paper 150305080149

Abstract

In this paper, Transfer Matrix Method and modified Maxwell equations are used to find the general expressions for reflection and transmission coefficients of periodic multilay- ered structure. The structure is placed in D dimension space where D is integer for Euclidean space and non-integer for Fractional space. Characteristics of these structure are studied when an electromagnetic wave strikes on it at both normal and oblique incident angle. The final expressions are the function of frequency, dimension and incident angle. Numerical results for multilayered periodic strong chiral — strong chiral structure are presented. This study provides motivation to investigate the electromagnetic waves propagation in multilayered structures at fractional boundaries.

1. Liu, C. H. and N. Behdad, "Tunneling and filtering characteristics of cascaded ɛ-negative metamaterial layers sandwiched by double-positive layers," Journal of Applied Physics, Vol. 111, No. 1, 014906, January 2012.
doi:10.1063/1.3673796 Google Scholar

2. Sabah, C. and H. G. Roskos, "Design of a terahertz polarization rotator based on a periodic sequence of chiral-metamaterial and dielectric slabs," Progress In Electromagnetics Research, Vol. 124, 301-314, 2012.
doi:10.2528/pier11112605 Google Scholar

3. 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 Google Scholar

4. 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 Google Scholar

5. Mandelbrot, B., The Fractal Geometry of Nature, Freeman, New York, 1982. Google Scholar

6. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific Publishing, 2000. Google Scholar

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

8. Naqvi, Q. A. and A. A. Rizvi, "Fractional dual solutions and corresponding sources," ProgressIn Electromagnetics Research, Vol. 25, 223-238, 2000.
doi:10.2528/pier99051801 Google Scholar

9. Lakhtakia, A., "A representation theorem involving fractional derivatives for linear homogeneous chiral media," Microwave and Optical Technology Letters, Vol. 28, No. 6, 385-386, 2001.
doi:10.1002/1098-2760(20010320)28:6<385::aid-mop1048>3.0.co;2-l Google Scholar

10. 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.
doi:10.2528/pier95051000 Google Scholar

11. Engheia, 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 Google Scholar

12. Mughal, M. J., S. K. Marwat, N. Amin, and M. Omar, "Analysis of periodic strong chiralmetamaterial structures as frequency selective surfaces and polarization rotators using transfer matrix method," International Conference on Metamaterials and Photonic Crystals and Plasmonics, 2014. Google Scholar

Safiullah Khan Marwat

Muhammad Junaid Mughal