Vol. 28
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2013-01-24
Behavior of Electromagnetic Waves at Dielectric Fractal-Fractal Interface in Fractional Spaces
By
Progress In Electromagnetics Research M, Vol. 28, 229-244, 2013
Abstract
In this paper, reflection and transmission coefficients at dielectric fractal-fractal interface are discussed. The ratio of permittivity of the two dielectric fractal media is kept constant, while the dimension is varied in order to get the desired results. Conventional results are recovered for the integer dimensions. The proposed expressions are useful to study the behavior of electromagnetic waves for non-integer dimensions, multiple fractal interfaces and waveguides. Moreover, it is also helpful to understand the variation in the magnitudes of reflection and transmission coefficients with the difference in dimensionality at interface of the two fractal media.
Citation
Muhammad Omar, and Muhammad Junaid Mughal, "Behavior of Electromagnetic Waves at Dielectric Fractal-Fractal Interface in Fractional Spaces," Progress In Electromagnetics Research M, Vol. 28, 229-244, 2013.
doi:10.2528/PIERM12121903
References

1. Mandelbro, B., The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.

2. Vicsek, T., "Fractal models for diffusion controlled aggregation," J. Phys. A: Math. Gen., Vol. 16, No. 17, 1983.
doi:10.1088/0305-4470/16/17/003

3. Wagner, G. C., J. T. Colvin, J. P. Allen, and H. J. Stapleton, "Fractal models of protein structure, dynamics and magnetic relaxation," J. Am. Chem. Soc., Vol. 107, No. 20, 5589-5594, 1985.
doi:10.1021/ja00306a001

4. Stillinger, F. H., "Axiomatic basis for spaces with noninteger dimension," J. Math. Phys., Vol. 18, No. 6, 1224-1234, 1977.
doi:10.1063/1.523395

5. Bollini, C. G. and J. J. Giambiagi, "Dimensional renormalization: The number of dimensions as a regularizing parameter," Nuovo Cimento B, Vol. 12, 20-26, 1972.

6. Baleanu, D. and S. Muslih, "Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives," Phys. Scripta, Vol. 72, No. 23, 119-121, 2005.
doi:10.1238/Physica.Regular.072a00119

7. Tarasov, V. E., "Electromagnetic fields on fractals," Modern Phys. Lett. A, Vol. 21, No. 20, 1587-1600, 2006.
doi:10.1142/S0217732306020974

8. Palmer, C. and P. N. Stavrinou, "Equations of motion in a non-integer-dimensional space," J. Phys. A, Vol. 37, 6987-7003, 2004.
doi:10.1088/0305-4470/37/27/009

9. Tarasov, V. E., "Continuous medium model for fractal media," Physics Letters A, Vol. 336, No. 2-3, 167-174, 2005.
doi:10.1016/j.physleta.2005.01.024

10. Martin, O.-S., "Electromagnetism on anisotropic fractals,", 2011,Eprint arXiv: 1106.1491.

11. Muslih, S. and D. Baleanu, "Fractional multipoles in fractional space," Nonlinear Analysis: Real World Applications, Vol. 8, 198-203, 2007.
doi:10.1016/j.nonrwa.2005.07.001

12. Baleanu, D. and A. K. Golmankhaneh, "On electromagnetic field in fractional space," Nonlinear Analysis: Real World Applications, Vol. 11, No. 1, 288-292, 2010.
doi:10.1016/j.nonrwa.2008.10.058

13. Zubair, M., M. J. Mughal, Q. A. Naqvi, and A. A. Rizvi, "Differential electromagnetic equations in fractional space," Progress In Electromagnetic Research, Vol. 114, 255-269, 2011.

14. 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.

16. 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.

17. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "An exact solution of spherical wave in D-dimensional fractional space," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 10, 1481-1491, 2011.

18. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "Electromagnetic fields and waves in fractional dimensional space," Springer Briefs in Applied Sciences and Technology, XII, 76, Springer, Germany, Jan. 28, 2012.

19. Mughal, M. J. and M. Zubair, "Fractional space solutions of antenna radiation problems: An application to Hertzian dipole," 2011 IEEE 19th Conference on Signal Processing and Communications Applications (SIU), 62-65, Apr. 20-22, 2011, doi:10.1109/SIU.2011.5929587.

20. Hira, A., M. Zubair, and M. J. Mughal, "Reflection and transmission coefficients at dielectric-fractional interface," Progress In Electromagnetics Research, Vol. 125, 543-558, 2012.

21. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York , 1989.