM 119 PIERM 118 PIERM 117 PIERM 116 PIERM 115 PIERM 114 PIERM 113 PIERM 112 PIERM 111 PIERM 110 PIERM 109 PIERM 108 PIERM 107 PIERM 106 PIERM 105 PIERM 104 PIERM 103 PIERM 102 PIERM 101 PIERM 100 PIERM 99 PIERM 98 PIERM 97 PIERM 96 PIERM 95 PIERM 94 PIERM 93 PIERM 92 PIERM 91 PIERM 90 PIERM 89 PIERM 88 PIERM 87 PIERM 86 PIERM 85 PIERM 84 PIERM 83 PIERM 82 PIERM 81 PIERM 80 PIERM 79 PIERM 78 PIERM 77 PIERM 76 PIERM 75 PIERM 74 PIERM 73 PIERM 72 PIERM 71 PIERM 70 PIERM 69 PIERM 68 PIERM 67 PIERM 66 PIERM 65 PIERM 64 PIERM 63 PIERM 62 PIERM 61 PIERM 60 PIERM 59 PIERM 58 PIERM 57 PIERM 56 PIERM 55 PIERM 54 PIERM 53 PIERM 52 PIERM 51 PIERM 50 PIERM 49 PIERM 48 PIERM 47 PIERM 46 PIERM 45 PIERM 44 PIERM 43 PIERM 42 PIERM 41 PIERM 40 PIERM 39 PIERM 38 PIERM 37 PIERM 36 PIERM 35 PIERM 34 PIERM 33 PIERM 32 PIERM 31 PIERM 30 PIERM 29 PIERM 28 PIERM 27 PIERM 26 PIERM 25 PIERM 24 PIERM 23 PIERM 22 PIERM 21 PIERM 20 PIERM 19 PIERM 18 PIERM 17 PIERM 16 PIERM 14 PIERM 13 PIERM 12 PIERM 11 PIERM 10 PIERM 9 PIERM 8 PIERM 7 PIERM 6 PIERM 5 PIERM 4 PIERM 3 PIERM 2 PIERM 1
All Journals
PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2018-03-13
Analysis of a Non-Integer Dimensional Tunnel and Perfect Electric Conductor Waveguide
By
Nayab Bhatti,

    Dr. Nayab Bhatti

    Department of Electronics

    Quaid-i-Azam University

    Pakistan

    Homepage

Qaisar Abbas Naqvi

    Dr. Qaisar Abbas Naqvi

    Department of Electronics

    Quaid-i-Azam University

    Pakistan

    Homepage

Progress In Electromagnetics Research M, Vol. 65, 165-174, 2018
doi:10.2528/PIERM18011604 | Google Scholar

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.
Download Full Article (865) View Full Article volume
Citation
Nayab Bhatti, and Qaisar Abbas 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
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        Google Scholar

2. Dimri, V. P. and R. P. Srivastava, Fractal Behaviour of the Earth System, 23-37, Springer Berlin Heidelberg, 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        Google Scholar

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        Google Scholar

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        Google Scholar

6. Zubair, M., M. J. Mughal, and Q. A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space, Springer-Verlag, 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        Google Scholar

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.        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

Download Full Article (865) View Full Article volume


The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.