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2015-09-30
Reflection and Transmission of an Electromagnetic Wave Due to Fractal Slab Sandwiched Between Ordinary Material
By
Progress In Electromagnetics Research Letters, Vol. 57, 1-7, 2015
Abstract
εThis paper presents an analytical solution to study the reflection and transmission of an electromagnetic wave impinged upon a multilayered structure. The structure is composed of a fractal slab sandwiched by ordinary material on either side. Modified Maxwell equations for fractional dimension space are used to represent the fields in a fractal slab. The electromagnetic characteristics of the structure are studied for different dimensions (D) and numerical results are presented for both the classical (D is integer) and fractal (D is non-integer) slabs. This study provides foundations for investigating the waveguides filled with fractal media and electromagnetic waves propagation in multilayered structures at fractional boundaries.
Citation
Safiullah Khan Marwat, Muhammad Junaid Mughal, and Qaisar Naqvi, "Reflection and Transmission of an Electromagnetic Wave Due to Fractal Slab Sandwiched Between Ordinary Material," Progress In Electromagnetics Research Letters, Vol. 57, 1-7, 2015.
doi:10.2528/PIERL15063005
References

1. Nikishkov, G. P., "Curvature estimation for multilayer hinged structures with initial strains," Journal of Applied Physics, Vol. 94, No. 8, 5333-5336, 2003.
doi:10.1063/1.1610777

2. Cory, H. and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave and Optical Technology Letters, Vol. 40, No. 6, 460-465, 2004.
doi:10.1002/mop.20005

3. Cory, H., S. Shiran, and M. Heilper, "An iterative method for calculating the shielding effectiveness and light transmittance of multilayered media," IEEE Transactions on Electromagnetic Compatibility, Vol. 35, No. 4, 451-456, 1993.
doi:10.1109/15.247859

4. Sihvola, A., "Electromagnetic emergence in metamaterials," Advances in Electromagnetics of Complex Media and Metamaterials, 1-17, Kluwer Academic Publishers, Dordrecht, 2003.

5. Liu, C. H. and N. Behdad, "Tunneling and filtering characteristics of cascaded-negative metamaterial layers sandwiched by double-positive layers," Journal of Applied Phyics, Vol. 111, 014906, 2012.
doi:10.1063/1.3673796

6. Oraizi, H. and M. Afsahi, "Design of metamaterial multilayer structures as frequency selective surfaces," Progress In Electromagnetics Research C, Vol. 6, 115-126, 2009.
doi:10.2528/PIERC09010508

7. Kalluri, D. K. and T. C. K. Rao, "Filter characteristics of periodic chiral layers," Pure and Applied Optics, Vol. 3, 231-234, 1994.
doi:10.1088/0963-9659/3/3/005

8. Cojocaru, E., "Electromagnetic tunneling in lossless trilayer stacks containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 113, 227-249, 2011.
doi:10.2528/PIER11010707

9. Bassiri, S., C. H. Papas, and N. Engheta, "Electromagnetic wave propagation through a dielectricchiral interface and through a chiral slab," Journal of the Optical Society of America, Vol. 5, 1450-1459, 1988.
doi:10.1364/JOSAA.5.001450

10. Sabah, C., F. Dincer, M. Karaaslan, E. Unal, H. T. Tastan, and K. Delihacioglu, "Transmission tunneling through the periodic sequence of double-negative and double-positive layers," 13th Conference on Microwave Techniques, 2013.

11. Smirnovaa, D. A., I. V. Iorshb, I. V. Shadrivova, and Y. S. Kivshara, "Multilayer graphene waveguides," Journal of Experimental and Theorectical Physics, Vol. 99, No. 8, 456460, 2014.

12. Liu, C. H. and N. Behdad, "High-power microwave filters and frequency selective surfaces exploiting electromagnetic wave tunneling through ε-negative layers," Journal of Applied Phyics, Vol. 113, 064909, 2013.
doi:10.1063/1.4790584

13. Sabah, C. and S. Uckun, "Mirrors with chiral slabs," Journal of Optoelectronics and Advanced Materials, Vol. 8, No. 5, 1918-1924, 2006.

14. Mandelbrot, B., The Fractal Geometry of Nature, Freeman, New York, 1982.

15. Balankin, A. S. and B. E. Elizarraraz, "Map of fluid flow in fractal porous medium into fractal continuum flow," Physical Review E, Vol. 85, 056314, 2012.
doi:10.1103/PhysRevE.85.056314

16. Balankin, A. S. and B. E. Elizarraraz, "Hydrodynamics of fractal continuum flow," Physical Review E, Vol. 85, 025302, 2012.
doi:10.1103/PhysRevE.85.025302

17. Sabatier, J., O. P. Agrawal, and J. A. Tenreiro Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007.

18. Wang, Z.-S. and B.-W. Lu, "The scattering of electromagnetic waves in fractal media," Waves in Random and Complex Media, Vol. 4, 97-103, 1994.
doi:10.1088/0959-7174/4/1/010

19. Engheta, N., "Use of fractional integration to propose some ‘fractional’ solutions for the scalar Helmholtz equation," Progress In Electromagnetics Research, Vol. 12, 107-132, 1996.

20. Engheta, N., "On the role of fractional calculus in electromagnetic theory," IEEE Antennas and Propagation Magazine, Vol. 39, No. 4, 35-46, 1997.
doi:10.1109/74.632994

21. 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

22. Naqvi, Q. A. and A. A. Rizvi, "Fractional dual solutions and corresponding sources," Progress In Electromagnetics Research, Vol. 25, 223-238, 2000.
doi:10.2528/PIER99051801

23. 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

24. Naqvi, Q. A., "Fractional dual interface in chiral nihility medium," Progress In Electromagnetics Research Letters, Vol. 8, 135-142, 2009.
doi:10.2528/PIERL09032405

25. Zubair, M., M. J. Mughal, and Q. A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space, 1st Ed., Springer, 2012.
doi:10.1007/978-3-642-25358-4

26. Marwat, S. K. and M. J. Mughal, "Characteristics of multilayered metamaterial structures embedded in fractional space for terahertz applications ," Progress In Electromagnetics Research, Vol. 144, 229-239, 2014.
doi:10.2528/PIER13110603

27. Omar, M. and M. J. 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

28. Asad, H., 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

29. 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.
doi:10.2528/PIERL11051105