volume | PIER Journals

Abstract

Simple normalized dispersion relations for transverse magnetic (TM) and transverse electric (TE) propagating modes in parallel-plate waveguides filled with DPS/DPS or DNG/DNG, and DNG/DPS bilayers are presented. The evanescent TE₀ mode of the waveguide filled with a DNG/DPS bilayer is characterized also by a simple normalized dispersion relation. Since an important behavior of the modes in the waveguide filled with a DNG/DPS bilayer is the existence of a turning point (TP) at which the power carried by the respective mode on the propagation direction equals zero and changes the sign, we present also implicit relations for determining the normalized parameters of the TM and TE modes at that TP. We show that the TP begins to exist at certain values of the normalized parameter v₂ characterizing the DPS layer. For both the TM and TE modes, the higher is the mode order, the greater is the v₂ parameter at which the TP begins to exist, but the behavior of the TP is different for the TM and TE modes.

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp., Vol. 10, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

2. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative refractive index of refraction," Science, Vol. 292, 77-99, 2001.
doi:10.1126/science.1058847

3. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

4. Smith, D. R. and N. Kroll, "Negative refraction index in left handed materials," Phys. Rev. Lett., Vol. 85, 2933-2936, 2000.
doi:10.1103/PhysRevLett.85.2933

5. Ziolkowski, R. W. and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E, Vol. 64, 056625, 2001.
doi:10.1103/PhysRevE.64.056625

6. Lindell, I. V., S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media-Media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett., Vol. 31, 129-133, 2001.
doi:10.1002/mop.1378

7. Lindell, I. V. and S. Ilvonen, "Waves in a slab of uniaxial BW medium," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 3, 303-318, 2002.
doi:10.1163/156939302X01164

8. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002.
doi:10.2528/PIER01082101

9. Nefedov, I. S. and S. A. Tretyakov, "Waveguide containing a backward-wave slab," Radio Science, Vol. 38, 1101, 2003.
doi:10.1029/2003RS002900

10. Wu, B.-I., T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys., Vol. 93, 9386-9388, 2003.
doi:10.1063/1.1570501

11. Shadrivov, I. V., A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E, Vol. 67, 057602, 2003.
doi:10.1103/PhysRevE.67.057602

12. Peacock, A. C. and N. G. R. Broderick, "Guided modes in channel waveguides with a negative index of refraction," Opt. Express, Vol. 11, 2502-2510, 2003.
doi:10.1364/OE.11.002502

13. Alu, A. and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech., Vol. 52, 199-210, 2004.
doi:10.1109/TMTT.2003.821274

14. Ran, L.-X., H.-F. Jiang Tao, H. Chen, X.-M. Zhang, K.-S. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," Progress In Electromagnetics Research, Vol. 51, 249-279, 2005.
doi:10.2528/PIER04040502

15. Mahmoud, S. F. and A. J. Viitanen, "Surface wave character on a slab of metamaterial with negative permittivity and permeability," Progress In Electromagnetics Research, Vol. 51, 127-137, 2005.
doi:10.2528/PIER03102102

16. Li, C., Q. Sui, and F. Li, "Complex guided wave solution of grounded dielectric slab made of metamaterials," Progress In Electromagnetics Research, Vol. 51, 187-195, 2005.
doi:10.2528/PIER04011203

17. Xiao, Z. Y. and Z. H. Wang, "Dispersion characteristics of asymmetric double-negative material slab waveguides," J. Opt. Soc. Am. B, Vol. 23, 1757-1760, 2006.
doi:10.1364/JOSAB.23.001757

18. Tsakmakidis, K. L., C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, "Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability," Phys. Rev. B, Vol. 73, 085104, 2006.
doi:10.1103/PhysRevB.73.085104

19. Wang, Z. H., Z. Y. Xiao, and S. P. Li, "Guided modes in slab waveguides with a left handed material cover or substrate," Opt. Commun., Vol. 281, 607-613, 2008.
doi:10.1016/j.optcom.2007.10.034

20. McCall, M. W., "What is negative refraction?," Journal of Modern Optics, Vol. 56, 1727-1740, 2009.
doi:10.1080/09500340903324818

21. Yang, H. W., P. Dong, and Y. Liu, "Transmission properties of asymmetric slab waveguides with left-handed materials," J. Russ. Laser Res., Vol. 30, 193-203, 2009.
doi:10.1007/s10946-009-9060-7

22. Dong, P. and H. W. Yang, "Guided modes in slab waveguides with both double-negative and single-negative materials," Optica Applicata, Vol. 40, 873-882, 2010.

23. Cojocaru, E., "Electromagnetic tunneling in lossless trilayer stacks containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 113, 227-249, 2011.

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

Dr. Eva Cojocaru