volume | PIER Journals

Abstract

This paper presents the frequency response of a stratified structure consisting of double-positive and dispersive double-negative chiral metamaterial layers. The structure is inserted between two half-spaces of fractional dimensions. Transfer matrix approach is used for the analysis. Dispersion within the double-negative chiral layers is realized by using Lorentz/Drude model. The effect of fractionality of the dimension is particularly investigated. Numerical results, for a five layer structure, are presented for various parametric values of the stratified structure and fractionality of the host media. It is shown that the fractionality of host media can be used as yet another parameter to control the frequency response of such a filtering structure. For integral values of dimensions, the results are shown to converge to the classical results thus validating the analysis.

1. 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

2. 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, 2009.
doi:10.1063/1.3263940

3. Bollini, C. G. and J. J. Giambiagi, "Dimensional renorinalization: The number of dimensions as a regularizing parameter," Il Nuovo Cimento, Vol. 12, No. 1, 20-26, 1972.

4. Muslih, S. I., "Solutions of a particle with fractional δ-potential in a fractional dimensional space," International Journal of Theoretical Physics, Vol. 49, No. 9, 2095-2104, 2010.
doi:10.1007/s10773-010-0396-0

5. Wilson, K. G., "Quantum field-theory models in less than 4 dimensions," Physical Review D, Vol. 7, No. 10, 2911, 1973.
doi:10.1103/PhysRevD.7.2911

6. Guo, X. and M. Xu, "Some physical applications of fractional Schrödinger equation," Journal of Mathematical Physics, Vol. 47, No. 8, 082104, 2006.
doi:10.1063/1.2235026

7. 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.

8. Palmer, C. and P. N. Stavrinou, "Equations of motion in a non-integer-dimensional space," Journal of Physics A: Mathematical and General, Vol. 37, No. 27, 6987, 2004.
doi:10.1088/0305-4470/37/27/009

9. Muslih, S. I. and D. Baleanu, "Fractional multipoles in fractional space," Nonlinear Analysis: Real World Applications, Vol. 8, No. 1, 198-203, 2007.
doi:10.1016/j.nonrwa.2005.07.001

10. Calcagni, G., "Geometry and field theory in multi-fractional spacetime," Journal of High Energy Physics, Vol. 2012, No. 1, 1-77, 2012.
doi:10.1007/JHEP01(2012)065

11. Ray, S. S., "A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends," Applied Mathematics and Computation, Vol. 202, No. 2, 544-549, 2008.
doi:10.1016/j.amc.2008.02.043

12. Tarasov, V. E., "Fractional hydrodynamic equations for fractal media," Annals of Physics, Vol. 318, No. 2, 286-307, 2005.
doi:10.1016/j.aop.2005.01.004

13. Barnsley, M. F., Fractals Everywhere: New Edition, Courier Dover Publications, 2013.

14. 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

15. Wang, Z. S. and B. W. Lu, "The scattering of electromagnetic waves in fractal media," Waves in Random Media, Vol. 4, No. 1, 97, 1994.
doi:10.1088/0959-7174/4/1/010

16. Asad, H., M. J. Mughal, M. Zubair, and Q. A. Naqvi, "Electromagnetic Green’s function for fractional space," Journal of Electromagnetic Waves and Applications, Vol. 26, No. 14-15, 1903-1910, 2012.
doi:10.1080/09205071.2012.720748

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

18. Tarasov, V. E., "Possible experimental test of continuous medium model for fractal media," Physics Letters A, Vol. 341, No. 5, 467-472, 2005.
doi:10.1016/j.physleta.2005.05.022

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

20. Sihvola, A., "Metamaterials in electromagnetics," Metamaterials, Vol. 1, No. 1, 2-11, 2007.
doi:10.1016/j.metmat.2007.02.003

21. Silva, A., F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, "Performing mathematical operations with metamaterials," Science, Vol. 343, No. 6167, 160-163, 2014.
doi:10.1126/science.1242818

22. Ziolkowski, R. W. and A. D. Kipple, "Causality and double-negative metamaterials," Physical Review E, Vol. 68, No. 2, 026615, 2003.
doi:10.1103/PhysRevE.68.026615

23. Hrabar, S., N. Engheta, and R. Ziolkowsky, "Waveguide experi-ments to characterize the properties of SNG and DNG metamaterials," Metamaterials: Physics and Engineering Explorations, 2006.

24. Wang, B., J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, "Chiral metamaterials: Simulations and experiments," Journal of Optics A: Pure and Applied Optics, Vol. 11, No. 11, 114003, 2009.
doi:10.1088/1464-4258/11/11/114003

25. Sabah, C., "Left-handed chiral metamaterials," Central European Journal of Physics, Vol. 6, No. 4, 872-878, 2008.

26. Wongkasem, N., A. Akyurtlu, and K. A. Marx, "Development of double negative chiral metamaterials in the visible regime," Antennas and Propagation Society International Symposium 2006, IEEE, 757-760, IEEE, 2006.
doi:10.1109/APS.2006.1710637

27. Sabah, C., H. Tugrul Tastan, F. Dincer, K. Delihacioglu, M. Karaaslan, and E. Unal, "Transmission tunneling through the multilayer double-negative and double-positive slabs," Progress In Electromagnetics Research, Vol. 138, 293-306, 2013.
doi:10.2528/PIER13013110

28. Sabah, C. and S. Uckun, "Multilayer system of Lorentz/Drude type metamaterials with dielectric slabs and its application to electromagnetic filters," Progress In Electromagnetics Research, Vol. 91, 349-364, 2009.
doi:10.2528/PIER09031306

29. 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

30. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media, 1994.

31. Sabah, C. and S. Uckun, "Physical features of left-handed mirrors in millimeter wave band," Journal of Optoelectronics and Advanced Materials, Vol. 9, No. 8, 2480-2484, 2007.

32. Balanis, C. A., Advanced Engineering Electromagnetics, Vol. 111, John Wiley and Sons, 2012.

33. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 5514, 77-79, 2001.
doi:10.1126/science.1058847

Dr. Aqeel Ahmad

Dr. Aqeel Abbas Syed

Dr. Qaisar Naqvi