Vol. 125
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2012-02-29
Fields in Fractional Parallel Plate dB Waveguides
By
Progress In Electromagnetics Research, Vol. 125, 273-294, 2012
Abstract
Time harmonic electric and magnetic fields inside a parallel plate DB boundary waveguide are derived and fractional curl operator is utilized to study the fractional parallel plate DB waveguides. The DB boundary conditions are incorporated by assuming the behavior of boundary as perfect electric conductor (PEC) for transverse electric mode and perfect magnetic conductor (PMC) for transverse magnetic mode. For this purpose a general wave propagating inside the parallel plate wave waveguide is assumed and decomposed into TE and TM modes. Behavior of the fields and transverse impedances of the walls of guide are studied with respect to the fractional parameter describing the order of the fractional curl operator. The results are compared with the corresponding results for fractional waveguides with PEC walls.
Citation
Akhtar Hussain, Sajid Naqvi, Ahsan Illahi, Aqeel Abbas Syed, and Qaisar Naqvi, "Fields in Fractional Parallel Plate dB Waveguides," Progress In Electromagnetics Research, Vol. 125, 273-294, 2012.
doi:10.2528/PIER11120701
References

1. Oldham, K. B. and J. Spanier, The Fractional Calculus, Academic Press, 1974.

2. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, 2000.
doi:10.1142/9789812817747

3. Podlubny, I., Fractional Differential Equations, Mathematics in Science and Engineering V198, Academic Press, 1999.

4. Das, S., Functional Fractional Calculus for System Identification and Controls, Springer-Verlag, 2008.

5. Debnath, L., "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Vol. 54, 3413-3442, 2003.
doi:10.1155/S0161171203301486

6. Engheta, N., "A note on fractional calculus and the image method for dielectric spheres," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 9, 1179-1188, 1995.

7. Engheta, N., "Use of fractional calculus to propose some fractional solution for the scalar Helmholtzs equation," Progress In Electromagnetics Research, Vol. 12, 107-132, 1996.

8. Engheta, N., "Electrostatic fractional image methods for perfectly conducting wedges and cones," IEEE Transactions on Antennas and Propagation, Vol. 44, 1565-1574, 1996.
doi:10.1109/8.546242

9. Engheta, N., "On the role of fractional calculus in electromagnetic theory," IEEE Antennas and Propagation Magazine, Vol. 39, 35-46, 1997.
doi:10.1109/74.632994

10. Engheta, N., "Phase and amplitude of fractional-order intermediate wave," Microwave and Optical Technology Letters, Vol. 21, 338-343, 1999.
doi:10.1002/(SICI)1098-2760(19990605)21:5<338::AID-MOP10>3.0.CO;2-P

11. Engheta, N., "Fractional paradigm in electromagnetic theory," Frontiers in Electromagnetics, Chapter 12, 523--552, IEEE Press, 1999.

12. Tarasov, V. E., "Universal electromagnetic waves in dielectric," J. Phys.: Condens. Matter, Vol. 20, 175-223, 2008.

13. Tarasov, V. E., "Fractional integro-differential equations for electromagnetic waves in dielectric media," Teoret. Mat. Fiz., Vol. 158, 419-424, 2009.

14. Musliha, S. I. and D. Baleanu, "Fractional multipoles in fractional space," Nonlinear Analysis: Real World Applications, Vol. 8, 198-203, 2007.
doi:10.1016/j.nonrwa.2005.07.001

15. Baleanua, D., A. K. Golmankhanehb, and A. K. Golmankhaneh, "On electromagnetic field in fractional space," Nonlinear Analysis: Real World Applications, Vol. 11, 288-292, 2010.
doi:10.1016/j.nonrwa.2008.10.058

16. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "The wave equation and general plane wave solutions in fractional space," Progress In Electromagnetics Research Letters, Vol. 19, 137-146, 2010.

17. Zubair, M., M. J. Mughal, Q. A. Naqvi, and A. A. Rizvi, "Differential electromagnetic equations in fractional space," Progress In Electromagnetics Research, Vol. 114, 255-269, 2011.

18. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "An exact solution of the cylindrical wave equation for electromagnetic field in fractional dimensional space," Progress In Electromagnetics Research, Vol. 114, 443-455, 2011.

19. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "On electromagnetic wave propagation in fractional space," Nonlinear Analysis: Real World Applications, Vol. 12, 2844-2850, 2011.
doi:10.1016/j.nonrwa.2011.04.010

20. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "An exact solution of the spherical wave equation in d-dimensional fractional space," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 10, 1481-1491, 2011.

