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 Google Scholar

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 Google Scholar

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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

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 Google Scholar

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. Google Scholar

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

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 Google Scholar

Dr. Eva Cojocaru