volume | PIER Journals

Abstract

The fields inside a rectangular waveguide with an internal coating of chiral nihility metamaterial are determined. These fields are then fractionalized utilizing the fractional curl operator to find the fields for the intermediate geometries which are also termed as the fractional order geometries. It is noted that no electric field exists inside the chiral nihility coating backed by perfect electric conductor (PEC) surface. The fractional order geometries are related through the principle of duality. The behavior of the fields with respect to the fractional parameter, α is analyzed.

1. Zouhdi, S., A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, 2008.

2. Jaggard, D. L., A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys., Vol. 18, 211-216, 1979.
doi:10.1007/BF00934418 Google Scholar

3. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media Norwood, Artech House, MA, 1994, ISBN 0-89006-684-1.

4. Mackay, T. G. and A. Lakhtakia, "Simultaneously negative and positive phase velocity propagation in an isotropic chiral medium," Microwave and Optical Technology Letters, Vol. 49, 1245-1246, 2007.
doi:10.1002/mop.22434 Google Scholar

5. Tretyakov, S., I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 5, 695-706, 2003.
doi:10.1163/156939303322226356 Google Scholar

6. Zhang, C. and T. J. Cui, "Negative reflections of electromagnetic waves in strong chiral media," App. Phys. Lett., Vol. 91, 194101, 2007.
doi:10.1063/1.2804124 Google Scholar

7. Cheng, Q., T. J. Cui, and C. Zhang, "Waves in planar waveguide containing chiral nihility metamaterial," Optics Communications, Vol. 276, 317-321, 2007.
doi:10.1016/j.optcom.2007.04.053 Google Scholar

8. Qiu , C. W., H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Physical Review B, Vol. 75, 245214, 2007.
doi:10.1103/PhysRevB.75.245214 Google Scholar

9. Qiu, C. W., H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction," Physical Review B, Vol. 75, 155120, 2007.
doi:10.1103/PhysRevB.75.155120 Google Scholar

10. Dong, J. F. and C. Xu, "Characteristics of guided modes in planar chiral nihility meta-material waveguides," Progress In Electromagnetics Research B, Vol. 14, 107-126, 2009.
doi:10.2528/PIERB09012201 Google Scholar

11. Naqvi, Q. A., "Fractional dual solutions to the Maxwell equations in chiral nihility medium," Optics Communications, Vol. 282, 2016-2018, 2009.
doi:10.1016/j.optcom.2009.02.022 Google Scholar

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

13. Dong, J. F., "Surface wave modes in chiral negative refraction grounded slab waveguides," Progress In Electromagnetics Research, Vol. 95, 153-166, 2009.
doi:10.2528/PIER09062604 Google Scholar

14. 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 Google Scholar

15. 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. Google Scholar

16. Ahmed, S. and Q. A. Naqvi, "Electromagnetic scattering from a chiral-coated nihility cylinder," Progress In Electromagnetics Research Letters, Vol. 18, 41-50, 2010.
doi:10.2528/PIERL10072807 Google Scholar

17. Oldham, K. B. and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.

18. Engheta, N., "On fractional paradigm and intermediate zones in electromagnetism: I. Planar observation," Microwave and Optical Technology Letters, Vol. 22, No. 4, 236-241, Aug. 20, 1999.
doi:10.1002/(SICI)1098-2760(19990820)22:4<236::AID-MOP6>3.0.CO;2-8 Google Scholar

19. Engheta, N., "On fractional paradigm and intermediate zones in electromagnetism: II. Cylindrical and spherical observations ," Microwave and Optical Technology Letters, Vol. 23, No. 2, 100-103, Oct. 20, 1999.
doi:10.1002/(SICI)1098-2760(19991020)23:2<100::AID-MOP12>3.0.CO;2-W Google Scholar

20. Engheta, N., "Fractional curl operator in electromagnetics," Fractional curl operator in electromagnetics, Vol. 17, 86-91, 1998. Google Scholar

21. Naqvi, Q. A. and M. Abbas, "Complex and higher order fractional curl operator in electromagnetics," Optics Communications, Vol. 241, 349-355, 2004.
doi:10.1016/j.optcom.2004.07.028 Google Scholar

22. Hussain , A., S. Ishfaq, and Q. A. Naqvi, "Fractional curl oerator and fractional waveguides," Progress in Electromagnetics Research, Vol. 63, 319-355, 2006.
doi:10.2528/PIER06060604 Google Scholar

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 Google Scholar

24. Hussain, A., M. Faryad, and Q. A. Naqvi, "Fractional curl oerator and fractional chiro-waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 8, 1119-1129, 2007. Google Scholar

25. Hussain , A. and Q. A. Naqvi, "Perfect electromagnetic conductor (PEMC) and fractional waveguide," Progress In Electromagnetics Research, Vol. 73, 61-69, 2007.
doi:10.2528/PIER07032401 Google Scholar

26. Hussain, A. and Q. A. Naqvi, "Fractional curl operator in chiral medium and fractional non-symmetric transmission line," Progress In Electromagnetics Research, Vol. 59, 199-213, 2006.
doi:10.2528/PIER05092801 Google Scholar

27. Faryad, M. and Q. A. Naqvi, "Fractional rectangular waveguide ," Progress In Electromagnetics Research, Vol. 75, 383-396, 2007.
doi:10.2528/PIER07052803 Google Scholar

28. Naqvi, Q. A., "Planar slab of chiral nihility metamaterial backed by fractional DUAL/PEMC interface," Progress In Electromagnetics Research, Vol. 85, 381-391, 2008.
doi:10.2528/PIER08081201 Google Scholar

29. Pozar, D. M., Microwave Engineering, 2nd Ed., 170176, John Wiley and Sons, 1998.

30. Lakhtakia, A., Beltrami Fields in Chiral Media, Contemporary Chemical Physics, World Scientific Series, 1994.
doi:10.1142/9789812812100

31. Harrington, R. F., Time-harmonic Electromagnetic Fields, McGraw-Hill Inc., New York, 1961.

32. Qiu, C. W., N. Burokur, S. Zouhdi, and L. W. Li, "Chiral nihility e®ects on energy °ow in chiral materials," J. Opt. Soc. Am. A, Vol. 25, No. 1, 55-63, 2008.
doi:10.1364/JOSAA.25.000055 Google Scholar

Mr. Arbab Abdur Rahim

Dr. Muhammad Junaid Mughal

Dr. Qaisar Abbas Naqvi