PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 125 > pp. 543-558

REFLECTION AND TRANSMISSION AT DIELECTRIC-FRACTAL INTERFACE

By H. Asad, M. Zubair, and M. J. Mughal

Full Article PDF (641 KB)

Abstract:
The transmission and reflection of electromagnetic waves at dielectric-fractal interface is studied, the fractal exhibits quasi fractional space properties.~The closed form expressions for transmission and reflection coefficients are formulated for such an interface. The classical results are obtained when integer dimensions, instead of fractional dimension are inserted in the said expressions. This work can be used to study behavior of electromagnetic waves in slabs and waveguides filled with fractal media.

Citation:
H. Asad, M. Zubair, and M. J. Mughal, "Reflection and Transmission at Dielectric-Fractal Interface," Progress In Electromagnetics Research, Vol. 125, 543-558, 2012.
doi:10.2528/PIER12012402
http://www.jpier.org/PIER/pier.php?paper=12012402

References:
1. Mandelbrot, 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., No. 17, 1983.

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

5. Ashmore, J. F., "On renormalization and complex space-time dimensions," Commun. Math. Phys., Vol. 29, 177-187, 1973.
doi:10.1007/BF01645246

6. Tarasov, V. E., "Continuous medium model for fractal media," Physics Letters A, Vol. 336, No. 2--3, 2005.

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

8. Stillinger, F. H., "Axiomatic basis for spaces with noninteger dimension," Journal of Mathematical Physics, Vol. 18, No. 6, 1224-1234, 1977.
doi:10.1063/1.523395

9. Sadallah, M. and S. I. Muslih, "Solution of the equations of motion for Einstein's field in fractional D dimensional space-time," International Journal of Theoretical Physics, Vol. 48, No. 12, 3312-3318, 2009.
doi:10.1007/s10773-009-0133-8

10. Muslih, S. I. and O. P. Agrawal, "A scaling method and its applications to problems in fractional dimensional space," Journal of Mathematical Physics, Vol. 50, No. 12, 123501-123501-11, 2009.
doi:10.1063/1.3263940

11. Wang, Z.-S. and B.-W. Lu, "The scattering of electromagnetic waves in fractal media," Waves in Random and Complex Media, Vol. 4, No. 1, 97-103, 1994.

12. Engheta, N., "Fractional curl operator in electromagnetics," Microwave Opt. Tech. Lett., Vol. 17, 86-91, 1998.
doi:10.1002/(SICI)1098-2760(19980205)17:2<86::AID-MOP4>3.0.CO;2-E

13. Naqvi, A., A. Hussain, and Q. A. Naqvi, "Waves in fractional dual planar waveguides containing chiral nihility metamaterial," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 11--12, 1575-1586, 2010.
doi:10.1163/156939310792149614

14. Naqvi, A., S. Ahmed, and Q. A. Naqvi, "Perfect electromagnetic conductor and fractional dual interface placed in a chiral nihility medium," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 14--15, 1991-1999, 2010.

15. Onufriyenko, V. M., "Electromagnetism of artificial fractal medium --- The physico-geometrical groundwork," Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies, 2007. The Sixth International Kharkov Symposium on MSMW'07, Vol. 2, 947-949, June 25--30, 2007.

16. Muslih, S. I. 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

17. Baleanu, D., A. K. Golmankhaneh, 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

18. 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.

19. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "On electromagnetic wave propagation in fractional space," Nonlinear Analysis B: Real World Applications, Vol. 12, No. 5, 2844-2850, 2011.
doi:10.1016/j.nonrwa.2011.04.010

20. 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.

21. 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.

22. 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.

23. 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, 2January 28, 012.

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

25. Martin, O.-S., "Electromagnetism on anisotropic fractals," Eprint ArXiv:1106.1491., June 2011.

26. Teng, H. T., H.-T. Ewe, and S. L. Tan, "Multifractal dimension and its geometrical terrain properties for classification of multi-band multi-polarised SAR image," Progress In Electromagnetics Research, Vol. 104, 221-237, 2010.
doi:10.2528/PIER10022001

27. Anguera, J., J. P. Daniel, C. Borja, J. Mumbru, C. Puente, T. Leduc, K. Sayegrih, and P. Van Roy, "Metallized foams for antenna design: Application to fractal-shaped sierpinski-carpet monopole," Progress In Electromagnetics Research, Vol. 104, 239-251, 2010.
doi:10.2528/PIER10032003

28. Siakavara, K., "Novel fractal antenna arrays for satellite networks: Circular ring Sierpinski carpet arrays optimized by genetic algorithms," Progress In Electromagnetics Research, Vol. 103, 115-138, 2010.
doi:10.2528/PIER10020110

29. Karim, M. N. A., M. K. A. Rahim, H. A. Majid, O. B. Ayop, M. Abu, and F. Zubir, "Log periodic fractal koch antenna for UHF band applications," Progress In Electromagnetics Research, Vol. 100, 201-218, 2010.
doi:10.2528/PIER09110512

30. Attiya, A. M., "Reflection and transmission of electromagnetic wave due to a quasi-fractional space slab," Progress In Electromagnetics Research Letters, Vol. 24, 119-128, 2011.

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


© Copyright 2014 EMW Publishing. All Rights Reserved