volume | PIER Journals

Abstract

A perfect electric conductor placed in chiral nihility medium and excited by a uniform plane wave has been considered as an original problem. Using fractional operators, solutions to Maxwell equations which may be regarded as intermediate step between the original solution and dual to the original solution are determined. Each fractional operator is composed of fractional curl operator. As more than one dual to original solution exists, so in each case, corresponding impedance of the fractional dual reflector has been determined.

1. Lakhtakia, A., "An electromagnetic trinity from negative permittivity and negative permeability," Int. J. Infrared and Millimeter Waves, Vol. 22, 1731-1734, 2001.
doi:10.1023/A:1015068715023

2. 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, 695-706, 2003.
doi:10.1163/156939303322226356

3. Qiu, C.-W., N. Burokur, S. Zouhd, and L.-W. Li, "Chiral nihility effects on energy flow in chiral materials," J. Opt. Soc. Am. A, Vol. 25, No. 1, January 2008.
doi:10.1364/JOSAA.25.000055

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

5. Naqvi, Q. A., "Fractional dual solutions to the Maxwell equations in chiral nihility medium," Opt. Commun., Vol. 282, 2016-2018, 2009.
doi:10.1016/j.optcom.2009.02.022

6. Naqvi, Q. A., "Fractional dual solutions in grounded chiral nihility slab and their effect on outside field," Journal of Electromagnetic Waves and Applications, Vol. 23, 773-784, 2009.
doi:10.1163/156939309788019958

7. Engheta, N., "Fractional curl operator in electromagnetics," Microwave and Optical Technology Letters, Vol. 17, No. 2, 86-91, February 5, 1998.
doi:10.1002/(SICI)1098-2760(19980205)17:2<86::AID-MOP4>3.0.CO;2-E

8. 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

9. Naqvi, Q. A., G. Murtaza, and A. A. Rizvi, "Fractional dual solutions to the Maxwell equations in homogeneous chiral media," Optics Communications, Vol. 178, 27-30, 2000.
doi:10.1016/S0030-4018(00)00651-9

10. 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

11. Naqvi, Q. A. and M. Abbas, "Fractional duality and metamaterials with negative permittivity and permeability," Optics Communications, Vol. 227, 143-146, 2003.
doi:10.1016/j.optcom.2003.08.041

12. 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

13. Hussain, A. and Q. A. Naqvi, "Fractional curl operator in chiral medium and fractional transmission line," Progress In Electromagnetics Research, Vol. 59, 319-335, 2006.
doi:10.2528/PIER06060604

14. Hussain, A., S. Ishfaq, and Q. A. Naqvi, "Fractional curl operator and fractional waveguides," Progress In Electromagnetics Research, Vol. 63, 319-335, 2006.
doi:10.2528/PIER06060604

15. Hussain, A., M. Faryad, and Q. A. Naqvi, "Fractional curl operator and fractional chiro-waveguide," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 8, 1119-1129, 2007.

16. 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

17. 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

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

19. Maab, H. and Q. A. Naqvi, "Fractional surface waveguide," Progress In Electromagnetics Research C, Vol. 1, 199-209, 2008.
doi:10.2528/PIERC08020801

20. Hussain, A., M. Faryad, and Q. A. Naqvi, "Fractional waveguide with impedance walls," Progress In Electromagnetics Research C, Vol. 4, 191-204, 2008.

21. Maab, H. and Q. A. Naqvi, "Fractional rectangular cavity resonator," Progress In Electromagnetics Research B, Vol. 9, 69-82, 2008.
doi:10.2528/PIERB08070101

22. Abbas, M., S. A. Naqvi, and Q. A. Naqvi, "Foster reactance theorem in fractional dual guiding structures," International Journal of Microwave and Optical Technology, IJMOT, Vol. 3, No. 2, April 2008.

23. Naqvi, S. A., M. Faryad, Q. A. Naqvi, and M. Abbas, "Fractional duality in homogeneous bi-isotropic medium," Progress In Electromagnetics Research, Vol. 78, 159-172, 2008.
doi:10.2528/PIER07090701

24. Naqvi, Q. A., "Planer slab of chiral nihility metamaterial backed by fractional dual/PEMC interface," Progress In Electromagnetics Research, Vol. 85, 381-391, 2008.
doi:10.2528/PIER08081201

25. Mustafa, F., M. Faryad, and Q. A. Naqvi, "Fractional dual solutions using calculus of differential forms," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2--3, 399-410, 2008.
doi:10.1163/156939308784160721

26. Veliev, E. I. and N. Engheta, "Fractional curl operator in reflection problems," 10th Int. Conf. on Mathematical Methods in Electromagnetic Theory, Ukraine, Sept. 14--17,2004.

27. Ivakhnychenko, M. V., E. I. Veliev, and T. M. Ahmedov, "Fractional operators approach in electromagnetic wave reflection problems," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1787-1802, 2007.

Dr. Qaisar Naqvi