21. Engheta, N., "On Fractional paradigm and intermediate zones in Electromagnetism: I. Planar observation," Microwave and Optical Technology Letters, Vol. 22, 236-241, 1999.
doi:10.1002/(SICI)1098-2760(19990820)22:4<236::AID-MOP6>3.0.CO;2-8

22. Engheta, N., "On Fractional paradigm and intermediate zones in Electromagnetism: II. Cylindrical and spherical observations," Microwave and Optical Technology Letters, Vol. 23, 100-103, 1999.
doi:10.1002/(SICI)1098-2760(19991020)23:2<100::AID-MOP12>3.0.CO;2-W

23. Lakhtakia, A., "A representation theorem involving fractional derivatives for linear homogeneous chiral media," Microwave and Optical Technology Letters, Vol. 28, 385-386, 2001.
doi:10.1002/1098-2760(20010320)28:6<385::AID-MOP1048>3.0.CO;2-L

24. Engheta, N., "Fractional curl operator in electromagnetics," Microwave and Optical Technology Letters, Vol. 17, 86-91, 1998.
doi:10.1002/(SICI)1098-2760(19980205)17:2<86::AID-MOP4>3.0.CO;2-E

25. Ozaktas, H. M., Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, Wiley, 2001.

26. 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

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

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

29. 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

30. Veliev, E. I., M. V. Ivakhnychenko, and T. M. Ahmedov, "Fractional boundary conditions in plane waves diffraction on a strip," Progress In Electromagnetics Research, Vol. 79, 443-462, 2008.
doi:10.2528/PIER07102406

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

32. 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

33. 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.

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

35. 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

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

37. Hussain, A. and Q. A. Naqvi, "Fractional rectangular impedance waveguide," Progress In Electromagnetics Research, Vol. 96, 101-116, 2009.
doi:10.2528/PIER09060801

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

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

40. Hussain, A. and Q. A. Naqvi, "Fractional rectangular impedance waveguide," Progress In Electromagnetics Research, Vol. 96, 101-116, 2009.
doi:10.2528/PIER09060801

41. Naqvi, S. A., Q. A. Naqvi, and A. Hussain, "Modelling of transmission through a chiral slab using fractional curl operator," Optics Communications, Vol. 266, 404-406, 2006.
doi:10.1016/j.optcom.2006.05.030

42. 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

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

44. Tretyakov, S., I. Nefedov, A. Sihvola, and S. Maslovski, "A metamaterial with extreme properties: The chiral nihility," Progress In Electromagnetics Research Symposium 2003, 468 Honolulu, Hawaii, USA, October 13--16, 2003.

45. 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

46. Tretyakov, S. A., I. S. Nefedov, and P. Alitalo, "Generalized field transforming metamaterials," New Journal of Physics, Vol. 10, 115028, 2008.
doi:10.1088/1367-2630/10/11/115028

47. 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

48. Zhang, C. and T. J. Cui, Negative reflections of electromagnetic waves in chiral media, arXiv:physics/0610172.

49. Dong, J. F. and C. Xu, "Surface polaritons in planar chiral nihility meta-material waveguides," Optics Communications, Vol. 282, 3899-3904, 2009.
doi:10.1016/j.optcom.2009.06.054

50. Naqvi, A., "Comments on waves in planar waveguide containing chiral nihility metamaterial," Optics Communications, Vol. 284, 215-216, 2011.
doi:10.1016/j.optcom.2010.08.017

51. 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

52. Naqvi, Q. A., "Planar slab of chiral nihility metamaterial backed by fractional dual/PEMC interface," Progress In Electromagnetics Research, Vol. 85, 381-391, 2009.

53. Naqvi, Q. A., "Fractional dual solutions in grounded chiral nihility slab and their effect on outside fields," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 5--6, 773-784, 2009.
doi:10.1163/156939309788019958

54. 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.

55. Illahi, A. and Q. A. Naqvi, "Study of focusing of electromagnetic waves reflected by a PEMC backed chiral nihility reflector using Maslov's method," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 7, 863-873, 2009.
doi:10.1163/156939309788355216

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

57. 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

58. Lindell, I. V. and A. H. Sihvola, "Zero axial parameter (ZAP) sheet," Progress In Electromagnetics Research, Vol. 89, 213-224, 2009.
doi:10.2528/PIER08120307

59. Lindell, I. V. and A. H. Sihvola, "Uniaxial IB-medium interface and novel boundary conditions," IEEE Transactions on Antennas and Propagation, Vol. 57, 694-700, 2009.
doi:10.1109/TAP.2009.2013431

60. Lindell, I. V. and A. Sihvola, "Circular waveguide with DB boundary conditions," IEEE Trans. on Micro. Theory and Tech., Vol. 58, 903-909, 2010.
doi:10.1109/TMTT.2010.2042638

61. Lindell, I. V., H.Wallen, and A. Sihvola, "General electromagnetic boundary conditions involving normal field components," IEEE Ant. and Wirel. Propag. Lett., Vol. 8, 877-880, 2009.
doi:10.1109/LAWP.2009.2028301

62. Sihvola, A., H. Wallen, and P. Yla-Oijala, "Scattering by DB spheres," IEEE Ant. and Wirel. Propag. Lett., Vol. 8, 542-545, 2009.
doi:10.1109/LAWP.2009.2022960

63. Lindell, I. V. and A. Sihvola, "Electromagnetic boundary and its realization with anisotropic metamaterial," Phys. Rev. E, Vol. 79, 026604, 2009.
doi:10.1103/PhysRevE.79.026604

64. Lindell, I. V. and A. Sihvola, "Zero axial parameter (ZAP) medium sheet," Progress In Electromagnetics Research, Vol. 89, 213-224, 2009.
doi:10.2528/PIER08120307

65. Naqvi, A., F. Majeed, and Q. A. Naqvi, "Planar DB boundary placed in a chiral and chiral nihility metamaterial," Progress In Electromagnetics Research Letters, Vol. 21, 41-48, 2011.